mechanisms of homogeneous nucleation of polymers of sickle cell anemia hemoglobin in deoxy state

Mechanisms of Homogeneous Nucleation of Polymersof Sickle Cell Anemia Hemoglobin in Deoxy State

Oleg Galkin and Peter G. Vekilov*

Department of ChemicalEngineering, University ofHouston, Houston, TX77204-4004, USA

The primary pathogenic event of sickle cell anemia is the polymerizationof the mutant hemoglobin (Hb) S within the red blood cells, occurringwhen HbS is in deoxy state in the venous circulation. Polymerization isknown to start with nucleation of individual polymer fibers, followed bygrowth and branching via secondary nucleation, yet the mechanisms ofnucleation of the primary fibers have never been subjected to dedicatedtests. We implement a technique for direct determination of rates andinduction times of primary nucleation of HbS fibers, based on detectionof emerging HbS polymers using optical differential interference contrastmicroscopy after laser photolysis of CO-HbS. We show that: (i) nucleationthroughout these determinations occurs homogeneously and not onforeign substrates; (ii) individual nucleation events are independent ofeach other; (iii) the nucleation rates are of the order of 106 –108 cm23 s21;(iv) nucleation induction times agree with an a priori prediction based onZeldovich’s theory; (v) in the probed parameter space, the nucleuscontains 11 or 12 molecules. The nucleation rate values are comparable tothose leading to erythrocyte sickling in vivo and suggest that themechanisms deduced from in vitro experiments might provide physiologi-cally relevant insights. While the statistics and dynamics of nucleationsuggest mechanisms akin to those for small-molecule and protein crystals,the nucleation rate values are nine to ten orders of magnitude higher thanthose known for protein crystals. These high values cannot be rationalizedwithin the current understanding of the nucleation processes.

q 2003 Elsevier Ltd. All rights reserved.

Keywords: sickle cell anemia; hemoglobin S polymerization; fibernucleation; homogeneous nucleation rate; nucleus size*Corresponding author

Introduction

Sickle cell anemia, or homozygous sickle celldisease, is a genetic disorder, which affects about250,000 children worldwide every year; many ofthem have multiple strokes and die before theyare two years of age.1,2 The disease is caused by anA-to-T mutation within the sixth codon of theb-globin coding region.3 As a result, the glutamicacid residues at the sixth position of the twob-subchains are replaced by non-polar valine.4 – 6

Unlike the normal hemoglobin (Hb) A, themutated hemoglobin has a high propensity topolymerize when in the tense (T) state in thevenous circulation.7 – 11 The polymerization alters

the shape and rigidity of the red blood cells,12 – 15

and triggers a sequence of pathogenicconsequences.15 – 17

Polymerization of HbS is one example of anumber of disorders caused by phase transitionsof abnormal proteins,18 which include the eyecataract, Alzheimer’s, Huntington’s, and the priondiseases, etc.19 –22 Phase transitions are ubiquitousin healthy organisms as well; examples includethe formation and modification of thecytoskeleton,23 the suspected microcompartmenta-tion of the cytosol,24 etc. Data on the kinetics ofphase transitions provide insights into their mech-anisms and governing physical parameters andmay help in the understanding of their normaland pathological effects in living systems.

As many other first-order phase transitions,25 – 27

the polymerization of deoxy-HbS starts withnucleation, in which a certain number of moleculesassemble into an embryo of the new phase.28 – 30

0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.

E-mail address of the corresponding author:[email protected]

Abbreviations used: Hb, hemoglobin; DIC, differentialinterference contrast.

doi:10.1016/j.jmb.2003.12.019 J. Mol. Biol. (2004) 336, 43–59

Although the progress of HbS polymerization hasbeen monitored by a variety of techniques (seeEaton & Hofrichter8 for a review), to date thereexists just one set of data on nucleation rates.28,31,32

These detailed determinations use an eleganttheoretical model33 to extract nucleation rates fromthe evolution of the intensity scattered fromgrowing polymer fibers.

Here, we implement a method for direct simul-taneous determination of two independent charac-teristics of the nucleation kinetics of HbS polymerfibers: the homogeneous nucleation rates and thenucleation induction times. After polymerizationis induced by laser photolysis of carbon monoxide-saturated HbS, nucleation of individual fibers ismonitored by optical microscopy with differentialinterference contrast (DIC) in slides of uniformthickness containing supersaturated solution. Therate of homogeneous nucleation and the inductiontimes are determined from the evolution of thestatistics of appearance of HbS spherulites.

The results obtained using this technique shedlight on the following questions: is nucleation ofHbS fibers compatible with the general theories ofnucleation of first-order phase transitions? Whatare the typical nucleation rates of the deoxy-HbSpolymers? How do the determined values compareto those leading to red cell sickling in vivo? How dothe determined values compare to those in other,protein and non-protein, systems? How applicableare the mechanisms determined from in vitro deter-minations to the nucleation of HbS polymers invivo? How many molecules are in the polymernucleus? Are they arranged in disks of seven pairsas in grown HbS fibers, or do they have a differentarrangement?

Results

Polymerization, nucleation, and nucleationrate determination

In brief, the determinations of the nucleation rateconsist of the following experimental procedures.A CO-HbS sample is held in a glass slide of 5 or10 mm uniform thickness. An area of ,90 mmdiameter is continuously illuminated with greenlaser or lamp to photolyze CO-HbS to deoxy-HbSand sustain the deoxy form. DIC microscopy isemployed to monitor the number of HbS fibersand spherulites appearing in the illuminated area.Assuming that each spherulite is generated by asingle nucleation event (see arguments supportingthis assumption in this subsection) we determinethe number of nuclei in the illuminated volumefor the time elapsed after illumination starts. Thenthe illuminated spot is moved to another,randomly selected location on the slide and thetime evolution of the number of nuclei is recordedagain. In most cases, this is done 82 times at eachtemperature. In some cases 200 and more determi-nations are carried out. The nucleation rate is

determined as the ratio of the mean number ofnuclei that appear for a certain time to the volumeoccupied by deoxy-HbS. Exhaustive details areprovided in Materials and Methods below.

If polymerization is driven by low-to-moderatesupersaturations, the fibers do not branch and thesolid phase consists of separate HbS fibers, suchas those in Figure 1(a).34 At the later stages ofpolymerization, the solution turns into a gelconsisting of straight fibers (Figure 1(b)). Sincespherulites are easier to detect than single fibers,we work at slightly higher supersaturations,which ensure spherulitic morphology of the HbSpolymer phase illustrated in Figure 1(c).

As in previous work (e.g. Briehl10), a basicassumption in the nucleation rate determinationsbelow is that each spherulite is generated by asingle primary nucleation event. The relative errorintroduced by this assumption is equal to the prob-ability of having two nucleation events within theslide area occupied by one spherulite. This prob-ability can be evaluated as the ratio of the areaoccupied by all spherulites in the slide to the totalarea, in which nucleation can occur. As shownbelow, nucleation rate data are extracted fromimages of slides with fewer than ten spherulites,each occupying an area of ,10 mm £ 1 mm. Theprobability of having a second spherulitehidden under or within one of the ten is about(10/5000)2 £ 10 ¼ 4 £ 1025.

Homogeneous nucleation or nucleation ona substrate?

For tests of whether the primary nucleation ofthe observed spherulites is facilitated by the upperand lower slide covers, or dust particles in thesolution, we record the locations of appearance ofthe spherulites in four repetitive identical runs atthe same area of a slide. The runs were separatedin time by 20–30 minutes, allowing complete dis-solution of the spherulites nucleated in thepreceding run. With slide thickness of 5 mm or10 mm, buoyancy-driven convection due topossible thermal gradients is suppressed.35,36 Thus,possible particles in the solution could only bemoved by Brownian diffusion, in which theexpected displacement Dx <

ffiffiffiffiffiffiffiffiffiffiffi4DDt

p< 10 mm for a

,1 mm particle with diffusivity D , 1029 cm2 s21

over Dt ¼ 1200 s. The predicted displacement iscomparable to the observed sizes of the spheruliticdomains, i.e. if such particles serve as substratesfor heterogeneous nucleation, the locations of thespherulites in subsequent runs would overlap.Figure 2 shows that no correlation exists betweenthe locations and orientations of the spherulites inthe four runs. We conclude that the nucleationevents that lead to the spherulites are notfacilitated at particular spots on the slide covers orby particles larger than 1 mm in the solution.

For further evidence for the mechanism ofprimary nucleation, we carried out several deter-minations of the mean (over ,100 identical runs)

44 Nucleation of HbS Polymers

number of nuclei that appear in solutions held inslides of 5 mm and 10 mm thickness after identicaltime periods and with special care to ensure equaltemperatures of the two runs, for details, seebelow. We found that the mean number of nucleiin the illuminated area in 10 mm slides is double

the number in 5 mm slides, i.e. the number ofnuclei generated over a certain time is proportionalto the solution volume. Furthermore, we observedthat spherulites are never firmly attached to thesurface of a glass slide. The latter two observationsrule out heterogeneous nucleation on the glasssurfaces.

Statistics of nucleation

The time required for complete dissolution of thespherulites is usually comparable or longer thanthe time of spherulite nucleation and growth.Hence, repetitive runs to determine the nucleationstatistics are carried out by illuminating randomlyselected different areas in the slide.

Figure 3(a) shows that as spherulites grow, theyget close to one another, fill the illuminated area,and interfere with the processes of further nuclea-tion. Hence, we only count spherulites before theirregions overlap. Furthermore, as shown below, thenucleation rates are determined from the earliestpart of the data on spherulite numbers, where thenumbers increase linearly with time.

In Figure 3(b), we show determinations of thenumber of spherulites n in the illuminated area as

Figure 1. Morphologies of polymer fibers observed during deoxy-HbS polymerization visualized in 10 mm slides at22 8C using differential interference contrast microscopy. (a) Single fibers ,20 nm thick observed at HbS concentration170 mg ml21. (b) Gel composed of long single fibers, conditions the same as in (a), long observation times.(c) Spherulites observed at HbS concentrations 200 mg ml21 and higher. (d) Thick gel with no individual fibersdiscernible at long polymerization times with HbS concentration of 250 mg ml21.

Figure 2. Locations and orientation of spherulites infour consecutive runs made at the same area on theslide, with full dissolution of fibers between the runs.T ¼ 22 8C; CHbS ¼ 232 mg ml21.

Nucleation of HbS Polymers 45

a function of the time, t, elapsed after CO-HbSphotolysis. These determinations were performedat identical conditions, within the same slide. Wesee that even in the limited number of runs dis-played, the delay times before the appearance ofthe first spherulites vary from 8 s to 13 s, thenumber of spherulites, for instance at 16 s, variesbetween one and five, and the shape of the n(t)dependence is unpredictable. These three factsillustrate the inherently stochastic nature of theprocesses of fiber nucleation.

In a stochastic process, the number of nuclei thatappear in a certain volume is a random variable:repetitions of an experiment under identical con-ditions could give, for instance, one, ten, or nonuclei. Representative statistical distributions ofthe number of nuclei resulting from 200 experi-ments under identical conditions are presented inFigure 4.

To verify if the individual nucleation events areindependent of each other, a prerequisite for theapplicability of the general nucleation theories, wedetermine the nucleation statistics. We compare

the distributions of the numbers of nuclei inFigure 4 with Poisson’s law:

PðnÞ ¼Nn

n!expð2NÞ ð1Þ

where n is the number of nuclei that appear involume V during nucleation time t, N is the meannumber of nuclei in all runs with the same V and treflected in the distribution.

For each distribution, we calculate Nfit from thebest fit to equation (1) and the algebraic meanof the data in the distribution N. The expressionð1 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiN=Nfit

pÞ was evaluated and its closeness to 0

was used as a criterion for the correspondence ofthe actual distribution of the data to Poisson’slaw.37 In all cases, it was ,0.065. For further testsof the goodness of the fit to the Poisson’s law,equation (1), we calculate the parameter x2:37

x2 ¼X

n

½Fn 2 PðnÞNfit�2

PðnÞNfitð2Þ

where Fn are the measured frequencies fromFigure 4 and P(n) are Poissonian best-fit values. Inmost such determinations, for instance the data inFigure 4, the x2 values correspond to confidencelevels in the Poissonian character of thedistributions of 90% or better; in a few cases theconfidence level was as low as 80%. The relativeerror in determination of N is evaluated asffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

N=ðnumber of runsÞp

: Thus, for 100 runs yieldingon the average one nucleus, it is 0.1.

Comparisons of the distributions of thespherulites in five series of 200 repetitive runsunder identical conditions show (data not dis-played) that although the number of spherulites israndom, the statistical distributions correspondingto experiments performed under the same con-ditions are reproducible. All five distributionshave the same shape, follow Poisson’s law, andhave very similar mean values.

The good correspondence of the experimentallydetermined distributions to Poisson’s law showsthat all individual nucleation events are indepen-dent of each other. Thus, the statistics of nucleationof the sickle cell hemoglobin polymers indicate thatunder the conditions probed here it follows thegeneral laws of nucleation of first-order phasetransitions.

The homogeneous nucleation rates

Figure 4 shows that with increasing nucleationtime t the distribution of the number of spherulitesshifts to the right, changing from near-exponentialat short times to near-Gaussian at long times.Figure 5 shows that the time dependencies ofmean number of spherulites found from 82 inde-pendent runs have a characteristic shape: after aninitial delay period, when no nuclei are seen, thenumber increases linearly with time. These linearparts of the dependencies in Figure 5 correspondto steady-state nucleation, characterized by the

Figure 3. Variation of the number of spherulites nappearing for time t at T ¼ 22 8C and HbS concentrationof 232 mg ml21. (a) Illustration of spherulite countingprocedures for determination of n. (b) Six dependencesnðtÞ at identical conditions.


nucleation rate J. The last part of the dependenciesreflects saturation due to growth of spherulitesand overlapping of their supply fields. These datawere not included in determinations of thenucleation rates. Note that all points in Figure 5

were taken from images similar to the first fiveframes in Figure 3(a), i.e. where the interactionbetween spherulites is not apparent. Thus, thetime dependencies of the averaged numbers ofnucleated spherulites offer a stricter criterion fornon-interacting spherulites, from which nucleationrates can be extracted.

The nucleation rate J, i.e. the number of nucleithat appear in a unit solution volume within aunit time, is determined for each dependence inFigure 5 as the slope of the straight linecharacteristic of the steady regime of nucleation.Figure 6(a) shows the dependence of the homo-geneous nucleation rate J on temperature T for asolution of deoxy-HbS with concentrationC ¼ 232 mg ml21 ¼ 3.32 mM in 0.15 M potassiumphosphate buffer with pH ¼ 7.35. The values inFigure 6(a) come from two independentexperiments, starting from solution preparation, asdiscussed in Materials and Methods below. Thegood correspondence between the two data sets isevidence for the reproducibility of the determi-nations by the technique used here.

As expected, the nucleation rate J in Figure 6(a)is a strong, exponential function oftemperature. The values of nucleation rate fromthis and other runs at similar HbS concentrationsand temperatures are in the range 105 –108 cm23 s21. Converting to units mM s21 asothers,31,32 J ¼ 108 cm23 s21 ¼ 1.66 £ 10210 mM s21,

Figure 4. Statistical distributions of the number of nuclei at times of the evolution of a polymerizing sampleindicated on the plots at T ¼ 25 8C, and CHbS ¼ 232 mg ml21. Bars represent experimental determinations, linesrepresent fits with the Poisson distribution.

Figure 5. The dependence of mean number of nuclei,determined by averaging over 82 runs on time at thetemperatures indicated in the plot andCHbS ¼ 232 mg ml21. The relative error in each datapoint is ,0.1. The linear portion of each dependence isfitted with a straight line, whose slope is taken as thehomogeneous nucleation rate. The intercept of thestraight line with the time axis determines the apparentnucleation delay time.


with log J ¼ 29:78: The publisheddeterminations31,32 were carried out at higher HbSconcentrations and in the 25–35 8C temperaturerange. If one extrapolates the decrease of J(denoted with f0

31,32) with decreasing HbSconcentration from 4.26 mM ¼ 275 mg ml21 to3.92 mM ¼ 253 mg ml21 at 25 8C reported by Cao& Ferrone32 to the concentration that we use, avalue close to ours obtains.

The driving force for polymerization

To evaluate the thermodynamic supersaturationDm=kBT ¼ ðmHbS

polymer 2 mHbSsolutionÞ=kBT (m is the

chemical potential of the HbS in the respectivephase, kB is the Boltzmann constant and T is theabsolute temperature) at the determination tem-peratures, we use the virial expansion38 – 40 limitedto the sixth-order term as justified:8,41

DmðC;TÞ

kBT¼ ln

C

CeqðTÞ

þX6

i¼1

i þ 1

iBiþ1½C

i 2 CeqðTÞi� ð3Þ

where C is the deoxy-HbS concentration, and Ceq isits value at equilibrium with the polymers. Thevalues of the virial coefficients Bi are obtained

using the expressions for non-interacting hardspheres from Hill:39 for justification, see Minton:42,43

B2 ¼8V

2M; B3 ¼

15V2

3=2M; B4 ¼

24:48V3

4=3M;

B5 ¼35:3V4

5=4M; B6 ¼

47:4V5

6=5M;

B7 ¼65:9V6

7=6M

ð4Þ

The specific volume V was determined from fits tore-plotted data on sedimentation equilibria;41 bestfits are obtained with V ¼ 0:79 cm3 g21, close tothe values for other proteins44,45 and to the Hbvalue reported.8 Since the virial coefficients fornon-interacting spheres are temperature-indepen-dent, the only temperature dependence in equation(3) comes from CeqðTÞ:

8

CeqðTÞ ¼ 0:319 2 0:000883ðT 2 273:15Þ

þ 0:000125ðT 2 273:15Þ2 ð5Þ

We find that the supersaturation levels aremoderate: for C ¼ 232 mg ml21 as in Figure 6(a),Dm=kBT does not exceed 1.7 even at the highesttemperature probed.

Nucleation induction time

An advantage of the method used here is that itallows independent determinations of thenucleation rate and of the nucleation delay time.As Figure 5 shows, we determine the nucleationdelay time from the intersection point with thetime axis of the dependence of the mean numberof nuclei on time. Another possibility is to averagethe individual delay times in plots similar to thosein Figure 3, which would yield a different charac-teristic of nucleation kinetics. As shown byKashchiev,46 the delay time resulting from theformer method contains the nucleation inductiontime u, and hence, this is the method used here.The time u is a measure of the rate of trans-formation of the molecular distribution in a meta-stable single-phase solution to the distribution in asolution in which nucleation of the new phaseproceeds at a steady rate.47,48

The delay times are plotted as a function of tem-perature in Figure 6(b). The data in the two seriesdiverge, while the reproducibility of the nucleationrates in Figure 6(a) is preserved. This discrepancyillustrates the independence of these two character-istics of the nucleation kinetics; an understandingof the physical phenomena underlying it is stillmissing at his point. The delay times are the sumsof two components: the nucleation induction timesu and the instrument detection times. Theinstrument detection times are determined by theresolution of the microscope of ,0.5 mm andthe growth rate of the spherulites. We measure thespherulite growth rates as 1.15–2.5 mm s21 at 19 8C

Figure 6. The dependencies of the homogeneousnucleation rate J in (a) and the nucleation delay time in(b) on temperature at the HbS concentration indicatedin the plots. Data in (a) and (b) have relative errors inthe range 0.05–0.11, determined by the relative errors ofthe points in Figure 5 and the their deviations fromlinearity. The error in temperature is ,0.5 deg. C, seediscussion of temperature non-uniformity in Materialsand Methods.


and C ¼ 232 mg ml21 and hence the detectiontimes are ,1 s. Thus, the apparent delay times inFigure 6(b) are good approximations to therespective u.

The nucleus size

The nucleation theorem has been used todetermine the nucleus size from data on thedependence of the homogeneous nucleation rate Jon supersaturation Dm.46,49,50 For non-isothermaldata sets, where supersaturation Dm is varied viatemperature, a more recent form of the nucleationtheorem applies. The resulting method employstwo data sets: the homogeneous nucleation rate Jand the nucleation induction time u:

np ¼ kBd

dDm½T lnðJuÞ� þ

kB

DselnðC0Þ ð6Þ

where C0 is the concentration of single HbSmolecules in the solution, and Dse is the entropyof HbS polymerization.46 Equation (6) is derivedassuming that Ju and C0 are in the same units,such as m23.

Figure 7 displays the nucleation kinetics datafrom Figure 6 plotted in the coordinates ofequation (6), i.e. the product T lnðJuÞ with Jrescaled in m23 s21 units, as a function of the super-saturation Dm rescaled with kB: The theories relatedto the nucleation theorem do not treat the interceptof the dependence of T lnðJuÞ on Dm. Thus, while itis likely that the different intercepts of the twolines in Figure 7 are linked to the deviations ininduction times between the two series inFigure 6(a), the physical phenomena that underliethese differences are unclear to us. However, forthe purposes of determination of the nucleus size,it is sufficient that the slopes of the linear fits are6.9 for both data series in Figure 7.

To evaluate the second term on the right-hand side of equation (6), we use that

TDS ¼ 7:4 kcal mol21 at 25 8C,8 resulting inDse ¼ 1:72 £ 10222 J K21. The concentrationC0 ¼ 232 mg ml21 ¼ 2.18 £ 1024 m23 and ðkB=DseÞln C0 ø 4:5: Combining this value with the slopefrom Figure 7, we get for the nucleus size:

np < 11:4 ð7Þ

i.e. sizes of 11 or 12 molecules are within the errorlimits of this determination.

Discussion

Nucleation of HbS polymer fibers

The polymerization of deoxy-HbS has been dis-cussed in terms of a double nucleation model.29

The first step in polymerization is homogeneousnucleation, in which single fibers are randomlygenerated in the bulk of a supersaturated solution.As the fibers grow, they serve as substrates for thenucleation of new fibers.10 This leads to thickeningand branching of the fibers.8,28 – 30 As withnumerous other phase transformations proceedingvia nucleation,51 – 54 the rate of polymerization wasfound to be a very strong, likely exponentialfunction of the concentration of HbS. Dependingon the range of concentrations probed, the strongdependence has been described as tenth to 20thpower55 to 30th and 50th power.32

The nucleation of secondary fibers on an existingfiber is often referred to as “heterogeneousnucleation”.8,28 – 30 Typically, the term hetero-geneous nucleation is used for nucleation on aforeign substrate.46,56,57 Nucleation on a substrate isenergetically different from that in bulk of the oldphase; the wetting of the substrate by the newphase is expected to decrease the nucleation barrierand render heterogeneous nucleation faster bymany orders of magnitude. In practice hetero-geneous nucleation is widespread and includesnucleation on foreign molecules (impurities),microscopic particles (dust or bubbles), etc. It mayoccur concurrently with homogeneous nucleationand care must be taken in data interpretation todistinguish between homogeneous and hetero-geneous nucleation. In the second stage of HbSpolymerization, the substrate is the newly appear-ing phase, i.e. the substrate is not a foreign object,and it is available only after HbS polymerizationhas started. In another deviation from “classical”heterogeneous nucleation, it is not always fasterthan homogeneous nucleation; at low-to-moderatesupersaturations single un-branched fibers, suchas those in Figure 1(a), are often observed.9,10,58

There have been some early claims that sicklingis akin to gelation of a colloid suspension59

supported by the fact that completely polymerizedsamples behave rheologically as a gel.13 Thisinterpretation was contradicted by the findingthat unlike gels, the polymer has constantdensity and structure, independent of external con-ditions for polymerization,60,61 indicating that HbS

Figure 7. Toward determination of the nucleus size.Plots of the data on nucleation rate J and nucleationinduction time u from Figure 6 in coordinates of thenucleation theorem, i.e. T lnðJuÞ as a function of thermo-dynamic supersaturation Dm rescaled with theBoltzmann constant kB:


polymerization is a first-order phase transition.62,63

In further analogy to first-order phase transitions,the changes of enthalpy, entropy, and molarvolume upon polymerization have beendetermined.8 It has recently been emphasized thatthis and other phase transitions, in which anordered solid (crystal, fibril, polymer) emerges fora dilute and disordered fluid (gas or solution)should be viewed as a transition along two orderparameters,64 density and structure.65 Thus, thefibers and spherulites in Figure 1(a) and (c) have ahigher concentration of HbS molecules than thesurrounding solution, and the molecular arrange-ment is ordered.

Homogeneous nucleation or nucleation ona substrate

The results in Figure 2 do not provide evidenceagainst heterogeneous nucleation on particles orpieces of the cell membrane smaller than 1 mm, oron protein molecules larger than hemoglobin; eachof these could serve as centers of heterogeneousnucleation.46,56,57 Indeed, if these entities have sizesof 100 nm or smaller, they could move about thesolution volume driven by Brownian diffusionand in subsequent runs induce nucleation at differ-ent locations. If their concentrations were constantthey would not lead to dependence of the numberof nucleated spherulites on the solution volume.However, dynamic light-scattering characterizationof Hb solutions prepared following proceduresidentical with those used here showed a singlespecies of a size between 5 nm and 6 nm,66 com-patible with the 5.5 nm known for hemoglobin.67,68

The high limit of the detection range of thesedeterminations is above 1 mm. In view of the highsensitivity of light-scattering to larger species (e.g.Eisenberg & Crothers69), we conclude that thesolutions that we use do not contain species orparticles that could serve as heterogeneous nuclea-tion centers. Thus, the spherulites observed hereare generated via homogeneous nucleation.

An important issue in the studies of the sicklecell hemoglobin polymerization is whether thenucleation of the primary fibers is enhanced at par-ticular sites on the membrane of the red bloodcells.15,70 Before this issue can be addressed in aquantitative manner, benchmark data on the trulyhomogeneous nucleation of HbS polymers isneeded. An added advantage of data on homo-geneous nucleation stems from the fact that its

rate depends on fewer parameters than the rate ofnucleation on foreign substrates. Hence, homo-geneous nucleation data serve as a firmerfoundation for conclusions about the nucleationmechanisms.

The nucleation rates

The values of J in Figure 6(a) are comparable tothose occurring in the cytosol of non-permanentlysickled erythrocytes. Indeed, a red blood cellwhose volume is ,94 femtoliters < 10210 cm23

spends from 10 s to 20 s in the venous circulation.71,72

During that time, one or a few nucleationevents,11,70,73 followed by fast growth (as shownabove, growth rates of the polymers are a fewmm s21) and branching, may lead to sickling of thecell. Thus, the nucleation rates of sickling of non-permanently sickled cells are of the order of109 cm23 s21.

Note that the conditions in the red cells aredifferent from those in our experiments. Mostimportantly, the HbS concentrations in the sicklered cells are in the range 320–460 mg ml21, with aconsistent mean of ,360 mg ml21 and this shouldresult in significantly faster nucleation rates.74 Thehigh HbS concentration is likely compensated bythe partial oxygenation of the HbS:73 due to theresidual oxygen vapor pressure of ,40 Torr, 70%of the Hb is in oxy-form.75 Furthermore, the redcell cytosol contains several compounds in concen-trations comparable to that of HbS,76 – 79 whoseeffects on polymerization and in particular onnucleation have only partly been studied.80 Inaddition, the role of the inside surface of the redcell membrane on the nucleation is unknown.11,15

Despite these factors that may affect nucleation invivo and take it along pathways different fromthose followed in vitro, the similarity of thenucleation rates suggests that the mechanisms ofnucleation deduced from in vitro experiments area relevant first step in the understanding ofpolymerization in the red cells of sickle cell anemiapatients.

The values of J of sickle cell hemoglobinpolymers are seven to ten orders of magnitudehigher than those of formation of other orderedsolid phases of proteins, summarized in Table 1.In fact, the HbS polymer nucleation rates aresimilar to the nucleation rates of water droplets atatmospheric pressure and room temperature:54 thephase-transition rates of small molecules are

Table 1. Homogeneous nucleation rates J and ranges of concentration C and supersaturation Dm=kBT during determi-nations for four proteins

Protein C (mg ml21) Dm=kBT J (cm23 s21) Ref.

Lysozyme 30–80 3–3.7 0.01–1 50,83,99Insulin 1–3 3.2–3.7 0.01–0.1 L. Filobelo, unpublishedHemoglobin C 10–20 2.5–3 ,0.01 66Apoferritin (estimates) 0.1–1 2.2–3.9 0.1–1 100,101


expected to be significantly faster. While theprotein concentrations in the determinations inTable 1 were significantly lower than the concen-trations of HbS in the determinations discussedhere, the supersaturation levels were higher. Sincethe nucleation rate is expected to be a linear func-tion of concentration and exponential function ofsupersaturation,46,81,82 the huge discrepancy cannotbe solely attributed to the action of protein concen-tration. One could argue that the nucleation ratesfor proteins crystals were determined under con-ditions optimized for crystal perfection and arenot the maximum possible for a given protein;often, multiple protein crystals form in a container.Even if one allows for 103 £ faster nucleation ofcrystals under “unfavorable” conditions, this stillleaves a discrepancy of four or five orders ofmagnitude between the two types of nucleation.

This discrepancy cannot be understood at thispoint. Still, we would like to offer two hypotheses,to be tested in further work. One can speculatethat it may be linked to the lower, one-dimensionaltranslational symmetry of the HbS polymers.Polymerization is a phase transition occurringalong two order parameters, density and structure,and arguments have been presented suggestingthat such transitions occur when a structurefluctuation is superimposed on a densityfluctuation.83 – 86 Thus, it is feasible that a lowerdegree of symmetry of the new phase could leadto lower barriers for the second stage of theprocess, ordering, occurring within a densityfluctuation.

Another possibility also linked to the super-position of density and structure fluctuations isthat the high nucleation rates of HbS polymersstem from the high fluidity of the concentratedhemoglobin solution within the quasi-droplet ofthe density fluctuation. As expected for suspen-sions of non-interacting particles, the viscosityof hemoglobin solutions at concentrations similarto those in the red cell cytosol is ,10 cP(1 P ¼ 1021 Pa s),87,88 i.e. barely above that of thesolvent, while solutions of other proteins with con-centrations ,200 mg ml21 are very viscous or gel-like. While the high fluidity of the concentratedsolutions should lead to linearly faster kinetics ofordering, it also leads to faster rate of probing ofvarious structures, i.e. of density fluctuationswithin the quasi-droplet of the density fluctuation,and this may result in exponentially faster rate offinding of the “right” structure. In support of thishypothesis, we note that dense liquid phases ofHbS enhance nucleation and growth of HbSpolymers.34 This is in contrast to the viscous denseliquid phases of other proteins,44,89 which suppressnucleation83 and growth90 of protein crystals.

The nucleation induction time

The delay time and the nucleation inductiontime u determined here are inherently differentfrom the nucleation time lag or the 1/10 time

determined by others:28,29,31,32,91 the latter tworepresent expectancy times until a polymer reachesa point from which light is scattered, or at whichthe solution turbidity is monitored. As such, theyare linked in a complex way to the mean timeseparating nucleation events in steady state.46 Asdiscussed above, the induction time u characterizesthe transformation of the molecular distribution inthe meta-stable single-phase solution to the distri-bution in a solution in which nucleation proceedsat a steady rate.47,48

Theoretically, the nucleation induction time u canbe evaluated as:47,48,82

u ¼ 2=3pZ2f p ð8Þ

The parameter Z, the Zeldovich factor, is also animportant component of the pre-exponentialfactor of the nucleation rate expression.47,81 It isproportional to the radius of curvature of the free-energy barrier for nucleation around its maximum;its lack of dimension stems from the scaling of thefree energy with kBT and using the number ofmolecules in the near-critical cluster as a spatialvariable. The Zeldovich factor accounts for thedeviations of the cluster size distribution from thatin the state of forced equilibrium in a nucleatingsystem, assumed in earlier nucleation theories.This equilibrium assumption requires the action ofa mechanism of decay of supercritical clusters,while in fact supercritical clusters undergouninhibited growth.81 Typical estimates are Z <0:1 at low supersaturations typical of phase tran-sitions with small molecules.82 For large biologicalmacromolecules, for which the characteristicsupersaturations during nucleation are several-fold the thermal energy, Z < 0:01 are likely.92 Notethat evaluations of Z using equation (6) arenecessarily only approximate: the small size of theHbS polymer nuclei suggests that the addition ordetachment of single molecules to near criticalclusters leads to significant changes in its thermo-dynamic characteristics. Thus, continuous con-siderations, such as those behind equation (6), canonly provide semi-quantitative understanding ofthe nucleation processes.

The parameter f p is the frequency of attachmentof molecules to the critical cluster (nucleus). It canbe evaluated from the rate of growth of,1 mm s21, see determination above, as f p ¼ 180molecules s21. Using these values of f p and Z; weget u , 12 s, with shorter u if higher attachmentrates apply. Although the induction times in thetwo series of determinations in Figure 6(b) differ,especially at low T values, for both series they areof the same order of magnitude as this estimate.In further agreement with the predictions of theZeldovich theory, they decrease as T is increased.

The nucleus size

The most important characteristic of the nuclea-tion process is the nucleus size np: The nucleus is


a cluster that has equal probabilities to grow anddissolve and is thus in unstable equilibrium at thepeak of the free energy landscape along the nuclea-tion reaction pathway.25,26 The size of the nucleuslargely determines the value of the free energy atthis peak, the free energy barrier for nucleation.The nucleation theorem examines how the nuclea-tion barrier varies in response to supersaturationchanges and shows that the respective derivativeallows determination of the nucleus size.46,49,93,94

Recently, it has been pointed out that thenucleation theorem relies on very few confiningassumptions about the nucleation process, and isthus a general, system-independent nucleationlaw.93,94

The earliest estimates of the nucleus size for HbSpolymerization were based on determinations ofthe delay time td of polymerization monitored viathe solution turbidity.95 In a quasi-chemicalapproach, the apparent reaction order m was deter-mined as a slope of the plot of logðtdÞ versus logðCÞ;obtaining a value around 32. In subsequentinvestigations, the necessity to account for thenon-ideality of HbS solutions was acknowledged,bringing the reaction order to 9 or 6.96 Still, deter-minations of the nucleus size n p from the reactionorder remained a difficult problem, with estimatesranging from np ¼ m þ 1 to np ¼ 2m:

In another series of studies, the apparentreaction order was determined from the timeevolution of the HbS polymerization monitoredwith light-scattering.30,31,91 Homogeneous nuclea-tion rates were extracted from the distributions ofthe time to achieve one-tenth of the final reactionyield,33 assuming that the primary nucleation ofHbS polymers is the only source of stochasticity ofthe data. The apparent reaction order was 47(^5).The authors found that no simple relation of thereaction order of the tenth-time to molecular par-ameters exists and employed the double nucleationmodel to determine the size of nuclei as 7.31 Notethat this result, obtained at higher supersaturation,does not contradict our finding: the nucleus size isexpected to decrease at increasing supersaturation.

Thus, the determination of nucleus size using thenucleation theorem offers advantages: the nuclea-tion theorem is a general nucleation law, whichdoes not rely on assumptions about the kineticpathway or the structure of critical nucleus.The data used in the evaluation of np are thedependencies of J and u on temperature and thethermodynamic properties of the HbS solution.

The determination of the nucleus size of the HbSpolymers calls attention to an interesting point: np

is smaller then 14, the number of HbS moleculesin the cross-section of the fiber. Obviously, suchsmall nuclei cannot contain one, or two, or several14-member “disks”. The question of whether thenucleus contains 10–12 molecules from the 14 inthe cross-section, or five or six pairs of moleculesin one of the Wishner–Love double strands,97 oranother ordered, or an altogether disordered con-figuration is an open one at this point.

Perspectives for future work

A line of intriguing and relevant questionsarising from analogies to recent findings on thenucleation mechanisms of crystals50,83 –85 and onthe phase behavior of hemoglobin mutants34 havenot been addressed here. Some of these are relatedto the fundamentals of the nucleation mechanisms:is the HbS polymer nucleus ordered or disordered?Does nucleation occur in one or two steps, i.e. isthere a disordered precursor to an ordered HbScritical cluster? What is the exact shape and struc-ture of the critical cluster? Others are related tothe participation of the cell membrane and otherred cell cytosol components in the nucleationprocess: is HbS polymer nucleation affected byany of the red cell cytosol components present inconcentration comparable to those of HbS?76,77 Isthe nucleation of HbS polymers enhanced atcertain areas of the inside of the red cellmembrane?

Materials and Methods

Solution preparation

Hemoglobin S was isolated from the blood of sicklecell anemia patients kindly provided by Dr R. E. Hirschfrom Albert Einstein College of Medicine. The bloodwas washed in isotonic 0.9% (w/v) NaCl solution andcentrifuged to remove white blood cells. The red bloodcells were lyzed with deionized water and the solutionwas centrifuged again to remove cell membranes. Theremaining Hb solution was filtered through a 0.45 mmSterivex-HV filter. To purify HbS, the solution wasdiluted into a large volume of 20 mM Tris buffer (pH8.5), and loaded onto a Q-Sepharose FPLC column (XK50, Amersham Biosciences). Separation of different Hbvariants was achieved by elution using a gradient ofNaCl. The purity of the fractions was checked by gelelectrophoresis (PhastSystem, Amersham Biosciences).After the purification procedure, the gels showed asingle band of HbS. The sample was concentrated bycentrifugation in Centricon Plus-20 filters (Millipore).For polymerization experiments, the solution wasdialyzed into 0.15 M potassium phosphate buffer (pH7.35), using Slide-A-Lyzer Cassettes (Pierce). Thesolution was finally concentrated to about 270 mg ml21.

After purification, Hb is in the oxy form. The quantumyield of O2-Hb is 50 times lower than that of CO-Hb98 soCO-Hb is better suited for use in photolysis experiments.To prepare CO-Hb we used the following procedure:1 ml of stock solution was placed for one hour in a tenliter glove box with an atmosphere of 100% CO saturatedwith water vapor at room temperature. While exposed toCO, the sample was carefully and mildly stirred fourtimes. During this step, HbS molecules lose oxygen andbind CO. After this the atmosphere in the glove boxwas changed to 100% He, saturated with water. Thesample was again mildly stirred four times. The secondstep reduces the concentration of free CO in the solution,allowing for full photolysis of Hb at lower laser power inthe subsequent experiments. After this procedure, theconcentration of the stock solution was determined, the


solution was stored as stock under liquid nitrogen andused as needed.

For each experiment a solution sample of CO-HbS wasprepared by mixing 20 ml of stock solution in 0.15 Mpotassium phosphate buffer at pH 7.35 with 1 ml ofsodium dithionite in the same buffer to give final concen-tration of 0.055 M sodium dithionite. About 3 ml of thissolution was placed on a standard 75 mm £ 50 mmmicroscope glass slide (Corning), covered with a22 mm £ 22 mm cover glass, and sealed with Mount-Quick (Daido Sangyo, Japan). All of the aboveprocedures were performed in a glove box under Heatmosphere saturated with water. Tests showed thatwhen handling volumes of several microliters, controlof humidity during sample preparation is crucial. Thus,the rate of evaporation of a 20 ml droplet of the phos-phate buffer used here was found to be 2.4 ml hour21 atrelative humidity of 55% and was still 0.4 ml hour21 at95% relative humidity.

After sealing, the spectrum of the solution in the slidein the range of 450–700 nm was determined to verifythat it contains 100% CO-HbS and no met-HbS. Allnucleation experiments were performed immediatelyafter the sample preparation; samples older than24 hours aged markedly, having higher nucleation ratesand smaller spherulites sizes, consistent with the obser-vations reported by Ferrone et al.28

To determine the solution concentration, we usedDrabkin’s reagent (Sigma). For concentrations of,260 mg ml21 the solution was diluted up to 500-fold.We measured the absorption at 540 nm using extinctioncoefficient 1 ¼ 0.6614 ml mg21 cm21. The procedure ofconcentration determination for HbS samples requiredparticular attention because of the strong dependence ofthe nucleation rate on concentration. The smallest pipettevolume used here was 1 ml with an accuracy of ,1.5%(Eppendorf Research Series 2100 pipetter). Using 500 mlsolution volumes with a 1 ml pipette with an accuracyof 0.5% (the pipette accuracies were taken from themanufacturers’ specifications and were independently

experimentally verified), and using the accuracy of thephotometric readout of 0.1%, we get 1.6% for theaccuracy of the concentration determination. For aconcentration of 260 mg ml21 it yields an error of^4.2 mg ml21.

Experiment setup

The experiment setup is built around a Leica DM Rfluorescence microscope and is shown in Figure 8.Observations of HbS fiber nucleation are made in trans-mitted light with DIC optics, a 63x HCX APO L U-V-Iwater immersion objective and a 0.90 S1 achromatic con-denser. Pictures are taken with VCC-151 color videocamera (Hitachi), FlashPoint-3D frame grabber (IntegralTechnologies Inc.) and custom-made software. With thecurrent configuration the shortest time between framesis 1 s.

Photolysis is achieved by a beam of a continuous-wave Nd:YAG laser (LCS-DTL-316 from Power Tech-nology Inc., l ¼ 532 nm, Itotal ¼ 2– 200 mW). Alterna-tively, we use a 100 W gas discharge Hg lamp (Leica).When laser is used, its beam is expanded by a spatialfilter assembly consisting of two objective lenses (focuslengths F1 ¼ 16:5 mm and F2 ¼ 60 mm) and a 12 mm pin-hole. The pinhole is positioned over the focus of the firstlens. The position of the second lens is varied to controlthe beam expansion ratio and its divergence so that anilluminated spot of a desired size in the working planeof the microscope could be achieved. Besides expansion,this arrangement provides for filtering of laser beamnon-uniformities.

The expanded and filtered beam is input through themicroscope’s light path for fluorescence excitationillumination. The diameter of the photolyzed regiontypically is ,90 mm, adjusted by a variable aperturediaphragm. A beam splitter with a dichroic mirror andfilter is used, respectively, to direct the photolyzingbeam towards the solution sample through the special-ized fluorescence objective and to reject the laser light

Figure 8. Schematic of theexperiment setup, see the text fordetails.


scattered in the direction of observation. Since the filtercompletely cuts off the photolysis wavelength from theviewing path, to measure and control the diameter ofthe photolyzing beam, we used a slide with Rhodamin6G dye in ethanol. To achieve precise timing and to auto-mate the data acquisition, a computer-controlled shutter(Melles Griot, opening time ,few milliseconds) is used.

With slide thickness of 5 mm and diameter of thephotolyzed region of ,90 mm, the total photolyzedvolume is ,3 £ 1028 cm3. The shortest times betweencaptured frames are 1 s, and since we can confidentlyresolve at most ten spherulites in the illuminatedvolume, these parameters determine the fastest nuclea-tion rate that we can measure as 108 cm23 s21. Fasternucleation rates can be measured by using a fastercamera.

Slide thickness uniformity

The nucleation statistics is determined through inde-pendent runs in different locations on the slide contain-ing HbS solution. This requires accurate determinationsof the slide thickness and verification of the thicknessuniformity throughout the slide. Furthermore, to preventsample overheating, low optical density of the slideloaded with a relatively high concentration of HbS,,200 mg ml21 and higher, is required. This can beachieved by using slides as thin as 5 mm or 10 mm. Todetermine the uniformity of the slide thickness, wemeasured the spatial distribution of slide optical density(OD) on spatial coordinates with a Beckmann DU-68spectrophotometer (sample thickness h is proportionalto the optical density because of Lambert–Beer lawOD ¼ 1Ch; where 1 is extinction coefficient, C is sampleconcentration). For these measurements, the slide wasplaced in the focus of the spectrophotometer light beamwith a spot size of 2 mm £ 0.3 mm, and scanned in twoperpendicular directions.

The determinations with slides without thickness con-trol revealed that their thickness was extremely non-uniform (Figure 9(a)), with variations of as much as50%. For thickness control, we used glass spheres (DukeScientific) placed between the slide and the cover slip.These glass spheres are available in diameters2.0(^0.5) mm, 4.9(^0.5) mm, 10.0(^1.0) mm. Using thesespheres as spacers, we achieve slide thickness uniformityof ^2% for 10 mm spheres and within ^5% for 5 mmspheres (Figure 9(b)). In most determinations, 5 mmthick slides were used that provided for lower overheat-ing due to absorption of the photolysis light.

Temperature of polymerization

To control the temperature of the sample we use a50 mm £ 50 mm £ 20 mm box assembled by gluingbrass side walls to a glass slide. The top of this assemblyis left open for microscope objective access. A RTE-100waterbath (Neslab) circulates deionized water throughthe box over the slide and sets its temperature between0 8C and 80 8C. The use of water immersion objectivesprovides for high quality DIC images in this arrangement.Temperature is measured with a HH 506R thermocouplethermometer (Omega Engineering Inc.) with 0.1 K accu-racy and is input to a computer using a serial port. Wechecked the temperature inside the slide by placing asmall thermocouple under the cover-slip; its temperaturereading was equal to that in the circulating water.

Because our sample absorbs light at the wavelength of

photolysis, the steady-state temperature rise in thephotolyzed region is different from the temperature out-side of the illuminated region. To measure this tempera-ture we deposited in a slide a ,10 mm grain ofOMEGASTICS crayon (Omega Engineering) that meltsat 40.5 8C. To determine the temperature near the centralaxis of the beam we masked half of it and positionedthe crayon grain near its center (Figure 11(a)). Then wevaried the temperature of the water circulating over theslide and recorded the temperatures at which crayonmelted with laser power on, as in Figure 11(b), and off.With the laser off, the crayon melted at the manu-facturer-specified 40.5 8C. The overheating due to laserlight increases roughly linearly with laser power, slidethickness and HbS concentration, and is about 4.5 deg. Cwith HbS concentration of 232 mg ml21, slide thicknessof 15 mm and laser power of 10 mW. Our observationsare consistent with those reported by Ferrone et al.,28

thus, we rely on their conclusion that the typical timesto reach steady temperature are of the order of severalmilliseconds, significantly shorter than our observationtimes of ,1 s.

Figure 9. Characterization of the slide thicknessuniformity using the proportionality of the spectrophoto-metrically determined optical density to local thickness.Optical density at 540 nm, normalized to 1, is plotted asa function of location along the slide. (a) Two slides with-out thickness control. (b) A slide with 10 mm spheresused as spacers between slide and coverslip. (c) Same as(b) but for 5 mm spacers.


The Gaussian profile of the laser beam (see below)gives rise to a non-uniform temperature field. To limitthis non-uniformity, we expanded the beam and used avariable aperture diaphragm to cut out the beamperiphery, where the intensity drops off. In the remain-ing central part of the beam, the intensity non-uniformitywas ,35%. With the above determination of the over-heating due to light absorption, the temperature non-uniformity at laser power 10 mW in a 5 mm slide, themost common arrangement used here, is ,0.5 8C.

Photolysis illumination intensity and uniformity

The total intensity of the photolysis illumination andits spatial distribution determine the extent of HbS con-version to deoxy-state, its spatial distribution, and thetemperature regime in a sample. We measured the inten-sity profile by scanning either a 12 mm diaphragm placedat the sample plane or a 0.5 mm diaphragm placed nearthe expanding lens of the telescope. Figure 10(a) showsthe intensity profile with laser illumination; it is ade-quately described by a Gaussian function. Tests showedthat the beam width does not depend on the laser inten-sity and can be adjusted in a wide range from several

mm to 200 mm. When the gas discharge lamp was used(Figure 10(b)), an essentially flat profile of intensityobtained.

We determined the attenuation of the light by thediaphragms and lenses in the optical pathway by placingthe detector of the light power meter in front of the laser,and in the slide focal plane. We found that theattenuation ratio is 0.52.

To determine the laser power needed to achieve fullphotolysis of the CO-HbS, we carried out the followingtests. We use the fact that CO-Hb has higher extinctioncoefficients at l ¼ 532 nm than deoxy-Hb. At low laserpower all Hb is in CO form and the optical density ishighest. When laser power is increased, more and moreHb molecules lose CO and the optical density dropsuntil, at a certain intensity setting, it reaches the level ofdeoxy-Hb. To determine the degree of photolysis, wedetermined the optical density of a slide loaded withCO-HbA (HbA was used to avoid interference fromfiber formation with the optical density measurements).We used the illuminating pathway of the microscope, inwhich a narrow band-pass interference filter (EdmundIndustrial Optics, l0 ¼ 436 nm, halfwidth 10 nm) wasmounted between the illumination lamp and the sample.

Figure 10. Intensity profiles of the photolyzing beamsin the plane of slide with HbS solution: (a) illuminationwith a laser beam, a 90 mm diaphragm around the centerof the beam leaves intensity non-uniformity of ,35%;(b) lamp illumination, 90 mm diaphragm around thecenter of the beam leaves near-uniformly illuminatedarea.

Figure 11. Measurement of overheating of the slide insteady state. (a) A ,10 mm grain of OMEGASTICKcrayon with Tmelt ¼ 40:5 8C is placed near the center ofhalf-blocked laser beam, not visible because of the filterthat absorbs photolyzing light reflected in the directionof observation. (b) The grain is intact at 35 8C, at 36.1 8Ca crescent-shaped molten area is detectable in the direc-tion of the beam; at higher temperature the molten areaincreases. Upon reversal of temperature changes, moltencrescent disappears at 36 8C.


The intensity of the light transmitted through the samplewas measured with 1830-C power meter (Newport)whose sensor was placed in the image plane of themicroscope, instead of the video camera in Figure 8. Toreject the reflected photolyzing laser beam, we usedthree short-pass filters (Melles Griot, l ¼ 500 nm) and apolarizer. A diaphragm set to an area of 16 mm diameterwas placed in front of the power meter sensor, andadjusted so that only the light transmitted through thecentral part of the illuminating sample reaches thepower meter. The laser power was varied in the range5–200 mW and was additionally attenuated by calibratedfilters with optical densities 1, 2 and 3. Two consecutivedeterminations, 1 and 2, were done with and withoutthe solution slide in the optical pathway (Figure 11).

Figure 12 shows that power density of 0.3 kW cm22,corresponding to at laser power of about 10 mW thephotolysis reaches ,100% in the whole illuminated areafor less than 1 s. At power densities .0.8 kW cm22, thetransmittance increases. We tentatively assign this effectto photochemical “bleaching” of the sample.

Thus, we chose laser power of 10 mW correspondingto power density of 0.3 kW cm22, at which the dis-sociation of the CO-HbS into deoxy-HbS is completedwithin a time period sufficiently short to only insignifi-cantly bias the determinations of the induction timesand nucleation rates.

Acknowledgements

We thank Rhoda Elison Hirsch for numeroushelpful suggestions and for providing some of thesickle cell and normal blood samples, RonaldN. Nagel for patient guidance through the field ofhemoglobin diseases, Gregoire Nicolis for insightinto viscosity effects, Bill R. Thomas for thedevelopment of a procedure for HbS isolation andpurification, Angela Feeling-Taylor for normal andsickle cell blood samples. This work was supportedby the Office of Physical and Biological Research,NASA, through grants NAG8-1854 and NAG8-1824.

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Edited by K. Nagai

(Received 14 August 2003; received in revised form 25 November 2003; accepted 2 December 2003)


mechanisms of homogeneous nucleation of polymers of sickle cell anemia hemoglobin in deoxy state

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