dialysis culture microorganisms: design, theory, and resultsmicroorganisms. in 1896, metchnikoffet...

BACTERIOLOGICAL REVIEWS, Mar. 1969, p. 147 Vol. 33, No. ICopyright © 1969 American Society for Microbiology Printed in U.S.A

Dialysis Culture of Microorganisms:Design, Theory, and ResultsJEROME S. SCHULTZ AND PHILIPP GERHARDT

Department of Chemical and Metallurgical Engineering, University of Michigan, Ann Arbor, Michigan 48104,and Department of Microbiology and Public Health, Michigan State University,

East Lansing, Michigan 48823

INTRODUCTION............................................................ 1DESIGN AND APPARATUS .................................................. 2Membrane Dialysis Culture................................................... 2Interface Dialysis Culture ............... ..................................... 6Colonial Growth with Dialysis ................................................ 8Methods of Operation........................................................ 9Types of Membranes........................................................ 10Membrane Permeability and Solute Sieving ........ ............................. 11Membrane Penetrability by Microorganisms .................................... 12

THEORY................................................................. 14Principles of Dialysis........................................................ 14Membrane characteristics................................................... 14Measurement of permeability............................................... 15Porosity................................................................. 15Hydrodynamics............................................................ 17Osmosis................................................................. 18

Growth in Dialysis Culture................................................... 19Basic considerations ....................................................... 19Completely continuous operation............................................. 20Completely batch operation................................................. 25Batch fermentor, continuous reservoir operation.............................. 28Continuous fermentor, batch reservoir operation................................ 29

Product Formation in Dialysis Culture.......................................... 29Basic considerations........................................................ 29Completely continuous operation............................................. 30Batch operations.......................................................... 31

Implications of Theory....................................................... 31Summary of Mathematical Abbreviations ......... .............................. 32Analogue Computer Program................................................. 32

RESULTS AND APPLICATIONS............................................. 34In Vitro Systems............................................................ 34Growth response and variables.............................................. 34Cell production........................................................... 37Formation of nondiffusible products.......................................... 38Production of diffusible compounds .......... ................................ 39Interbiosis................................................................ 40Gas exchange............................................................. 40

In Vivo Systems................................ ''I ....... 41Peritoneal dialysis......................................................... 41Hemodialysis............................................................. 43Solid tissue implants....................................................... 43Embryonated egg.......................................................... 43Rumen symbiodialysis ................ ..................................... 43

LITERATURE CITED........................................................ 44

INTRODUCTION an illustrative example occurs in the placentalRegulation of a constant milieu interieur is a envelopment of the embryo. One may also think

prime characteristic of life systems (71), with the of analogous situations where a population ofcontrol often exercised by a membrane. Although growing microorganisms is nurtured within abest exemplified with individual cells, the prin- membrane-enclosed environment-a classic in-ciple applies as well to multicellular organisms- stance is seen with bacterial peritonitis.

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SCHULTZ AND GERHARDT

Efforts to simulate this disease situation led tothe first uses of artificial membranes for culturingmicroorganisms. In 1896, Metchnikoff et al. (98)implanted collodion sacs containing cultures ofcholera vibrios into the peritoneal cavity of ani-mals to establish tout d'abord that there existed adiffusible cholera toxin. This new and simpletechnique was promptly exploited by Nocard andRoux (110) to achieve cultivation of the "peri-pneumonia" organism (mycoplasma), and byNovy (112) to enhance virulence of pneumococciby animal passage without phagocytosis.A logical modification of these in vivo experi-

ments was the suspension of a collodion sac con-taining bacterial culture in a laboratory flask withordinary medium. This step was promptly takenby Carnot and Fournier (20) in 1900 in theirsearch for a diffusible toxin from pneumococci;they reported that properties different from thosein ordinary culture were acquired, such as greatercapsulation, prolonged viability, and more per-sistent virulence. In the same year, Ruffer andCrendirpoulo (142) described a similar culturearrangement, but only proposed possible uses.Shortly thereafter, in 1904, Frost (41) exploitedthe technique to study the antagonism of soil orwater organisms toward typhoid bacteria, observ-ing what now would be called antibiotic effects.These pioneering uses of semipermeable mem-

branes in culturing microorganisms involveseveral principles that distinguish the methodfrom ordinary ones. The primary feature is thatthe microbial population is sequestered into amilieu on one side of the diffusion barrier. Onthe other side is the greater environment, whichcontains the nutrients for metabolism and growth.These nutrients diffuse through the barrier intothe culture compartment, and diffusible metabolicproducts diffuse away from the culture-that is,exchange dialysis occurs.With in vitro dialysis culture systems, the cul-

ture compartment contains a population of micro-bial cells that usually is in a liquid medium and isin some way mixed so as to obtain a homogeneoussuspension. For the system to be effective, thevolume of the reservoir must be relatively large incomparison with that of the culture compartment,or else it must be replenishable. Regulation of thesystem is achieved through alteration of the ratioof culture-to-reservoir volume and through selec-tion of the type of inert membrane and adjust-ment of its area. These factors are irreduciblycontrolling in any dialysis culture system. Butother parameters must also be considered, suchas the rate of liquid flow, liquid turbulence, con-centrations of essential nutrients and diffusibleproducts, and osmotic effects. Refinements onsimple dialysis (such as electrodialysis, adsorption

dialysis, and ultrafiltration) also seem applicablebut as yet appear not to have been studied.What we seek to do first in this article is to

present briefly the evolution in the design of appa-ratus for managing dialysis culture. The technicallimitations of the original membrane-sac tech-nique have largely been overcome, and presentlyavailable systems enable a larger scale of size,better control of the essential elements, and theuse of different types of membrane material inmembrane sheets. It will become evident thatdialysis culture can be operated in a batch cycle,continuously under steady-state conditions, or incombined modes. The principles of dialysis canbe extended to systems that employ a filter mem-brane, a solution-transport membrane, or aninterface, rather than the usual dialysis mem-brane.With development of a generalized design, it

became possible for us to derive new mathemati-cal models that describe the expected behavior ofsome simplified dialysis culture systems. Thistheoretical analysis represents the second objec-tive of this article. The simplifying assumptionthat allows such a theoretical analysis is the limit-ing nutrient concept (102), since it provides thecommon feature that enables one to relate dialysiskinetics to growth kinetics. The resulting equa-tions and their graphical solutions lead to attrac-tive predictions about dialysis culture, some ofwhich are verified from existing experimental dataand others of which are remarkable but untested.Perhaps the most important purposes of a simpli-fied mathematical analysis are to focus attentionon the more important parameters deservingattention in experiments, and to challenge in-vestigators to greater exploitation of the method.Our third objective is to describe the differences

in growth response that distinguish dialysis cul-ture from ordinary propagation systems, and todefine some of the more important controllingvariables. The remarkable consequences ofdialysis culture have led to application of thetechnique for a range of useful purposes, whichwe will review, and have opened prospects for anumber of new uses, which we will attempt inpart to preview. If through design, theory, orapplication of dialysis culture the course offurther research is illuminated, then the centralpurpose of this effort will be accomplished.

DESIGN AND APPARATUSMembrane Dialysis Culture

The surprising fact about the evolution of thedialysis culture technique is that so little advance-ment was made in basic designs for so many years.Only recently have significant improvements ap-

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FIG. 1. Preparation of implantable filter-membrane envelopes for in vivo dialysis culture. Acetone is employedtofuse the edges. Reproducedfrom Wong et al. (166).

peared with in vitro systems, and these havegreatly increased the applicability and study ofthe method.For in vivo studies, however, the original im-

plantable "diffusion chamber" method still per-sists with little modification. Algire (6) describedseveral effective arrangements for peritoneal in-sertion, in which filter membranes are sealed withsolvent to small Plexiglas rings so as to providean implantable chamber. Wong et al. (166) de-vised a neat method for preparing envelopes madefrom cellulose acetate filter membranes fusedaround the edges with acetone (Fig. 1). Suchimplantable envelopes or chambers are easilymultiplicable but do not allow access for samplingwhile in place. This can be accomplished with the"Vivar" diffusion chamber developed by Fina etal. (37), which they applied to a study of thebovine rumen. The device is shaped like a drum,with the two heads comprised of membrane heldin place by nuts and rubber washers. An accesstube for sampling extends as a side arm and ispassed through a fistula in the animal. A compar-ably employed device (28) is designed as a longinsertable tube of dialysis membrane supportedinside and out by cylindrical polythene netting.

In the first in vitro experiments, the arrange-ment mimicked that used for in vivo studies,except that a glass vessel of medium replaced theperitoneum or rumen. The membrane sac wasmade by coating a tube or thimble with collodionand then removing the mold, or by tying the endof a tube of parchment, cellophane, or similarmembrane material. The simplest arrangement,

however, is to employ a length of dialysis mem-brane tubing that is intussuscepted so as to forma double-walled tube, in the annular space ofwhich the culture is contained (165). The scale ofsize attainable with such a device obviously islimited, although Sterne and Wentzel (155)managed a toxin production system of this typewith 3.5 liters of culture surrounded by 35 litersof medium in a carboy (Fig. 2).The first really basic change in design intro-

duced the distinctive concept of carrying outgrowth in a culture vessel that is remote from butin communication with a nutrient reservoir vessel(44). This separation of the principal compart-ments of a dialysis culture system makes it pos-sible for each to be controlled independently andmore effectively. The concept was at first appliedby coiling dialysis membrane tubing around asupport in either the culture or the reservoir ves-sel, with the respective contents continuouslycirculated through the tubing by means of apump. Both of these systems, however, had in-herent limitations in capability for control, scale-up, and use with different types of membranes.To overcome these limitations, all three re-

gions-culture, reservoir, and dialysis-wereseparated. In the system thus evolved (Fig. 3),the culture vessel and the nutrient reservoir bothcan be of conventional fermentor design withoutany special modifications, and in principle anytype of vessel could be employed. Remote fromthese vessels but connected with them by tubingand pumps is a dialyzer through which the cultureand medium are continuously circulated. An

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FiG. 2. Representative sac-dialysis culture system.A tube of dialysis membrane is intussuscepted so as toform a double walled sac (C), the annular space ofwhich contains culture (B). The medium (A) is con-tained in a carboy. There also is a tubefor sampling andinoculating (D) anda harvesting siphon (E). Reproducedfrom Sterne and Wentzel (155).

important attribute of this system is that it allowsthe use of membranes in sheet form, which arecommercially available in a range of materials andtypes. Experiments demonstrated that this new"dialyzer-dialysis system" is inherently capable ofindependent control of the component opera-tions; for example, the culture can be agitated andaerated as much as necessary while the reservoiris held quiescent to help guard against contamina-tion. Furthermore, the system apparently couldbe adapted to any size simply by scaling up eachpart in proportion. An example is illustrated inFig. 4, where a 14-liter glass fermentor with 10liters of culture is shown attached to a 250-litersteel fermentor charged with 100 liters of medium.The key to effective operation of the above

dialyzer-dialysis culture system is a suitably de-signed dialyzer. The best principle of design ap-pears to be one resembling a plate-and-framefilter press, but holding a series of membranesheets. An industrial chemical dialyzer was em-ployed initially (44). Subsequently, Gerhardt andco-workers (Abstract, Meeting Am. Chem. Soc.,New York, 1966) designed and constructed a

multimembrane dialyzer especially suitable fordialysis culture and other biological applications.The resulting instrument (Fig. 4) consists of twoend plates that compress an alternating series ofthin metal frames, sheet membranes, and moldedrubber separators. All of the parts withstand re-peated autoclaving and are not toxic to micro-organisms or mammalian cells. The plates aremade of stainless steel or Pyrex glass and theframes, of stainless steel. The separators (Fig. 5)are custom molded from medical-grade siliconerubber. Each separator in one piece providesgasketing, entry holes and ports, and fields ofmembrane-support elements. Each such elementis an equilateral pyramid which causes a mini-mum of masking yet provides uniform supportof the membrane and also promotes turbulencein the flow of liquid, with consequent increase indialysis efficiency and prevention of the lodgmentof cells. The flow of liquids through the dialyzercan be upward or downward, cocurrent or coun-tercurrent, and slow or fast. Any type of sheetdialysis or filter membrane can be employed.With the development of more functional fer-

mentor systems, there also became evident a needfor more convenient flask dialysis culture systems,so that a number could be used at one time. Theresult was an efficient, twin-chambered dialysisflask (Fig. 6), constructed mainly from stockcomponents and designed for mounting on ashaking machine (51). A supported membrane isclamped between a reservoir of medium in thebottom and a small volume of culture above. Thelower reservoir is stirred by the rotation of aTeflon-coated steel ball, and is accessible byhypodermic needle through a rubber diaphragm.The culture in the upper chamber is aerated andagitated by baffled swirling, and is accessiblethrough a removable cotton closure on the topopening. The flask is constructed of stock fittings.of commercial Pyrex pipe and can be made in anydesired size.Nurmnikko (115) also had designed a flask

dialysis system, in which the membrane is heldbetween flanged side arms in the base of each oftwo adjoined flasks. A stagnant pocket of liquidcan occur in the side arms and the relative area ofmembrane is low, so that the efficiency of dialysisprobably is low. Furthermore, adequate mixingand aeration appear difficult to achieve in this.system. However, dialysis flasks of similar designare commercially available.A simple and effective dialysis flask can be

assembled from two L tubes of stock Pyrex pipe,with a gasketed membrane positioned betweenthe opposing arms by means of stock clamps(Zaccharias, personal communication).

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FIG. 3. Dialyzer-dialysis culture system. The nutrient reservoir is on the left, the dialyzer in the center, and theculture fermentor on the right. P designates a pump and V designates a valve. The arrows show the direction ofcirculation ofmedium and culture. Reproducedfrom Gallup and Gerhardt (44).

FIG. 4. Pilot-plant adaptation of dialyzer-dialysis culture system. An ordinary glass-jar fermentor assemblycontaining 10 liters ofculture is at the left; the dialyzer and two circulatingpumps are at center; and a stainless-steelreservoir containing 100 liters ofsterile medium is at the right. Reproducedfrom Gerhardt and Schultz (53).

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FIG. 5. Enlarged dimensional view of the silicone rubber separator used in the Gerhardt dialyzer.

Another dialysis flask was devised by Langloiset al. (83) for propagation of chick myeloblastcell suspensions. It embodied the useful featureof a separate medium reservoir, which was con-nected by tubing and a pump to the base of theflask so that the medium could be replenishedeasily (Fig. 7). The flask could be mounted on ashaker.Yet another design inventively made use of the

Venturi principle to induce turbulence arounddialysis tubing held in an hourglass-shaped flask,which is mounted on a reciprocating shaker (J.N. Dews, G. W. Schmersahl, and W. C. PatrickIII, U.S. Patent 3,321,086, 1967).

Interface Dialysis CultureOne usually thinks of dialysis as diffusion

through a membrane, but the diffusion barrieralso can be an interface between two physicallydifferent phases. For example, an ordinary brothculture in a test tube may be considered a dialysissystem in which a nutrient (gaseous oxygen) froma large reservoir (the atmosphere) diffuses across abarrier (the gas-liquid interface) and into solu-tion in the culture; carbon dioxide similarlydialyzes away as a product. Interfacial dialysissituations can be visualized as useful in microbialgrowth not only in such a gas-liquid biphasicsystem but also in solid-liquid and gas-solidsystems. Furthermore, liquid-liquid systems arepossible if two immiscible solutions are employed,

and a solid-solid system, in a sense, is exemplifiedby ordinary colonial growth upon nutrient agar.

This extended concept of dialysis has been ap-plied to microbial propagation in solid-liquid sys-tems directly analogous to the membrane dialysisflask system of Gerhardt and Gallup (51). Proto-zoologists apparently have employed the principlefor years, without clearly explaining its effects orsystemically studying its basis. The origin of thetechnique may be found in the work of McNealand Novy (90), who employed the liquid ofsyneresis on blood-agar slants to grow trypano-somes. This was followed by a series of redis-coveries that an overlay of liquid on an agar baseprovides a useful culture system. An early exampleis in the work of Drbohlav and Boeck in 1924(30), who described a biphasic medium for thecultivation of Entamoeba. Whole egg was mixedand inspissated in a tube, thus providing a solidreservoir of nutrient. This or blood-agar wasoverlaid with Ringer's or Locke's solution plusdiluted serum, into which the protozoa wereinoculated. The result was a solid-liquid dialysisculture system, with the solid phase serving as areservoir and the interface serving as a diffusionbarrier. The method was extended to obtaingrowth of trypanosomes by Kelser (79), with thenecessary blood restricted to the agar-solidifiedbase. Chang and Negherbon (24) described typi-cal growth curves. Although the protozoa areknown to be obligate aerobes, active aeration of

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FIG. 6. Dialysis culture flask, designed to be held ona carriage mounted on a rotary shaking machine. Thebottom compartment is filled with sterile medium whichis stirred by the rotating ball. The top compartmentholds the culture, which is turbulently aerated by swirl-ing and baffling. Reproducedfrom Gerhardt and Gallup(51).

cultures (e.g., placing a biphasic flask on a shak-ing machine) apparently has not been attempted.A convenient review of the cultivation of trypano-somes has been provided by Tobie (158).

Apparently the firstl use for interfacial dialysisculture in bacteriology was devised by Hestrin etal. (68). Aerobacter levanicum was grown in a

thin layer of aqueous sucrose over a base ofnutrient agar in a flask. The cells were then har-vested, washed, and autolyzed to obtain endo-cellular levansucrase.A solid-liquid biphasic flask system for grow-

ing bacteria in interfacial dialysis culture was de-veloped and studied in principle by Tyrrell et al.(161). In their system, an Erlenmeyer flask ispartially filled with hot medium containing 2%,agar. After the agar base has solidified, it is over-

laid aseptically with a small volume of broth,which then is inoculated. The flask thus preparedcan be clamped on a shaking machine to provideagitation and aeration during incubation, can bemade in numbers, and is adaptable to any size offlask up to several liters. Its effectiveness islimited mainly by the immobilization of thenutrient within a solid matrix. The movement ofnutrients is thus dependent on internal diffusion.Consequently, in practice the agar base must belimited to a depth of 5 cm or less. The agar also issubject to breakup from shaking, and some caremust be taken to prevent hydrolysis from over-heating. Breakup also can be minimized by im-mobilizing the agar by use of a square or indentedflask, and by precoating the flask with a film ofagar in order to obtain better bonding. If all ofthe medium components are incorporated intothe agar base, the overlay can be distilled water.After an equilibration period, the organisms canbe inoculated into the resulting clear diffusate.For bacteria such as gonococci, which normallymust be grown in a turbid medium enriched withblood and starch, a relatively clean crop of cellscan thus be harvested (52).The above solid-liquid dialysis culture systems

may be confused with the well-known doublemedium of Castaneda (21), which was devised forsimplifying blood cultivation procedures in thediagnosis of brucellosis. In this method, liquidmedium is placed in the base of an upright culturebottle, which is periodically tipped to inoculate alayer of agar medium on one of the side walls.The principle of dialysis, however, is not involved.The feasibility of using a liquid-liquid biphasic

culture system was explored by Puziss and Heden(132), in an approach based on the extensive useof immiscible polymer solutions for separationprocedures (5). A 2% solution of dextran (mo-lecular weight, 480,000) separates as a lower phasefrom a 12% solution of polyethylene glycol(molecular weight, 4,000). Incorporated into anagitated culture system for Clostridium tetani, thesolutions were kept dispersed as droplets duringthe course of growth and toxin formation. Uponcompletion of the production cycle, the cell-containing dextran phase was permitted to coa-lesce to the bottom and then was withdrawn.Toxin was equally distributed in the two layers,but was recovered mainly in the top glycol phasebecause of its greater volume. The main feature ofthis liquid-liquid biphasic culture system, there-fore, appears to be dialytic removal of a macro-molecular product into a dispersed reservoir ofextracting solvent.

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FIG. 7. Dialysis flask (A) usedfor production of virusfrom myeloblast cell culture, with provision for circulationofmedium from a separate reservoir (B). The pump (C) consists ofa rubber tube with check valves, which is posi-tioned within a glass chamber and activated by air pressure delivered by a reciprocating motor. The remaining com-ponents are self explanatory. Reproducedfrom Langlois et al. (83).

Colonial Growth with DialysisThe discussion thus far has tacitly assumed that

the microbial populations were homogeneouslysuspended in liquid culture. Within or on a solidmedium, however, microorganisms generallydevelop as a localized mass of cells. This colonialgrowth usually occurs in a situation governed bydialysis, but the nature of growth is quite differentfrom that in liquid culture.

Initially, cells in a colony are largely physio-logically homogeneous and multiply exponen-tially with time. But after a few generations, thepopulation becomes more heterogeneous and theorder of growth may become very complex, prob-ably because of the close proximity of the cellsand their relative location within the colony.Since nutrients from the substratum can reachcells only by diffusion, any given cell at the top ofthe colony is in competition for nutrients with theentire metabolizing mass of cells beneath it.Conversely, any given cell at the bottom mustcompete with the respiring barrier of cells above

it. These two cells in a colony only 1 mm thickmay be separated by hundreds of competing cells,and even greater competition gradients exist be-tween cells in the center and on the periphery ofthe colony. Consequently, colonial growth posessevere limitations in the design of controllablesystems, the development of rational theory, andeven the application to practical needs.

Despite these limitations, there are a number ofmethods for colonial growth with dialysis, manyof which are cited in a recent monograph onminiaturized methods (64). Only selected andexemplifying techniques will be cited here.The classical method of growing microorga-

nisms on medium solidified with agar or other gelsmay be considered as an interfacial dialysis cul-ture system. Although mainly used in petri platesor as slants in test tubes, agar microcultures alsohave been devised in ingenious variety by "hang-ing-block" techniques (64).

Placed on the surface of agar medium, an inocu-lated limiting membrane can subsequently be

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lifted off, and the colonial growth on it can bereadily examined in situ and even preserved.Apparently introduced by Birch-Hirschfeld (13),the technique was redescribed and applied tovarious uses in morphology (64). The familiarmembrane-filter technique is a modification inwhich the organisms strained from a large anddilute sample are subsequently cultured by plac-ing the membrane on nutrient agar.The feasibility of employing membranes or

other porous solid surfaces for producing massesof microorganisms in colonial growth has beenexplored from time to time (126, 134). Invariably,-these have proven impractical; in principle, they-are inefficient, and the resulting cells are physio-logically heterogeneous. However, colonial sur-face cultures may be eminently useful in certainindustrial fermentation processes, notably, trick-ling filter beds for sewage and the "quick process"generator for vinegar.

Colonial growth on membranes in contact witha reservoir of liquid medium has unexcelled meritfor certain microscopic applications. Both simple(119) and elaborate (128) techniques have been-devised by Powell and his colleagues to permit theexamination of microcultures. The latter tech-nique permits circulation of the medium beneath-the membrane, variation in the gaseous environ-ment above the membrane (including anaerobio-sis), control of the amount of liquid around indi-vidual cells, micromanipulation of the cells, anduse of reflected, transmitted, or phase-contrastoptics. Hillier et al. (69) described a method forgrowing microcultures on a collodion membrane-so that they could be transferred undisturbed forexamination in an electron microscope.A natural membrane dialysis system is pro-

vided by the chorioallantoic membrane of theembryonated chicken egg. This serous surfacewith its underlying reservoir of nutrient has longbeen employed for propagating colonies of anumber of microorganisms. An ingenious anduseful extension of this method has been made byimplanting on the natural membrane a diffusionchamber with a cellulose-acetate filter membrane.Human leukocytes grow better in this environ-ment than in vitro, reaching a maximum mitoticrate 72 hr after implantation (117), and the im-mune response elicited by other in vivo environ-ments is avoided. The method also has beenfound valuable for growing a number of differenttypes of embryonic tissues and for obtainingdifferentiation of neural tissue (12).

Although these techniques for obtaining/colonial growth with dialysis have been very use-ful in specific circumstances, all of the followingdiscussion will be directed toward the more un-restricted situations where the growing microbial

populations are homogeneously suspended indialyzed liquid culture.

Methods of OperationThe classical method of growing microorgan-

isms (e.g., a broth culture in a cotton-plugged testtube) may be said to be operated as an approxima-tion of a closed system, in which all reactants,products, and energy are contained and insulatedwithin a completely closed vessel. It is obviousthat a microbial culture system only roughly

a) BATCH RESERVOIR AND FERMENTOR

b)CONTINUOUS RESERVOIR AND FERMENTOR

c) BATCH RESERVOIR, CONTINUOUS FERMENTOR

VrFr Sr

d) CONTINUOUS RESERVOIR, BATCH FERMENTORFIG. 8. Four modes of operating a dialysis culture.

Although a dialyzer-dialysis system is diagrammed, theprinciples are intrinsically applicable to any design. Thesymbol F is the flow rate, S is the substrate concentra-tion, V is the volume, and X is the cell concentrationinto, within, and out from the reservoir and fermentorvessels. Reproduced, with revisions, from Gerhardt andSchultz (53).

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approximates this ideal, because gaseous nutrientsand products are free to exchange with the at-mosphere through the plug and also because heatis freely lost from the system. In common par-lance, this is a batch culture. It is characterized bythe familiar population growth cycle and a pat-tern of nutrient depletion and product accumu-lation.

Dialysis cultures usually have been operated asbatch cultures, as illustrated diagrammatically inFig. 8a. A fixed volume of medium is charged intothe fermentor (Vf) and reservoir (Vr), with aninitially fixed concentration of limiting substratein each (Sf, Sr). Microorganisms are inoculatedinto the fermentor, also at an initially fixed con-centration (X). The resulting growth cycle indialysis culture appears similar to that seen in anordinary batch culture, differing mainly in a pro-longation of the exponential phase so that themaximal stationary phase occurs at a higher level(see below, section on In Vitro Systems)

It is now well known that microorganisms alsocan be grown in an open system, in an approxima-tion of a steady state. In common parlance, thisis a continuous culture. A constant concentrationof organisms and a constant rate of growth occurwhen dynamic equilibrium is reached.

Dialysis culture also can be operated as a con-tinuous culture, although the experimental trialshave been limited (58, 59, 65; Gallup, Ph.D.Thesis, Univ. of Michigan, Ann Arbor, 1962).As illustrated in Fig. 8b, both the fermentor andthe reservoir can be operated in steady state, butthe option also exists to operate in a partiallycontinuous mode with the fermentor in steadystate and the reservoir not (Fig. 8c), or vice versa(Fig. 8d). Continuous operations are directlyamenable to mathematical analysis. The equationsfor the batch situation can be handled best bycomputer simulation or by an approximatinganalytical approach. The above four possiblemodes of operating a dialyzer-dialysis fermentorsystem are treated in the section on Theory (seebelow, Growth in Dialysis Culture).

Types of Membranes

Three main types of membranes applicable todialysis culture presently are available commer-cially. The type usually considered is ordinarydialysis membrane, exemplified by the tubingmade of regenerated cellulose by the Viskingprocess. The rated average pore size is in theorder of 5 nm in diameter but varies with thesize of tubing, which is available in various diam-eters. This type of membrane retains large mole-cules such as enzymes and toxins but permits thepassage of small molecules such as sugars and

salts. Wall thickness varies with size of the tubing,the percentage of void~space differs, and theporosity changes with the degree of hydration.This type of membrane may be fabricated fromcollodion, parchment, cellophane, or a variety ofplastics. A recently introduced type of membraneis described as anisotropic, but essentially is avery thin (and therefore efficient) film of ultra-microporous polymer cast on a supporting layerof coarsely porous material. This permselectivefilm can be cast with pore sizes from 0.3 to 10nm. It will be convenient to refer to such ultra-microporous membranes in general as dialysismembranes.A second principal type of membrane is micro-

porous. The rated mean pore diameter for micro-biological use is in the order of 200 nm, but theavailable range of porosity extends down toabout 25 nm. This type of membrane retainsparticles such as bacteria but permits the passageof most solutes, including macromolecules.These membranes are exemplified by several onthe market made from cellulose-acetate, and con-veniently may be called filter membranes (ormembrane filters). Materials of construction mayvary widely and recently have tended towardplastics such as polyvinyl alcohol. Asbestos, un-glazed porcelain, and sintered metal or glass alsohave been used to fabricate membrane filters, aswell as the more usual filter candles and funnels.The disadvantages for dialysis applications liesmainly in the relative thickness and coarseporosity of membranes made from such materials.A third type of membrane has a more restricted

applicability in dialysis culture, because onlygases can penetrate it. This type, made from mate-rials such as silicone rubber or Teflon, shows noevidence of porosity but instead behaves as asolvent in which dissolved molecules migrate bydiffusion. Such membranes will be called solution-transport membranes.

Selection from the above membrane types is, ofcourse, determined by those properties which bestserve experimental requirements. In general,however, microbiological applications requirethat a membrane be capable of withholding or-ganisms during the culture period, sterilizable byautoclaving, durable in construction, undigestibleby bacterial enzymes, and efficient in the rate ofsolute diffusion. Although membrane porosity,void space, and thickness mainly govern diffusionrates, it is desirable to make direct comparisonswith glucose or some other representative nu-trient as a test or reference solute. Such a repre-sentative comparison of membranes has beenpublished (51). Theoretical aspects of membranecharacteristics, permeability measurements, po-

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FIG. 9. Electron micrograph showing the ultrastructure ofa typical filter membrane. Reproduced with permissionof Gelman Instrument Co., Ann Arbor, Mich.

rosity, and hydrodynamics are presented later inthis article (see Principles of Dialysis).

Membrane Permeability and Solute SievingIn both dialysis and filter membranes, the

mechanisms for permeation of solutes are relatedto membrane ultrastructure. Both are made fromessentially linear polymers, the macromolecularfibrils of which are cross-linked by chemical bondsto form a tertiary heteroporous matrix. Consider-able study has been made of membrane ultra-structure by means of electron microscopy (18,91). A dimensional representation of this ultra-structure is depicted in Fig. 9. It is important toremember the spongelike or foamlike nature ofporous membranes, because quite a differentimage often is conjured, e.g., something like aperforated sheet. Our model embodies openingsor pores of various sizes distributed randomly inthe membrane and creating a tortuous passage-way for penetration. It would be desirable, ofcourse, if the pores were uniform in size, but suchisoporous membranes are not known to be avail-able except in much coarser porosity, as withscreens or fabrics, or in much finer porosity, aswith crystal lattices.

Since the openings of membranes usually arefilled with water, small solute molecules can eitherdiffuse through the passageway or be carriedthrough by net flow of water. This latter mecha-nism of transport in dialysis may not be as com-monly recognized as diffusion, but it accounts fora substantial part of the total, especially if pres-sure differentials occur.

In solution-transport membranes, a completelydifferent mechanism of permeability prevails.The membrane is not a gel with water-filled open-ings, but is instead a sol. The solute penetrates,therefore, by dissolving in the substance of themembrane, passing through by diffusion, andthen leaving on the other side. The solute canenter or leave the membrane either from thegaseous state or liquid solution.The withholding or sieving of molecules is

related to solubilities in the case of solution-transport membranes and to maximum pore sizein the other two types of membrane. Althoughelectrostatic charge and other factors have aninfluence, it is mainly the largest passageway inthe dialysis or filter membrane which determinesthe maximum size of molecule or particle that canpenetrate. Molecules large enough to be withheld

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by a dialysis membrane usually will be polymers,typically linear ones. Such long macromoleculestend to coil or agglomerate in solution and be-have as spheres or rods; their equivalent diffusiondiameter can be determined by the Einstein-Stokes formulation.

Membrane Penetrability by MicroorganismsIt is obvious that special precaution must be

exercised against the possibility of penetration ofmicroorganisms through rents or holes in defec-tive membranes. Each piece of membrane to beused can be examined for pinpoint leaks by flood-ing the membrane with alcohol while it rests on adark blotter, or by flooding the membrane withwater while it lies on an indicator mixture of 98%sugar and 2% crystal violet (63). Small leaks alsocan be detected by bubble-testing in a device ar-ranged so that above one side is water and underthe other is an air pressure chamber; if the mem-brane is adequately supported with a flat screen ora sintered plate, a pressure of 15 psi will discloseflaws. At high pressures, a relationship existsbetween bubble-threshold pressure and porosity,and the method can be employed to calibrate theporosity of coarsely porous membranes, such asfilter membranes.Given a flawless membrane of proper porosity,

it is generally assumed that cellular microorga-nisms such as bacteria cannot penetrate it. Theability to filter bacteria is dependent not only on apore structure smaller in size than the organisms(usually less than about 0.2 Mim) but also on theuse of a pressure differential. This causes theorganism to become impinged mainly on the sur-face of the filter, but also in the tortuous passage-ways. The mechanism by which bacteria are fil-tered has been examined by electron microscopyof bacteria-clogged filter membranes (101).The filtration process is not absolute, however.

It is common knowledge among those who em-ploy filter membranes for sterilizing biologicalsthat bacteria can be forced through the barrier ifthe filtration time is prolonged. It also has beendiscovered that deformable organisms such asmycoplasma will pass through a filter membranedirectly in proportion to the pressure applied(Morowitz, unpublished results).In dialysis culture (and in many other situa-

tions in which membranes are employed in micro-biology), the critical factor of pressure-inducedimpingement is not present, and consequentlymuch greater concern must be given to the possi-bility of penetrability of the unclogged membraneby microorganisms. This seemingly has not beena practical limitation in earlier systems, but in adifferential dialysis flask system it was discovered

that a bacterium such as Staphylococcus aureusapparently can penetrate a filter membrane withpores far smaller than the size of the cells (67).Besides the absence of a pressure differential, thesituation was distinctive in the requirement for anextended incubation period and perhaps also inthe membrane supporting structure, which couldtrap organisms in contact with the membrane.This occurrence prompted a literature search forother experimental evidence that organisms canpenetrate membranes with pores seemingly muchtoo small.The phenomenon of apparent dialyzability of

bacteria was traced, with some diligence, first to aLetter to the Editor in the Journal of the Indone-sian Medical Association by Gan (45), and thenceto a full report with experimental results (46).In these accounts, Gan told of controlled experi-ments in which some 21 different bacteria andcommon yeast were found to be capable of pene-trating intact dialysis (Visking) tubing Thisastonishing observation, if verified, would havebasic implications not only for dialysis culturebut also for a number of tenets in microbiology.Consequently, Gan's findings will be summarizedin some detail and his method will be scrutinized.

It should at once be recognized that the experi-ments apparently were performed with great careand with anticipation of incredulity (criticism wasobtained from two eminent biophysicists beforepublication of the results). The test apparatus wascrude but suitable: hydrated dialysis tubing wasinverted on itself, forming a double-walled cy-lindrical sac which was hung in the bulb of aSmith fermentation tube (Fig. 10). The testorganism and medium were inserted into themembrane sac, and the dialyzing fluid was placedin the tube proper. Appropriate precautions ap-parently were taken to prepare, assemble, sterilize,inoculate, and sample in the experiments.The demonstration experiments were conducted

with a good representation of organisms: gram-positive and gram-negative, motile and nonmotile,large and small, and morphologically different.At least 2, and on occasion as many as 23, repli-cations were made with a given organism. Withdialysis into distilled water, penetration of dif-ferent organisms was observed within 5 days with11 to 100% consistency. The presence of orga-nisms in the dialysate was determined by inoculat-ing a 0.1-ml sample onto an agar medium.Most importantly, control experiments were

conducted with protein molecules and virusparticles. Hemoglobin, vaccinia virus, or bac-teriophage, present in the dialysis sac togetherwith a test bacterium, did not penetrate, whereasthe organism did. Moreover, dialysis tubing did

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FIG. 10. Apparatus used to test the penetration of dialysis membrane by bacteria. Reproducedfrom Gan (45).

not become permeable to hemoglobin after ex-posure to six test bacteria, singly or together, for15 days. One might criticize these experiments onthe basis that one bacterium penetrating the mem-brane would multiply and so would be observed,whereas one penetrating virus might not be in-cluded in the sample transferred to a plaque testand so might escape observation.

Several variables were examined by Gan, in-cluding the culture age, the quantity and type ofdiluting medium used with the test cells, and thepH and type of the dialyzing fluid. In retrospect,the last variable is believed especially critical.Distilled water and phosphate solution, in aboutthree times the volume of the culture medium,were found to be the most effective in causing cellpenetration of the membrane. Unfortunately, thecontrol situation was apparently not included inwhich the medium employed with the cells wasalso used as the dialyzing fluid.We have come tentatively to accept Gan's

conclusions that several kinds of bacteria in facthave the ability to penetrate the pores of dialysistubing under certain experimental conditions andthat the results are not attributable to leakage.We further accept his admonition that the find-ings require confirmation by other workers.Two later and entirely independent studies on

permeability of membranes to bacteria were foundin the literature on food technology. Hartman,Powers, and Pratt (63) reported that cellulose-acetate or polyethylene membranes seemedpermeable to bacteria but cellophane membranesdid not. They felt it necessary, however, to useunsterilized membranes and therefore had to re-sort to a statistical estimate of the probability ofpenetration after test sacs were incubated for 72hr. Furthermore, a considerable number of pin-hole leaks were detected after the growth testswere completed. The cellophane bags were per-forated more often than any of the others. Thisobservation deserves attention in evaluating Gan's

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1SCHULTZ AND GERHARDT

results (above), although his use of protein andvirus as controls would seem to preclude thepossibility.

Ronsivalli et al. (140) subsequently also in-vestigated food-packaging films and concludedthat all were impermeable to bacteria. However,their actual data seem inconsistent with theirconclusions, e.g., two of six defect-free poly-ethylene sacs were indicated to have allowedbacteria to pass into and grow in the surroundingmedium.

If the dialyzability of bacteria is tentativelytaken as fact, the mechanism of passage is imme-diately in question. Gan (46) interpreted his find-ings to indicate that the transfer of the bacterialmultiplying activity through the membrane mustoccur by units smaller than the normal bacterialcell. In further studies, Gan (47) employedShigella sonnei at low temperature in an attemptto exclude active multiplication, and alleged that3-hr "dialysates" (diffusates) contained sub-microscopic viable units different in nature fromthe parent test bacteria. These particles were pur-ported to be filterable through a collodion filterand not to be sedimented after centrifugation for2 hr at 16,000 to 20,000 rev/min. Morphologicalexamination was said to reveal the presence, afterincubation of the diffusate for 1 hr, of minute(0.20 to 0.35 ,um) undifferentiated granules; after3 hr of incubation, these increased in diameter to1 to 2 ,um and became pleomorphic; after 4 hr,typical bacterial growth occurred. Obviously,critical confirmation is needed.An alternative mechanism also might account

for bacterial dialyzability, namely, an infiltratinggrowth process by diapedesis through the open-ings of the membrane. Capalbo et al. (19) foundthat mouse peritoneal cells were excluded fromimplanted diffusion chambers only if the filtermembranes were 0.1 ,um or less in average poros-ity, which is far smaller than the size of the cells.Sectioned and stained membranes of coarserporosity were observed to have cell processespenetrating them. Keller and Sorkin (78) furthernoted that the presence of a chemotactic agentenhanced the migration of such cells through afiltering barrier. This could explain the observedgrowth of staphylococcal L forms through filtermembranes of a pore size as small as 0.05 Amwhen placed on agar medium (100). In the situa-tions in which Gan (46) reported membrane pene-tration by a number of bacteria, the cells weredialyzed against distilled water or phosphatesolution. The ionic and osmotic gradients thusestablished across the membrane conceivablycould have caused plasmoptysis of the bacteria,with resulting formation of a spheroplast or bleb.These plastic forms conceivably could have

traversed the membrane and generated normalcells on the other side.Although the occurrence and mechanism of the

reported penetration of membranes by bacterianeeds critical confirming study, the likelihood ofsuch an occurrence clearly must be taken intoaccount in the practice of dialysis culture and inother comparable situations in microbiology.

THEORYPrinciples of Dialysis

Membrane characteristics. Even if the micro-geometry of all the tortuous paths through amembrane were known exactly, it still would beimpossible to predict precisely the excursion ofmolecules through the membrane. Therefore, asemiempirical approach, based on Fick's law ofdiffusion, has been adapted to characterize mem-brane permeability. Fick's law states that therate of diffusion through a uniform film of liquidis related to the concentration gradient across thefilm and to other parameters as shown below:

D°AN= pAS (1)

where N is the rate of permeation (g/hr), D° isthe diffusivity of the solute in the liquid (cm2/hr),Ap is that part of the total membrane area (i.e.,pore area) available for diffusion (cm2), Lp is thelength of the diffusion path in the pores (cm),and AS is the concentration difference across thefilm (g/cm3).A dialysis membrane may be regarded as a thin

film of liquid retained within the porous matrixof membrane material, but usually the diffusivityof solute within the membrane and the distribu-tions of pore areas and lengths are not known.Therefore, these unknown factors are combinedto give an empirical factor, the permeabilitycoefficient (Pm), which must be experimentallydetermined for each membrane and solute.

Equation 1 is rewritten (160) as:

(2)N = PmAmAS

which defines Pm as

NPM = AmAS

where Am is the total area of the membrane (whichis larger than Ap , defined above), and the perme-ability coefficient (Pm) has the units cm/hr.

Equation 2 states that the rate of molecular dif-fusion through an inert porous membrane is directlyrelated to the permeability coefficient, membranearea, and concentration difference across themembrane.

(3)

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Measurement of permeability. A method formeasuring the overall permeability coefficient of amembrane for a particular compound undergiven hydrodynamic conditions is suggested byequation 3. Experimentally, one can separate twochambers with the membrane, and then measurethe rate at which the compound diffuses from oneside to the other and the concentration of thecompound on each side of the membrane. If twowell-mixed closed chambers are used, only oneconcentration needs to be measured as a functionof time. The following formula gives the relation-ship of concentration and time to permeability(94):

USi (V + V-)-(2+ V1)In ( ) (4)

-( 1 + PmAmt

where Si is the concentration in chamber 1 at anytime, Si0 and S20 are the initial concentrations inchambers 1 and 2, and V1 and V2 are the volumesof chambers 1 and 2.

If the concentration in one of the chambers isinitially zero (S1i = 0), the left-hand side ofequation 4 is simplified so that

InSe V + V27 PmAm t (5)

Where Se is the final equilibrium concentrationin both chambers,

Se = 520V2/(V1 + V2) (6)

The time to reach half of the equilibrium con-centration (t = ET50) is sometimes used (27, 51).This number is related to the permeability coeffi-cient by the following formula, when Si = Se/2:

In (1- 5-)(=In

(V1 + m 6

Rearranging, we find

nV2

I1.

0.

,- 0.

%

-- U.mw 0.

(7) a-O

WO.

wZ 0.

O.

(8)

Thus, the half-equilibration time is dependent onthe chamber volume and the membrane area. There-fore, it has limited usefulness in characterizing

membrane permeability. For example, Craig (27)and Gerhardt and Gallup (51) give ETso values of3.5 and 2.5 hr, respectively, for glucose throughVisking dialysis membranes. On the basis of thesedata, it would seem that there was not much dif-ference in the permeability of glucose throughthese two membranes. But if one calculates Pmfor each membrane by equation 8, Pm for Ger-hardt and Gallup's membrane was 9.69 cm/hr,whereas Pm for Craig's membrane was 0.23 x

10- cm/hr; i.e.,they in fact differed by a factor of300. This result is not surprising, because Craigpurposely treated his membranes to reduce theirpore size and so to separate glucose and sucroseby dialysis, but the effect of this treatment onmembrane permeability is not apparent from thereported ET50 data.

Porosity. There are several methods for esti-mating the effective pore size of a membrane.These methods are based on resistance to liquidflow, capillary surface tension, void content, anddiameter of diffusing molecules (118, 135). Noneof these methods is entirely satisfactory, but, fromthe work that has been done in this field, it is cer-tain that the passage of molecules through a mem-brane is impeded as the size of the molecule ap-proaches the dimensions of the pore opening.For example, Manegold (94) showed that the

permeation of sucrose through a series of mem-branes increases as the average pore size of themembrane increases. Some of Manegold's dataare replotted in Fig. 11. It can be seen that therelative permeability of membranes with thesmallest pores is about 40% of the maximum.

Experiments by Spandau and Gross (151) showedthat the converse is also true; that is, the perme-

10 20 30 50 70 100 200 300 500ONE-HALF "EQUIVALENT SLIT WIDTH" OF

MEMBRANE PORES (A0)

FiG. 11. Permeation of sucrose through a series ofmembranes graded in porosity. Data from Manegold(94), replotted.

To.98-s7 /7

.5

.4-

.3-

.2

.1 _

0I

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ability of a given membrane to a series of in-creasingly larger molecules decreases more rapidlythan does the diffusivity of the molecules insolvent alone.Renkin (135) and Craig (27) have corroborated

this effect. Thus, for a given membrane, Pm de-creases with increasing molecular size. If a mix-ture of compounds is dialyzed, the individualcomponents will diffuse through the membraneat different rates, even with the same concentra-tion driving force across the membrane. Craig(27) developed this principle for the separation ofsmall protein fragments, and Siggia et al. (149)used it to measure the relative amounts of sugarsor amino acids in a mixture.The various explanations that have been pro-

posed to account for the effect shown in Fig. 11are all related to pore size and membrane struc-ture. Three main explantations exist: restricteddiffusion of a molecule, decreased effective openarea, or increased length of the diffusion path.All three properties can be affected when the poresize approaches molecular dimensions.

It has been proposed in the first case that dif-fusion is hindered when a molecule diffusesthrough a capillary pore, an effect similar to thereduction in sedimentation velocity of particlesin small tubes. Correlations for the wall effect onsedimentation have been used for predicting theeffect of pore size on hindered diffusion (82, 118).Two such correlations, suggested by Faxen (34)and Francis (40), are

f=-Do=1-2.104 R-(r )3 ( r5+ 2.091 - 0.95

and

f D= (1 -)

(9)

Ir0

(10) U

z0

where f is the ratio of the permeation rate of asubstance through the membrane to the permea-tion rate through an equivalent thickness of puresolvent, Dm is the effective diffusivity of the sub-stance in the membrane, r is the molecular radiusof the substance, and R is the effective radius ofthe pore in the membrane.A second possibility is that the effective open

area available for diffusion decreases with in-creasing molecular size because of the low proba-bility that an incident molecule will actuallypenetrate the pore. Ferry (35) suggested that theeffective available area for diffusion is related to

C-,w

0u-

the true open area by the following formula:

=e =(1-R2 (11)

where A e is the effective open area of the pore andAp is the true open area of the pore. Note theresemblance of this equation to the empiricalformula given in equation 10.The two previous explanations are based on an

isoporous membrane model. However, a mem-brane is madeup ofmany interconnected passage-ways of various sizes. All of the holes would beeffectively open for very small molecules, but forlarge molecules the number of suitable passage-ways would be reduced, and the average distancea large molecule would have to travel to getthrough the membrane would be longer.

In other words, for larger molecules the effec-tive open area of the pores will be smaller andalso the effective diffusion path will be longer.This can be expressed as

(_r)( )

(i+jn)(12)

where the numerator represents the decrease inopen area, the denominator represents the in-crease in diffusion path for decreasing pore size,and n is an empirical constant which is found bycurve fitting.

Equations 9-12 are plotted in Fig. 12, and theyall exhibit the same form shown in Fig. 11. Each

2 3 5 7 10 20 30 50 70 100RATIO PORE RADIUS TO MOLECULAR RADIUSR

FIG. 12. Calculated models for the effect of mem-brane pore size on permeability. The correction factor,f, is the ratio of the actual diffusion rate through themembrane to the diffusion rate (by Fick's law) calcu-latedfor a film of solvent having equal geometric thick-ness and open area.

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TABLE 1. Calculated effect of membrane pore sizeon the separation of molecules A and B, where

the molecular size of B is twice aslarge as that of A

Radius of Radius of Ratio of Relative per-pore/radius pore/radius permeation meation rate

of A of B rates, fA/fBa of A,fAa.b

100 50 1.03 0.9820 10 1.14 0.8810 5 1.35 0.775 2.5 2.04 0.573.3 1.67 4.50 0.412.5 1.25 15.5 0.28

a Calculated from equation 10.bRelative to an equivalent thickness for solvent

alone.

of the above equations for the correction factorf,or combinations of them, can be used to correlateexperimental data on membrane coefficients (Pm)for various substances relative to the diffusionrates of the same substance in solvent alone. Theyshould, therefore, be looked upon as semiempiri-cal rather than fundamental formulations.

There are several interesting consequences ofthese correlations insofar as dialysis culture isconcerned. One of the potential advantages ofdialysis culture is the differential segregation ofmolecules of different sizes (51). It can be seenfrom Fig. 11 and 12, however, that an effectiveseparation of molecules of similar size by a singlemembrane is not practical. For example, con-sider two molecules A and B where the diameterof B is twice as large as that of A. The relativediffusion rates of these two molecules are a func-tion of pore size, as shown in Table 1. To achievean appreciable difference in the rates of penetra-tion ofA andB through a membrane (column 3),a membrane has to be selected with a mean poresize about five times the molecular diameter of A.However, as shown in column 4, this separation isobtained at the expense of a considerable reduc-tion in the penetration rate of A. If A were glu-cose (molecular weight, 180), then B would corre-spond to a compound with a molecular weight ofabout 1,440 (assuming the molecular diameter isproportional to the cube root of molecularweight).

In addition to molecular size, there may beother factors which influence the passage ofmolecules through membranes. Ryle (143)showed that polyethylene glycol (Mn about15,000) passed through dialysis tubing which re-tained hemoglobin. However, this polymer ap-peared at the same holdup volume as hemoglobinwhen passed through a gel chromatography

column (Sephadex G-100). Since both dialysisand gel filtration depend on the principle ofhindered diffusion, there must be some interac-tion between the diffusing molecules and theporous media.From these considerations, it is apparent that

the use of a single membrane to separate microbialproducts produced in dialysis culture will be practi-cal only if there are large differences in the molecu-lar sizes of the products.The use of membranes with small pores, rela-

tive to the molecular size of the nutrients in thereservoir, may result in different permeation ratesinto the culture chamber and a correspondingimbalance in the dialyzed medium. Furthermore,if the prime purpose of the membrane is to separatethe microbial cells from the nutrient supply, thenthe durability of the membrane is probably a moreimportant consideration than the pore size, as longas the pore size is more than about 15 times thediameter of the largest nutrient molecule. FromFig. 12, it is seen that there is little difference indiffusion rate if the pore size is between 15 and100 times the molecular diameter.Hydrodynamics. The rate of dialysis is strongly

dependent on the liquid velocity at the membranesurface. A typical experimental curve, for thedialysis of sucrose (54), is shown in Fig. 13. Thisbehavior is rationalized by postulating theexistence of a thin zone of nonturbulent liquid(Nernst film) in the immediate vicinity of themembrane surface, as pictured in Fig. 14. Thethickness of this liquid film decreases as the bulkliquid velocity near the membrane increases. Asfar as the permeant molecule is concerned, there

_ 0.4

E

E0-I_ 0.3zw

U-U.w° 0.2

-J

mI 0.1

a-

00 1000

STIRRER SPEED (rev/min)2000

FIG. 13. Effect of liquid agitation on membranepermeability to sucrose. Data from Ginzburg andKatchalsky (54), replotted.

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F I

the added resistance of the liquid films is probablynever completely eliminated. Ginzburg andKatchalsky (54) estimated that a limiting filmthickness of 25 nm remains, even at extreme stir-ring rates. These authors also stated that the

i relative importance of the liquid film decreasesas larger permeant molecules are considered be-cause Pm° is more sensitive to molecular size than

____ i_ Pi and P2.J,~, Osmosis. Whenever a permeable membrane is

interposed between different solutions, there is apossibility of water transport across the mem-

_ brane by osmosis. In dialysis culture, concentra-tion gradients of nutrients and products acrossthe dialysis membrane will occur and thereforecause some movement of water either into or out

MEMBRANE of the culture chamber. Water will tend to movetoward the region of higher osmotic pressure. Therate of water flow through a membrane is given

L M by equation 15 (77, 152):

TURBULENCE

FIG. 14. Representation of fluid flow past the op-

posing faces of two membranes, with a laminar filmimmediately along each surface and turbulent bulkflowin the central channel.

are effectively three barriers that must be pene-trated: a liquid film on each side of the dialysismembrane, and the dialysis membrane itself.The permeability coefficient, as calculated by

equation 3, reflects the overall resistance of thecomposite barrier. It can be shown that the over-all permeability coefficient is related to the truemembrane permeability coefficient (Pm0) by thefollowing equation

1=

1 1 1±+o + (13)Pm P PmP2

where

Do DoPi = P2= (14)

61 2

D' is the diffusivity of the substance in water, anda is the thickness of the unstirred liquid film.As the bulk liquid velocity near the membrane

increases, the liquid film decreases (61 and 52 be-come smaller) and Pm approaches Pm0 (the truepermeability of the membrane). It can be seen inFig. 13 that the overall permeability coefficient,Pm , can be increased by afactor of two or three byvigorous stirring or high flow rates near the mem-brane. A point of diminishing returns is reachedinsofar as the value of providing extremely highturbulence near the membrane, however, because

Q = Kf(AP - RTE oijSj)i

(15)

where Q is the filtration rate of water through themembrane (cm3/hr cm2 of membrane area), Kfis the filtration coefficient for the membrane(cm3/hr atm cm2), AP is the hydrostatic pressureacross the membrane, R is the gas constant[82.05/cm3 atm/(g mole 'K)], T is the absolutetemperature (0K), AS1 is the concentrationgradient of a solute across the membrane (gmole/cm3), and ai is the reflection coefficient forthe solute.

Usually, dialysis cultures are carried out underconditions where there is no net external pressureacross the membrane (i.e., AP = 0), and thenequation 15 becomes

Q = -KfRT E ojAS1i

(16)

The reflection coefficient takes into account thefact that membranes are not ideally semiperme-able, and that lower osmotic pressures are exertedby freely diffusable solutes. For nonpermeantmolecules, a = 1. For permeable substances, a isless than one and approaches zero for freely per-meating molecules. Ginzburg and Katchalsky(54) give values for a with 0.1 M sucrose, 0.1 M

glucose, and 0.15 M urea solutions, respectively,of 0.114, 0.072, and 0.013 with a Visking dialysismembrane.A sample calculation of the magnitude of

water flow one might obtain in dialysis culture isinstructive. The filtration coefficient (Kf) fordialysis tubing is about 6 X 10-2 cm3/atm hr (54,135). If a glucose gradient of about 0.1 M is main-tained between the reservoir and culture cham-

At

1(A

k

T /-f1A (A I /f

AIl1'-

MEMBRANE

K1tFILM

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bers, then, from equation 16

Q=6X10-2 cm3atm hr cm2

x 82.05 g mole 'K X 298 X 0.072 X 0.1 (17)

X 10-3 g mole = 1.06 X 10-2 cm3cm3 hr cm2

If the membrane area were 100 cm2, and the dura-tion 50 hr, then the total volume of water leavingthe culture chamber would be 1.06 x 102 X100 x 50 = 50 ml. This amount of fluid wouldmake quite a difference if the culture chambercontained 100 to 250 ml initially. Actually, largeosmotic transfers of water are not found in prac-tice, probably because metabolic products in theculture chamber tend to minimize the osmoticpressure gradient and also because it is commonpractice to place saline in the culture chamberinitially to counterbalance the osmotic pressure ofthe reservoir chamber. However, transfers ofwater may occur if disparate amounts of proteinin the nutrient reservoir exert a Donnan effector if positive pressure from aeration in the culturechamber causes mass solvent flow with ultrafil-tration.

Growth in Dialysis Culture

Basic considerations. A valid approach towardquantitatively characterizing the proliferation ofmicroorganisms requires that only one factor at atime be considered, with the others invariant. Thisrequirement can be approximated with a culturein which a metabolic steady state is maintainedby means of an open system, i.e., in a continuousculture. Although this technique dates far back inthe art of fermentation, it was not until 1942 thatMonod (102) introduced the important modifica-tion of limiting the rate of growth and metabolismby regulating the concentration of a single re-quired nutrient. A finite relationship exists be-tween nutrient concentration and growth rate ofthe organism, and also between nutrient utiliza-tion and the amount of cell substance produced.Consequently, growth can be characterized insimple mathematical expressions (103, 111):

rg =iX (18)

Sf\M (K8~~ ~JMm (19)y Ka + Sf) ()

where rg is the rate of increase of cells due tomultiplication of the organism, (g/cm3 hr). We

use the symbol rg instead of the more conven-tional dX/dt to emphasize the fact that equation18 is a kinetic rate expression which reduces todX/dt only for the specific case of a completelybatch system. Sf is the concentration of sub-strate, X is the concentration of cells (g/cm3)IMis the specific growth rate constant (hr-'), Am isthe maximum growth rate constant (hr'1), andK. is a proportionality factor for the particularlimiting substrate.A number of other mathematical models for

growth have been derived from this concept(26, 42, 102, 105, 129, 131, 141, 156). As will beshown below, many of our conclusions are inde-pendent of the growth model chosen.Although the limiting-nutrient concept is par-

ticularly adaptable to continuous culture, it alsois exemplified in a number of other situations. Inordinary batch culture, unless all the nutrientsrequired by an organism are supplied in exactlythe right proportions, a condition is soon reachedwhere one of the nutrients begins to limit growthand metabolism. With aerobic bacteria in a testtube, for example, the supply of oxygen rapidlybecomes depleted and growth becomes limited bythe relatively slow diffusion of air through thetube closure and dissolution in the medium. Insome instances, different nutrients may succes-sively become the limiting growth factor. Anexample is the familiar diauxie phenomenon,exhibited by yeast grown in a medium containingboth glucose and maltose (102): first, the cellspreferentially utilize glucose until it is depleted,and then a second growth cycle results aftermaltose-degrading enzymes are induced.The limiting-nutrient concept is the common

feature that allows one to relate dialysis kineticsto microbial growth kinetics, since dialysis issimply another method by which nutrient can befed to a culture. The basic equations for moleculardiffusion through inert porous membranes can becombined with the mathematical models that de-scribe cell proliferation as a function of nutrientconcentration, first for continuous (steady state)culture and then for batch (nonsteady state)culture. The resulting equations prove difficult tosolve explicitly but can, however, be solved easilywith an analogue computer (see below).To relate dialysis kinetics to growth kinetics,

one has to establish not only the relationshipbetween nutrient concentration and growth rate(equation 19) but also the relationship betweennutrient utilization and cell production. A usefulmodel was proposed by Marr et al. (95) andsubsequently used by others (2, 133):

-r= rg + YEXYx

(20)

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where -r. is the rate of substrate utilization dueto growth and metabolism, rg is the rate of growthof the organism, and Y. and YE are empiricalrate constants. The first term on the right of equa-tion 19 represents the portion of the substratethat is used in cell growth, and Y. is the yieldcoefficient. The second term is the portion that isused by the organism to maintain itself, and YEis called the "specific maintenance rate" (95). Ifthe first term is zero, with no cell growth, then thesecond term is equivalent to the substrate utilizedin maintenance metabolism. The maintenancerequirement becomes significant at low growthrates or high cell densities.An idealized diagram of a dialysis culture sys-

tem operated in the four possible ways is shownin Fig. 8. The four basic modes correspond to thefollowing: (a) batch reservoir and fermentor,where Fr and Ff = 0; (b) continuous reservoirand fermentor, where Fr and Ff > 0; (c) batchreservoir and continuous fermentor, where F, =0 and Ff > 0; and (d) continuous reservoir andbatch fermentor, where F7 > 0 and Ff = 0.The mathematical analysis consists of making

suitable material balances on both chambers forthe generalized situation. First, a balance on thelimiting substrate in the reservoir chamber resultsin the following equation:

In + Production = Out + Accumulation

FrSro + 0 = FrSr + PmAm (Sr - Sf)

+ V dSr (21)r dt

where Sro is the concentration of substrate in thereservoir influent, Sr is the concentration of sub-strate in the reservoir effluent, Pm is the perme-ability of the membrane to substrate, Am is thearea of the membrane, and Vr is the volume of thereservoir. FrSr' and FrSr represent bulk flow ofsubstrate into and out of the reservoir, andPmAm(Sr - Sf) represents the removal of sub-strate by dialysis. In these derivations, it is as-sumed that circulation through the dialyzer israpid enough so that the same concentrationsexist in the dialyzer as in the chambers.A similar balance on the limiting substrate in the

fermentor chamber can be established:Ff Sf° + PmAm (Sr - S) + Vf r,

FfS + V dSf (22)

where S° is the concentration of substrate in thefermentor influent and Vf is the volume of thefermentor.

Third, a balance on cells in the fermentor

chamber, when cells enter in the feed stream at aconcentration, X°, and no transport of cellsacross the dialysis membrane occurs, results inthe following equation:

FfX + Vfrg= FfX+ VfdXdt (23)

In the usual situation, no cells are present in thefeed stream and FfX" reduces to zero. Cells maybe present in the feed stream, however, if thefermentor is part of a multistage cascade or if cellsare recycled in a single-stage unit.These three material balance equations plus

model equations 18, 19, and 20 are mathemati-cally sufficient to determine cell and substrateconcentrations in dialysis culture.Completely continuous operation. The subject of

ordinary continuous culture has been thoroughlyreviewed by several authors (50, 70, 92, 93, 97,150). A simplified theoretical analysis of con-tinuous dialysis culture was attempted by Gori(58), but the specific effects of membrane areaand membrane permeability were not taken intoaccount.

Although this is the most difficult operationto achieve in practice, it is the simplest type ofdialysis culture to solve mathematically, since asteady state can be assumed to occur in bothchambers. In steady state continuous culture, thetime derivatives dSr/dt (equation 21), dSf/dt(equation 22) and dX/dt (equation 23) are allequal to zero.From equation 23, the growth rate can be re-

lated to the flow through the fermentor and cellconcentration in the fermentor,

Firg = v(X-XO) = D(1-Rx)X (24)

where D(hr-1) is the dilution rate defined as theflow rate into the fermentor divided by the fer-mentor volume, and R. is the ratio of the cellconcentration in the feed to that in the outlet(R, = X"/X). When no cells are present in thefermentor feed stream, RX = 0.

Similarly, from equations 20 and 24 the sub-strate utilization rate can be related to the flowrate and cell concentration,

(1- RX) Fir. = - - - YEX (25)

This value for r8 can be substituted into equa-tion 22 so as to obtain,FfSfi + PmAm(Sr - S)

- Vx[(( -

+ YE]Y = FiSi (26

20 BAmrRIoL. REV.


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Also, equation 21 can be solved for Sr in termsof Sf, and the results substituted into equation26. The following equation is obtained for thecell concentration in terms of the operatingparameters and Sf, the substrate concentrationin the fermentor:

[Sr_- ~+Fi(Sf-SOlX = LPmAm+Fr 1 (27)

[Ff(I - R) + YEVf]

Note that equation 27 was derived without re-course to the growth models given in equations18 and 19. The only assumptions in its develop-ment are those corresponding to the substrate-utilization model, equation 20. To use this equa-tion in a predictive fashion, Sf must be related tothe operating parameters.Now, from equations 24 and 18,

M=Vf (1-Rx) = D(1-RX) (28)

which shows that the specific growth rate con-stant, g, is numerically equal to the dilution ratewhen no cells are present in the feed stream (i.e.,RX = 0).The fermentor substrate concentration is deter-

mined by combining equation 28 and the growthmodel equation 19:

D(I - R3) = JAMX Sf 5 (29)

Rearranging, we find that

S1 Ks (30)JMm

D(l - R) 1

The equations given above are quite generalfor the behavior of cells in continuous culture,subject to the validity of the models chosen.Effects of dialysis, maintenance metabolism, andcells in the feed stream on effluent cell and sub-strate concentration can be evaluated. Simpler,more restrictive equations can be obtained bygiving a zero value to the appropriate constant.For example, the interrelations between flow rate,feed cell concentration, and maintenance metabo-lism for nondialysis continuous culture can becalculated from these equations by allowing Pmto become zero. To emphasize the effects ofdialysis in the discussion and equations that fol-low, we will restrict our considerations to asingle-stage fermentor with no cells in the feedstream (i.e., R. = 0)

Note that the fermentor substrate concentrationterm (Sf) given in equation 30 was derived with-out recourse to equations 21 and 22, which havedialysis terms, nor to equation 20, the substrate-utilization model. Therefore, the substrate con-centration in the fermentor (Sf) and in the fer-mentor effluent is independent of membranepermeability (Pm) and membrane area (Am), andis altogether independent of the dialysis opera-tion. Also, it is independent of yield coefficientsY. and YE. The substrate concentration in thefermentor is in fact exactly the same as would beobtained in normal continuous culture at thesame dilution rate.However, the maximum or critical dilution

rate (D0), i.e., where washout occurs, is definitelya function of dialysis. The flow rate for washoutcan be found by letting R. = 0 and solving equa-tions 27 and 29 simultaneously:

K,, 1 l+PmAm Fr -

(31)

For the particular situation where the samemedium is used in the fermentor and the reser-voir, i.e. Sr0 = SfO, equation 31 reduces to

¢ JKs+ 1Sfo

(32)

This is the same condition for washout as innormal continuous culture (66).

Another important point is that the reservoirvolume, Vr, does not appear in any of the ex-pressions 27 to 31. This means that the perform-ance of fully continuous dialysis culture is com-pletely independent of the reservoir volume, and thereservoir can be made as small as is operationallyfeasible. This remarkable result has importantimplications for the design of large-scale continu-ous dialysis culture systems, since the reservoirneed not be scaled-up in the same proportion as thefermentor or dialysis unit.A comparison of continuous dialysis culture

with normal continuous culture is best served bya numerical example. The example is based onthe same hypothetical organism used by Herbertet al. (66) in their discussion of continuous cul-ture. If glucose is the limiting substrate, thepermeability coefficient, Pm, of cellulose-acetatemembranes is approximately 0.42 cm/hr (82).A realistic value to assume for Am is 1 cm2 per

ml of culture volume, based on the following lineof reasoning. If a separate dialyzing unit is used,

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SCHULTZ AND GERHARDTs~~~~~g_ ~~~~~bX 8

04 DIALYSIS

J3w

2 _ NON-DIALYSIS

C

0 0.1 0.2 0.3 04 0.5 0.6 0.7 0.8 0.9 1.0DILUTION RATE (HOUR)

pz

IL)

z

0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

DILUTION RATE (HOUR-')

FIG. 15. Calculated comparison of dialysis and nondialysis continuous culture with respect to cell density (a),productivity (b), and efficiency (c). Thefollowing conditions were assumed: fermentor volume, Vf = I liter; growthrate constant, Am = I hr-'; growth constant, K. = 2 X 10-4 g/ml; yield constant, Y.k = 0.5; maintenance constant,YE = 0; substrate concentration in fermentor and reservoirfeed, Sr0 = Sf0 = 10- g/ml; flow rate through reser-voir, Fr = 500 ml/hr; product ofmembrane permeability and area, PmAm = 420 cm'/hr.

the holdup in the dialyzer probably should notexceed 10% of the fermentor volume, or 100 mlper liter of fermentor volume. A dialyzer canreasonably be fabricated with 1 mm clearancebetween the membrane and supporting structure.This would result in 0.1-ml holdup per cm2 ofmembrane area. A 100-ml holdup would allow1,000 cm2 of membrane area per liter of fermentorvolume. If an integral type unit is used, the mem-brane area might be as high as 10 cm2 per ml ofculture fluid.The calculated example based on these assump-

tions is shown in Fig. 15.The most striking and important difference be-

tween nondialysis and dialysis continuous culture(Fig. 15) is the much higher cell densities attainable

in dialysis culture, especially at low dilution rates.The reason for this behavior is easily seen if onerealizes that in normal continuous culture all thesubstrate enters the fermentor with the feedstream. Therefore, at low dilution rates, the cellpopulation is limited by the substrate concentra-tion in the feed stream. In fully continuous dialy-sis culture, however, an additional supply of sub-strate is made available to the fermentor throughthe dialysis membrane. This essentially increasesthe net substrate concentration available. Conse-quently, a much higher cell concentration can beestablished. The rate at which cells are producedin a continuous dialysis culture is obtained simplyby multiplying the flow rate by the concentrationof cells in the effluent stream and by taking

22 BACrERIOL. REV.


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R. = 0:

Production rate = XFf =

F Ff i Sr0 - Sf[ + Ff(Sf -Sf) (33)

[-+YEVfJ }33

LYx JLPmAmn Frwhere Sf is obtained from equation 30.

In Fig. 15b, one also sees that the productivityof fully continuous dialysis culture will be higherthan that of a normal continuous culture through-out the entire range of dilution rates, with thesame medium flowing through both chambers.The flow rate through the fermentor which

corresponds to a maximum production rate isfound by differentiating equation 33 with respectto the flow rate through the fermentor (Ff) andsetting the result equal to zero. If we neglectmaintenance metabolism (YE = 0), the followingequation results:

Ffmax Vfi.m

- 4/~K8(+Sf ( mVfPmAm + Fr)]

(34)In comparing this equation with that given by

Herbert et al. (66) for a normal continuous fer-mentation, it is seen that the maximum productionrate in continuous dialysis culture is achieved at alower dilution rate than in nondialysis continuousculture.The efficiency of cell production, defined as the

actual production rate divided by the productionrate equivalent to complete utilization of thesubstrate supplied, is given by:

XFfEfficiencyC= Yx(FrSro + FfSfS)

Ff Sro - 5f + f(Sff)1Ff + YEYXVfI + Fr 0 )

FrSrO + FfSfO(35)

An example of the variation in efficiency withdilution rate is also shown in Fig. 15c. The highcell densities obtainable in continuous dialysisculture at low dilution rates are achieved at theexpense of lower efficiencies in converting sub-strate to cells. Also, the efficiency of continuousdialysis culture is always less than that of non-dialysis continuous culture. The difference be-tween the two is attributable to the unused sub-

strate which passes out of the system with thereservoir effluent stream.The relative cell density for dialysis culture (X)

and nondialysis culture (Xnd) at the same flowrates can be calculated from equation 27. Thecell density in nondialysis culture with mainte-nance metabolism is obtained from equation 27by setting PmAm = 0:

FfXF(Sf0 - Sf)

(-+ YEOf) (36)

The ratio X/X-d at the same dilution rate is

x

Xnd

SrO - Sf

Pnm + Ff(S10 Sf)

+ 1(37)

Notice that the maintenance coefficient, YE,does not appear in this equation, so that therelative effect of dialysis on cell density is the samewhether or not maintenance metabolism occurs.An examination of Fig. i5a shows that the

substrate concentration in the fermentor, Sf , ismuch smaller than Sf0 or Sr0 at low dilution rates,i.e., if D < 0.7 D0. An approximate expressionfor the relative cell density X/X-d, neglectingSf in equation 37, is

X SrO

Xnd F / 1 1 (38)PmAm Fr/

Data given by Hauschild and Pivnick (65) canbe used to check the validity of equation 38(Table 2). The-necessary values for operatingconditions, which are needed to calculate theincrease in cell concentration with dialysis, wereestimated from their description of the experi-mental apparatus. It can be seen by comparing

TABLE 2. Comparison of measured and calculatedvalues for cell production of Brucella abortus

in dialysis and non-dialysis continuousculture"

Viable bacteria per mlMedium Measured Calculated

lot With dialysis Without X/Xnd X/Xnd(X) dialysis (Xnd)

A 375 X 109 152 X 109 2.46 2.42B 80 X 109 38 X 109 2.10 2.42

The following operating conditions were used:Pm = 0.5 cm/hr; Am = 90cm2; =S - f, Fr = 20.8ml/hr; Ff = 10 ml/hr. Data from Hauschild andPivnick (65).

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24 SCHULTZ AND GERHARDT

en Fn

'D < a5x Cfl;xI. >- °

en04f-

a F

-j Z

>-0D iR-)IZiJ W

.4w o

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0DDILUTION. RATE (hour')

Fia. 16. Calculated effect of the substrate concen-tration in reservoirfeed on the cell density in continuousdialysis culture, plottedas relative cell density in dialysisculture (X) to nondialysis culture (Xnd) at the same di-lution rates. Assumptions: product ofmembrane perme-ability and area, PmAm = 500 cm'/hr; substrate con-centration in fermentorfeed, S = It g/ml; S,0/Stas shown; all else the same as in Fig. 15.

the last two columns of Table 2 that the pre-dicted results are very close to the measuredvalues.

Also, in the region of flow rates where Sf isnegligible, the cell concentration is practicallyindependent of the model chosen for the effect ofsubstrate concentration on growth rate, equation19. The cell concentration is determined princi-pally by the total substrate available in the feedstreams and the yield coefficients, Y., and YE .Some appreciation of the effect of the substrate

concentration in reservoir feed (Sr'), feed rate(F,), and membrane permeability and areas(PmAm) can be obtained from the calculatedexamples given in Fig. 16-18. An increase in con-centration of substrate in the reservoir influent,S,', is reflected in an almost directly proportionalincrease in cell density. The cell density is lesssensitive to changes in PmAm and Fr (Fig. 17 and18), especially at the higher dilution rates.An interestingfeature offully continuous dialysis

culture is that high cell densities can be obtained atlow dilution rates, even withfeed solutions contain-ing very low substrate concentrations. To achievethe same effect in nondialysis continuous fer-mentation, a portion of the cells must be sepa-rated from the fermentor effluent stream andrecirculated.

BACrERIOL. REV.

This feature of high cell densities at low dilu-tion rates would be expected to be displayed incontinuous dialysis culture even if the organismhad a significant level of maintenance metabo-

WmLtD 5 , Pm Am- 500 cm Ar

sJ: 5U~~~~n~~3,

nBIRD, 40 t PmAm 250cm /hr4-

40Z03

"Ix >-Z 3 Pm Am-/125 cm/hr

ztW W

W

.-ooWj

W

40

0 .1 .2 .3 4 .5 .6 .7 .8 .9 1.0DILUTION RATE (hour')

Fio. 17. Calculated effect of the membrane perme-ability and area (PmAm) on the cell density in con-tinuous dialysis culture, plotted as relative cell densityin dialysis culture (X) to nondialysis culture (Xnd) at thesame dilution rates. Assumptions: PmAm as shown; allelse the same as in Fig. 15.

6W

-5 5 ,Fr - 500 cm3hr

Em 4>U (n 4 Fr = 250cm3/hr

40

3 Fr 125 cmd'hr

- oW (jLuz2Hj

40EEH~_

DILUTION RATE (hour')

FIG. 18. Calculated effect of the flow rate throughreservoir (F,) on the cell density in continuous dialysisculture, plotted as relative cell density in dialysis culture(X) to nondialysis culture (Xnd) at the same dilutionrates. Assumptions: PmA. = 500 cm3/hr; F, as shown;all else the same as in Fig. 15.


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o 0.1 0.2 03 0.4 0.5

DILUTION0.6 0.7 0.8 09 1.0

RATE (Hour-1)

FIG. 19. Calculated effect of maintenance me-tabolism on cell density in dialysis and nondialysis con-

tinuous culture with the limiting substrate present in thefermentor feed stream.

lism. This is in contrast to the behavior of suchan organism in normal continuous culture, wherethe cell density drops to zero at low dilution rates.For example, Marr et al. (95), in continuousculture studies, showed that the specific mainte-nance rate, YE, had the numerical value of 0.028hr-1 for a strain of Escherichia coli with a growthrate constant of 1.0 hr-1. The expected behaviorif such a culture is grown in a continuous dialysissystem is shown in Fig. 19.

In situations where none of the limiting sub-strate is presented in the feed to the fermentor, aswhen cells are grown on the dialysate of a com-

plex medium, dialysis culture is not as advan-tageous for growing concentrated cultures. Figure20 shows the response to dilution rate (D) ex-

pected for this type of operation. High cell con-centrations are only obtained at very low dilutionrates. Cell densities below "normal" are obtainedthrough a wide range of flow rate, unless of coursethe substrate concentration in the reservoir isseveral times higher than "normal." A commonexperimental situation analogous to the condi-tion of no substrate in the fermentor feed is thatwhich occurs with aerobic continuous cultureswhen oxygen is the growth-limiting nutrient (123).

Completely batch operation. The remainingthree basic modes of operating dialysis cultureare essentially nonsteady-state in nature. Becausethe defining equations are nonlinear, they are bestsolved by computer (see below).

Completely batch operation results when thereis no flow through either the fermentor or reser-voir chambers (Fig. 8a). Mathematically, this isequivalent to letting Ff and Fr equal zero inequations 21 to 23.The expected growth pattern for this type of

operation is shown in Fig. 21. The growth cyclecan be separated into two phases: first, cells willgrow exponentially until the substrate concentra-tion in the fermentor falls to a level which limits

14 -

3 \NooDialysisContinuous cu/lure (SAC)

12-

I0

9J5

X 69>7

Lii Non-dialysis Continuous Cu/lture5.

111()I

Fio. 20. Calculated comparison of nondialysis con-tinuous culture with the dialysis situation when the limit-ing substrate is not present in thefermentorfeed streamand the culture has no maintenance requirement.

z

0

I-i

z

w s.roz

0

ui

tcTI ME

FIG. 21. Expected changes in cell density and limit-ing substrate concentrations for dialysis culture systemoperated with batch fermentor and reservoir. X, Sf, andSr, respectively, are cell density, fermentor-substrateconcentration, and reservoir-substrate concentrationduring culture period. The critical time when substratediffusion through membrane becomes limiting is shownas t,.

\ Dialysis

- Maintenance Mel- \ --- No Maintenance

F Non-odlolysls <

-1 1L -I 171

'3

12

11-J" D6

z

Lii1 5

u) 4

3

2

25VOL. 33, 1969

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the growth rate; afterwards, the growth rate willbe governed by the diffusion rate of substrateinto the fermentor from the reservoir, and sobecome linear.

Ideally the concentration of cells formed inbatch dialysis culture should be directly relatedto the amount of nutrients available to the culturefrom the fermentor and reservoir chambers. Bymaterial balance and neglecting maintenancemetabolism, the final cell concentration is givenby the equation

Vf(X - X0) = Yx(VfSf0 + VrSro) (39)

where X0 is the concentration of cells presentinitially as inoculum. For ordinary (nondialysis)batch culture, the final cell yield is given by thebalance

(Xnd - X) = YxSf° (40)Therefore, the concentration ratio achieved bydialysis is

X VrSr0=1 + VS0(41)Xnd Vfsf (1

where X is the cell concentration in the culturechamber of the dialysis flask, Xnd is the cell con-centration in an equivalent-volume, nondialysisflask, and X0 is small relative to the final cell con-centrations. The concentration ratio is seen to de-pend on the relative nutrient concentration in thereservoir and culture chambers, Sr/Sfo, and onthe ratio of chambers, Vr/Vf . In the experimentsreported by Gerhardt and Gallup (51), the samemedium was used in both chambers (i.e., the ratioSr0/Sf0 = 1.0) and the cell density in dialysisculture was proportional to 1 + Vr/Vf . Thus, ifthe ratio of reservoir volume to fermentor volume(Vr/Vf) is 10:1, it is possible to attain a cell densityin dialysis culture which is 11 times greater thanin a nondialysis batch culture. However, higher celldensities also can be obtained by using highernutrient concentrations in the reservoir.The period of exponential growth in batch

dialysis culture will depend upon the rate of cellu-lar growth relative to the rate of substrate diffu-sion through the dialysis membrane. If the genera-tion time of the cells is short, diffusion may be-come limiting early in the fermentation. On theother hand, if the cells grow slowly or the mem-brane area is very large, diffusion may never be-come limiting. Usually it is desirable to employexcess membrane area so that substrate diffusiondoes not limit the growth rate.

With dialysis culture, the exponential growthphase is extended because of the additional nu-

trient which is provided by the reservoir via themembrane. An approximate expression for theincrease in exponential-phase cells that can beobtained in dialysis culture relative to nondialysisculture is

+ PmAm)(42)

X Sr (

Xnd Sfot

where Sr° is the initial substrate concentration inthe reservoir for dialysis culture, and Sf is theinitial substrate concentration in the fermentorfor nondialysis batch culture.

This result, which is independent of whether ornot the cells have a large maintenance metaboliccomponent, is important for cases where it is de-sirable to obtain high concentrations of ex-ponentially growing cells. For example, the en-zymes involved in protein synthesis are oftenfound in highest concentration during the ex-ponential growth phase, and so large amounts ofexponential cells are required to isolate theseenzymes.The increased exponential phase in dialysis cul-

ture also means that the cells are maintained in amore constant environment for a longer periodof time than in nondialysis culture. The relativebenefit of dialysis culture mainly stems from theterm PmAnj/Vft.Lm. The ratio is related to thediffusion rate of substrate through the dialysismembrane per unit volume of fermentor. Thelarger this value is in comparison to the specificgrowth rate constant, jum , the greater will be thebenefit of dialysis culture. For fast-growing (e.g.,bacterial) cells, one might obtain only twice theamount of exponential growth, but for slower-growing (e.g., mammalian) cells, the amount ofexponential growth might be increased 10-fold.The influence of membrane permeability and

area on the kinetics of batch dialysis culture isshown in Fig. 22. As the magnitude of the termPmAm is made smaller, a longer period of time isrequired for a given cell yield to be obtained. Fora given cell yield, the relationship is approxi-mately

ConstantPmAm

Thus, if PmAm is halved, it takes about twice thetime to reach the same cell yield.The effect of changing the reservoir volume

alone is shown in Fig. 23. Two consequences areapparent: first, reducing the reservoir volume cur-tails the maximum cell yield; second, the final cellyield is approached faster with- lower reservoir vol-umes, because a larger portion of the cells isformed during the exponential-growth phase.

26 BACTERIOL. REV.

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- 50m

a / Pm Am - 250 cm3/hr>. 40-

Pm Am /25 cm3/hrz

~30-j

20-

0 10 20 30 40 50 60 70 80 90 100TIME (HOURS)

FIG. 22. Computed effect ofmembrane permeability and area (PmAm) on cell density in fully batch dialysis cul-ture. Assumptions: ratio of reservoir volume to fermentor volume, Vr/Vf = 10; fermentor volume, Vf = I liter;initial substrate concentration in reservoir andfermentor, Sr' = Sf" = 10-2 giml; cell inoculum, X0 = S X 10-6g/ml; PmAm as shown; growth constants as given in Fig. 15.

Both of these predictions have been confirmedexperimentally (44, 51; unpublished data).The efficiency of batch dialysis culture should

approach 100% if the fermentation is allowed torun long enough. But, if the membrane perme-ability or area is too small relative to thefermentor volume, a point may be reached whenthe rate of substrate diffusion can only satisfythe maintenance metabolism of the organism andnot the growth requirements. On the other hand,the cells might begin to autolyze before all thesubstrate in the reservoir is utilized.The effect of maintenance metabolism on batch-

culture kinetics is striking. Figure 24 shows thedecrease obtained in final cell yield for variousvalues of the specific maintenance rate, YE .

Relatively low levels of maintenance metabolismhave a profound effect on the maximum cell yieldobtainable, because at high cell densities an in-creasing proportion of the substrate is used inmaintenance rather than for building more cellsubstance. Even if the reservoir were continuallyreplenished with fresh substrate (Fig. 8d), thecell population in the fermentor would reach afinal stable level when the amount of substratediffusion into the fermentor became equal to theamount used for maintenance. The maximumcell density obtainable is calculated (by lettingdX/dt and dSf/dt = 0):

PmAm(Sr- Sfmin) = VfYEXmax (44)

and, if the substrate concentration in the reservoiris much larger than in the fermentor (Sro >> Sfm in)

when the cell concentration becomes constant,

PmAmSr,X~a3C = V YE (45)

Equation 45 suggests another unique use fordialysis culture, namely as an experimentalmethod for determining the specific maintenancerate, YE . By growing a culture in a batch dialysissystem with continual replenishment of the reser-voir fluid, one can experimentally determine thevalues of X.,b,, and Sfm in. With a knowledge ofthe other quantities, Pm, Am, Sr", and Vf, a

30TIME (HOURS)

FIG. 23. Computed effect of reservoir volume on celldensity in fully batch dialysis culture, plotted with theratio of reservoir volume to fermentor volume (Vr/Vf)as a parameter. Assumptions: product of membranepermeability and area, PmAm = 50O cm3/hr; Vr/Vf asshown; all else as given in Fig. 15.

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0

x

'J60-11

cn

0:500

_ cr-iw%.. C,' , 40x z

I-Zz

-Jo

Z Zt 30

0

lLU

4W r

10I-en

U,

0 10 20 30 40 50 60 70 80TIME (HOURS)

FIG. 24. Computed effect ofmaintenance metabolism onfinal cell yield in batch dialysis culture. Assumptions are-the same asfor Fig. 15 except that values of the maintenance coefficient, YE, were assumed to give the values of theratio, YE/lpm, shown as the parameters on the curves.

value for YE can be calculated from equation 45.A series of such experiments with different en-vironmental conditions and a variety of substrateswould reveal important information about main-tenance metabolism.

Batch fermentor, continuous reservoir operation.In this type of operation, a continuous streamcontaining substrate is passed through the reser-voir, but no additions to or withdrawals from thefermentor chamber are made (Fig. 8d). The ex-pected behavior is shown in Fig. 25. Assuming nolag, the cells grow exponentially at first; i.e., thenumerical value of the substrate concentration inthe fermentor will be much greater than thegrowth rate constant (Sf >> K.). The exponentialgrowth period will depend on many parametersof the system, as discussed in the previous section.However, eventually the substrate concentrationin the fermentor will drop to a low constant value,and growth will depend almost entirely on diffu-sion of nutrient from the reservoir. Under theseconditions, the substrate concentration in bothchambers will approach constant values; i.e.,dSf/dt and dSr/dt - 0.The material balance equations can be solved

to obtain an approximate expression for the

growth rate after the exponential phase:

dX=YxPmAm(Sr- Sf) _ YEY-X (46)

dt Vf YYX(6

If the maintenance factor (YE) is negligible,the second term will drop out and growth will belinear with time. Thus, under these conditions,one should be able to control the linear growthrate by varying the parameters Pm, Am,XfVand Sr. Of course, the cell density cannot in-crease indefinitely since eventually some otherfactor such as aeration or mixing effects will be-come limiting.On the other hand, if maintenance metabolism

is important, the second term in equation 46 can-not be neglected and the growth rate (dX/dt) willeventually go to zero. Under these conditions,the final cell yield is given by the equation

X PmAm(Sr - Sf)YEVf

where the reservoir substrate concentration (Sr)can be calculated from equation 21 by letting

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~z Phase Phase X

</z

s,ls/z Sr

X0

TIME

FIG. 25. Expected changes in cell density and limit-ing substrate concentrations for dialysis culture systemsoperated with a batch fermentor and continuous reser-voir. X, Sf, and Sr, respectively, are cell density, fer-mentor-substrate concentration, and reservoir-substrateconcentration during culture period. The critical timewhen substrate diffusion through membrane becomeslimiting is shown as tc.

dS,/dt = 0:

S PmAmSf + FrSr (48)

If the flow rate through the reservoir (Fr) ismuch greater than PmAmX then Sr = Sr0, andthe final cell concentration will be given by theequation

x PmAm (SrO - Sf) (49)YEVf

Equation 49 is essentially the same as for com-pletely batch operation (equation 45). Therefore,this mode of operation can also be used to de-termine the magnitude of the endogenouscoefficient, YE.

Continuous fermentor, batch reservoir opera-tion. In this type of operation, there would becontinuous flow through the fermentor but notthrough the reservoir (Fig. 8c). This is inherentlya nonsteady-state operation, since the concentra-tion of substrate in the reservoir is always chang-ing with time. The expected behavior of the sys-tem will depend somewhat on the start-up pro-cedure. If the fermentor chamber is inoculatedfirst and if circulation through the dialyzer isstarted only after the fermentor has reached acontinuous steady state, the behavior will be asshown in Fig. 26.

There would seem to be little point to thismethod of operation, since the cell density willslowly decay towards the original steady-statevalue as substrate in the reservoir is utilized, ex-cept that it is easier to have a batch reservoir than

a continuous-flow type. Almost fully continuousdialysis culture could be achieved if the reservoirwere periodically replenished. How often thereservoir needs to be replenished can be estimatedafter a decision is made as to how much substratewaste is feasible.

Product Formation in Dialysis CultureBasic considerations. The degree of complexity

increases immeasurably when one considersproduct formation in relation to dialysis culture.The word "product" can refer to any of thethousands of materials that can be generated bymicrobial systems, and the detailed kinetics offormation of any particular product in relation tomicrobial growth may be unique. The intricaciesof fitting a mathematical model to the kineticsof product formation is well illustrated by thework of Chen et al. (25) on steroid conversions,where phenomena such as substrate solubility,coprecipitation, feedback inhibition, and sub-strate inhibition had to be taken into account. Inanother study, Shu (148) showed that cell agedistribution is an important factor in lysine for-mation. Just as there is no general formulationwhich accounts for the kinetics of ordinary reac-tions, it is clear that a general mathematical modelfor all microbial reactions will not be forthcomingsoon.However, if one does have a kinetic model for

the production of a particular microbial productin nondialysis culture, it is not too difficult to pre-dict the behavior in dialysis culture. The onlyadditional information needed is the permeabilitycharacteristics of the product for the membrane

Sro XMax

o X4-

U Sf

TIME

FIG. 26. Expected changes in cell density and limit-ing substrate concentrations for dialysis culture systemoperated with continuous fermentor and batch reservoir.Xnd = steady-state cell density and Sf d = steady-statesubstrate concentration in fermentor before starting ofdialysis; Sr, = initial substrate concentration in reser-voir; X, Sf, and Sr, respectively, are cell density, fer-mentor substrate concentration, and reservoir-substrateconcentration after dialysis is initiated.

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materials that are used in the dialysis culture ap-paratus.Some of the characteristics of product forma-

tion in dialysis culture can be illustrated with thesemiempirical product model proposed by Luede-king and Piret (88):

rp = arg + (X (50)where rp is the total rate of product formation dueto metabolism, rg is the cell growth rate, and a and( are empirical constants. This model states thatthe net rate of product formation is the sum of theproduct formed that is directly related to growthrate (first term) and the product formed that isdirectly related to cell concentration (secondterm). This model has been chosen here becauseit probably represents a good one for "main-line"metabolic products, such as lactic acid andgluconic acid, where the product is a result ofenergy metabolism. The model clearly has limi-tations in that it predicts continued product for-mation after growth ceases, i.e., after rg = 0.However, this deficiency will only be importantin the later stages of batch culture.

In addition to a kinetic model for product for-mation, a complete analysis requires an account-ing for the amount of product in each of thechambers of the dialysis culture apparatus. Ma-terial balances for the reservoir and fermentorchambers are obtained in the same manner as thesubstrate balances given earlier in equations 21and 22:

In + Production = Out + Accumulation

For the reservoir chamber:

P'mAm(Pf - Pr) + 0 = FrPr + Vr dP, (51)\dt/

For the fermentor chamber:

0 + Vfrp = P'mAm(Pr - Pf) + FfPf

+ Vf (dPf\ (52)

where Pf is the concentration of product in thefermentor chamber, Pr is the concentration ofproduct in the reservoir chamber, and P'm is thepermeability of the membrane to product. Ofcourse, if the product is intracellular, this situa-tion can be handled by letting P'm equal zero.These equations can readily be accommodatedinto the analogue computer program for cell for-mation (see below) to give a complete solutionfor any mode of operation. However, someanalytical solutions are possible for particularsituations, and these will be discussed to illustratethe behavior of the dialysis system.

Completely continuous operation. The equa-tions can be solved algebraically because the timederivatives (dPr/dt and dPf/dt) are zero and,from equation 24, rg = (Ff/Vf)X.The product concentration within the fer-

mentor chamber is directly related to cell concen-tration by the following formula:

XVf(aFf/Vf + ()

(PmAm + Ff f(53)

where the cell concentration X is given by equa-tion 27.

If the product is nondialyzable, (P'm = 0) andif ( = 0 (i.e., if product formation is related onlyto cell growth), the equation reduces to

Pf = aX (54)

For this specific case, product concentrationin the fermentor is directly proportional to cellconcentration. The relation between product con-centration and dilution rate will be the same asshown in Fig. 15-20, except that the ordinate ismultiplied by a.

If a = 0 (i.e., if product formation is only re-lated to cell concentration), the equation reducesto

Pf = X Vf (55)

This equation indicates that, as the dilution ratedecreases, i.e., as the flow rate through the fer-mentor (Ff) becomes smaller, the product con-centration (Pf) becomes a higher and highermultiple of the cell concentration. The actualshape of the curve for product concentrationversus dilution rate will depend on the relativemagnitudes of a and (3. But as the (3 term becomesdominant, the theory predicts very high productconcentrations at low dilution rates. The ex-pected behavior is shown in Fig. 27.

Productivity of a nondialyzable product isgiven by:

Productivity = Pf Ff = XFf ( + ) (56)

Since the term XFf is the productivity of cells,the productivity of product (PfFf) is obtainedsimply by multiplying the cell productivity curveby the factor (a + Vf(/Ff). This is shown in Fig.27 for various magnitudes of a and (. Again,the influence of the (3 term is seen; as ( becomeslarger, productivity of product no longer goesthrough a maximum but actually increases at lowdilution rates.

Similar equations for product formation in

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E

0.

Zi

(e2PfF \$=I)=I

I: or

P P(0 (=,0=O)

00

Pf F l(a= 1,ll0

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

DILUTION RATE (Hr-1)FiG. 27. Expected changes in product concentration

and productivity in continuous dialysis culture when theproduct is not dialyzable. Assumptions are the same as

in Fig. 15.

nondialysis continuous culture are readily ob-tained by using equation 36 for cell concentration(X), rather than equation 27.

If the product is dialyzable (P'm o 0), then itwill be distributed between the fermentor andreservoir chambers. The concentration of productin the reservoir chamber is given by the equation

Pf

Fr (57)P' mAm

where Pf is given by equation 53.If the membrane is very permeable, or its area

is large, or the flow through the reservoir is small,then 1 >> Fr/PmAm and the product concentra-tion in the reservoir will approach its concentra-tion in the fermentor. In no case can the productsolution concentration in the reservoir becomegreater than that in the fermentor chamber, be-cause a concentration gradient from the fermentorto the reservoir chamber must exist in order fordiffusion to occur.The fraction of the total product formed which

will be removed in the reservoir effluent stream isgiven by FrPr(FrPr + FfPf), and by substitutionwith equation 57 this fraction is given by theequation,

Fr Pr 1

FrPr + FfPf1 + F (1 Fr

f~ PmAm Fr)

Therefore, in order to obtain a large fraction ofthe product in the reservoir effluent free fromcells, both the permeability (PmAm) and thereservoir flow rate (Fr) must be large numbers incomparison to the fermentor flow rate (Ff). Thistype of operation would result in a low concentra-tion of product in the reservoir effluent streamand perhaps also in difficulty with recovery of theproduct.

However, if the product happens to be an in-hibitor of metabolism, or if it is desired to main-tain the fermentor chamber at relatively constantenvironmental conditions and essentially freefrom metabolic products, then the usefulness ofequation 53 becomes apparent for predicting thevalues of P'mAm and Fr needed to reduce theproduct concentration in the fermentor chamber(Pf) to any desired level.Batch operations. Product formation in non-

steady-state dialysis culture cannot be meaning-fully discussed in general terms because of themany patterns to be expected from various com-binations of flow, product syntheses, and perme-abilities. For any particular set of circumstances,the expected behavior can be predicted with theanalogue computer program.

Completely batch operation (Fig. 8a) deservessome comments, however, because it is the mostlikely system to be used for experimentalpurposes. If the product is dialyzable, it willeventually distribute between the fermentor andreservoir chambers so that the concentration isthe same in both chambers. This means that thefraction of product that will be obtained in thereservoir chamber, free from cells, will be givenby the volume ratio, Vr/(Vr + Vf). The fractionof product remaining in the fermentor chambercan be made as small as desired merely by increas-ing the volume of the reservoir. However, thisis accomplished at the expense of diluting theproduct.

Another factor to be considered in this type ofoperation is that the product concentration in thereservoir will lag behind the concentration in thefermentor, because of the membrane diffusionbarrier between the two chambers. Figure 28shows an example of this type behavior. The rateof equilibration between the two chambers de-pends on the factor P'mAm(Pf - Pr). If theproduct concentrations are very low, then a verylarge membrane area will be needed to obtainacceptable rates of equilibration.

Implications of TheoryIn the preceding analysis, we have shown, on

the basis of a few simple models, how the be-havior of dialysis culture can be predicted for avariety of operational systems. The extent to

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Z

X0

100

z PRODUCT CHAMBER

0 20 40 60 80 100

HOURS

FIG. 28. Comparison of the changes in concentrationofa product, staphylococcal enterotoxin, in the productand culture chambers of a differential dialysis flask.Reproduced from Herold, Schultz, and Gerhardt (67).which the performance of any real dialysis culturematches that predicted by the analysis will de-pend on how closely the models reflect reality.

It is apparent that the behavior of these systemsis more closely linked to the operation of thefermentor chamber than that of the reservoirchamber. Therefore, the first step in designing adialysis culture system is to choose between batchand continuous culture. The relative advantagesof each type of operation for normal culturemethods have been discussed at length by Maxon(97), Ellsworth et al. (33), and Gerhardt andBartlett (50). The arguments can be summarizedas security and flexibility of batch culture as

opposed to uniformity and economy of continu-ous culture.

There are additional factors to be consideredfor dialysis culture. Fully continuous dialysisculture requires two systems to be simultaneouslyoperable, one for the fermentor and the other forthe reservoir. Therefore, the chances for mishapsare compounded. In theory, the reservoir need notbe maintained sterile if a dialysis-type membraneis used, but growth of an unwanted organism inthe reservoir would reduce the nutrient supply tothe fermentor and deleteriously affect cell yield.

Fully batch dialysis culture has the inherentadvantage that higher efficiencies can be attainedin the conversion of substrate to cells. But, ifthe process is to be scaled up to industrial stand-ards, extremely impractical reservoir volumesmay be required. For example, if a 10:1 increasein cell density were desired over that attainable innormal batch culture, the reservoir would haveto be nine times as large as the fermentor. If thefermentor were 20,000 gallons, the reservoirwould have to be a staggering 180,000 gallons.

As mentioned previously, continuous dialysisculture does not require proportional scale-up ofthe reservoir.

The equations presented provide a point of de-parture for experimentation and design. Theo-retically, one needs to determine the values ofonly five parameters, Pm X, su , K. , Y,, and YE,to design a dialysis system to produce cells.Membrane permeability, Pm,, can be measuredindependently by normal dialysis, and the con-stants for the cell metabolism and growth modelscan be found by ordinary continuous-culturestudies. However, the model parameters are notreally constant but are a function of environ-mental conditions, especially pH and dissolvedoxygen concentration. Unless these conditionsare controlled, the prevailing environment indialysis culture may differ from that in anordinary culture. Other factors such as toxicproduct formation may lead to differences be-tween the growth model for dialysis and ordinaryculture methods.A sounder approach to dialysis culture design

would be to use the equations developed here as aguide in experimental pilot-scale studies. De-pending upon the objective, whether it be highcell densities, high productivity, or efficientutilization of substrate or growth on dilute media,one can estimate the effect of the many inde-pendent variables and map out an experimentalregion which will provide design information forscale-up studies.An examination of the equations shows that

scale-up can be achieved by increasing volumes,flow rates, and membrane area proportionally,with the concentrations of substrate and inocu-lum kept constant. Not all of the independentvariables are of equal importance in scale-up.For instance, in continuous dialysis culture at lowdilution rates, cell density is more sensitive tochanges in flow rate than in membrane area. Butat high dilution rates the opposite is true. In batchdialysis culture it is more important to maintainthe ratio of fermentor to reservoir volume than theratio of fermentor volume to membrane area. If,as is often the case, equipment limitations preventequivalent scale-up of all components, the givenequations allow one to choose operating condi-tions to attain the desired objectives.

Summary of Mathematical AbbreviationsThe mathematical abbreviations used through-

out the section on Theory are defined in Table 3.

Analogue Computer Program

A general analogue computer program was de-vised to solve simultaneously for cell concentra-tion, substrate concentrations, and product con-

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TABLE 3. Summary of mathematical abbreviations

InitialAbbreviation Definition Units equa-

tion

A,AmApDD,DoDm

ET50

f

FFfmaxKf

K,LpNnPm

Ptm

Pm0P1,2

APPQrRRRx

rgrpr,SSeTtVxXndXmax

YEYxof

aa'

JAuAmSubscript fSubscript rSubscript 1, 2Superscript °

Effective open area of membrane for diffusionGeometric area of membraneCross-sectional pore or void area of membraneDilution rateCritical dilution rate for cell washoutFree diffusion coefficient of substrate in waterHindered diffusion coefficient of substrate in mem-brane

Measure of membrane permeability, expressed astime to reach one-half equilibrium diffusion con-centration

Ratio of actual diffusion rate through a membraneto rate expected for solvent of equal thicknessand area

Flow rate through a chamberFlow rate for maximum cell production rateFiltration coefficient for water flow through mem-brane

Cell growth model constantLength of diffusion path in poresPermeation rate through membraneEmpirical constantOverall membrane permeability coefficient for sub-

strateOverall membrane permeability coefficient for prod-

uctTrue permeability coefficient for membrane aloneEffective permeability coefficient of "unstirred

liquid layers"Hydrostatic pressure gradient across membraneProduct concentrationFiltration rate of water through membraneMolecular radiusPore radiusGas constantRatio of cell concentrations into and out of con-

tinuous fermentor, X0/XRate of cell growthRate of product formationRate of substrate "formation," negative valueSubstrate or solute concentrationEquilibrium solute concentrationTemperatureTimeChamber volumeCell concentrationCell concentration in nondialysis cultureMaximum cell concentration in batch cultureSpecific maintenance rateYield coefficient for conversion of substrate to cellsYield coefficient for product formationSpecific product formation rateThickness of unstirred liquid layerReflection coefficient for substrate by membraneSpecific growth rate constantMaximum specific growth rate constantFermentor chamberReservoir chamberDiffusion chambersInitial concentration in batch cases, or feed con-centration in continuous cases

cm2cm2cm2hr-'hr-1cm2/hrcm2/hr

hr

cm3/hrcm3/hrcm3/(hr atm cm2)

g/cm3cmg/hr

cm/hr

cm/hr

cm/hrcm/hr

atmg/cm3cm,/ (hr cm2)nmnmcm3 atm/gmole OK

g/cm3 hrg/cm3 hrg/cm3 hrg/cm3g/cm3OKhrcm3g/cm3g/cm3g/cm3hr-'g of cells/g of substrateg of product/g of cellshr-cm

hr-1hr"

1121

243119

7

9

213415

1911

122

51

1313

155115991524

18502015

15441836442020505014151819

33L


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centrations. Although applicable for any mode ofoperation of dialysis culture, it was especiallyuseful for the nonlinear equations derived forbatch operations. To facilitate programming, thepertinent equations were put in dimensionlessform by defining new dimensionless variables:-time, r = tAunt; substrate concentration in reser-

voir, Er = Sr/Sr0; substrate concentration infermentor, Sf = Sf/Sr0; cell concentration, X =

XlYxSr0; and product concentration, Pr =

lPr/Sro, Pf = Pf/Sr0. With these new variables,most of the concentration parameters will havenumerical values between zero and one.The pertinent equations in dimensionless form

become:

TgAX

Sf

IS + Sf

= rg + X -Xdr f

4dSr PmAm -3f)dr Vrpm(SrAm

4dSfi PmAm _ 9½)dr VfVim

+ VrpM(l - r)

YE YX -rg - X

JAm

Fif-

Of Mum3 S

rp= aYr +JEm

.dpi Fi m_ m=rp _ Ff f Vsmm (iiPrfdT JAM VQAM4dPr P'mAm Fr

-= r (-mV'r Vr'/m P

Pg rg/YxSr0Am , Ks/Sro, r? =

.rp/Sr0.

A schematic drawing of the analogue computerprogram is shown in Fig. 29, and the physicalmeaning of the various potentiometers is given inthe legend.

RESULTS AND APPLICATIONSIn Vitro Systems

Growth response and variables. A comparisonof schematic growth curves for dialysis and non-,dialysis batch cultures is representative of theexperimental results obtained with a number of

different organisms in several different systems(Fig. 30). The growing of cells in a dialysis systemdoes not usually affect the lag period or the rate ofexponential multiplication. In some situations,dialysis seems to reduce the growth rate, prob-ably because diffusion has been allowed to be-come rate-limiting (44). The main result ofdialysis conditions is a prolongation of activemultiplication to reach a higher maximum popu-lation, which often is extraordinarily dense.Viable-cell counts during the growth cycle havebeen compared with total cell counts, dry weightand deoxyribonucleic acid analyses, and tur-bidity measurements (44, 51). Viability approxi-mated 100% of the total counts throughout thegrowth and plateau phases of dialysis cultures,but the percentage of living cells decreasedrapidly after growth ceased in nondialysis cul-tures. A remarkable, but unexplained, two-stagecurve became evident when the two measures ofcell mass were plotted for the growth cycle in thedialysis fermentor system (51), but not in theflask system (44).A second main consequence of growing cells in

dialysis culture is a stabilization of the maximumstationary phase and the terminal phases of thegrowth cycle: viability is sustained both in theculture (161) and after the cells are washed andstored (E. A. Tyrrell, Ph.D. Thesis, Univ. ofMichigan, Ann Arbor, 1962), slow but activemultiplication actually may occur (161), andautolysis may be allayed (11, 55; Tyrrell, Ph.D.Thesis). The last mentioned result is particularlyapparent with some organisms that are suscep-tible to autolysis (e.g., Listeria monocytogenes)but not with others (e.g., Diplococcus pnue-moniae), probably because of differences in thecauses of autolysis. In some cases, spore forma-tion may be prevented (55, 99), but in others suchmorphogenesis proceeds uninterrupted, with theuseful consequence that a relatively clean sus-pension of spores is produced (145; Tyrrell,Ph.D. Thesis).Under usual conditions, the primary variable

controlling the extent of growth attainable indialysis culture is oxygen supply, as influenced byaeration and agitation of the culture. Final celldensity is affected by oxygenation to a greaterdegree in dialysis than in ordinary cultures (44).Most culture systems in common use are grosslyinadequate in providing for oxygenation of aero-bic cultures. In keeping with modern bioengineer-ing principles, flask dialysis systems must beusable on a shaking machine, contain baffles tocause turbulence, use a proportionally smallvolume of liquid culture (less than 20% of the

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dSrdr

FIG. 29. Analogue computer program for dialysis culture. Potentiometer parameters are as follows: (1) S3r,<2) Ff/Vri.m, (3) Fr/Vrpm, (4) PmAm/Vfum, (5) VfI/Vr, (6) X01 (7) Ff/Vfl., (8) YE/.am, (9) FfiVf/;m, (10) PI,(11) Ff1VfIm,, (12) aY1, (13) I3Yx/pm, (14) K8, (15) Pfo, (16) Ff/JMm, (17) Pm'Am/Vfjm, (18) Prog (19) Fr!/Vrym,(20) Pm'Am/Vfiim.

flask volume), and employ a cotton-gauze padclosure having a minimal resistance to gas ex-change. Fermentor dialysis systems similarly mustbe provided with a high rate of humidified spargedair (more than one volume of air per minute pervolume of liquid culture), efficient and vigorousagitation, baffling, and an effective antifoamingagent. Under such conditions, the measured oxy-gen-transfer rate should exceed 1 mmole of 02 perliter per min.When oxygen demand is met in dialysis cul-

tures, media thought to be optimal at the usuallylimiting oxygen levels may actually be suboptimalin nutrients, and carbon starvation in particularoften ensues. Supplemental feeding then can pro-

duce an astonishingly high population, unob-tainable in ordinary systems. With Serratiamarcescens, for example, the viable-cell count wasextended to 2.5 X 1012 cells per ml in 48 hr, withthe cell pack occupying half of the volume in atube of the culture after centrifugation (44).The relative geometry of a batch dialysis cul-

ture system also determines the degree of concen-tration achievable (see Fig. 23). That is, as thevolume of the culture compartment is reducedrelative to the volume of the reservoir compart-ment while the efficiency of nutrient conversionremains constant, then the degree of cell concen-tration will increase in direct proportion. In prac-tice, this relationship holds up to a reservoir to

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! ~~~~~~~~~~DIALYIS5

, ' NON-DIALYSIS

0

0

TIME - v

FIG. 30. Schematic representation of growth curvesin dialysis and ordinary batch culture systems.

fermentor ratio of about 10:1, beyond which theconversion efficiency suffers (44, 51). The 10-foldratio appears to be about optimal (58, 154).Another obviously controlling variable in

dialysis culture is the area of membrane availablefor diffusion (51). In general, the rate of growthshould not be limited by the membrane area andrate of diffusion; if so, a linear rather than an ex-

ponential rate of growth may result, and at a

lower mean rate (see Fig. 21). It is probably forthis reason that active growth under dialysisconditions tends to change from exponential tolinear when very high population densities are

attained (44). That is to say, a greater area ofmembrane is needed to maintain exponentialgrowth at high cell concentrations than at lowones.Morowitz and Maniloff (104) have observed

that Mycoplasma undergoes synchronized multi-plication when passed through a filter membraneand inoculated onto Formvar-coated electronmicroscope grids placed on nutrient agar. Thismethod of inducing synchronized cellular divi-sion may depend upon initial dispersion of cellaggregates and sizing of cells due to passagethrough the filter. Alternatively, cells may be de-pleted of internal primary food reserves andthereby reduced to a common base of metabolicactivity. The cells then will receive nutrients fromthe medium at a rate limited by diffusion throughthe supporting membrane and, consequently,initiate synthesis and divide synchronously for a

generation or more. This method has been usedto study morphogenesis during the cellular di-vision cycle.

It becomes evident from the above that the

diffusional supplying of nutrient is a major con-trolling factor in dialysis culture. Likewise, thediffusional removal of metabolic products maydirectly or indirectly increase growth. The netresult of dialysis is to lower the concentration ofsuch inhibitors per cell, because the product isdiluted into the reservoir volume and the cells areconcentrated within the growth chamber. In manysituations, the nature of the inhibitory productis not known. With bacteria such as lactobacilli,however, the observed enhancement of growthunder dialysis conditions (51) is attributable toremoval of inhibitory hydrogen ions and undisso-ciated lactic acid molecules. A more dramatic andbetter-defined example is provided by studies onthe usual inability of the obligate autotrophThiobacillus thiooxidans to grow on glucose. It wasreasoned that a toxic material is formed fromglucose metabolism. This material subsequentlywas identified as pyruvate and was shown to beinhibitory at 0.2 mM, in either glucose- or sulfur-containing media. By continual dialysis of theculture to remove the toxic metabolite, however,the organism was grown readily in glucose-con-taining medium (17).

Adsorption may sometimes account for resultsseemingly attributable to dialysis. This was ele-gantly demonstrated in a series of experimentsconducted 30 years ago by McClean (89) in aninvestigation of the cause of the increased produc-tion of hemolysin when staphylococci were grownin a cellophane sac. He clearly demonstrated thatthe result was not due to dialysis but instead toadsorption by the cellophane, which removed anunidentified substance from the medium. Thissubstance did not affect cell growth but onlyaffected hemolysin production. Other adsorbents(e.g., agar, kieselguhr, filter paper) were shown toduplicate the effect of the cellophane. Such aneffect could account for the growth enhancement.occasionally reported with use of dialyzed media(158).A synergistic effect of agar on the yield of cells.

has been observed when some species of bacteriaare grown in interface dialysis systems. WithSalmonella typhi in an agar-liquid biphasic flask,for example, the density of population was in-creased as much as 20-fold over nondialysis.yields, whereas the geometry of the system wouldexplain only a 5-fold increase (161). Presumably,the effect could be duplicated in a dialyzer-dialysis.system by including a particulate or macro-molecular adsorbing agent in the liquid mediumreservoir or, alternatively, the reservoir contentscould be continuously circulated through an ion-exchange bed.

If the aim of a dialysis system is to produce as.

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concentrated a slurry of cells as possible, thenadvantage can be taken of osmosis and hydro-philic colloids. After the conclusion of the growthcycle in a dialyzer-dialysis system, the spent me-dium can be supplemented or replaced by a con-centrated suspension of a material such as highmolecular weight polyethylene glycol or dextran.As it is circulated opposite to the cell suspensionin the dialyzer, water passes from the cell suspen-sion into the reservoir until the culture becomes sothick that pumping is precluded. Although rela-tively slow, such osmotic dehydration provides auseful and safe method for terminally concen-trating pathogenic microorganisms without theneed for centrifugation and additional equip-ment (44).

Another important exploitation of the dialysismethod is for the production of cells free fromcontamination by macromolecular constituentsof the medium. This is accomplished simply byincorporating all of the medium constituents intothe reservoir of a membrane dialysis system orinto the solidified base of an interface-dialysissystem, with only water initially in the culturezone. After allowance for a period of diffusionalequilibration, the organism can be inoculatedand grown in the clear diffusate. The principlehas been applied to the propogation of gonococci(52), mammalian cells (32), and Haemophilus in-fluenzae (51) in water diffusates of the protein-enriched media that otherwise would have beenmandatory. The idea also is applicable to theproduction of uncontaminated macromolecularproducts such as enzymes and toxins (67, 125). Apractical application is exemplified in the produc-tion of brucella cells for use as a live vaccine.Sterne (153) devised a semicontinuous method inwhich filter-sterilized medium was continuouslycirculated outside a dialysis tube that containedabout 500 ml of a saline diffusate culture ofBrucella abortus. This was harvested every 3 to 4days; the material harvested was replaced withfresh saline, and another batch of cells was al-lowed to regenerate.

Cell production. Because of the concentratingeffect during growth, which allows the attainmentof extraordinarily high population density, themain use of dialysis culture has been in cell massproduction. The obvious application is in themanufacture of vaccines.

Seemingly, the types of microorganism thatcan be propagated efficiently in dialysis culturesystems are unrestricted. Table 4 lists representa-tive genera that have been used, and provides keyreferences. Although the general principles of thedialysis method may be expected to apply to anyorganism used, nonetheless special modificationswill be required to accommodate certain types.Aerobic organisms require provision for adequate

TABLE 4. Genera of microorganisms studied withdialysis culture in vitro

Microorganism Selected reference

AlgaeScenedesmus..........

BacteriaAerobacter ...........Bacillus..............

Bacteroides...........Bordetella ............Brucella ..............

Clostridium...........

Corynebacterium.Diplococcus...........Escherichia...........Haemophilus..........Lactobacillus.........

Mycobacterium .......Mycoplasma ..........Neisseria .............Nitrobacter...........Nocardia.............Pseudomonas .........Rhizobium ............Salmonella...........Serratia ..............

Shigella ..............Staphylococcus . . .. ..

Streptococcus.........Streptomyces.........Thiobacillus ..........Vibrio................

FungiMycotorula ...........Neurospora ...........Oospora..............Pencillium............Phytopthora ..........Saccharomyces .......

ProtozoaEntamoeba ...........Eudiplodinium ........Leishmania ...........Ophryoscolex.........Polyplastion..........Tetrahymena .........Trypanosoma......

Tissue CellsKB, HeLa, L

fibroblast...........Sarcoma 180, L

fibroblast...........KB, HeLa, HEp......Avian myeloblast.....

159

6851, 55, 57, 68, 132,

137, 1615115, 7257, 65, 108, 134,

153, 16180, 132, 154, 155,

162106, 16120, 14251, 57, 115, 144, 16151, 13851, 114, 115; Fried-

man, Thesisa1091245216, 157

Mobile Oil Corp.b51, 1616141, 57, 134, 16146, 51, 52, 161; Ger-

hardt and GallupC47, 16151, 67, 89, 10751, 139511748, 51

311511551, 84, 1469651

30312431315124, 36, 79, 90, 113,

158

32

4358, 5983

a Columbia Univ., New York, N.Y., 1967.b British Patent 1,110,999, 1968.C U.S. Patent 3,186,917, 1965.

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aeration ifmaximum growth rate and extent are tobe attained (see preceding section); anaerobes,growing only at a relatively reduced Eh, requirethe exclusion of air; and the growth of some types(e.g. Bordetella pertussis) is greatly improved ifthey are cultured symbiotically (see below). Pro-visions to insure safety of the operator have beenbuilt into systems designed for producing patho-genic microbes, especially by arranging for com-

pletely diffusional gas exchange (see below).Mammalian cells usually have been propagatedwith a view toward virus production (see follow-ing section). Not all types of organisms have beensuccessfully managed in dialysis culture; e.g.,

inexplicably, Streptococcus lactis does little betterin a dialysis flask system than under ordinaryconditions.

Formation of nondiffusible products. The conse-

quences of dialysis culture that apply to cellsthemselves in the main also apply to their non-

diffusible products, i.e., particles or macromole-cules that do not pass through ordinary dialysismembranes with a porosity of less than about 10nm. (Obviously, this definition of "nondiffusible"is arbitrary because of the availability of mem-branes in almost a complete gradation of po-rosity.) For the most part, the production ofprotein exotoxins has been studied, but the prin-ciples seem applicable to the formation of othermaterials that accumulate extracellularly, e.g.,endotoxins, enzymes, antigens, allergins, poly-mers, and even viruses and cell particles. Thepotential for application of dialysis culture is thusgreatly extended, as indicated in Table 5.

Practical results are exemplified in the develop-ment of dialytic methods for the production ofbotulinum toxin, for use as toxoid. Polson andSterne (125) first employed a regenerated-cellu-lose sac with saline, into which Clostridiumbotulinum was inoculated after allowing time forequilibration with the medium in the reservoir.Type D toxin was obtained in 7 to 10 days insteadof 3 weeks and was 80 times more potent thanthat obtained from broth alone in an ordinaryculture system. The seemingly faster productionrate may only have been a reflecton of the con-centrating effect of dialysis culture, which al-lowed detection earlier. The method then wasscaled up by employing a sac containing 3.5 litersof saline diffusate surrounded by 35 liters of me-dium (155). The resulting toxin reportedly was50 to 100 times more effective. These improve-ments are much greater than what is expectedfrom the 10:1 ratio of reservoir to culture volumeand probably reflects a concomitant increase inpurity of the product, since potency is expressedin terms of toxicity per unit weight of isolatedprotein. Barron and Reed (11) reported com-

TABLE 5. Nondiffusible products studiedwith dialysis culture in vitro

Product Organism Selected

AntigensAnthrax pro- Bacillus anthracis 55

tectiveantigen

EnzymesHyaluronidase Streptococcus 139

haemolyticusPolysaccharidesLevan B. subtilis 68

ToxinsAnthrax toxin B. anthracis 132Botulinum Clostridium botuli- 155, 162

toxin numDiphtheria Corynebacterium 106

toxin diphtheriaeEnterotoxin Staphylococcus 67, 89

aureusGangrene Clostridium 154

toxins chauvoeiHemolysin S. aureus 85, 89

Pseudomonas sp. 86Tetanus toxin Clostridium tetani 80, 132

VirusesAdenovirus KB 59BAI avian Avian myeloblast 83

leukosisvirus

Poliovirus HeLa 59

parable success in producing type E botulinumtoxin, and the principle has been demonstratedto be applicable to the production of a number ofother bacterial toxins.

In the above methods, the macromolecularproduct remains with the cells, withheld by thedialysis membrane. Theoretically (see above, sec-tion on Porosity), it is possible to separate andconcentrate a macromolecular product from thecells by adding a small intermediate productchamber, with a microporous membrane filter be-tween product chamber and culture chamber, andwith an ultramicroporous dialysis membrane be-tween product chamber and reservoir. The cellswill be restricted to the culture chamber; themacromolecules will diffuse through the mem-brane filter and into the product chamber, but nofurther; nutrients and products of low molecularweight will exchange freely among the threechambers.

This concept of differential dialysis culture was-embodied in a prototype flask, tested in principlewith the production of diphtheria toxin (P.Gerhardt and D. M. Gallup, U. S. Patent3,186,917, 1967), and then examined further withan enterotoxigenic staphylococcus (67). The total

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amount of enterotoxin formed was about seventimes greater than in the nondialysis control; two-thirds of this amount was separated in the productchamber, free from cells or macromolecular con-stituents of the medium and at about twice theconcentration found in nondialysis culture. Incomparison with ordinary dialysis culture, thedifferential system proved less concentrating (by80%) and less productive in total toxin yield (by20%). The choice between ordinary and differen-tial dialysis culture will depend on the importanceof separating the macromolecular product fromthe culture.

In principle, one might also exploit the fact thatthe porosity of agar gel increases with decreasingagar concentration. Consequently, a differentialinterfacial dialysis system probably could be de-vised.

Just as cell suspensions can be concentrated to athick slurry by use of a hyrophilic colloid to re-place spent medium, so also could macromolecularproducts be further concentrated by this sup-plemental method. The principle has been demon-strated with proteins (39, 81).

Use of dialysis culture for preparation of en-zymes has been virtually unexploited. Rogers(139) employed a membrane dialysis system forproducing hyaluronidase and also made an im-portant ancillary observation. In studying theformation of two different types of hyaluronidase,he found not only that the concentrations of theenzymes were about six times higher than inordinary cultures but also that the distribution ofenzymes was different in dialysis culture. Just aswas observed for cells grown in continuous cul-ture, it appears that a different physiological bal-ance is created by growth in dialysis culture. Onecannot expect a priori to extrapolate directly fromone condition of growth to another.

Another instance in the use of dialysis culturefor enzyme production is afforded in a limitedsense by the study of Hestrin et al. (68). Theyemployed a solid-liquid interface system to growAerobacter levanicum and then extracted theendocellular levansucrase after autolysis. Theyalso used a dialysis membrane system to enhancethe production of levan by Bacillus subtilis, whichexcretes its levansucrase.

Several efforts have been made toward propa-gating mammalian cell suspensions for virus pro-duction in dialysis systems. Langlois and associ-ates grew dialysis-cultured myeloblast cells fromleukemic chickens in an effort to enhance theproduction of leukosis virus (83). Populations ofnearly 2 x 108 viable cells per ml were maintainedby a replacement technique with a shaken dialysisflask, in which the medium reservoir was con-tinuously recirculated.

Gori (58) devised a dialysis-fermentor systemin which several mammalian cell lines were propa-gated under conditions approaching steady-state.Populations of about 0.6 x 106 to 1.2 x 108 cellsper ml were maintained with HeLa 53-1, KB, andHEp-2 lines. Subsequently, poliovirus was grownon the HeLa cells with a yield of 421 TCID5o percell, and adenovirus was grown in the KB cellswith a yield of 116 TCID5o per cell (59).

Production of diffusible compounds. Surpris-ingly, there has been relatively little work reportedon the use of dialysis culture for the production ofdiffusible metabolic products. In principle, thetechnique may allow a higher productivity perunit quantity of cells because toxic products maybe continuously removed. Such a product may benonspecific in its toxic effect, as with the accumu-lation of an acid that increases hydrogen ion andundissociated molecular concentration, or it maybe specific, as when the concentration of threonineexerts feedback inhibition on the activity ofhomoserine kinase.

Demonstration in principle of the former situa-tion is afforded by results with lactic acid produc-tion. Gerhardt and Gallup (51) reported that theamount of titratable acid, as well as cell growth,was greatly increased by dialysis culturing ofLactobacillus acidophilus. Quantitative confirma-tion has been provided by a study of L. delbru-eckii grown in ordinary batch culture, batch cul-ture with continual nutrient addition, and batchdialysis culture (M. R. Friedman, Eng. Sc.D.Thesis, Columbia Univ., New York, N.Y., 1967).The results showed that lactate inhibits its ownproduction at concentrations above 10 g/liter.With dialysis, lactate could be maintained belowthis critical level so that a maximum rate of pro-duction per cell could be achieved along withhigher cell concentration. Thus, markedly higheroverall acid production rates were obtained.A convincing hypothesis for increased produc-

tion of threonine has been developed by Abbott(personal communication). Even though tested ex-perimentally only in a preliminary way, it de-serves description as an exemplifying model fordialysis fermentation. Only threonine accumu-lates in cultures of Escherichia coli W, if appropri-ate auxotrophic mutants are selected that relieverepression and feedback controls on threoninesynthesis and prevent diverted synthesis of lysineand methionine from aspartate (75). In thissituation, a primary hindrance toward higherthreonine yield appears to be a feedback inhibi-tion by threonine on homoserine kinase. Ap-parently, this and comparable blocks can be re-lieved by dialyzing away the product as it is re-leased from the organism, thereby maintainingthe lowest possible intracellular levels of the con-

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trolling metabolite. This type of approach wouldseem to have important implications for industrialfermentations.

Interbiosis. A natural extension of the use ofdialysis culture for study of diffusible metabolicproducts is to bring together two or more popu-lations of organisms on the opposite sides of oneor more membranes, so that their metabolites caninterchange. The situation may be beneficial toone population (parasitism) or both (symbiosis),and may be harmful (antibiosis) or innocuous(commensalism). Of course the entire applicationto in vivo situations represents such "interbiosis,"but the concepts also have been examined with invitro systems.The search for a diffusible "toxin" to explain

the parasitism of infectious disease agents moti-vated some of the pioneering research with dialy-sis culture (20), and Frost in 1904 used the methodto show that diffusible products from saprophyticorganisms inhibit typhoid bacilli (41). And, ofcourse, the now common agar-diffusion methodfor detecting formation of an antibiotic com-pound by one organism active upon another is buta modification of the same principle.

Investigation of symbiotic relationships be-tween population pairs has employed dialysisculture techniques in a number of different situa-tions. Ritter (138) grew Haemophilus influenzaewith Staphylococcus aureus across a membrane.Black (15) found that higher densities and pro-longed survival of Bordetella pertussis were ob-tained when it was grown in a dialysis flask withCorynebacterium pseudodiphtheriticum. Marx andHaasis (96) discovered that sporangial formationwas induced in Phytophthora cumamoni bydiffusates from adjacently growing soil bacteria;sporangial formation was 10 times higher when afilter membrane was used instead of a dialysismembrane, suggesting that a large molecular sub-stance was causing the effect. A symbiotic protec-tive action was illustrated in the work of Schaum-berg and Kirsch (144), who used dialysistechniques to show that Escherichia coli couldsubstitute for reducing agents to stimulate thegrowth of anaerobic methane-forming bacteria.The E. coil culture was interposed between themethane bacteria and the atmosphere to scavengeoxygen and maintain a low Eh .The most precise investigation of "symbiodialy-

sis" was made by Nurmikko (114, 115). He grewauxotrophic mutants deficient for a specific aminoacid in conjunction with strains producing it in anattempt to measure the specific formation rate. Hereasoned that the amino acid was removed fromthe system by the symbiotic culture as it wasformed, thereby eliminating feedback inhibitionmechanisms. However, as shown by mathematical

theory, a concentration of the amino acid mustbuild up so as to provide a driving force fordiffusion, and consequently the feedback inhibi-tion can be alleviated but never completelyeliminated.

Symbiotic mixed cultures in sewage sludge di-gestion were studied in dialysis culture by M. JLHammer (Ph.D. Thesis, Univ. of Michigan, AnnArbor, 1964). He employed a dialyzer-dialysissystem to separate and optimize the acid and thegasification stages of anaerobic digestion. Rawsewage solids were fed into the primary fermenta-tion vessel to establish a mixed enrichment culturefor production of volatile organic acids, whichdiffused through a vinyl dialysis membrane into asecondary vessel to establish another enrichmentfor production of methane and other gases. Thestudy demonstrated that the two stages could beseparately controlled (e.g., in Eh and pH) andthat the acid fermentation stage was rate-limitingin the process. It also nicely demonstrated the po-tential usefulness of dialysis culture as an enrich-ment method for obtaining microorganisms.Gas exchange. Another little exploited feature

of dialysis culture is the ability to provide oxygenor other required gases, and to remove carbondioxide or other gaseous products, solely by dif-fusion. The principle seems especially applicable.to the propagation of oxygen-requiring butfragile organisms, such as protozoan or mam-malian cells, which may be injured by directgassing or the addition of antifoam agents. Itmight also be useful for regulating the oxygensupply of microaerophilic organisms. An im-portant practical consequence will be a greatlyimproved safety factor in the production of patho-genic microorganisms for vaccines, where a mainpotential hazard is aerosol formation. In currentprocedures, the culture vessel is usually aeratedunder pressure, and leaks, especially around theagitator shaft, almost inevitably arise. Withdialysis aeration, the passage of air is removedfrom the culture to the opposite side of the mem-brane. Furthermore, it becomes evident that thesupply of air need not be separately sterilized insuch a system, thus eliminating a substantialsource of contamination as well as a difficult andcostly mechanical problem.The possibility of dialysis aeration was first

explored by Gladstone (55), who used the methodto produce a cell-free protective antigen for an-thrax without the danger of denaturation bygassing or from antifoam agents. Gerhardt andGallup (51) further demonstrated the principle byinoculating a facultatively aerobic bacterium intothe bottom chamber of a dialysis flask, rather thanthe top as in the usual procedure, and comparingthe effectiveness of a dialysis membrane and a

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filter membrane. The latter proved much thebetter and supported growth surprisingly nearthat attained with normal aeration.The effective use of this principle depends on

newly developed solution-transport membranes(see above, section on Types of Membranes),which selectively and rapidly transport gases.Humphrey and Gerhardt (unpublished data) em-ployed silicone rubber membranes in a dialyzer-dialysis culture system, with humidified air con-tinuously circulated through the dialyzer. Vari-ables affecting the efficiency of oxygen transportincluded air velocity, culture liquid velocity,membrane area, partial pressure of oxygen, andculture mixing. Even though the measured oxygentransfer rates were less than 25% of those in well-sparged fermentors, the dialysis-aerated culturesattained population densities at least as great asthose in conventionally aerated cultures. Similarresults were obtained when dialysis aeration wasused in conjunction with nutrient dialysis ofcultures.

In Vivo SystemsMicrobial growth within animal tissues is recog-

nized often to differ from that in artificial media,as exemplified by the common observation ofchanges in virulence, antigenicity, metabolism,and morphology when infectious agents are trans-planted into the laboratory.Two general conditions distinguish the in vivo

environment: antibacterial factors of the hostand the nutritive quality of its tissues. These can-not be differentiated in tests in which the micro-organism is introduced directly into the tissues,but can be if the agent is implanted within a mem-brane chamber. All known nutrients are smallenough to diffuse through dialysis membranes,whereas phagocytic cells, antimicrobial factorsassociated with serum proteins, and other macro-molecules are excluded.The in vivo nutritive environment is distin-

guished by two further conditions that are lesscommonly recognized. First, there often is a flowof fluids and a limitation of nutrients that ap-proach steady-state conditions. Second, the nu-trient supply usually is regulated by diffusionthrough one or more membranes, surroundingeither an organ or a cell in which the parasiticmicroorganism is localized. Thus, in vivo growthcan best be simulated by continuous culturegoverned by dialysis.The animal has a number of organs and tissues

-with a fluid environment in which dialysis culturecan be managed experimentally. For the mostpart, this has been accomplished by implanting a

sac or chamber directly into the region. In somecases, a number have been implanted so that one

after another could be removed for examination.In other cases, a single device has been used, withan excess tube for sampling.

Peritoneal dialysis. The most obvious organ forin vivo dialysis culture is the peritoneum, andhistorically it was the first used, in the demonstra-tion of bacterial toxigenesis (98). A considerablebody of literature ensued along a similar vein ofdemonstrative experiment, including the cultureof supposedly obligate parasites (110), alterationof virulence (112), prolongation of multiplication(49), and the role of phagocytosis (62). In vir-tually all of this early work, collodion sacs wereused.

Cellophane, which is much more reliable thancollodion and of known ultramicroporosity, cameinto use for in vivo propagation of microor-ganisms about 10 years ago. An excellent andexemplifying quantitative study was made byGladstone and Glencross (56), who investigatedgrowth of and toxin production by staphylococciin vivo. They employed a cellophane tube fittedwith a fine nylon tube for inoculation andsampling, which was filled with saline and im-mersed in the peritoneal fluid. Filter-sterilizedserum was used as an in vitro control. A total of28 strains of staphylococci, both coagulase-posi-tive and -negative, were grown in vivo with dialy-sis, and 5 strains were studied quantitatively inmice, rats, guinea pigs, and rabbits. In comparisonwith the in vitro control, the in vivo growthcurves usually exhibited both a prolonged lagphase and a slower rate of exponential growth. Amore rapidly growing mutant often arose andcould be selected, especially with rabbits as thehost animals. When the production of a hemolysinand a leukocidin were compared, however,staphylococcal strains that had failed to producethese toxins in vitro did so in vivo with dialysis.Furthermore, other strains produced toxin inamounts far exceeding those produced under thebest conditions in vitro. The results nicely demon-strated the entirely different growth conditionsfor bacteria that prevail within an animal.

Later results demonstrated that the virulence ofstaphylococci was directly related to a diffusiblehemolysin (74). When S. aureus was implantedintraperitoneally in a diffusion chamber equippedwith filter membranes, necrosis usually occurredin the vicinity of the implant; but, when thechamber was fitted with dialysis membranes, nonecrosis occurred. Analysis of the latter contentsshowed that hemolysin was still produced butevidently did not cause necrosis because hemol-ysin could not diffuse away. Growth curves withthe two types of membranes appeared much thesame, and the maximal populations were re-

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ported to be about one log higher than in "typi-cal" broth cultures.The loss or gain of virulence after passage of in-

fectious microorganisms through animals is acommon phenomenon. Ogg et al. (116) investi-gated this phenomenon by implanting cellophanesacs inoculated with Pasteurella pestis into guineapigs. In contrast to usual behavior, a virulent cul-ture did not lose its virulence, nor did avirulentstrains revert. Apparently, more intimate contactbetween the microorganisms and the host is re-quired. In addition, they noted that a lower cellpopulation was achieved in vivo than in anaerated in-vitro control. This last result wouldseem opposite to that reported by Houser andBerry for staphylococci (74). The fallacy in bothcomparisons, of course, is that neither employeda really comparable control situation such as wasdevised by Gladstone and Glencross (56).

Lorincz, Priestly, and Jacobs (87) found thatmice have an interesting defense mechanismagainst a dermatophyte. The organism Trichophy-ton mentagrophytes was inhibited from prolifera-tion when implanted intraperitoneally within afilter-membrane chamber, and the inhibition wasnot relieved when dialysis membrane was substi-tuted for the more porous membranes. The evi-dence points to a dialyzable, water-soluble sub-stance which is present in the serum and interfereswith the growth of dermatophytes. Studies suchas these should lead to a fuller understanding ofin vivo defense mechanisms.Mammalian cells and tissues also have been

propagated in vivo within implanted dialysischambers. The earliest attempts apparently weremade about 1933 by Rezzesi (136) and Bisceglie(14), using collodion sacs and Ehrlich carcinomacells. The method was revived and modified in1954 by Algire and co-workers (130). Their"diffusion chamber technique" utilized micro-porous filter membranes to separate the cell cul-ture from host cells, so that other noncellulargrowth-controlling influences of the host wereallowed to act.

Quantitative measurement of cell growth invivo was attempted first by Amos and Wakefield(10), who used direct counting methods on ascitestumor cells growing in free suspension within thediffusion chamber. The cells were found to growexponentially only for a short period and afteran initial drop in cell concentration.A comparison of the growth rate of tissue cells

in vivo and in vitro was made by Gabourel andFox (43), employing lactate dehydrogenase ac-tivity as an index of cell numbers. A specialdouble-membrane diffusion chamber was used toseparate the implanted cells from the host cellsthat grew on the outer membrane surface. The

growth of L-fibroblast and sarcoma 180 cells ap-peared to be exponential, both in vivo and invitro, with over a 100-fold increase in cell density.However, a somewhat larger inoculum of the L-fibroblast cells was required in vivo to obtainconsistent results. The generation times for bothlines were similar, but they were much longer forthe respective in vivo cultures. The slower in vivogrowth rate may be caused by nutrient deficienciesdue to low diffusion rates through the membranesurfaces and hindrance by cell growth on theoutside membranes. However, directly compar-able conditions in the two situations were notachieved.The implant chamber technique has also been

used to study cell differentiation in vivo. Sheltonand Rice (147) presented evidence that normalleukocytes develop into plasma cells and fibro-blasts within filter-membrane diffusion chambers;collagen accumulates concomitantly. These ob-servations were substantiated by Petrakis, Davis,and Lucia (121), who used diffusion chambers-implanted subcutaneously to demonstrate thathuman leukocytes differentiated to form macro-phages and "polyblasts" initially and then de-veloped into histiocytes and fibroblast-like cells.After 4 to 6 weeks, collagen formation was ex-tensive and in some instances fat cells wereformed. Over the same period, initially maturegranulocytes underwent disintegration. In experi-ments with guinea pigs, in which normal andascorbic acid-deficient leukocytes were used,Petrakis (120) further showed that ascorbic acidwas required for the differentiation of leukocytes.into fibroblastic cells.The concept of the intact animal as a con-

trolled environment has been used to study anti-body production by tissue cells contained withina diffusion chamber. Holub (73) found that sus-pensions of spleen cells, lymph nodes, or lym-phatic cells would produce antibodies againstbacterial antigens when incubated within diffu-sion chambers in the peritoneal cavity of rabbits.He also showed, by trypan blue diffusion studiesand microscopic examination, that the membranewalls were eventually blocked by occlusive cellgrowth on the membrane surface. Diffusion ratesbetween the chamber and surrounding fluiddropped by a factor of about 8 over a 10-dayperiod. Weiler (164) showed that antibody pro-duction by immunologically competent cellsstarted 4 days after implantation intraperitoneallyin a diffusion chamber and peaked between 8 and15 days. No new exposure to antigen was neededto elicit this response. The evidence provided bytiter analysis indicated that antibody was pro-duced inside the chamber and not outside by thehost cells. A further contribution, made with the

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aid of diffusion chambers and important to anunderstanding of antibody formation, was re-ported by Fishman and Adler (38). They demon-strated that nonimmune lymph node cells in animplanted chamber could be stimulated to pro-duce novel and specific antibody (to bacterio-phage) by addition of a cell-free homogenate frommacrophages that had been specifically stimu-lated in vitro. The active principle in the ho-mogenate was found to be a low molecularweight ribonucleic acid (RNA) fraction, whichwas inactivated by ribonuclease. Diffusion cham-bers have an adjuvant effect on soluble antigens(1), however, and the possibility remains that theRNA carried bacteriophage fragments as an anti-gen-RNA complex. Antibody-synthesizing cellsalso can be explanted and maintained in vitro in afunctioning state for at least 2 weeks, by use of adialysis apparatus and a continuous flow of me-dium through the reservoir compartment (4).

In a series of studies on the growth and survivalof tissue homografts, Algire et al. found that pro-longed survival of the implanted tissue could beattained if the grafted tissue was protected fromdirect cellular contact with the host by peritonealimplantation within a finely porous diffusionchamber. However, if a membrane-filter materialwith pores large enough to allow lymphocytes toenter the diffusion chamber was used, the graftswere destroyed in a manner similar to unprotectedimplants. These results indicate that humoralfactors are not responsible for graft rejection, butrather that antibodies transported by lymphocytescause graft destruction (6, 9, 130, 163). In furtherwork, in which heterografts were used, it wasfound that the survival time was reduced to a fewdays if the host was previously immunized, evenwhen the transplant was placed in cell-im-penetrable chambers (7).

Potter and Haverback (127) examined thyroidtissue within diffusion chambers implanted intra-peritoneally in thyroidectomized dogs. Althoughthe implanted tissues lasted for 10 months, theyslowly deteriorated. This led the authors to con-clude that the technique would not be satisfactoryfor clinical purposes.

Hemodialysis. A dialyzer can be connected intoa bypass of the venous circulatory system to per-mit communication through a membrane with anexternal reservoir. Such hemodialysis systemshave been widely employed as artificial kidneysand lungs, for detoxification, and for adminis-tration of anesthetics. The reader is referred topapers in the Proceedings of the Society for Arti-ficial Organs and in a recent engineering sym-posium (29). Developments in this field oftenhave application to dialysis culture of micro-organisms, especially in the development of

membranes and dialyzers. Although a mainconcern in artificial organ work is asepsis, hemo-dialysis would seem to offer considerable promisefor extracorporeal study of septicemia. However,we have been unable to find such efforts reportedin the literature and, in preliminary experimentalwork, have discovered only that a culture dialyzerand pump efficiently destroy erythrocytes (Mol-stad and Gerhardt, unpublished results).

Solid tissue implants. Membrane diffusionchambers containing cells can be implanted uponsolid tissues as well as within the more usualliquid tissues employed in dialysis culture in vivo.Essentially colonial growth occurs. The tech-nique has mainly been applied to the study oltissue homografts, but would seem to offer con-siderable promise for examination of virulencefactors in infections.Much of the study on tissue homografts and

heterografts by Algire et al. (see preceding sec-tion) was accomplished with diffusion chambersimplanted subcutaneously as well as intraperi-toneally (6, 9), or only subcutaneously (8).Essentially the same results were obtained withthe two sites (see above).

Similarly, the study of cell differentiation invivo by Petrakis, Davis, and Lucia (121) was ac-complished with subcutaneous implantation(see preceding section).

Castellanos and Sturgis (22) extended the workon graft transplants within diffusion chamberspositioned intraperitoneally by studying the func-tion as well as survival of endocrine gland trans-plants within chambers positioned subcu-taneously. Ovarian tissues were transplanted tocastrated rats, and uterine development was ob-served over a period of 2 months. They foundconclusive evidence of estrogenic stimulation ofthe uterus, which implies that the grafted tissuemaintained functional estrogenic capabilities overthis period. Similar experiments with monkeysover a span of 7 months also showed continuedfunctional performance (23).Embryonated egg. Mention should be made of

the chorioallantoic and other membranes of fowleggs as natural dialysis systems, which were dis-cussed earlier in the section on Colonial Growthwith Dialysis. Although these have found con-siderable use in microbiology, the resultingmicrobial growth is colonial in character.Rumen symbiodialysis. The biochemical reac-

tions occurring in the rumen of cattle and otherruminant animals result from the digestive ac-tivity, mainly cellulolytic, of a mixed populationof symbiotic microorganisms. The wall of therumen itself acts as a dialysis barrier, so that theorgan represents an enormously complex dialysisculture system. In vitro techniques applied to

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study this ecosystem have been extensive (76),and include artificial rumen systems in whichmembrane chambers are filled with samples ofrumen contents and allowed to dialyze againstvarious media in an effort to simulate naturalabsorption. Some of these have incorporated thesignificant concept of operation under steady-state conditions (60).The comparable in vivo studies are those in

which some form of dialysis chamber is cannu-lated through a fistula and immersed in the rumenof an animal. Although much of the effort to dateseems to have been expended in developing andtesting apparatus, some progress has been madetoward characterizing cellulose digestion (122),fatty acid production (37), hydrogenation of fattyacids (28), mixed microbial growth (28, 31), andprotein synthesis (28).

In discussing applications of the dialysis tech-nique to problems of rumen ecology, Fina andassociates (37) pointed to vistas of study nowsusceptible to investigation: examination of purecultures and defined mixtures in context withtheir natural environment, cultivation of fastidi-ous organisms heretofore not cultivatable in pureform, and isolation of enzymes that are producedin the milieu. Such visions might well be extendedto the dialysis culture technique in general. Itremains to be seen, however, how well and howgenerally this promise is realized.

ACKNOWLEDGMENTS

We appreciatively acknowledge the library assistance of LynnE. Sorensen and the resource of reference material accumulated inthe theses of Elizabeth A. Tyrrell, D. M. Gallup, J. U. Pedersen,J. D. Herold, and H. E. B. Humphrey, Jr.

Figures are reproduced from other articles with the permissionof the authors and of the publisher for the journal cited.

The experimental work by the authors and preparation of thisarticle were supported by contracts from the Department of theArmy, Fort Detrick, Frederick, Md., and by Public Health Servicegrants GM-15152 and AI-06999 from the National Institutes ofHealth.

This is article no. 4504 from the Michigan Agricultural Experi-ment Station.

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