effect of length, topology, and concentration on the microviscosity and microheterogeneity of dna...

Effect of Length, Topology, and Concentration on theMicroviscosity and Microheterogeneity ofDNA Solutions

Alan Goodman1, Yiider Tseng1,2 and Denis Wirtz1,2,3*

1Department of ChemicalEngineering, The JohnsHopkins University, 3400North Charles Street, BaltimoreMD 21218, USA

2Graduate Program inMolecular Biophysics, TheJohns Hopkins UniversityBaltimore, MD 21218, USA

3Department of MaterialsScience and Engineering, TheJohns Hopkins UniversityBaltimore, MD 21218, USA

The viscoelastic behavior of chromosomal DNA, which is heterogeneouslydistributed within the nucleus, may influence the diffusion of nuclearorganelles and proteins. To identify some of the parameters that affectDNA viscoelasticity, we use the high-throughput method of multiple-particle nanotracking to measure the microviscosity and degree of hetero-geneity of solutions of chromosomal DNA, linear DNA, and circulardouble-stranded DNA over a wide range of concentrations and lengths.The thermally excited displacements of multiple fluorescent microspheresimbedded in DNA solutions are monitored with 5 nm spatial resolutionand 30 Hz temporal resolution, from which mean-squared displacement(MSD) and viscosity distributions are generated. For all probed DNAsolutions but the most concentrated solution of the longest molecules, theensemble-averaged MSD increases linearly with time at all probed timescales, a signature of viscous transport. The associated mean viscosity ofthe DNA solutions increases slowly with concentration for circular DNAand more rapidly for linear DNA, but more slowly than predicted bytheory. The heterogeneity of the DNA solutions is assessed by computingthe relative contributions of the 10%, 25%, and 50% highest values ofMSD and viscosity to the ensemble-averaged MSD and viscosity. Forboth linear DNA and circular DNA, these contributions are much largerthan observed in homogeneous liquids such as glycerol. The microhetero-geneity of the linear DNA solutions increases with concentration moresignificantly for linear DNA than circular DNA. These in vitro resultssuggest that the topology, local concentration, and length of DNAinfluence the microrheology and microheterogeneity of the DNA withinthe nucleus.

q 2002 Elsevier Science Ltd. All rights reserved

Keywords: genomic DNA; particle nanotracking; microrheology; nucleusorganization*Corresponding author

Introduction

Much evidence supports the view that nuclearDNA is dynamically and heterogeneouslyorganized within the nucleus.1 Many cellular pro-cesses such as gene expression rely on the trans-

port of molecules between dynamic DNA-richcompartments created by relatively immobile bind-ing or assembly sites.2,3 Heterochromatin, the mostgenetically active transcribed DNA, whichcoincides with nuclear regions of relatively highDNA concentration, are distinguished fromeuchromatin, the least active form of DNA, bystaining more intensely with the fluorescent stain-ing dye 40-6-diamidino-2-phenylindole (DAPI)during interphase. The movement of chromatin inthe nucleus is not uniform; in particular, the lociat nucleoli or the nuclear periphery are signifi-cantly less mobile than other, more nucleoplasmicloci.4 Such spatio-temporal fluctuations in DNAconcentration become even more discernibleduring cell division where condensed mitotic

0022-2836/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved

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

Abbreviations used: MPT, multiple-particle tracking;MSD, mean squared displacement; SK, pBlueScript IISK þ ; pET, pET21a; pEYFP, pEYFP-IRS-1; DAPI, 40-6-diamidino-2-phenylindole.

doi:10.1016/S0022-2836(02)00893-8 available online at http://www.idealibrary.com onBw

J. Mol. Biol. (2002) 323, 199–215

chromosomes undergo large re-organization.Furthermore, in eukaryotic cells, chromosomes arelocally organized into large loops. During DNArecombination, transcription, and packaging intochromosomes, DNA segment ends can join andform loops. Hence, DNA topology and concen-tration display large spatio-temporal fluctuationsin the nucleus. How DNA topology and concen-tration affect the local dynamics and viscoelasticityof the nuclear DNA mesh is unknown.

Local variations in DNA viscosity may affect theoverall physical properties of the nuclear region aswell as the transport of nuclear organelles andnuclear proteins. For instance, the guanidinenucleotide exchange factor RCC1 for Ran, a smallGTPase that regulates nucleocytoplasmic traffick-ing and spindle assembly, is transiently associatedwith chromatin.5 The nuclear mobility of RCC1creates a RanGTP gradient around chromosomes.This nuclear transport of RCC1 is believed to beaffected by its transient binding to DNA and bysteric obstacles (i.e. local mesh size) created bylocal fluctuations in DNA concentration.6 Spatialvariations in DNA concentration could also affectthe local viscoelastic properties of the nucleus. Atlow enough concentrations, DNA would formmostly viscous structures, and the transport ofnon-binding proteins would be purely diffusional.Here, small random forces created by the move-ments of water and other small molecules onto thenuclear proteins are quickly dissipated. At highDNA concentrations, DNA molecules may overlapand entangle, generating an elastic polymer mesh.Elasticity may in turn greatly slow down the trans-port of nuclear organelles and proteins, which maybecome sub-diffusive. Here, medium-mediatedrandom forces applied to the proteins are met byrestoring elastic forces, which limit free viscousdiffusion and rapid viscous dissipation within theDNA mesh. Such an elastic DNA mesh mayprovide additional structural strength to thenucleus. It is generally believed that in eukaryoteslong, fragile DNA molecules do not provide pro-tection against the mechanical forces generated bythe cytoskeleton, a protection mostly provided bythe nuclear membrane.7 Genomic DNA forms arelatively rigid macromolecular assembly,8 whichhas the potential to form a stiff network. Becausethe local viscoelastic properties of DNA in vivo areunknown, it is unclear whether nuclear DNA dis-

plays elasticity that could enhance the overallstiffness.

Here, we use reconstituted DNA networks tobegin to investigate how some key molecular andsolution parameters, such as DNA concentration,DNA topology and length, may affect both theglobal and local viscoelasticity of DNA solutions.We also investigate whether solutions containingphysiological concentrations of chromosomalDNA possess elasticity. We use the recently intro-duced method of multiple-particle microrheologyto quantitatively assess both the mean viscoelasticproperties of DNA solutions, as well as the magni-tude of viscoelastic fluctuations. The in vitromeasurements presented here establish a frame-work to begin to analyze measurements of theviscoelastic properties of nucleoplasm in livingcells.

Results

Quantifying the microviscosity of DNAsolutions using multiple-particle tracking

The general procedure to analyze local variationsof the local mechanical properties of DNA sol-utions using multiple-particle tracking (MPT) isillustrated in Figure 1. The thermally excited dis-placements of 1-mm diameter microspheresimbedded in solutions of either linear or circularDNA of contour lengths of 1.00 mm, 1.84 mm or3.57 mm (Table 1) were video monitored with 5 nmspatial resolution and 30 Hz temporal resolutionusing a custom MPT software (see Materials andMethods) (see Figure 1(a) for illustration). Thetime-dependent coordinates ½xðtÞ; yðtÞ� (t ¼ elapsedtime) of the centroids of the microspheres wererecorded (Figure 1(a)) and transformed intofamilies of time-averaged mean squared displace-ments (MSDs), kDr2ðtÞl ¼ k½xðt þ tÞ2 xðtÞ�2 þ ½yðt þtÞ2 yðtÞ�2l (t ¼ time scale or time lag) (Figure1(b)), from which distributions of MSDs (Figure1(c)) and distributions of viscosity (Figure 1(d)) ofthe DNA solutions were obtained.

We first present microrheological measurementsfor circular, supercoiled DNA. Microspheresembedded in solutions of circular pBlueScript IISK þ (SK) DNA (2.9 kbp), pET21a (pET) DNA(5.4 kbp), and pEYFP-IRS-1 (pEYFP) DNA

Table 1. Properties of the DNA molecules tested here

DNA mol-ecules

Shortname

Molecular massn (kbp)

Contourlength L (mm)

Radius of gyration (C , C p)Rg ¼ ðLLp=3Þ0:5 (mm)

Overlap concentration Cp ¼3Mr=ðNA4pR3

gÞ (mg/ml)

pBlueScriptII SK þ

SK 2.96 1.00 0.13 0.33

pET21a pET 5.40 1.84 0.17 0.27peyfp-IRS-1 pEYFP 10.51 3.57 0.22 0.25

The contour length of the molecules is L ¼ n £ 0:34 mm, where the molecular mass n is expressed in kilobase pairs (kbp);Lp ¼ 0:05 mm is the persistence length of DNA;37 NA is Avogadro number; Mr ¼ n £ 6:1 £ 105 Da is the molecular mass of the DNAmolecules expressed in Daltons.

200 Microviscosity of DNA

Figure 1. MPT of microspheressuspended in DNA solutions. (a) Adilute suspension of 1 mm-diameterfluorescently labeled polystyrenemicrospheres is mixed with a DNAsolution of controlled concen-tration; their thermally excitedmotion is simultaneously moni-tored with ,5 nm spatial resolutionover a 120 mm £ 120 mm field ofview. Trajectories are recorded at arate of 30 Hz (see details inMaterials and Methods). The fluctu-ating microspheres subject theirmicroenvironment to localizedforces; the response may locally dif-fer within the solution as shown by(b) variations in the MSDs of themicrospheres in solution. Inset:typical two-dimensional trajectoryof a microsphere from which theMSD is calculated. (c) Distributionof MSDs ðn ¼ 120Þ estimated at atime scale of 0.1 second. (d) Distri-bution of local viscosity ðn ¼ 120Þof the DNA solution. The type ofDNA probed here is circular pET(contour length 5.4 kbp ¼ 1.8 mm);the concentration of pET is 1.6 mg/ml.

Microviscosity of DNA 201

(10.5 kbp) displayed seemingly unrestricted ran-dom displacements over a wide range of concen-trations as qualitatively shown by their trajectories(for illustration, see inset, Figure 1(b)). Accor-dingly,9 MSD profiles increased linearly with timeat least at short time scales (Figure 1(b)). This is a

signature that the microenvironment surroundingthe particles responds like a viscous liquid:10

stresses that are locally applied to the DNA solu-tion by the fluctuating movements of the particlesare quickly relaxed by viscous dissipation. TheseMPT measurements show that, over a wide range

Figure 2. Ensemble-averaged MSD, viscosity, and compliance of circular and linear DNA solutions. (a) Ensemble-averaged compliance of 1.6 mg/ml solutions of circular pET (5.4 kbp), pEYFP (10.5 kbp) and SK (2.9 kbp) as a functionof time scale. Compliance characterizes the extent of deformation of the DNA solution as a function of stress (force perunit area). Inset: MSD versus time scale for microspheres imbedded in a 1.6 mg/ml pEYFP solution. Upper curverepresents raw data; lower curve represents data corrected for specimen convection. (b) Ensemble-averaged com-pliance evaluated at a time scale of 0.1 second as a function of the concentration in circular pET, pEYFP, and SK.(c) Ensemble-averaged viscosity as a function of the concentration in circular pET, pEYFP, and SK. (d) Ensemble-averaged compliance of 1.6 mg/ml solutions of linear pET, pEYFP, and SK. Inset: Diffusion coefficient versus timescale for SK solution (upper curve) and pEYFP and pET solutions (lower curves). (e) Ensemble-averaged complianceevaluated at a time scale of 0.1 second as a function of concentration of linearized pET, pEYFP, and SK. (f) Ensemble-averaged viscosity as a function of concentration in linear pET, pEYFP, and SK. n , 120 for each solution.


of concentrations, solutions of circular DNAbehave mostly like viscous liquids at least at smalltime scales.

At long time scales, the profile of the MSDs wasaffected by slight convection of the DNA specimen,which is difficult to avoid for low-viscosity fluids.To eliminate the non-random component of themovements of the microspheres, we analyzed thetime-dependence of the MSD profiles (inset, Figure2(a)). The existence of convection effects duringparticle tracking is readily detected by the (slight)

upturn shape of the microspheres’ apparent diffu-sion coefficient ð¼ kDr2ðtÞl=4tÞ at long time scales(not shown here). The polynomial RDr2ðtÞS ¼4Dtþ v2t2 was fitted to the ensemble-averagedMSD, RDr2ðtÞS; where D is the mean diffusionconstant and v is the mean convection velocity ofthe microspheres. This functional form contains arandom diffusion component, 4Dt; which domi-nates at short time scales, and a directed-transportcontribution, v2t2; which dominates at long timescales. From the fit, we found that convection

Figure 3. Concentration-dependent MSD distributions of microspheres embedded in solutions of circular DNA ofdifferent length. MSD distribution of micrspheres imbedded in solutions containing (a) 0.1 mg/ml, (a0) 0.4 mg/ml,(a00) 0.8 mg/ml, and (a000) 1.6 mg/ml circular pET. (b–b000) Circular pEYFP, and (c–c000) circular SK. n , 120 for eachsolution. All MSDs are evaluated at a time scale of 0.1 second.


created detectable deviations from Brownian dif-fusion only beyond a time scale of t , 2 seconds(for illustration, see inset, Figure 2(a). For alltested circular DNA solutions, the corrected MSDprofiles showed a linear increase up to that timescale.

The viscosity of DNA solutions is obtained fromStokes–Einstein equation, which relates the diffu-sion coefficient of the probe microspheres to theviscosity of the DNA solution, D ¼ kBT=6pah:9

Here kB is Boltzmann constant, T is the specimentemperature, a is the radius of the microsphere,and h is the viscosity of the solution. However,microspheres imbedded in some of the linearDNA solutions showed sub-diffusive behavior. Toextract viscoelastic parameters, each MSD profilewas transformed into a so-called creep complianceprofile, GðtÞ; via a simple manipulation, since GðtÞ

is proportional to kDr2ðtÞl (see Materials andMethods) (Figure 2(a)). The magnitude of GðtÞdescribes the degree of deformability of the DNAsolution while the time scale dependence of GðtÞdetermines the viscoelastic character of DNA. Forinstance, in a viscous liquid subjected to a (small)mechanical stress, the compliance is proportionalto time and inversely proportional to the viscosityh, GðtÞ ¼ t=h; the time dependence shown by theDNA solutions at short time scales. In an elasticHookean solid, the compliance is independent oftime and inversely proportional to the elasticmodulus G0; GðtÞ ¼ 1=G0: All solutions, but themost concentrated one of the longest linear DNAmolecules (see below), displayed compliance pro-files that scaled linearly with time scale (data notshown). Hence, up to a concentration of 1.6 mg/ml, solutions of circular and linear pEYFP DNA

Figure 4. Concentration-dependent viscosity distributions of solutions of circular DNA of different length. Distri-bution in solutions containing (a) 0.1 mg/ml and (a0) 0.4 mg/ml circular pET, (b) 0.1 mg/ml and (b0) 0.4 mg/ml circu-lar pEYFP, and (c) 0.1 mg/ml and (c0) 0.4 mg/ml circular SK. n , 120 for each tested solution.


solutions displayed a liquid-like behavior. Theensemble-averaged shear viscosity of 1.6 mg/mlsolutions of circular pEYFP, pET and SK DNAmolecules was 6.1 cP, 2.9 cP, and 4.1 cP, respec-tively (Figure 3(c)). By comparison, the viscosity ofwater at 20 8C is 1 cP ( ¼ 0.01 Poise ¼ 0.001 Pa s).The ensemble-averaged compliance estimated at a

fixed time scale (here 0.1 second) declined slowlywith concentration (Figure 2(b)); the same resultheld at all tested time scales (t ¼ 0.03–10 seconds).Accordingly, the shear viscosity measured fromMPT experiments increased slowly for concen-trations between 0.1 mg/ml and 1.6 mg/ml (Figure2(c)).

Figure 5. Statistical analysis of MSD and viscosity distributions in solutions of circular DNA. (a) Relative contri-butions of the 10%, 25%, and 50% highest MSD values to the ensemble-averaged MSD of microspheres embedded incircular pET solutions. (b) Relative contributions of the 10%, 25%, and 50% highest MSD values to the ensemble-averaged MSD of microspheres embedded in circular pEYFP solutions. (c) Relative contributions of the 10%, 25%,and 50% highest MSD values to the ensemble-averaged MSD of microspheres embedded in circular SK solutions.These contributions would be exactly equal to 10%, 25%, and 50% in a perfectly homogeneous solution. (d) Relativecontributions of the 10%, 25%, and 50% highest viscosity values to the ensemble-averaged viscosity of circular pETsolutions. (e) Relative contributions of the 10%, 25%, and 50% highest viscosity values to the ensemble-averagedviscosity of circular pEYFP solutions. (f) Relative contributions of the 10%, 25%, and 50% highest viscosity values tothe ensemble-averaged viscosity of circular SK solutions. First columns in (a)–(f) represent solutions of 0.1 mg/ml;second columns, 0.2 mg/ml; third columns, 0.4 mg/ml; fourth columns, 0.8 mg/ml; and fifth columns, 1.6 mg/ml.All MSDs are evaluated at a time scale of 0.1 second. n , 120 for each solution.


Microheterogeneity as measured by multiple-particle tracking: effect of DNA length andDNA concentration

To quantify the degree of heterogeneity ofsolutions of the circular DNA, MSD values werecollected into distributions (Figure 3). As expected,MSD distributions shifted towards low values forincreasing DNA concentration, a result that heldfor SK DNA (Figure 3(a)–(a000)), pET DNA (Figure3(b)–(b000)), and pEYFP DNA (Figure 3(c)–(c000)).MSD distributions were relatively symmetric andnarrow (Figure 3). However, comparing the shapeof distributions that encompass different values ofan observable could be misleading. To analyze theshape of the MSD distributions (Figures 3 and 4),we used the so-called bin-partition analysis (Figure5).11 – 13

In this analysis, MSD values evaluated at a giventime scale are sorted and the contributions ofthe 10%, 25%, and 50% highest MSD values to theensemble-averaged MSD are evaluated. We pre-viously showed that these parameters are 11%,26%, and 52%, respectively, for a homogeneoussolution of glycerol, contributions that are closeto 10%, 25%, and 50% predicted for a perfectlyhomogenous liquid, for which all MSDs should be

equal.11 For circular DNA solutions, the contri-butions of the 10%, 25%, and 50% highest MSDvalues to the mean MSD were larger than thosedisplayed by glycerol (Figure 5(a)–(c)). Thisindicates that the DNA vector solutions were lesshomogenous than the control glycerol solution,despite the fact that, like glycerol, DNA solutionsdisplayed a strong liquid-like character. Relativecontributions of the highest MSD values to themean MSD increased for increasing DNA concen-tration (compare columns in Figure 5, A–C ),which indicates that the microheterogeneity ofDNA solutions increased for increasing concen-tration, a result that held for all tested DNAlengths (Figure 5(a)–(c)). We found that solutionsof pET, SK and pEYFP displayed similar micro-heterogeneity parameters (Figure 5(a)–(c)).

Having verified that at short time scales alltested DNA solutions behaved like viscous liquids,we used the Stokes–Einstein relationship to gener-ate distributions of the local viscosity (Figure 4).As expected, the viscosity distributions shiftedtowards high values for increasing DNA concen-tration (Figure 4). Viscosity distributions alsowidened for increasing concentration, an effectobserved for pET, SK, and pEYFP DNA solutions(compare (a)–(c) with (a0)–(c0), Figure 4). Follow-ing the MSD distribution analysis describedabove, we computed the relative contributions ofthe 10%, 25%, and 50% highest values of the localviscosity to the ensemble-averaged viscosity(Figure 5(d)–(f)). Since viscosity is inversely pro-portional to the MSD (see Materials and Methods),these parameters complement those computedfrom the 10%, 25%, and 50% highest MSD valuesdescribed above: they characterize the MSDdistributions at low MSD values. We found thatthe degree of heterogeneity in the viscosity ofDNA solutions increased with concentrationand increased slightly with DNA length (Figure5(d)–(f)).

Linear and circular DNA

To begin to test the effect of DNA topology onthe overall viscous response of the solutions, themolecules were subjected to enzymatic treatmentthat linearized DNA. Samples of each solutionwas run in an agarose gel to ensure completedigestion and verify the uniformity of the lengthof the molecules. We hypothesized that solutionsof linear DNA molecules, which a priori have agreater tendency to overlap and, possibly, a greaterradius of gyration than circular DNA molecules,would be more viscous than solutions of circularDNA of the same concentration. To test thishypothesis, we applied the MPT microrheologymethod described in Figure 1 to solutions of linearDNA. We found that the compliance (i.e. thedeformability) of solutions of linear DNA waseither similar or slightly smaller than the com-pliance of solutions of circular DNA at low concen-trations (Figure 2(d)). Moreover, as in the case of

Figure 6. Typical MSD profiles of microspheresembedded in solutions of linearized DNA. The concen-tration of linear pET is (a) 0.1 mg/ml; (b) 0.8 mg/ml.


circular DNA, the transport of the microspheres inlinear DNA solutions was diffusional over theprobed time-scale range (Figures 2(d) and 6), i.e.linear DNA solutions were viscous (not elastic) atlow DNA concentrations. The compliance of linearDNA solutions, however, decreased with concen-tration much more sharply than observed for circu-lar DNA (Figure 2(e)). In addition, unlike circularDNA, the compliance of pEYFP DNA solutionswas lower than that of solutions of the shorterpET and SK DNA molecules, respectively (Figure2(e)). Accordingly, the viscosity of linear DNA

solutions was much more concentration-dependentthan the viscosity of circular DNA, a viscosity thatincreased with the length of the molecules (Figure2(f)). At long time scales, the averaged complianceof the 1.6 mg/ml solution of linear pEYFP DNAincreased less rapidly than linearly with timescale, RGðtÞS , ta where a , 1; a signature ofviscoelastic behavior (Figure 2(d)). The corre-sponding ensemble-averaged elastic modulus of1.6 mg/ml solutions of pEYFP was 0.5 dyn/cm2 ata frequency of 0.1 Hz. The elasticity of pET andSK DNA solutions was either negligible or too

Figure 7. Concentration-dependent MSD distributions of microspheres embedded in solutions of linear DNA ofdifferent length. MSD distribution in solutions containing (a) 0.1 mg/ml, (a0) 0.4 mg/ml, (a00) 0.8 mg/ml, and (a000)1.6 mg/ml linear pET. (b–b000) Linear pEYFP, and (c–c000) linear SK. All MSDs are evaluated at a time scale of 0.1 second.n , 120 for each solution.


small to be measured by MPT microrheology.Therefore, the linear DNA solutions studied heredisplay a purely viscous liquid character; the mostconcentrated DNA solution behaves like a pureliquid at high frequencies (i.e. short time scales)and is slightly elastic at low frequencies (i.e. longtime scales).

To quantify the microheterogeneity of linearDNA solutions and following the methodologydescribed in Figures 4 and 5, MSD profiles such asthose shown in Figure 6 were collected into MSDdistributions and statistically analyzed. We foundthat the MSD and viscosity distributions for linearDNA solutions were as wide and skewed as circu-lar DNA (Figures 7 and 8). The contributions of the10%, 25%, and 50% highest MSDs to the ensemble-averaged MSD for linear DNA and circular DNAsolutions were similar (Figure 9(a)–(c)). The contri-

butions of the 10%, 25%, and 50% highest viscosityvalues to the ensemble-averaged viscosity werealso larger for linear DNA solutions than for circu-lar DNA solutions (Figure 9(d)–(f)). Those contri-butions were relatively independent of DNAlength (Figure 9).

The microviscosity of genomic DNA in vitro

We tested the microviscoelastic properties ofgenomic DNA purified from Swiss 3T3 mousefibroblasts. Using the MPT method presentedabove, we found that solutions of genomic DNAwith concentrations ranging between 0.1 mg/mland 1.6 mg/ml displayed viscoelastic and struc-tural properties similar to those of DNA vectors.Despite its length (see Discussion), solutions ofgenomic DNA displayed a mostly viscous-like

Figure 8. Concentration-dependent viscosity distributions of solutions of linear DNA of different length. Distri-bution in solutions containing (a) 0.1 mg/ml and (a0) 0.4 mg/ml linear pET, (b) 0.1 mg/ml and (b0) 0.4 mg/ml linearpEYFP, and (c) 0.1 mg/ml and (c0) 0.4 mg/ml linear SK. n , 120 for each solution.


behavior as shown by the linear dependence ofthe MSD with time scale (Figure 10(a)). The meanviscosity increased from 7 cP to 39 cP for concen-trations between 0.1 mg/ml and 1.6 mg/ml (Figure10(d)). The distributions of MSDs were slightly

more asymmetric as detected by computing thecontributions of the 10%, 25%, and 50% highestMSD values to the mean MSD (Figure 10(b) and(c)). Microheterogeneities in solutions of genomicDNA decreased with concentration (Figure 10(c)).

Figure 9. Statistical analysis of MSD and viscosity distributions in solutions of linear DNA. (a) Relative contributionsof the 10%, 25%, and 50% highest MSD values to the ensemble-averaged MSD of microspheres embedded in linearpET solutions. These contributions would be exactly equal to 10%, 25%, and 50% in a perfectly homogeneous solution.(b) Relative contributions of the 10%, 25%, and 50% highest MSD values to the ensemble-averaged MSD of micro-spheres embedded in linear pEYFP solutions. (c) Relative contributions of the 10%, 25%, and 50% highest MSD valuesto the ensemble-averaged MSD of microspheres embedded in linear SK solutions. (d) Relative contributions of the10%, 25%, and 50% highest viscosity values to the ensemble-averaged viscosity of linear pET solutions. (e) Relativecontributions of the 10%, 25%, and 50% highest viscosity values to the ensemble-averaged viscosity of linear pEYFPsolutions. (f) Relative contributions of the 10%, 25%, and 50% highest viscosity values to the ensemble-averaged vis-cosity of linear SK solutions. First columns in (a)–(f) represent solutions of 0.1 mg/ml; second columns, 0.2 mg/ml;third columns, 0.4 mg/ml; fourth columns, 0.8 mg/ml; and fifth columns, 1.6 mg/ml. All MSDs are evaluated at atime scale of 0.1 second. n , 120 for each solution.


Analysis and Discussion

We measured the microviscoelastic properties ofDNA solutions as a function of concentration(0.1–1.6 mg/ml), molecular topology (linear versuscircular) and contour length of the molecules(1.0–3.6 mm). Most DNA solutions tested hereshowed a viscosity that was very small and closeto the viscosity of water ðh0 , 1 cPÞ: Commerciallyavailable rheometers, including strain-controlledand stress-controlled rheometers, fare typicallybadly when testing fluids of low viscosity, pro-viding poor accuracy. MPT microrheology usedhere not only offers the possibility to probe smallamounts of low-viscosity liquids, but also providesinformation about the microheterogeneity of theDNA solutions and allows us to test a largenumber of DNA specimens readily.

Sometimes subtle, but significant, differences inthe microstructural and microrheological proper-ties of DNA were captured using the MPT method.We found that solutions of circular DNA were lessviscous and the concentration dependence of theviscosity was much more pronounced than for

linear DNA. DNA solutions displayed non-negli-gible heterogeneity, which, surprisingly, increasedwith concentration. The degree of heterogeneity ofsolutions of linearized DNA was higher than solu-tions of circular DNA, and relatively independentof contour length in both cases. While contourlength had a minimal effect on circular DNA’sproperties, it had a profound effect on linear DNArheology. We discuss separately our results in thedilute and semidilute regimes.

Dilute DNA solutions

We first consider the dilute regime and estimatethe average distance between linear molecules indilute conditions, i.e. for concentrations lower thatthe critical concentration C , Cp: Since the persist-ence length of DNA in TE buffer, Lp , 0:05 mm,14

is much smaller than the contour length L of theDNA molecules tested here, pEYFP, pET, and SKlinear molecules can be considered to be flexiblepolymers of L=Lp ¼ 72; 36, and 20 randomlyoriented segments, respectively.15 In TE buffer andfor the lengths of polymers considered here, DNA

Figure 10. Particle tracking microrheology of genomic DNA in vitro. (a) MSD profiles of microspheres embedded in a1.6 mg/ml solution of genomic DNA. These profiles show faster-than-linear increase at long time scales due to slightconvection of the specimen. Inset: ensemble-averaged MSD corrected for convection. (b) MSD distribution evaluatedat a time scale of 0.1 second for a 1.6 mg/ml solution of genomic DNA. (c) Statistical analysis of MSD distributions ingenomic DNA solutions. Relative contributions of the 10%, 25%, and 50% highest MSD values to the mean MSD.First columns represent a solution of 0.1 mg/ml; second columns, 0.4 mg/ml; third columns, 0.8 mg/ml; and fourthcolumns, 1.6 mg/ml. (d) Distribution of viscosity for the 1.6 mg/ml solution. Inset: mean viscosity versus concen-tration. n , 200 for each tested solution.


molecules can be considered as ideal randomwalks for which steric intramolecular interactionsare mostly negligible.14,16,17 In dilute conditions,the estimated radius of gyration, Rg ¼ ðLLp=3Þ0:5;of pEYFP, pET, and SK DNA molecules is 0.22 mm,0.17 mm, and 0.13 mm, respectively (see Table 1).In non-overlapping conditions, the average dis-tance between DNA molecules is given by d ¼Rgf

21=3 where f is the volume fraction of DNA insolution. The volume fraction is given approxi-mately by f ¼ ðCNA=MrÞð4pR3

g=3Þ where Mr ¼n £ 6:1 £ 105 Da is the molecular mass of the DNAmolecules expressed in Da (average molecularmass of a base-pair is 610 Da), n is the number ofkbp in DNA molecules ( ¼ 10.5, 5.4, and 2.9 forpEYFP, pET, and SK molecules, respectively), C isthe DNA concentration, and NA is Avogadronumber. The volume fraction of a 0.1 mg/ml solu-tion of SK, pET, and PEYFP DNA is 31%, 38%,and 42%, respectively, and the average distancebetween molecules is 0.19 mm, 0.23 mm, and0.29 mm, respectively. Hence, on average the probemicrospheres are in contact with one or moreDNA molecules. Next, we analyze the MSD ofmicrospheres in these dilute DNA suspensions.

The fact that the MSDs of microspheres in diluteDNA solutions grew linearly with time scalewithout a break as a function of time is somewhatsurprising. One can envision that the transport ofthe microspheres in dilute DNA conditions isdescribed by two different diffusion coefficients.At short time scales, the diffusion of the micro-spheres is fast and set by the (low) viscosity ofthe buffer. At long time scales, the diffusion ofthe microspheres is reduced by the presence of theDNA molecules, which create soft obstacles to thetransport of the probe microspheres. The crossovertime scale between these two regimes depends onthe average time for the microsphere to encountermolecules, i.e. the crossover time would decreasewith DNA volume fraction, which sets the averagespacing between molecules described above. Thiscrossover time would therefore (slightly) decreasewith the molecular mass of the molecules byincreasing the radius of gyration of the moleculesand therefore diminishing the time between bead/polymer collisions. For three different DNA sizes,we found no such crossover behavior. This resultsuggests that this simple picture of microspheretransport is at least incomplete.

This “static” view of DNA solution organizationneglects the relatively fast diffusion of the DNAmolecules themselves. The diffusion coefficient ofthe (linear) SK, pET, and pEYFP molecules,approximately D , kBT=6ph0Rg; is larger than thediffusion coefficient of the probe microspheresby a factor R=Rg ¼ 3:9; 2.9, and 2.3, respectively.The average time required for the DNA moleculesto diffuse their radius of gyration is aboutt , R2

g=D ¼ 5 ms, 11 ms, and 25 ms for SK, pETand pEYFP DNA, respectively. In contrast, theaverage time required for the probe microspheresto diffuse their radius R is tR , R2=DR ¼ 2:3

seconds. All tested (linear) DNA molecules movedmuch faster than the microspheres. A bettermodel for the diffusion of the particles wouldassume a cloud of very fast moving DNA mol-ecules forming a continuum and therefore makingthe particles diffusion smoother. We note that inthe dilute regime, linear and circular DNA mol-ecules form liquid solutions of similar viscosity,which indicates that the exact topology of themolecules does not influence their hydrodynamicbehavior in dilute conditions.

Theory predicts that, at low volume fractions,the viscosity of a dilute suspension of flexiblepolymers increases linearly with concentration ash ¼ h0ð1 þ ½h�CÞ ¼ h0ð1 þ 1:49fÞ; where ½h� ¼0:425NAð

ffiffiffi

6p

RgÞ3=Mr is the Flory–Fox intrinsic

viscosity.18 Hence, the predicted viscosity of a0.1 mg/ml solution is 1.49 cP, 1.57 cP, and 1.62 cP,for pEYFP, pET, SK molecules, respectively, whichare all lower than measured by MPT. The fasterthan-linear increase of the viscosity with concen-tration (Figure 2) suggests that even for the lowesttested concentrations, non-linear contributions tothe viscosity need to be incorporated.

Semidilute DNA solutions

DNA solutions with concentrations higher thanthe theoretically predicted critical concentration C p

form suspensions of overlapping polymers (Table1). The degree of heterogeneity of semidilute DNAsolutions is significantly higher than that of homo-geneous glycerol solutions. However, the MSDdistributions of microspheres in DNA solutionsare relatively narrow and symmetric compared tothose observed in other complex fluids, includingsolutions of actin filaments,19 actin bundles,12

keratin suspensions,20 and the cytoplasm of livingcells,21 but wider than glycerol.11 Accordingly, therelative contributions of the 10%, 25%, and 50%highest values to the mean MSD were smallerthan in those complex fluids, but higher than inglycerol.

The fact that the microheterogeneity of DNAsolutions increases with concentration is a surpris-ing result. Intuitively, local DNA concentrationshould greatly fluctuate in dilute conditions. Inthose conditions, each polymer has on average amicroenvironment devoid of other polymers; thelocal volume fraction alternates between 0% and100% at length scale equal to that of the radius ofgyration. Above the critical concentration, poly-mers overlap and concentration fluctuations arepredicted to diminish.18 At length scales largerthan the mesh size of the solution, the volume frac-tion is close to unity. However, as discussed above,dilute DNA solutions are better modeled as acloud of fast moving molecules at the time scalesprobed by particle tracking, which may explainwhy fluctuations are seemingly very small in thedilute regime. There may exist a concentrationabove which these fluctuations would begin todiminish, a regime seemingly not probed here


despite the fact that we investigated concentrationsas high as 6.4 times the overlap concentration (i.e.C=Cp ¼ 6:4 for pEYFP). In support of this, wefound that concentration fluctuations in genomicDNA solutions, which display much higher ratiosof C=Cp; decreased for increasing concentrations(Figure 10(c)).

We find that the concentration dependence of theviscosity of linear DNA solutions is biphasic: itincreases slowly at low DNA concentrations, andthen rapidly above a threshold concentration(Figure 2(f)). At low DNA concentrations, the vis-cosity of solutions of linear DNA is similar to thatof circular DNA. At high concentrations, however,a crossover behavior occurs at a threshold concen-tration beyond which the viscosity of linearmolecules increases rapidly with concentration. Incontrast, the viscosity of circular DNA increasesmonotonically with concentration over the entireprobed range of concentrations (Figure 2(c)). Wefind that this crossover concentration decreaseswith increasing DNA length (Figure 2(f)). Theexistence of a crossover concentration beyondwhich the viscosity increases rapidly is typicallyinterpreted as the onset of new interactionsbetween molecules.18 This experimentally deter-mined crossover concentration is found to besimilar to the theoretically predicted criticalconcentration, the concentration at which DNAmolecules begin to interact (i.e. to overlap).Circular DNA solutions do not display elasticity,which is presumably due to the fact that, whileoverlapping, these molecules do not form topo-logical entanglements capable of generating elasticbehavior.

Theory predicts that polymer solutions displayelasticity when molecules entangle,15 which occursfor polymer concentrations larger than the criticalconcentration C p. All solutions, but the 1.6 mg/mlpEYFP solution, display a strongly viscous charac-ter (i.e. non-elastic). pEYFP molecules form theonly solution that displays a non-negligible elas-ticity. Similar elastic behavior was previouslyobserved with the much longer linear l-phageDNA ðL , 17 mmÞ and T2 DNA ðL , 52 mmÞ;22,23

for which the movement of microspheres was sub-diffusive over the same time scale range as probedhere. The predicted elastic modulus is G , kBT=j3

where j is the mesh size of the solution, jðCÞ ¼RgðC=CpÞ21: This prediction holds for uncross-linked solutions of flexible, ideal (i.e. random-walk) polymers such as the linear DNA solutionsconsidered here (see Discussion above). For con-centrations between C p and 1.6 mg/ml, jðCÞdecreases from 130 nm to 27 nm for SK, from170 nm to 29 nm for pET, and from 220 nm to34 nm for pEYFP. Accordingly, we find that thepredicted elastic modulus of the tested solutions isextremely small, at most G ¼ 0:2 dyn/cm2, for themost concentrated solution (1.6 mg/ml) of thelongest molecules (pEYFP), in agreement with ourexperimental observations. Recent models on semi-flexible polymer rheology predict that the modulus

of a semidilute solution is G ¼ ð7=5ÞðrkBT=leÞ24

where r ¼ ðCNA=MrÞðn £ 0:34 mmÞ is the concen-tration of DNA contour length per unit volume,which ranges between 3.4 mm22 and 53.7 mm22 forconcentrations between 0.1 mg/ml and 1.6 mg/ml, and le ¼ lpðrl2pÞ

22=525 is the so-called entangle-ment length which ranges between 0.3 mm and0.1 mm over the same concentration range. Wefound elastic moduli that were even smaller thanthose predicted for flexible polymers, indepen-dently of DNA length. Hence, the assumption thatthe linear DNA vectors are flexible random-walkpolymers,16,17,26,27 which form overlapping solu-tions is supported by an agreement with classicaltheory of polymer solutions.

Above C p, the viscosity of a semidilute solutionof linear flexible polymers is expected to dependstrongly on polymer concentration and length: h ,ðC=CpÞ6 , L3C6 (for C . Cp). We find much weakerconcentration and length dependencies for h, evenabove C p (Figure 2). This suggests that, while over-lapped, linear DNA molecules in the tested solu-tions are not sufficiently entangled to verify theassumptions of the theory. This interpretation issupported by the fact that only the most concen-trated solutions of the longer DNA molecules dis-played elasticity (see above). The fact that ourmeasured viscosity is lower than predicted couldalso be due to the increasing degree of hetero-geneity of the solutions for increasing concen-tration. We find that the viscosity can locally differby up to a factor of 5. Ensemble-averaged visco-metric measurements, such as those obtained byaveraging all local measurements (this study) orusing macroscopic methods such as rheometersand viscometers,28 may be dominated by weakstructural points within the solution which locallyyield under shear deformation. We indeed findthat by considering only the 90% highest values ofviscosity (90% lowest MSDs), the apparent meanviscosity increases by up to a factor of 2, i.e. out-liners contribute disproportionately to the meanviscosity.

DNA rheology in vitro and in vivo

The physical state of nuclear DNA is clearlymuch more complex in vivo than that of reconsti-tuted DNA networks. Nevertheless, insight intopossible mechanisms of DNA microviscoelasticityin vivo can be derived from our results in vitro.Since the human genome contains n , 2:9£106 kbp (mouse genome contains , 2:6 £ 106 kbp),the mass of nuclear DNA in a normal human cellis ðn £ 6:1 £ 105Þ=NA , 2:9 pg ( ¼ 2.9 £ 10212 g).Therefore, for a nuclear volume of ,525 mm3 (thenucleus is assumed to be a sphere of radius 5 mm),the mean concentration of DNA is ,5.5 mg/ml;if the nuclear volume is 7240 mm3 (radius,12 mm, the approximate radius of many culturedfibroblasts such as Swiss 3T3 used here), then themean concentration of DNA becomes ,0.4 mg/ml. These are very approximate estimates, since,


for instance, large fluctuations in DNA concen-tration occur within the nucleus (see Introduction).Nevertheless, the concentrations used here havethe same order of magnitude as the mean physio-logical concentration of DNA in the nucleus. Thefact that chromosomal DNA is much longer thanthe DNA should only affect the viscosity, not theelastic modulus and the network mesh size, ofDNA solutions of longer molecules. Indeed, in asemidilute solution, viscoelastic moduli and meshsize do not depend on polymer length.18 For com-parison, human mitotic chromosome (no confiningnuclear membrane), which has an average molecu-lar mass of 6.3 £ 105 kpb, has a predicted radius ofgyration of ,135 mm and corresponding overlapconcentration of Cp ¼ 0:06 mg/ml, ignoring thepossible confining effects of the plasma membraneand the presence of DNA-binding proteins, suchas histones, which tightly package chromosomalDNA in vivo. The mesh size is expected to increaseto about 1 mm for a concentration of 5.5 mg/ml.Therefore, the intrinsic elastic modulus of chromo-somal DNA is expected to be very small, which issupported by our in vitro microrheological studiesof solutions of genomic DNA.

The viscosity of nucleus is typically measuredby comparing the diffusion coefficient of smallmolecules, DNA fragments or polymers, in thenucleus and buffer. For instance, fluorescencerecovery after photobleaching (FRAP) was utilizedto determine the diffusion of microinjectedFITC-labeled dextrans.29 When injected into thenucleus of Swiss 3T3 fibroblasts and MDCK cells,the macromolecule diffusion of dextran was foundto be , four times slower than in aqueous solu-tions. This suggests that the mean viscosity of thenucleus is ,4 cP,30 which is similar to the viscosityof DNA vectors, but smaller than the viscosity ofreconstituted chromosomal DNA. This is a surpris-ing result, since chromosomal DNA is much longerthan the DNA vectors tested here (see above). Thismay be due to the fact that dextran’s size may besmaller than the average mesh size, effectivelyprobing the (small) interstitial viscosity of chromo-somal DNA. If larger than the DNA mesh size,dextran may be excluded from the dense regionsof DNA. In contrast, DNA fragments were nearlyimmobile, which suggests that DNA fragmentsexhibit extensive binding to immobile obstaclesand/or because of molecular crowding.30,31

We recently used particle tracking micro-rheology21 to measure the viscoelastic propertiesof the nucleoplasm (Y.T. and D.W., unpublishedresults). We found viscoelastic moduli that weremuch larger than those of purified DNA. Thesmall viscosity of DNA in vitro suggest that tran-sient crosslinkers may greatly enhance the elas-ticity of the nuclear region. Histones in particulardramatically increase the local concentration ofDNA and locally modify the topology of DNA.Moreover, recent studies show the localization ofthe intermediate filaments lamin both in thenuclear periphery and its interior.32 Intermediate

filaments tend to form relatively stiff gels at highconcentrations.33,34 We are currently investigatingthe microviscoelasticity of the nucleoplasm usingMPT microrheology. Small microspheres microin-jected into the nucleus of adherent cells areallowed to undergo Brownian motion. Using thesame approach discussed here, we measure theviscoelasticity of the nucleoplasm. Preliminarymeasurements indicate that the viscosity and elas-ticity of the nucleoplasm of living cells are muchhigher than those of reconstituted DNA solutionsconsidered here. The in vitro results presentedhere therefore show that concentrated solutions ofgenomic DNA do not contribute directly to theoverall viscoelasticity of the nucleoplasm.

Materials and Methods

Preparation of DNA

A Megaprep (Qiagen, Valencia, CA) was performedon plasmid-transformed Escherichia coli competent cellstrains XL-1 Blue (Stratagene, La Jolla, CA) followingthe Qiagen protocol. These strains were transformedwith three different DNA vectors, including pEYFP(Clontech, Palo Alto, CA) with a specialized insert of afull length cDNA of insulin receptor substrate 1 (IRS-1)to make pEYFP-IRS-1 of length 10.5 kbp (contour lengthL ¼ 3:6 mm), pET21a (Novagen, Madison, WI) of length5.4 kbp ðL ¼ 1:8 mmÞ; and pBlueScript II SK þ (Strata-gene) of length 2.9 kbp ðL ¼ 1:0 mmÞ: The last threesteps of the Qiagen protocol were modified to ensureDNA purity. Once the DNA was eluted, it was precipi-tated by adding 0.1 volume of 3 M sodium acetate tothe DNA solution, then adding 2 £ the volume of theDNA/salt mixture of 100% (v/v) ethanol to the mixtureand mixed well. The solution was placed at 270 8C for40 minutes and centrifuged at 12,000g for 30 minutes at4 8C. The pellet was rinsed with 70% ethanol, dried in avacuum, and redissolved in a suitable volume of TEbuffer. After measuring the A260 of each DNA solution,DNA was concentrated to 1.6 mg/ml using the precipi-tation method described above. These concentrated solu-tions were serially diluted for the MPT experiments toprobe a wide range of concentrations.

To make linear DNA, a single cut was made in eachcircular DNA molecule using a restriction enzyme. ForpEYFP-IRS-1, Sac I was used; for pET21a, Bam HI wasused; for pBlueScript II SK þ , Xho I was used (allenzymes from New England Biolabs, Beverly, MA). Allenzymes were incubated in 1.6 mg/ml DNA solutions,at a dilution of 1:10, at 37 8C for 24 hours. Oncecompleted, a sample from each solution was run in anagarose gel to ensure a complete digestion and that thelinear DNA was at a proper length. Finally, the A260 wasmeasured and the linear DNA solutions were concen-trated to 1.6 mg/ml for the MPT experiments.

For convenience, pBlueScript II SK þ is denoted SK;pET21a is denoted pET, and pEYFP-IRS-1 is denotedpEYFP (Table 1). The estimated radius of gyration ofthese molecules in the dilute regime, Rg, and criticalconcentration, C p, for linear pEYFP, pET, and SK DNAmolecules are 0.22 mm and 0.25 mg/ml, 0.17 mm and0.27 mg/ml, and 0.13 mm and 0.33 mg/ml, respectively(Table 1). Therefore, the linear DNA solutions testedhere are either in the dilute ðC , CpÞ or the semidilute


regime ðC . CpÞ where the tested DNA concentration Cranges between 0.1 mg/ml and 1.6 mg/ml. This rangeof concentration was selected to coincide with estimatedconcentration of DNA in the nucleus of the cell (seeDiscussion). We note that, in dilute conditions, all testedDNA molecules have a radius of gyration smaller thanthe microsphere radius ( ¼ 0.5 mm).

Genomic DNA was prepared from six flasks of conflu-ent, cultured Swiss 3T3 fibroblasts (,20 £ 106 cells/flask)using a DNeasy Tissue Kit from Qiagen (for a total of 24preps). All of the preps were combined and the genomicDNA was concentrated to ,0.44 mg/ml (measuredusing spectrophotometry at wavelengths of 260 nm and280 nm). This DNA was then precipitated and resus-pended in a 1% solution of 1 mm beads in PBS to preparea DNA concentration of 1.6 mg/ml. The beads weretracked in this solution and then serially diluted 2 £and tracked until a concentration of 0.1 mg/ml wasreached.

A total of 35 DNA solutions differing in molecularcontour length, molecular topology (linear versus circu-lar), and concentrations were studied. This underlies theextraordinary ability of MPT for high-throughput testingand screening of biologicals.

Multiple-particle tracking (MPT)

Yellow-green fluorescent carboxylated 1 mm-diameterpolystyrene microspheres (Molecular Probes, Eugene,OR) were mixed with each DNA solution. Movies of thefluctuating fluorescent microspheres were recorded witha silicon-intensifier target (SIT) camera (VE-100 Dage-MTI, Michigan City, IN) mounted on an inverted epi-fluorescence microscope (Eclipse TE300, Nikon, Melville,NY).35 Displacements were monitored with a 100 £ PlanFluor oil-immersion objective (N.A. 1.3) at a spatial reso-lution of ,5 nm over a 120 mm £ 120 mm field of view.19

Images of the microspheres were analyzed by a customMPT routine incorporated into the software Meta-morph/Metaview (Universal Imaging Corp., WestChester, PA) as described.12 The displacements of theparticle centroids were monitored in the focal plane ofthe objective for 20 seconds at a rate of 30 frames/second. Individual time-averaged MSDs, kDr2ðtÞl; wheret is the time lag, were calculated from the two-dimen-sional trajectories of the centroids of each microsphere.kDr2ðtÞl is proportional to the local compliance of thecomplex fluid, GðtÞ ¼ ðpa=kBTÞkDr2ðtÞl; in response tothe small local force created by the fluctuatingmicrosphere.36 Here, kB is Boltzmann’s constant, T is theabsolute temperature of the specimen, and a is the radiusof the probe microsphere. After verifying that the MSDscaled with time linearly (i.e. we did not assume dif-fusional transport a priori ), the viscosity of the solutionwas derived using the Stokes–Einstein relation, h ¼2kBTt=3pakDr2ðtÞl; which is independent of t for a purelyviscous liquid because kDr2ðtÞl , t; or equivalently, fromthe slope of the compliance trace (see Results).

Acknowledgements

The authors acknowledge financial support fromthe NSF (CTS007227 and NIRT CTS0210718) andthe Materials Research Society. The authors thank

Yixian Zheng, Joseph G. Gall, Alex Levine, andRegina List for useful discussions.

References

1. Manders, E. M., Kimura, H. & Cook, P. R. (1999).Direct imaging of DNA in living cells reveals thedynamics of chromosome formation. J. Cell Biol. 144,813–821.

2. Carmo-Fonseca, M., Mendes-Soares, L. & Campos, I.(2000). To be or not to be in the nucleolus. NatureCell Biol. 2, E107–E112.

3. Carmo-Fonseca, M. (2002). The contribution ofnuclear compartmentalization to gene regulation.Cell, 108, 513–521.

4. Chubb, J. R., Boyle, S., Perry, P. et al. (2002). Chroma-tin motion is constrained by association with nuclearcompartments in human cells. Curr. Biol. 12,439–445.

5. Wilde, A. & Zheng, Y. (1999). Stimulation of micro-tubule aster formation and spindle assembly by thesmall GTPase Ran. Science, 284, 1359–1362.

6. Smith, A. E., Slepchenko, B. M., Schaff, J. C. et al.(2002). Systems analysis of Ran transport. Science,295, 488–491.

7. Alberts, B., Bray, D., Lewis, J., et al. (1994). MolecularBiology of the Cell, Garland Publishing, Inc, NewYork.

8. Houchmandzadeh, B., Marko, J. F., Chatenay, D. et al.(1997). Elasticity and structure of eukaryote chromo-somes studied by micromanipulation and micro-pipette aspiration. J. Cell Biol. 139, 1–12.

9. Berg, H. C. (1993). Random Walks in Biology, PrincetonUniversity Press, Princeton, NJ.

10. Palmer, A., Xu, J., Kuo, S. C. et al. (1999). Diffusingwave spectroscopy microrheology of actin filamentnetworks. Biophys. J. 76, 1063–1071.

11. Xu, J., Tseng, Y., Carriere, C. J. et al. (2002). Micro-rheology and microheterogeneity of wheat gliadinsuspensions studied by multiple particle tracking.Biomacromolecules, 3, 92–99.

12. Tseng, Y. & Wirtz, D. (2001). Mechanics and multiple-particle tracking microhetrogeneity of alpha-actinin-cross-linked actin filament networks. Biophys. J. 81,1643–1656.

13. Tseng, Y., An, K. M. & Wirtz, D. (2002). Microhetero-geneity controls the rate of gelation of actin filamentnetworks. J. Biol. Chem. 277, 18143–18150.

14. Marko, J. F. & Siggia, E. D. (1995). Stretching DNA.Macromolecules, 28, 8759–8770.

15. de Gennes, P.-G. (1991). Scaling Concepts in PolymerPhysics, Cornell University Press, Ithaca.

16. Haber, C., Alom-Ruiz, S. & Wirtz, D. (2000). Shapeanisotropy of a single random-walk polymer. Proc.Natl Acad. Sci. USA, 97, 10792–10795.

17. Haber, C. & Wirtz, D. (2000). Magnetic tweezers forDNA micromanipulation. Rev. Sci. Instrum. 71,4561–4570.

18. Doi, M. & Edwards, S. F. (1989). The Theory of PolymerDynamics, Clarendon Press, Oxford.

19. Apgar, J., Tseng, Y., Federov, E. et al. (2000). Multiple-particle tracking measurements of heterogeneities insolutions of actin filaments and actin bundles. Bio-phys. J. 79, 1095–1106.

20. Ma, L., Yamada, S., Wirtz, D. et al. (2001). A hot-spotmutation alters the mechanical properties of keratinfilament networks. Nature Cell Biol. 3, 503–506.


21. Yamada, S., Wirtz, D. & Kuo, S. C. (2000). Mechanicsof living cells measured by laser tracking micro-rheology. Biophys. J. 78, 1736–1747.

22. Mason, T. G., Ganesan, K., van Zanten, J. V. et al.(1997). Particle-tracking microrheology of complexfluids. Phys. Rev. Letters, 79, 3282–3285.

23. Mason, T. G., Dhople, A. & Wirtz, D. (1997). Concen-trated DNA rheology and microrheology. InStatistical Mechanics in Physics and Biology (Wirtz,D. & Halsey, T. C., eds), vol. 463, pp. 153–158.

24. Morse, D. C. (1998). Viscoelasticity of concentratedisotropic solutions of semiflexible polymers. 2.Linear response. Macromolecules, 31, 7044–7067.

25. Morse, D. C. (1998). Viscoelasticity of concentratedisotropic solutions of semiflexible polymers. 1.Model and stress tensor. Macromolecules, 31,7030–7043.

26. Haber, C. & Wirtz, D. (2000). Shear-induced l-phageDNA assembly. Biophys. J. 79, 1530–1536.

27. Wirtz, D. (1995). Direct measurement of the transportproperties of a single DNA molecule. Phys. Rev.Letters, 75, 2436–2439.

28. Mason, T. G., Dhople, A. & Wirtz, D. (1998). Linearviscoelastic moduli of concentrated DNA solutions.Macromolecules, 31, 3600–3603.

29. Seksek, O., Biwersi, J. & Verkman, A. S. (1997). Trans-lational diffusion of macromolecule-sized solutes incytoplasm and nucleus. J. Cell Biol. 138, 131–142.

30. Lukacs, G. L., Haggie, P., Seksek, O. et al. (2000). Size-dependent DNA mobility in cytoplasm and nucleus.J. Biol. Chem. 275, 1625–1629.

31. Kues, T., Peters, R. & Kubitscheck, U. (2001). Visuali-zation and tracking of single protein molecules in thecell nucleus. Biophys. J. 80, 2954–2967.

32. Moir, R. D., Spann, T. P., Lopez-Soler, R. I. et al.(2000). Review: the dynamics of the nuclear laminsduring the cell cycle—relationship between structureand function. J. Struct. Biol. 129, 324–334.

33. Ma, L., Xu, J., Coulombe, P. A. et al. (1999). Epidermalkeratin suspensions have unique micromechanicalproperties. J. Biol. Chem. 274, 19145–19151.

34. Yamada, S., Wirtz, D. & Coulombe, P. A. (2002).Pairwise assembly determines the intrinsic potentialfor self-organization and mechanical properties ofkeratin filaments. Mol. Biol. Cell, 13, 382–391.

35. Leduc, P., Haber, C., Bao, G. et al. (1999). Dynamics ofindividual flexible polymers in a shear flow. Nature,399, 564–566.

36. Xu, J., Viasnoff, V. & Wirtz, D. (1998). Compliance ofactin filament networks measured by particle-track-ing microrheology and diffusing wave spectroscopy.Rheol. Acta, 37, 387–398.

37. Hagerman, P. J. (1988). Flexibility of DNA. Annu. Rev.Biophys. Biophys. Chem. 17, 265–286.

Edited by M. Moody

(Received 3 May 2002; received in revised form 19 August 2002; accepted 19 August 2002)


effect of length, topology, and concentration on the microviscosity and microheterogeneity of dna...

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