Physical manipulation of the Escherichia colichromosome reveals its soft natureJames Pelletiera,1, Ken Halvorsenb,c,1, Bae-Yeun Had, Raffaella Paparconea, Steven J. Sandlere, Conrad L. Woldringhf,Wesley P. Wongb,c,2, and Suckjoon Juna,g,2

gDepartment of Physics and Section of Molecular Biology, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093; aFAS Center forSystems Biology, Harvard University, 52 Oxford Street, Cambridge, MA 02138; bImmune Disease Institute, Boston Children's Hospital and Department ofBiological Chemistry and Molecular Pharmacology, Harvard Medical School, 3 Blackfan Circle, Boston, MA 02115; cRowland Institute at HarvardUniversity, 100 Edwin H. Land Boulevard, Cambridge, MA 02142; dDepartment of Physics and Astronomy, University of Waterloo, Waterloo, ON, CanadaN2L 3G1; eDepartment of Microbiology, University of Massachusetts, Amherst, MA 01003; and fMolecular Cytology, Swammerdam Institute for LifeSciences, Faculty of Science, University of Amsterdam, 1098 SM Amsterdam, The Netherlands

Edited by T. C. Lubensky, University of Pennsylvania, Philadelphia, PA, and approved August 21, 2012 (received for review May 23, 2012)

Replicating bacterial chromosomes continuously demix from eachother and segregate within a compact volume inside the cell calledthe nucleoid. Althoughmany proteins involved in this process havebeen identified, the nature of the global forces that shape and seg-regate the chromosomes has remained unclear because of limitedknowledge of the micromechanical properties of the chromosome.In this work, we demonstrate experimentally the fundamentallysoft nature of the bacterial chromosome and the entropic forcesthat can compact it in a crowded intracellular environment. Wedeveloped a unique “micropiston” and measured the force-com-pression behavior of single Escherichia coli chromosomes in con-finement. Our data show that forces on the order of 100 pN andfree energies on the order of 105 kBT are sufficient to compressthe chromosome to its in vivo size. For comparison, the pressurerequired to hold the chromosome at this size is a thousand-foldsmaller than the surrounding turgor pressure inside the cell.Furthermore, by manipulation of molecular crowding conditions(entropic forces), we were able to observe in real time fast(approximately 10 s), abrupt, reversible, and repeatable compac-tion–decompaction cycles of individual chromosomes in confine-ment. In contrast, we observed much slower dissociation kineticsof a histone-like protein HU from the whole chromosome duringits in vivo to in vitro transition. These results for the first timeprovide quantitative, experimental support for a physical modelin which the bacterial chromosome behaves as a loaded entropicspring in vivo.

chromosome segregation ∣ depletion forces ∣ polymer physics ∣mother machine ∣ optical trap

Like many other model bacterial organisms such as Bacillussubtilis andCaulobacter crescentus,Escherichia coli has a single

circular chromosome. In vivo, the chromosome exists in a highlycompacted state, occupying only a subvolume of the micron-sizedrod-shaped cell. As early as 1956, Mason and Powelson observedthat compact E. coli chromosomes exhibit dynamic morphologi-cal changes during DNA replication and segregation before celldivision (1). Undoubtedly, the changing chromosome morpholo-gies during the cell cycle reflect a dynamic balance between thepolymeric nature of the chromosome and the active and passiveforces acting on the chromosome by other molecules inside thecell. It is odd, then, that our understanding of the micromecha-nical properties of bacterial chromosomes is almost completelylacking, especially considering the detailed knowledge of themolecular factors involved in replication and protein synthesisthat influence the chromosome (2). For instance, despite a largenumber of proposed models (3–17), we have not been able toexperimentally answer obvious questions such as how much forceis required to maintain the in vivo chromosomes in their com-pacted state or to segregate them during DNA replication. Canwe characterize experimentally the nature of the forces that shapethe bacterial chromosome?

For the much smaller (and biochemically simpler) system ofviruses and their genomes, we now have a comprehensive under-standing of the role of physical properties of viral DNA on itspackaging into and ejection from the capsid (18, 19). For themuch larger (and more easily manipulable) system of eukaryoticchromosomes and spindles, a combination of biophysical andbiochemical methods has begun to unravel their micromechanicalproperties (20–22). In contrast, despite some of the earlierpioneering biophysical work (23), experimental progress for bac-terial chromosomes has lagged behind, because of compoundexperimental difficulties (ı.e., small in size but complex in mole-cular and biochemical detail).

In this work, we measured the force-compression curves (ratherthan more traditional force-stretching curves) of individual wholebacterial chromosomes in confinement. Because the spatial di-mensions of the confinement were comparable to the size of thecell, we developed a new experimental system that brings togetherimaging, microfluidics, and single-molecule manipulation techni-ques. Importantly, by combining the microfluidic “mother ma-chine” (24) and an optical trap, we developed the micropiston tocompress isolated single chromosomes confined in long narrowmicrochannels.

The measured force-compression curves are consistent with anentropic spring model (11, 17, 25). The quantitative agreementbetween the data and the model allows us to estimate the forceand free energy required to compress the in vitro chromosometo its in vivo size. In stark contrast to the viral DNA in a capsid,our experiments demonstrate that the bacterial chromosome isfundamentally “soft” and can be readily influenced by entropicforces. These experimental results, combined with a physicalmodel, provide quantitative and mechanistic insights into thephysical nature of the bacterial chromosome.

ResultsExperimental System for Gentle and Synchronous Lysis of Cells in aConfined Space. To investigate the micromechanical propertiesof isolated bacterial chromosomes in confinement, we had toovercome considerable technical challenges imposed by the 1-μm

Author contributions: S.J. designed research; J.P., K.H., B.-Y.H., R.P., C.L.W., W.P.W., and S.J.performed research; S.J.S. contributed new reagents/analytic tools; J.P., K.H., W.P.W., andS.J. analyzed data; and J.P., K.H., B.-Y.H., S.J.S., and S.J. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1J.P. and K.H. contributed equally to this work.2To whom correspondence may be addressed. E-mail: wong@idi.harvard.edu orsuckjoon.jun@gmail.com.

See Author Summary on page 15978 (volume 109, number 40).

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1208689109/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1208689109 PNAS ∣ Published online September 14, 2012 ∣ E2649–E2656

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length scale of the E. coli cell. The small size of the cell preventedthe use of micropipettes (20) or microneedles (21) that have beensuccessful in probing much larger eukaryotic chromosomes andspindles. Instead, we started from previous work that demon-strated the proof of principle of bacterial chromosome extractionin a microfluidic device (26) and lysis in suspension (27). As illu-strated in Fig. 1A, the mother machine (24) was ideally suited forthis purpose. The E. coli chromosomes could be extracted andconfined directly in long microchannels about as wide as the cells.In brief, the cells were loaded into the microchannels. Then, su-crose buffer and lysozyme were added to the media. Synchronouslysis was achieved when this cell wall digestion buffer was re-placed with the relatively dilute HEPES buffer at a specific ionicstrength dictated by the concentration of NaCl (23). Experimentswere conducted for cells prepared in two different physiologicalconditions (exponential and stationary phase). To visualize thechromosome, we made use of a previously characterized, fullyfunctional fusion of the fluorescent protein mCherry to one of themost abundant nucleoid-associated proteins, HupA (part of thehistone-like HU protein dimer) (28). Thus, morphological andbiochemical changes of the chromosomes during the in vivo toin vitro transition were easily observable (Fig. 1B–E).

During the experiments, the biochemical contents of the reser-voir main trench were controlled with multiple syringes and avalve. Importantly, this allowed switching from one ambientbuffer to another in seconds, without subjecting the chromo-somes to direct flow. SI Appendix, Sections I.A.2–4, describes themicrofluidic system and lysis protocol in full detail.

Bacterial Chromosomes Show Spring-Like Fast Expansion During Lysis.Chromosome expansion following cell lysis is a visually strikingprocess (see Movies S1 and S2), starting with an abrupt “explo-sion” of the chromosome from the cell and continuing with amoregradual equilibration within the new in vitro environment. Fig. 1Cshows a typical time series of the expansion dynamics of exponen-tial and stationary phase chromosomes during lysis. Although in-dividual chromosomes exhibited some variation, on average eachchromosome showed a 2- to 3-fold expansion to half its equili-brium length in approximately 10 s (Fig. 1D, green and orangelines illustrating the mean chromosome length). After the fastinitial expansion, the chromosomes slowly continued to expand tomany times their in vivo volumes over a period on the order of102–103 s before plateauing to their final equilibrium lengths.

The in vitro Chromosomes Show Physiology-Dependent Morphologi-cal Dynamics. The chromosomes exhibited distinct morphologiesafter lysis, likely reflecting their in vivo physiological state. Toquantify the morphological dynamics, we employed principalcomponent analysis, a powerful method commonly used in pat-tern recognition with a wide range of applications in many fields(29, 30). The basic idea is to extract eigenmodes of the chromo-some morphologies from the time-lapse images of each chromo-some-containing microchannel. See SI Appendix, Section I.A.7,for full description and analysis.) The top eigenmodes, or the top“eigenChromosomes,” often resembled space-filling helicoids ofright-handed, left-handed, or mixed handedness. We can visualizethe morphological dynamics in a lower dimensional space by pro-jecting the original time-series of chromosome images onto theeigenChromosomes. The projection coefficients form trajectories

A B

C

D

E

Fig. 1. Experimental setup and chromosome dynamics during lysis (100 mM NaCl). (A) Illustration of the device: A main trench connects multiple inlets toone outlet, with thousands of protrudingmicrochannels. Cells were loaded intomicrochannels (typically one per channel) and lysed, causing rapid expansion ofchromosomes. The microchannels containing the chromosomes equilibrated with the reservoir via passive diffusion in seconds (24). (B) Typical E. coli cell and itsnucleoid in exponential phase. The nucleoids (in red) occupy a subvolume of the cell. (C) Time-lapse pictures showing expansion and morphological relaxationof representative exponential and stationary phase chromosomes. (D) Normalized chromosome length vs. time shows rapid expansion of chromosomes to halftheir equilibrium length in tens of seconds. (E) Morphological relaxation analyzed by principal component analysis. Multiple time-lapse chromosome images,such as shown in C, were normalized and projected onto the top eigenmodes [the “eigenChromosomes (eC)”] (representative trajectories of individual chro-mosomes are in color). Consistent with D, the chromosomes from exponential phase cells show longer relaxation times (approximately 1,000 s) than those fromstationary phase cells (approximately 300 s).

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moving forward in time. Fig. 1E shows such projections onto thetop two eigenChromosomes.

Notice in Fig. 1E that the exponential phase chromosomesshow spiral trajectories and converge to the top eigenChromo-somes after on the order of 103 s; whereas the stationary phasetrajectories decay faster and converge to zero (ı.e., no apparentmorphological features) in on the order of 102 s. These physiol-ogy-dependent morphological dynamics are also consistent withour observations in Fig. 1 C–D and Movies S1 and S2. That is, theexponential phase chromosomes always look more structured,and they equilibrate more slowly than the stationary phase chro-mosomes (Fig. 1 C–E). We attribute the differences to differentreplication topologies, transcription levels, and nucleoid-asso-ciated protein activities between the two physiological states (31).

After Lysis, a Histone-Like Protein HU Dissociates Slowly from theWhole Chromosome. HU is a histone-like protein in bacteria thatbinds DNA nonspecifically. Phenotypic analyses of HU mutantspoint to many important roles in global transcription regulation,DNA replication, and DNA repair (31–33). Reported in vitromeasurements for key parameters such as the dissociation rate(koff) and the equilibrium dissociation constant (KD) vary morethan 10-fold (34, 35).

Our system can directly monitor dissociation of HU from theentire chromosomes during the in vivo to in vitro transition. Fig. 2shows the normalized integrated fluorescence of a functionalsubunit HUα-mCherry after lysis. The integrated fluorescence ex-hibited nonexponential decay for approximately 103 s. This mightreflect a wide range of binding affinities across the whole chro-mosome. Eventually, all chromosomes showed exponential de-cay. The dissociation rate from this last stage shows that DNAbinding of HU can be remarkably stable: 1∕koff ≈ 523 min forexponential and 68 min for stationary phase chromosomes at100 mM NaCl. See SI Appendix, Section I A. 6, for full analysisof KD, kon, and koff at NaCl concentrations ranging from 40to 200 mM.

HU is one of the most abundant nucleoid-associated proteinswith high DNA binding affinities (36). Thus, in light of the se-paration of time scales, we hypothesize that the fast initial chro-mosome expansion in Fig. 1 C–D is driven mainly by the releaseof micromechanical energy stored in the in vivo chromosome,rather than by dissociation of nucleoid-associated proteins. Wecannot exclude the possibility that fast dissociation of unlabeled

nucleoid-associated proteins or Mg2þ contributed to chromo-some expansion or modulated the unbinding rates of other nu-cleoid-associated proteins (37); however, lysed in suspension(27), chromosomes expanded to comparable in vitro volumesin the presence and absence of Mg2þ and adenosine-5′-tripho-sphate (ATP) (see SI Appendix, Section I D).

The Optical-Trap Micropiston Enables Direct Measurement of theForce-Compression Curves of the Bacterial Chromosome. Becausethe chromosome expands like a loaded spring, one should beable to measure its “spring constant.” Because confinement is themajor physical constraint that characterizes the bacterial chromo-some, it was necessary to measure micromechanical propertiesof individual chromosomes in confinement. To this end, we de-veloped the micropiston, a unique system that couples opticaltweezers and the mother machine. Unlike most prior work in sin-gle-molecule manipulation that focuses on pulling or stretchingbiomolecules, the micropiston enables the direct measurementof force-compression curves of in vitro chromosomes (Fig. 3and Movie S4).

From the raw force-compression curves (Fig. 3B, Inset), weidentified two distinct populations corresponding to one andtwo nucleoids. Each of these exhibits nonlinear behavior thatappears to be asymptotic at high forces.

The next challenge was modeling the data. In general, spatialconstraints pose formidable technical barriers to analyticaltheory. In fact, we found only one theoretical expression for theforce-compression behavior of a confined polymer that has beentested against numerical simulations (25). It is the loaded entro-pic spring model written by some of us and used to explain,among other phenomena, a physical mechanism of chromosomesegregation in bacteria:

fA

¼�RR0

�−�RR0

�−2; [1]

where f is the applied force, A ¼ k∕wβ is the rescaled springconstant for the dimensionless spring constant k (w is the widthof the piston), β ¼ 1∕kBT (kB is the Boltzmann constant and Tthe absolute temperature), R the measured chromosome lengthduring compression, and R0 the chromosome length under noexternally applied force.

An important implication of Eq. 1 is that, if we rescaleR by theequilibrium length R0 and f by the spring constant A, all datashould collapse onto a single master curve. That is, the force-compression relationship is universal. It can be used to test thepolymeric nature of confined chromosomes, independently ofmolecular details that determine R0 and A. Indeed, as seen inFig. 3, the chromosome data collapse onto a single curve andare in excellent quantitative agreement with Eq. 1 *. Further-more, the equilibrium force-compression data and Eq. 1 appearto be consistent with the expansion dynamics of the chromosomeduring lysis (see SI Appendix, Section II.A).

The quantitative agreement between the data and the modelallowed us to calculate the force and free energy required tocompress the chromosome back to its in vivo size. Extrapolatingour data to stronger compression using Eq. 1, we estimated thatabout 100 pN force and 105 kBT free energy are required to fullycompress the in vitro chromosome to its in vivo size (roughly 1∕10of the equilibrium length).

Fig. 2. Dissociation of HU from whole chromosomes at 100 mM NaCl, afterstart of acquisition phase with negligible photobleaching. (Main) HU dissoci-ates slowly after lysis (data shown from 100 s after lysis). Initially, dissociationis nonexponential, perhaps due to a wide range of HU binding affinitiesof the whole chromosome. Eventually, the dissociation kinetics reached anexponential decay regime, from which we estimated the off-rates, koff.Dissociated HU that escaped from the channel via diffusion was washed fromthe device. (Inset) At themoment of lysis, the integrated HU intensity showedan abrupt initial drop due to loss of cytoplasmic HU. Our measurements al-lowed us to estimate KD and kon. Movie S3 and SI Appendix, Section I A.6,discuss cytoplasmic HU during lysis in more detail.

*Interestingly, Eq. 1 agrees with our chromosome data for a wider range of R∕R0 (up toR∕R0 ≈ 0.2) than with the numerical data [up to R∕R0 ≈ 0.5; (25)]. The difference isperhaps due to the size fluctuations and softness of the chromosomal “beads” (asopposed to the monodisperse hard-spheres of the chain in the simulations). In apolymer-physics language, softer beads will result in more gradual crossover fromsemidilute to concentrated regimes, in which f ∼ ðR∕R0Þ−3 .

Pelletier et al. PNAS ∣ Published online September 14, 2012 ∣ E2651

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Depletion (Entropic) Forces by Molecular Crowding Alone Can Com-press Chromosomes to in Vivo Size. The findings presented aboveraised the question of why a nucleoid occupies only a subvolume

of the cell but expands to several times the size of the cell uponlysis (Fig. 1). Three possibilities have been discussed in the litera-ture (31): nucleoid-associated proteins such as HU and H-NSthat can hold DNA together, DNA supercoiling, and the entropiceffect of molecular crowding. However, most HU remained onthe chromosome during the fast initial expansion of the chromo-some after lysis (Figs. 1D and 2). Further, recent experimentsdemonstrated that supercoiling has only a minor effect on the sizeof in vitro chromosome (38).

Are depletion forces by molecular crowding sufficient to causecompaction of the chromosome in vivo? A typical E. coli cellcontains on the order of one million proteins in the cytoplasm(ref. 2, chap. 3). Because each depletant has an effect of orderkBT (39), the change in free energy due to molecular crowdingavailable for chromosome compaction may be approximately106 kBT. This is about one order of magnitude more significantthan the estimated approximately 105 kBT free energy storedmechanically in the in vivo chromosomes.

We tested this idea by using high molecular weight polyethy-lene glycol (PEG 20000) to simulate the crowded cytoplasmicenvironment in our device (Fig. 4A). Here, the response of thechromosomes to molecular crowding can be monitored in realtime by controlling the ambient buffer. The results were striking.

Fig. 4B and Movie S5 show that the addition of high-concen-tration PEG caused sudden collapse of the chromosomes in mi-crochannels. Conversely, removal of the PEG rapidly restored thechromosomes to their expanded conformations. This compac-tion–decompaction by PEG was completely reversible and repea-table for many cycles, over the course of more than 1 h, similar tothe compression-decompression by mechanical force observed inthe micropiston experiments.

We repeated the experiments with a wide range of PEG con-centrations. Only at or above the PEG volume fraction compar-able to that of cytoplasmic proteins (about 12% to 17%) (40) didwe observe compaction of the chromosomes back to their in vivo

A

B

Fig. 3. Mechanical compression of equilibrated chromosomes. (A) A poly-styrene microbead held by optical tweezers was used to compress thechromosome against the closed channel end. The residual membrane of thecell after lysis was used as a gasket to prevent leakage of the chromosome. (B)(Inset) Raw force-compression data shows two groups of curves that representone and two nucleoids. The error bars denote the standard deviation (SD) ofmultiple measurements. When rescaled by the fitted “spring constant” Aand the equilibrium length R0 (mean A ¼ −2.04 pN with SD ¼ 1.24 pN, meanR0 ¼ 10.1 μm with SD ¼ 2.2 μm) all data collapsed onto a single master curve.By integrating to the equivalent in vivo size (R∕R0 ¼ 0.1, about half thesmallest measurement R∕R0 ≈ 0.2), we estimated the micromechanical energystored in the in vivo chromosome to be on the order of 105 kBT .

A B C

Fig. 4. Depletion (entropic) forces bymolecular crowding induce chromosome compaction. (A) Illustration of depletion interactions. (Upper) When twomacroobjects (red squares) are in each other’s proximity such that the volume ΔV between them is inaccessible to the depletants (white), there is effective attractionbetween the macro objects due to random collisions with the depletants. By integrating the ideal gas law over the volume ΔV in the illustration, we obtain thefree-energy reduction ΔF ≈ ΔV · c · kBT , where c is the concentration of the depletants, (Lower) Essentially the same physics applies to long chains; ı.e., deple-tion interactions can cause collapse of the chains (see SI Appendix, Section II.C). (B) Addition of PEG at a volume fraction comparable to that of cytoplasmicproteins caused full compaction of the equilibrated chromosomes (multiple traces in grey) back to their in vivo volume. Removal of PEG caused the chromo-somes to spring back to their equilibrium in vitro volume in about 10 s, comparable to the expansion timescale after initial lysis. The experiment was repeatablefor at least 11 successive cycles of PEG addition and removal. (C) Effective size of the chromosomes at different PEG concentrations. (Experiment) Just below thetransition point (PEG volume fraction 11–13%), we observed interesting coexistence of compacted and decompacted regions within individual chromosomes(arrows in the snapshots). The areas of the purple and yellow circles represent the relative fraction of the decompacted and compacted regions within thechromosomes, respectively. The fraction of the decompacted chromosomes (purple) drops sharply before transition. (Theory) The solid line shows the meanchromosome length as a function of PEG concentration calculated using Eq. 1 and amodified Odijk theory (23). (The dashed line shows the result of the originalOdijk theory.) Our theory predicts collapse of the chromosome at ½PEG� ¼ 18% volume fraction, in a reasonable agreement with the data (11–19%). In both ourtheory and the Odjik theory, the volume of completely collapsed DNA is zero.

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size (Fig. 4C). These results clearly show that molecular crowdingalone can cause compaction of the nucleoid in vitro at a suffi-ciently high (e.g., in vivo) concentration of depletants. In vivo,however, the effects of molecular crowding may be complementedby contributions from nucleoid-associated proteins and supercoil-ing. Furthermore, because depletion interactions tend to reduceinter-DNA spacing and thus enhance looping, molecular crowdingmay indirectly enhance binding of nucleoid-associated proteins.Further work is needed to make quantitative predictions in vivodue to significant differences in microscopic detail between PEGand cytoplasmic proteins.

The Compaction–Decompaction Transition in the Microchannels Ap-pears To Be Abrupt. In the above experiments, we noticed an inter-esting phase coexistence of compacted and decompacted regionswithin individual nucleoids (see snapshots with yellow and purplearrows in Fig. 4C). This, together with the fast collapse of thechromosomes in the presence of high-concentration PEG (Fig. 4Band Movie S5), is typical of a first-order phase transition and re-miniscent of the coil-globule transition of a stiff chain (41).

To understand the nature of the compaction–decompactiontransition, and to explore the extent to which Eq. 1 describes theobserved behavior of the bacterial chromosomes, we revised thetheoretical approach by Odijk and colleagues (23). That is, weincorporated Eq. 1 to compute the expected size of a linear en-tropic spring in response to depletion forces in microchannels.

Fig. 4C shows the theoretical predictions against the data. Animportant prediction of our theory is that the entropic spring(nucleoid) is expected to collapse completely at a concentrationof 18% PEG. This compares favorably to the data (11%–19%).Also important, the predicted size of the entropic spring de-creases rapidly, albeit continuously, around the transition point.Taken together, the compaction-decompaction transition is con-sistent with a weakly first-order transition (42) †.

Our conclusion is different from the previous work by Odijkand coworkers, who concluded that the compaction–decompac-tion transition is second-order (23) (see Fig. 4C for comparison).In SI Appendix, Section II.C, we show that the results criticallydepend on the form of the force-compression expression usedin the theory.

DiscussionShape Influences the Volume of the in Vitro Chromosome, Consistentwith Polymeric Behavior. When injected into a long narrow tubewith open ends, a lump of clay or an agarose gel (polymer gel)maintains constant volume and changes only its shape, whereas along chain with excluded-volume interactions decreases its con-tainment volume as well (43). The equilibrium volume of the invitro chromosomes isolated in microchannels is several timessmaller than the ones isolated in the absence of confinement(Table 1 and SI Appendix, Section II.B). This shape-dependentdecrease in total chromosomal volume is consistent with a poly-mer model of the bacterial chromosome (11, 17, 44).

The Bacterial Chromosome Behaves as a Cross-Linked Polymer. Be-cause the entropic spring model in Eq. 1 describes the force-com-pression curves remarkably well, it is plausible to model thebacterial chromosome as a linear or ring-like “string of beads,”in which molecular details determine the spring constant k. In thebare entropic spring model, the absolute value of k should be oforder 1 (25). In contrast, the spring constant obtained by fitting

our data has the much larger magnitude of k ¼ −794� 483(Fig. 3 and Table 1; see also ref. 15).

The large numerical value of k is a salient feature of cross-linked polymers (43). In particular, based on the recent theore-tical results by Metzler et al. (45), we infer that our measured k isdirectly proportional to the number of cross-links that may tight-en large DNA loops (see Fig. 5, lower right). If we interpret thebacterial chromosome as a linear or ring polymer described byEq. 1, we can estimate the number of cross-links to be 63 or284 per cell (see Table 1 and SI Appendix, Section II.B). Similarly,we can also estimate the size of individual “beads” comprising thechromosome, which ranges from 130 to 440 nm (see Fig. 5 and SIAppendix, Section II.B), with the former being in a reasonableagreement with the results obtained by Krichevsky and coworkersusing fluorescence correlation spectroscopy (38).

What constitutes the cross-links is not clear. The nucleoid-associated proteins are the obvious candidates (31). In particular,although not essential for cell viability (46), the MukBEFcomplex is an interesting possibility because of its ring-like struc-ture (47), role in chromosome organization and segregation (4),and copy number [several hundreds (46, 48), comparable to thenumber of cross-links we estimated above]. Furthermore, MukBbinds to DNA very strongly, shows cooperativity, and acts as amacromolecular clamp (49). Other candidates may include tran-scription for its direct and indirect effect on chromosome com-paction (50).

Based on our discussion above, two types of nucleoid-asso-ciated proteins will influence the physical properties of the chro-mosomes. The first type, which we will refer to as Type I, changesthe local physical properties (e.g., by bending), whereas the sec-ond type, which we will refer to as Type II, cross-links the DNA atlong distance. Most nucleoid-associated proteins appear to beType I, whereas MukB (and perhaps H-NS) seems to be Type II.Type I nucleoid-associated proteins will influence the excluded-volume interactions between the beads, whereas Type II maychange the effective spring constant significantly (e.g., slip-links)(Fig. 5). It will be of interest to measure how the spring constantwill change for the cells that lack a specific type of nucleoid-associated protein.

Comparison with Viral DNA in a Capsid Reveals the Soft Nature ofthe Bacterial Chromosome. To understand the nature of the forcesrequired to shape and segregate the in vivo bacterial chromo-somes, it is useful to highlight the similarities and differences be-tween the viral DNA packaged in a capsid and the bacterialchromosome.

On the surface, both genomes are confined to spaces muchsmaller than their fully stretched lengths (e.g., 6.6-μm longdsDNA in an approximately 50-nm ϕ29 capsid, and a millimeter-long dsDNA in a micrometer-long E. coli or Bacillus subtilis cell).Also, both virus and bacteria have been shown to package ortranslocate their entire genome equivalents of DNAusing power-ful motor proteins that can exert several tens of piconewtons offorce [the portal complex for ϕ29 (18) and FtsK/SpoIIIE forE. coli/B. subtilis (51)]. These force scales are consistent with ourdata in Fig. 3. Extrapolation of this result implies that about100 pN force is sufficient to fully compress the in vitro chromo-some to its in vivo size.

However, if we consider the origin of the internal pressure ofthe capsid and the cell, the two genomes reveal astonishing dif-ferences in their materials properties. For the virus, the 50 atmo-sphere internal pressure of the capsid is a direct result of thestrong bending of and electrostatic repulsions between the stiff,negatively charged dsDNA (18, 19). In stark contrast, the pres-sure (applied force perμm2 of nucleoid surface area; Fig. 3) re-quired to compress the chromosome to its in vivo size is about athousand-fold smaller than the approximately 1 atmosphere tur-gor pressure exerted by the cytoplasm inside the bacterial cell

†Although the theoretical results clearly capture the major features of the data, severalassumptions/simplifications made in the theory need to be noted. (i) Depletion inter-actions have an effect only along the long axis of the microchannel. The transversedimensions of the nucleoid are fixed by the width of the microchannel. (ii) The chainis a homo-polymer, whereas the chromosome may not be. (iii) The chain interacts onlywith itself through excluded-volume interactions (i.e., we ignore proteins and otherpotential biological factors). See SI Appendix, Section II.C) for more details.

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(52). That is, the bacterial chromosome in vivo is fundamen-tally “soft.”

The softness of the bacterial chromosome, together with thefast timescale of its global motion (Figs. 1 and 4), means thatentropic forces can readily and dynamically influence the chro-mosome, from segregation and organization (11, 13, 17, 44) tocompaction (3, 23), as suggested previously and demonstratedin this work.

ConclusionsChromosomes are the basis of many cellular processes in all livingcells, and confinement is the key condition that constrains thephysical properties of chromosomes. In this work, we directlymeasured the micromechanical properties of individual bacterialchromosomes confined in microchannels. We found that thebacterial chromosomes are soft in that the compaction pressuresare only approximately 1∕1000 of the surrounding turgor pres-sure inside the cell. Our view is that the softness is important tounderstanding the dynamic balance between various intracellularforces acting on the chromosomes in vivo. Many of these forcesare entropic in nature (e.g., depletion). They can cause fast, glo-bal changes in chromosomemorphology and size with only tens ofpiconewtons of force.

Our measurements were possible because of technologicaldevelopment bringing together imaging, optical tweezers, and amicrofluidic device. Although pulling on single-molecules has

been well established over decades (53), pushing molecules hasbeen a much more formidable challenge with few published ex-amples exclusively focusing on a single DNA molecule (54–57).

Our optical trap micropiston expands the optical tweezer plat-form to allow for single-chromosome compression, enablingnew studies on the biologically important role of the physicalproperties and spatial organization of confined chromosomes.For example, our approach could be extended to study the prop-erties and interactions of multiple eukaryotic chromosomes.Here, underlying biological principles may be revealed if we un-derstand the forces governing the organization of interphasechromosomes in mammalian nuclei (58) and chromosomal indi-vidualization in eukaryotes (59).

In previous work, we suggested how chromosome segregation(demixing) can be driven by physical processes using a confinedpolymer model (11, 17, 44). Considering the intriguing quan-titative agreement between our measurements and the samemodel (Figs. 3 and 4), physical properties of the bacterial chro-mosome may indeed provide major driving forces for chromo-some segregation in vivo. That is, although the diversity of life isthe consequence of evolution, quantitative understanding ofthe physical properties of biological systems, such as the micro-mechanical properties of the bacterial chromosomes presentedhere, may provide deeper insight into the basic processes sharedby all life forms.

Fig. 5. Bacterial chromosome model with summary. The in vivo chromosome consists of physical structural units with an effective “bead” size on the order of100 nm, which are dynamically cross-linked. The effect of dynamic cross-links can be modeled using the idea of a slip-link (lower right) (45). Upon lysis, thestructural units remain mostly intact, although the dynamic bridges either break or stretch. In fast-growing cells, we envision that, on ensemble average, themajority of the DNAmass is found near the envelope. See also Fig. 1B. A possible model is that a significant part of the in vivo chromosome is collapsed onto theenvelope assisted by molecular crowding (Fig. 4A), with the cross-section of the cell as illustrated above. For slowly-growing cells with a smaller cell diameter,the nucleoid on average may occupy the center of the cell (see figure 2 in ref. 17). In stark contrast to viral DNA, the E. coli chromosome is soft (see Discussion).

Table 1. Summary of the experimental parameters for nucleoids isolated from a single cell (four chromosomeequivalents for our growth conditions)

V0, nucleoid volume 25.5� 10.7 μm3 (40 mM NaCl)(4 chromosome equivalents) 27.3� 7.4 μm3 (100 mM NaCl)

V free, unconfined nucleoid volume 18 μm3 (ref. 38), 27 μm3 (ref. 23)(1.6 chromosome equivalents)

A, rescaled spring constant (fit) −2.04 pN ± 1.24 pNk, dimensionless constant (fit) −794 (see Eq. 1)ξ, size of structural unit 130–440 nmmξ, minimum number of structural units (assumed equal to mcrosslinks) 63–284f , force of compaction on the order of 100 pNF, stored mechanical energy per nucleoid on the order of 105 kBTτglobal, timescale of global motion of the nucleoid approximately 10 s

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Materials and MethodsLysis and Molecular Crowding Experiments. Polydimethylsiloxane (PDMS) mi-crofluidic channels were cast from a master mold, constructed via standardsoft lithography techniques as previously described (24). The PDMS devicewas passivated with PLL-g-PEG to prevent adsorption of the chromosomesto the inner walls of the device (60). The lysis protocol was derived fromref. (27): E. coli cells expressing HU-mCherry or HU-GFP were grown in liquidLBwith varying growth conditions depending on the physiological conditionsof interest. The cells were plasmolyzed in 20% sucrose buffer (pH 7.3–7.4) andloaded to the device, approximately one cell per channel. Loaded cells wereincubated with lysozyme for digestion of the cell wall. Dilute buffer contain-ing NaCl (varying concentrations from 40 to 200mMNaCl) was infused to lysethe cells synchronously. After cell lysis, fresh dilute buffer was continuouslyinfused at a reduced flow rate to create a constant chemical environment.During and after lysis, fluorescent HU was imaged to measure the chromo-some size, morphology, and occupancy by fluorescently labeled HU. Molecu-lar crowding experiments were performed by cyclic addition and removal ofdepletant-containing buffer (PEG 20000) using an automated syringe pumpsystem (Harvard Appratus Pump 22, Upchurch valve, LabVIEW). A detaileddescription of experimental conditions and image analysis is provided in SIAppendix, Section I.A.

Mechanical Compression Experiments. The confined chromosomes weremanipulated by moving an optically trapped bead (piston head) relativeto the chromosome-filled microchannel (piston chamber). The optical trapacts as a soft spring, with bead displacement reporting the force requiredto compress and decompress the chromosome at various degrees of confine-ment. These experiments utilize an optical trap setup that integrates a nearIR laser (Coherent Compass 1064-4000 M) into an inverted light microscope(Nikon TE2000-U). The microfluidic device is mounted onto a piezo scanningstage (Physik Instruments PI-562.3CD) to move the channels relative to theoptical trap. Transmitted light images at 160x total magnification are pro-jected onto a CCD camera (Prosilica GE680) to track the trapped bead andfiducial marks on the stage with a one-dimensional accuracy of 4 nm (61).

Chromosomes in the microfluidic channels were prepared with BSA pas-sivated microspheres (Spherotech, nominal diameter of 1 μm) included withthe lysis buffer. Fluorescent images of channels were taken after lysis toidentify channels containing potentially compressible chromosomes and acell ghost at the open end of the channel (empirically, we found that the cellghost acted as gasket to create a tight seal, preventing chromosome escapeduring compression). An optically trapped bead was then aligned with themicrochannel and moved relative to the channel to repeatedly compress anddecompress the chromosome in 500 nm increments. After the experiment,most beads were individually calibrated by measuring fluctuations of atrapped bead (just outside the channel) at low power and fitting with theblur-corrected power spectrum fit (61). A detailed description of the experi-mental conditions and data analysis is in SI Appendix, Section I.B.

Principal Component Analysis. Principal component analysis (PCA) is a methodthat interprets the distribution of data geometrically. To analyze chromo-some morphologies using PCA, we built an image stack for each chromo-some. For every frame, the bounding box of the chromosome was com-puted automatically. The chromosome image in the bounding box wasrescaled and interpolated to a fixed size of an L × M matrix using a cubicspline algorithm in Igor Pro (WaveMetrics). Further, each pixel intensitywas normalized by the total intensity of the bounding box. The results wereported in this work were insensitive to the choice of L and M.

Once a normalized image-stack of chromosome images has been con-structed, we performed a standard PCA. Briefly, we computed an averagechromosome profile h ~Φti from the image stack f ~Φtg, and calculated the

residual, δ ~Φt ¼ ~Φt − h ~Φti, at each time-index t. The main step of PCA is diag-onalization of the covariance matrix

C ¼ 1

N∑N

t¼1

δ ~Φtδ ~ΦTt ¼ 1

NAAT; [2]

where the data matrix A ¼ ½δ ~Φ1δ ~Φ2…δ ~ΦN �. Because C is symmetric, all itseigenvalues are positive real and its eigenvectors ~ui form an orthornormalbasis that diagonalizes C. The eigenvectors are ordered by eigenvalues,and the resulting ordered set of eigenmodes ( ~ui) are the principal com-ponents.

To analyze the morphological dynamics of the chromosome, we projectedthe original chromosome image ~Γ into the principal components by thefollowing simple operation,

ωi ¼ ~uTi ð ~Γ − h ~ΦiiÞ∕j ~uij · j ~Γ − h ~Φiij: [3]

The projection coefficient, ωi , has a value between −1 and 1 as seen in Fig. 1D.For example, ω1 ¼ þ1 means that the system (chromosome) is in the highesteigenmode (first eigenChromosome). SI Appendix, Section I.A.7, provides afull description and the results of PCA of the chromosome expansion data.

Theory. To predict the size of the in vitro chromosomes in the microchannelsat a given PEG concentration, we solved the following two equations simul-taneously:

wo þ k2w2o þ 2k3w3

o ¼ wi þ k2w2i þ 2k3w3

i

þ 0.349wi

Vþ 9.85w9∕4

i

V

þ 3.34 × 10−8�−

∂∂V

�FchrðV ÞkBT

[4]

lnwo þ 2k2wo þ 3k3w2o ¼ lnwi þ 2k2wi þ 3k3w2

i

þ 0.349V

þ 9.85w5∕4i

V; [5]

where V is the envelope volume of the chromosome (in units of μm3),wo andw i are the weight fraction (in units of g∕ml) of PEG outside and inside V , andFchrðVÞ is the free energy of the confined chain inferred from Eq. 1 (25). Thefirst equation describes mechanical equilibrium across the boundary, and thesecond equation represents chemical equilibrium of PEG. The constantsk2 ≈ 56.75 and k3 ≈ 99.43 are two-body and three-body contributions calcu-lated without the chromosome (23). SI Appendix, Section II, provides detailedinformation about various theoretical methods used in this work.

ACKNOWLEDGMENTS. S.J. thanks Bela Mulder, Marileen Dogterom, andSander Tans at Foundation for Fundamental Research on Matter Institutefor Atomic and Molecular Physics (FOM Institute AMOLF) for their generoussupport in the early stage of this work; Wei Lien Dang, Jay Fisher, PeterGalajda, and Nancy Kleckner for helpful discussions; and Jean-Yves Bouetfor help with biochemistry and for fruitful discussions. This work was sup-ported by Natural Sciences and Engineering Research Council of Canada(B.-Y.H.), the Rowland Junior Fellows program at Harvard University and Im-mune Disease Institute/Harvard Medical School/Boston Children's Hospitalstartup funds (W.W.), and the Bauer Fellows program at Harvard University,the National Institutes of Health Grant P50GM068763, and University ofCalifornia San Diego startup funds (S.J.).

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