Role of DNA–DNA sliding friction and nonequilibrium dynamics in viral genome ejection and packaging

Abstract Many viruses eject their DNA via a nanochannel in the viral shell, driven by internal forces arising from the high-density genome packing. The speed of DNA exit is controlled by friction forces that limit the molecular mobility, but the nature of this friction is unknown. We introduce a method to probe the mobility of the tightly confined DNA by measuring DNA exit from phage phi29 capsids with optical tweezers. We measure extremely low initial exit velocity, a regime of exponentially increasing velocity, stochastic pausing that dominates the kinetics and large dynamic heterogeneity. Measurements with variable applied force provide evidence that the initial velocity is controlled by DNA–DNA sliding friction, consistent with a Frenkel–Kontorova model for nanoscale friction. We confirm several aspects of the ejection dynamics predicted by theoretical models. Features of the pausing suggest that it is connected to the phenomenon of ‘clogging’ in soft matter systems. Our results provide evidence that DNA–DNA friction and clogging control the DNA exit dynamics, but that this friction does not significantly affect DNA packaging.


INTRODUCTION
Many double-stranded DN A (dsDN A) viruses, including tailed bacterial viruses ('phages') and some human / animal viruses such as herpesviruses, employ ATP-powered molecular motors to package DNA into preformed viral capsid shells (1)(2)(3). The DNA is very tightly packed, reaching densities as high as ∼660 mg / ml ( ∼50% volume fraction). This density is well above that at which short DNA segments in solution form liquid crystal phases. X-ray scattering measurements indicate that the spacing between adjacent ∼2 nm diameter DNA segments is only ∼0.5-1 nm. The remaining volume is occupied by thin layers of water molecules and ions (4)(5)(6).
Viral packaging motors exert large forces to translocate DN A into the proca psid through a portal nanochannel against large forces resisting DNA confinement that arise from factors including electrostatic self-repulsion of DNA segments, DNA bending rigidity, and changes in DNA hydration and entropy (7)(8)(9)(10). Part of the work done by the motor is stored as potential energy, giving rise to what has been termed 'DNA pr essur e' or 'internal force'. While this for ce r esists packaging, it plays an important role in driving DNA ejection when the virus infects a host cell (11)(12)(13)(14)(15).
The dynamics of motor-dri v en DNA packaging in phages phi29, lambda and T4 have been e xtensi v ely studied via single-molecule measurements with optical tweezers ( 3 , 16-24 ). The motors generate forces > 60 pN, placing them among the strongest kno wn ATP-po wered motors. DNA packaging begins ra pidl y, a t ra tes ranging from ∼150 to 2000 bp / s depending on virus and condition, but then slows as the capsid fills ( 16-18 , 23 ). This is due, in part, to the buildup of internal force that loads the motor ( 20 , 24 ). In phage phi29, the force reaches ∼25 pN at the end of packaging ( 20 , 24,25 ), which is consistent with theoretical predictions and the experimentally determined DNA ejection force in phage lambda, which packs DNA to similarly high density ( 25 , 26 ).
DNA ejection from phages T5 and lambda has been measured in vitro with fluorescently labeled DNA ( 12 , 27-29 ). Although the force that dri v es ejection is highest at the beginning of the process and decreases as ejection proceeds, a notable finding was that the DNA ejection velocity has an initially incr easing tr end. It was proposed that this is due to hydrodynamic drag forces acting on the confined DNA that decrease with decreasing DNA packing density. After about half of the genome is ejected, there is another regime in which the velocity decreases, which is attributed to decreasing internal force. Viral DNA ejection in vivo has also been studied ( 14,15 , 30 ) and is more complex because it involves interactions with the cytoplasm or nucleoplasm. We focus here on in vitro ejection to investigate the fundamental question of how DNA mobility is affected by the very high density packing. This question is also of interest in soft matter / polymer physics since DNA is a model for semiflexible polymers in general and viral packaging is a model for studying how confinement affects polymer dynamics.
Another surprising finding is that long pauses of up to ∼100 s were observed during T5 DNA ejection ( 12 , 29 ), but no pauses were observed with phage lambda. The T5 studies also found that the ejection dynamics depend on the concentration of dye used to label the DN A ( 31 ), w hich is likely due to the dye binding affecting the physical properties of DNA. It is thus advantageous to de v elop methods to measure ejection without dye labeling ( 32 ).
Here, we introduce a method to probe the DNA mobility by using optical tweezers to pull single DNA molecules out from single phi29 viral capsids. The method provides higher r esolution measur ement of DNA exit dynamics, avoids the use of fluorescent dyes and allows us to study how exit velocity depends on driving force. We find that during the initial stages of DNA exit the velocities are much lower than those previously reported for T5 and lambda, and there is a much sharper increase in the velocity as ejection proceeds. We find evidence that DN A-DN A sliding friction controls the initial ejection speed rather than hydrodynamic drag. We also observe frequent pauses during ejection but find that they have a different character from those observed in the phage T5 studies by fluorescence imaging.

MATERIALS AND METHODS
Methods for initiating and measuring DNA packaging are similar to those described previously ( 51 ). Fiberless phage phi29 proheads (empty capsids) and recombinant gp16 packaging ATPase proteins were produced as described previously ( 52 , 53 ). A biotin-labeled 25-kb dsDNA packaging substrate was produced via polymerase chain reaction as described previously ( 54 ).
Prohead-motor complexes were prepared by mixing 2 g of proheads with 0.4 g of gp16 ATPase in 10 l of 0.5 × TMS buffer (25 mM Tris-HCl, pH 7.5, 50 mM NaCl, 5 mM MgCl 2 ) and incubating for 4 min, before adding ␥ S-ATP to a final concentration of 0.5 mM. Complexes were then incuba ted a t 4 • C f or 1 h bef ore use. The DNA constructs wer e tether ed to str eptavidin-coated 2.3 m microspheres and the prohead-motor complexes were attached to 2.1 m protein G-coated microspheres coated with IgG antibodies against the phage capsid protein, gp8.
Packaging was initiated in a fluid chamber in the optical tweezers instrument by bringing a microsphere carrying DNA into near contact with a microsphere carrying prohead-motor complexes in a buffer containing 0.5 mM ATP, as described previously ( 51 ). In measurements where Na + was the dominant ion screening the DNA charge, the packa ging b uffer contained 25 mM Tris-HCl (pH 7.5), 50 mM NaCl and 5 mM MgCl 2 , whereas measurements with Mg 2+ as the dominant screening ion were conducted in a buffer containing 1 mM Tris-HCl (pH 7.5) and 30 mM MgCl 2 . After packaging close to 100% of the genome length (which takes, on average, ∼8 min), complexes were moved into a region of the fluid chamber containing an identical b uffer b ut without ATP. A gentle flow was maintained so that no ATP could diffuse into this region. Based on the measured kinetic rates of the packaging motor, any bound ATP would be spontaneously hydrolyzed on a timescale less than the time it takes to finish the solution exchange and initiate measurement of the DNA exit (i.e. in < 1 s) ( 20 , 55 ).
Measur ements wer e made with a dual-trap optical tweezers system at room temperature ( ∼23 • C) as described previously ( 51 ). The force signal was recorded at 1 kHz and measur ements wer e conducted in for ce-clamp mode, wher e the position of the movable trap is adjusted by a feedback control system to keep the applied force on the DNA constant. The tweezers were calibrated as described previously ( 56 ). The tether length was computed from the measured force versus fractional extension relationship that is accurately described by the e xtensib le w orm-lik e chain model for DN A elasticity. The instantaneous ca psid filling le v el was computed by subtracting the current tether length from the initial tether length at the start of packaging. DNA exit velocities were calculated by linear fits to DNA tether length versus time in a 0.5 s sliding window. These velocities were averaged together in 5% filling bins to determine a velocity versus filling profile for each complex, and then averaged across complexes to calculate the mean velocity versus filling le v el. DNA e xit from an individual complex was r equir ed to cover at least half of a filling bin to contribute to the average. Pauses were detected using the method described by Kalafut and Visscher ( 57 ). A lower resolution limit for both pause duration and change in tether length between pauses was determined by measuring experimental noise / drift le v els in control da tasets (sta tic DNA tethers held at constant force) and comparing the velocity in a time interval t during the pause or between pauses to one standar d de viation from the mean of the distribution of velocities of control data measured in time intervals of duration t .
Internal force values were determined based on previous optical tweezers measurements via interpolation of the mean force-filling relationship ( 24 , 58 ). Inferred internal force and the applied pulling force were added for each complex and then averaged across different complexes for each filling bin. Error bars on averaged quantities r epr esent standard errors calculated by bootstrap sampling.

Measurement of DNA exit trajectories
The experimental method is illustrated in Figure 1 A and builds on methods we de v eloped pre viously for measuring motor-dri v en packaging ( 59 ). We first initiate packaging by bringing a trapped microsphere with tethered DNA near a second trapped microsphere carrying capsid-motor complexes in a solution with ATP. Packaging proceeds until the capsid filling (% of the 19.3 kb viral genome length in the capsid) reaches ∼100% and then the complex is moved to a region without ATP. This causes the motor to release its grip and the DNA exits the capsid. We apply a small 5 pN force to keep the DNA stretched so that the length that has exited can be measured. Further details are gi v en in the 'Materials and Methods' section.
Examples of measured DNA exit trajectories are shown in Figure 1 B. Striking features are that the initial velocities ar e extr emel y low (m uch lower than those observed in the prior T5 and lambda studies with dye-labeled DNA) and at high filling le v els ther e ar e pauses of widely varying dura- tion. As DNA exit proceeds, the pausing decreases and the av erage v elocity increases, e v entually e xceeding ∼12 kb / s, which is the maximum we can measure with our instrument. At this point, the velocity is so high that it has negligible influence on the overall DNA exit time.
We measured an ensemble of events to determine average DNA e xit v elocity and assess dynamic heterogeneity. Transient velocity versus filling level was determined and av eraged across comple x es in 5% bins. A tr end of incr easing av erage v elocity with decreasing filling le v el is observ ed regardless of whether the pauses are included or excluded in the velocity calculations ( Figure 2 A and Supplementary Figure S1). We hereafter use the term 'velocity' to refer to transient velocity not including pauses. Strikingly, the average velocity increases exponentially as the capsid filling le v el decreases from ∼100% to 80%, going from ∼200 to ∼2000 bp / s. In Figure 2 , we plot av erage v elocities from 80% to 100% filling, where the transient velocities for all complex es wer e low enough to be measur ed. This range dominates the overall ejection time.
In many e v ents, DNA e xit could be measured to lower filling le v els (Supplementary Figure S2A). We emphasize that although previous studies of DNA ejection from phages lambda and T5 observ ed v elocity decreases below ∼50% filling, attributed to decreasing internal driving force with decreasing filling, our present measurements differ because we have a constant 5 pN applied force. Because this applied force dominates over the internal force in the low-filling regime (below ∼70%), a velocity decrease is not generally expected if the DNA mobility is ra pidl y increasing with decreasing filling. In Supplementary Figure S3, we plot velocity versus filling for each e v ent measured below 70% filling. The av erage v elocity for this subset showed an increasing trend down to the lowest measured filling le v el (45%; Supplementary Figure S4). Our measurements therefore imply that, on average, the r esisting friction for ces decr ease with decreasing filling. Individual events also generally exhibit an increasing velocity trend, although both increases and decr eases ar e observed between adjacent filling bins, indica ting tha t the v elocity for indi vidual comple xes fluctuates. Statistically, there is no evidence for significant deviations from the trends of decreasing velocity with decreasing filling (Supplementary Figure S5).
Howe v er, we do find evidence in a small fraction of e v ents ( ∼20%) for large transient velocity decreases. In these e v ents, the v elocity initially increased to a value higher than we could track, causing the applied force to drop to zero. But then, at lower filling le v els (ranging from ∼20% to ∼40%), an increase of the force back to 5 pN was briefly detected, indicating a velocity decrease ( Supplementary Figure S6). These e v ents were brief, lasting < 400 ms, after which the velocity increased back to a value higher than we could measure. Although infrequent and brief, these e v ents interestingl y impl y that the resisting friction can occasionall y sharpl y increase e v en though the filling le v el has decr eased. This pr esumably occurs due to the formation of peculiar nonequilibrium DNA conformations.

Pausing during DNA exit and nonequilibrium dynamics
We observe significant pausing during DNA exit. The pauses occur stochastically across all capsid filling le v els down to ∼50% and have widely varying durations as long as ∼15 s. We measure individual pauses with high resolution and determine their frequencies and durations. The mean frequency and mean duration decrease monotonically with decreasing capsid filling le v el ( Figure 2 C and D). The percent time spent paused decreases from ∼60% near 100% filling to ∼20% at 80% filling (Figure 2 E). These pauses dominate the overall ejection kinetics, comprising 57% ( ±3%) of total exit time.
We also observe br oad heter o geneity in DN A exit dynamics between different indi vidual comple xes, clearly seen in the length versus time and velocity measurements (  Figure S7). The velocity limit of ∼12 000 bp / s is reached at quite variable filling levels in each complex, ranging from ∼40% to 80% filling (mean of 73 ± 3%). Overall exit times, which are dominated by dynamics in the high-filling regime, vary widely between complexes, ranging from ∼10 to 100 s (Figure 2 B), consistent with the process being con-trolled by nonequilibrium dynamics of the tightly packed DNA.

Dependence on ionic screening
Ionic screening of the DNA phosphate backbone charge is expected to be an important parameter because it influences the strength of electrostatic DN A-DN A interactions ( 60 , 61 ). Phage lambda ejection studies with fluorescent DNA found that increasing the screening, thus reducing DNA charge repulsion, slowed ejection ( 27 , 28 ). We repeated our measurements with higher screening by omitting NaCl and increasing MgCl 2 to 30 mM; divalent cations result in an ∼25% lower effecti v e DNA charge per unit length ( 62 ). DN A-DN A interactions are net repulsi v e in both conditions, but weaker with Mg 2+ ( 63 , 64 ). We find that the mean DNA exit velocity is r educed (Figur e 2 A). Velocities measured for individual complexes are shown in Supplementary Figure S2B, again sho wing lar ge heterogeneity. Whereas the trend of exponentially increasing average exit velocity remains similar, velocities are reduced by ∼50% across the whole range compared to the lower screening condition. Both the mean pause duration and mean pause frequency follow a similar trend with filling as in the lower scr eening condition (Figur e 2C and D). P ause duration is increased significantly in the high screening condition and pause fr equency incr eases at the highest filling le v els, leading to a ∼30% increase in the fraction of time spent paused during DNA exit. As shown in Figure 2 B, the distribution of DNA exit times shifts toward higher values.

Dependence on driving f or ce
A unique advantage of our method using optical tweezers is that we can a ppl y controlled pulling forces to vary the force driving DNA exit. An unanswered question in the field is whether frictional forces restricting the movement of the tightly packed DNA ar e pr edominantly due to hydrodynamic drag or some type of DN A-DN A sliding friction. For hydrodynamic drag, a linear relationship between velocity and force, v = μF , was predicted, where μ is a mobility constant. This relationship was used to interpret the phage lambda ejection data, but this model has not been tested experimentally. To test this, we repeated DNA exit measurements with a significantly higher applied pulling force of ∼20 pN (Supplementary Figure S8).
We observe qualitatively similar exit dynamics as with 5 pN pulling force, but the mean velocity is higher across the whole range of capsid fillings (Figure 3 A). Velocities measured for individual complex es ar e shown in Supplementary Figure S2C, again showing significant heterogeneity, and the frequency and aver age dur ation of pauses ar e decr eased ( Figure 3 C and D). A notable finding is that the relationship between exit velocity and total driving force [sum of the internal force and applied pulling force ( 20 , 24 )] is not linear as predicted by hydrodynamic drag models. This is shown in Figur e 3 B, wher e the ratios of the e xit v elocities and ratios of total driving forces with the high and low applied forces ar e compar ed. The magnitude of the friction for ce opposing DNA exit is equal to the total driving force since the molecular motion is ov er damped on the timescale of measurement. The ratio of the velocities is notably higher than the ratio of forces across the measured range of filling levels (Figure 3 B), which shows that the relationship v = μF does not hold.

DISCUSSION
DNA ejection through the ∼3-4 nm diameter portal channel ( 65 ) in the viral shell is dri v en by the internal forces resisting tight confinement of the charged biopolymer that build up during packaging. The dynamics of ejection, howe v er, depend on friction forces that resist DNA exit. The nature of this friction has been considered in some theoretical models, but experimental data have not been available to investigate this.
In one influential early model, Gabashvili and Grosberg considered that the main source of the friction could be hydrodynamic drag acting on the DNA inside the capsid ( 33 ). They proposed that, due to the high-density packing, DNA segments might undergo a reptation-like motion during ejection, akin to that of entangled polymers in concentrated solutions. Entanglements restrict a polymer to move primarily in a fluid-filled tube-like volume parallel to its own contour. The viral DNA is envisioned to behave as a selfentangled polymer and to experience hydrodynamic drag force proportional to e xit v elocity v, such that F = v/μ, where μ is a mobility factor. Applying classical continuum fluid mechanics, μ was predicted to increase as the DNA packing density decreases because the confining tube diam-eter would incr ease, r esulting in decr eased hydrodynamic shear forces ( 33 ). This model could thus explain a trend of initially increasing DNA exit velocity (provided that the internal force does not decrease too ra pidl y as the DNA ejects). Howe v er, the assumption that the friction force at each capsid filling le v el is proportional to DNA exit velocity is inconsistent with our findings (Figure 3 B). Moreover, the predicted hydrodynamic drag forces are much smaller than those we detect. For example, when ejecting at 93% capsid filling, we detect a friction force of ∼20 pN at a mean exit velocity of ∼300 bp / s, which is much higher than the ∼0.01 pN predicted by the hydrodynamic model for this velocity (see Supplementary Data).
Other r esear chers have proposed that sliding friction between adjacent, tightly packed DNA segments may be important. Odijk considered the possibility of simple Coulomb (macroscopic solid-like) sliding friction ( 34 ). The friction force depends on normal forces that press adjacent segments together, proposed to be proportional to internal force. Since these internal for ces decr ease as ejection proceeds, this model could also explain a trend of increasing velocity as ejection proceeds. A similar idea was explored by Ghosal ( 35 ), who modeled DNA as a semifle xib le elastic rod initially arranged in an inverse spool and subject to Coulomb sliding friction. Howe v er, the friction force assumed in these models is, at each capsid filling le v el, independent of DNA exit velocity, which is inconsistent with our findings (Figure 3 B).
Rather, our measurements provide evidence that DNA exit is controlled by a type of nanoscale biopolymer sliding friction described recently. Ward et al. used macromolecular cro w ding to press two actin filaments together and measured the force required to slide one past the other ( 66 ). The friction force was found to increase lo garithmicall y with velocity. This finding was shown to agree with the predictions of a Frenk el-Kontoro va-type model for nanoscale friction that accounts for effects of the periodic atomic-scale 'bumpiness' of individual polymers and the role of thermal fluctuations. The model predicts that friction force follows known as the Prandtl-Tomlinson r elationship, wher e μ is an effecti v e mobility factor, kT is the thermal energy and d is the spacing between monomers in the biopolymer ( 66 ). This was shown to fit the actin data with d = 5 nm set equal to the monomer spacing for F-actin filaments. Our measurements provide evidence that an analogous type of DN A-DN A sliding friction acts during the initial stages of slow DNA exit. The ratios of e xit v elocities we measure with high and low externally applied forces agree with the predictions of the Prandtl-Tomlinson relationship with a d value consistent with the 0.34 nm monomer spacing (per bp) of dsDNA over the whole range of filling le v els where the velocity is exponentially increasing (Figure 3 B). Fits of the data to Equation ( 1 ) yield an average d = 0.33 ± 0.06 nm. This sliding friction likely contributes to the very long timescale for DNA reorganization we observed in previous studies in which packaging complex es wer e stalled at ∼75% filling le v el ( 59 ). As ejection proceeds to lower filling le v els and the average spacing between DNA segments increases, a crossover to a regime where the friction is dominated by hydrodynamic drag is expected ( 27,28 , 63 ). Howe v er, as discussed abov e, at this point the e xit v elocity is so fast that it has a negligible effect on the overall kinetics.
Our findings further allow us to consider whether DNA-DNA sliding friction has any significant effect on motordri v en DNA packaging. Since the friction is mainly dependent on the spacing between adjacent segments of dsDNA, we expect that at equivalent capsid filling le v els the nature of the friction will be similar during ejection and packaging.
Howe v er, since packaging is much slower than ejection, the Prandtl-Tomlinson relationship implies much lower friction forces during packaging. Our measurements find that the average DNA translocation velocity during packaging, at room temperature and with saturating ATP, decreases from 55 to 11 bp / s as the filling increases from 80% to 100%. At these velocities, the Prandtl-Tomlinson relationship predicts friction forces < 0.1 pN (see Supplementary Data), which are negligible compared to the internal forces resisting packaging ( ∼5-30 pN).
We note that if the phi29 motor were translocating at the maximum value of ∼160 bp / s and did not slow with capsid filling as observed ( 16 , 20 , 24 ), then the predicted friction forces would be significant ( ∼25 pN). The downregula tion of transloca tion velocity a t high filling le v els may be a feature that was favored by evolutionary pr essur e as it reduces friction forces that could otherwise increase the chance of motor stalling. On the other hand, the lambda and T4 motors tr anslocate consider ably faster than phi29 (up to ∼10 × faster in the case of T4) ( 17 , 18 ), so it is possible that DNA sliding friction could play a role in those systems.
DNA ejections from phages T5 and lambda, which pack DNA to similar density as phi29, were studied using fluorescentl y labeled DN A. Mangenot et al . de v eloped a method in which T5 phages were attached to a surface, ejection was triggered with purified host cell membrane protein, and the exiting DNA was stretched in a flow and imaged by fluor escence microscop y ( 12 ). Mor e detailed studies wer e conducted by Chiaruttini et al . ( 29 ), and the method was extended to study phage lambda by Grayson et al . ( 27 ) and Wu et al . ( 28 ).
For phage lambda, Grayson et al . reported initial average ejection velocities of ∼25 000 bp / s increasing to ∼30 000 bp / s at 80% filling ( 27 ). Using a lower dye concentration, Wu et al. measured ∼3000 bp / s at 85% filling, rising to ∼6000 bp / s at 80% filling ( 28 ). In both cases, the velocity initially increased approximately linearly with decreasing filling le v el. In contrast, in a similar ionic condition, for phi29 with unlabeled DNA we measure a much lower initial average velocity of ∼200 bp / s at ∼100% filling and a much sharper, exponential increase in the velocity to ∼2000 bp / s at 80% filling. Wu et al . also studied the dependence of lambda ejection on ionic screening and observed that it slows with increased screening, attributed to decreased internal force due to reduced electrostatic DN A-DN A repulsion ( 28 ). Although our velocities are systematically lower and dependence on filling le v el is different, we observed a similar trend of decreased velocity with increased ionic screening.
For phage T5, Chiaruttini et al . reported much higher DNA e xit v elocities than we observe for phi29 with unlabeled DNA: ∼7000 bp / s at 100% filling ( 29 ), which is ∼35fold higher than we measure in a similar ionic condition. Their velocity figure also averaged in pauses, which implies e v en higher transient velocities. They also observed a less than linear increase in velocity from 100% to 80% filling, compared to the much sharper (exponential) increase we observe.
We observe frequent pausing that dominates the overall DNA exit kinetics. While pausing was also observed in the T5 studies ( 12 , 29 , 31 ), the character of the pausing we observe is quite different. The pauses we observe occur stochastically with a frequency and dura tion tha t decreases with decreasing filling le v el, whereas those reported for T5 occurred mainly around a few specific filling levels (94 ± 1%, 88 ± 4% and 60 ± 12%). It was suggested that those pauses might be caused by liquid crystal phase transitions of the DNA, a proposal guided by electron microscopy studies of partly ejected T5 phages that found evidence for partial ordering of the DNA in liquid crystal-like phases ( 31 ).
Howe v er, it is unclear whether this explains the pauses since they did not occur at the same density le v els as the phase transitions.
The large differences in DNA exit dynamics we measure compared with those reported in the T5 and lambda studies are surprising since these phages all pack DNA to similarly high densities. Recent X-ray scattering studies that probe the spacings between packed DNA segments in phage particles suggest that the packing density is only slightly higher in phi29 (615 ± 50 mg / ml versus 540 ± 20 mg / ml for T5 and 525 ± 20 mg / ml for lambda), where the differences are not much larger than the uncertainties in the measurements ( 67 ). Other differences are that lambda and T5 have genome and capsid sizes that are ∼2.5-fold and ∼6-fold larger than phi29, respecti v ely, and hav e isometric (spherically symmetric) capsids, whereas phi29 is prolate (slightly elonga ted). These dif ferences would make the DNA bending energy per unit length higher for phi29, which would increase the internal force. Howe v er, this difference would be expected to cause the DNA exit velocity to be higher rather than lower.
Another difference is that our method does not r equir e the DNA to be labeled with dye. Studies with phage T5 found that the ejection dynamics is affected by the concentra tion of d ye used to label the DN A ( 31 ). This likel y occurs due to changes in the physical properties of DNA such as contour length, bending rigidity and net charge caused by dye binding ( 68 , 69 ). The studies of sliding friction between actin filaments also showed that the sliding friction is sensiti v e to perturbations to the biopolymer structure ( 66 ). Changes in DNA structure caused by dye binding might ther efor e affect ejection dynamics by altering DN A-DN A sliding friction.
There have been a wide variety of theoretical studies of DNA ejection: we identified 48 published studies, including analytical models and simulations (see r efer ences in Supplementary Data for a full list). Above we discussed three analytical models that proposed explicit models for friction during ejection but showed that these are inconsistent with our findings. Most of the other analytical studies have focused on predicting energetics of ejection and / or scaling laws for ejection time. Se v eral considered ejection dynamics but predict only monotonically decreasing velocity, attributed to decreasing driving force as ejection proceeds ( 42 , 46-48 ). Only one of these studies, by Wang et al. ( 49 ), predicts an initially increasing velocity. This study modifies the hydrodynamic model ( 33 ) by adding a compressi v e osmotic force that increases drag force per length of the confined DNA. Howe v er, it again predicts a much smaller friction force ( ∼0.4 pN) than we measure. Notably, all of these models assume that sliding friction between adjacent segments of dsDNA is negligible compared to hydrodynamic forces.
Many simulation studies have also been conducted, all using coarse-grained bead-spring pol ymer DN A models. Unlike in analytical models where DNA-DNA sliding friction would need to be explicitl y included, sim ulations have the potential to account for such friction via steric interactions betw een beads. How e v er, it has remained unclear to what extent these models correctly predict features of the ejection dynamics. We identified 10 studies (36)(37)(38)(39)(40)(41)(42)(43)(44)(45) that make predictions that can be directly compared to our findings, summarized in Supplementary Tables S1 and S2. Some of these studies predict features in accord with our findings at a qualitati v e le v el (Supplementary Tab le S2). First, se v eral predict large variations in the dynamics between individual ejection e v ents and link this to variability in initial DNA conformations ( 37,38 , 43-45 ). Second, three studies predict an initially increasing v elocity ( 36 , 38,39 ). Thir d, se v eral predict stochastic pausing ( 36-39 , 43-45 ). The nature of the stochastic pausing we observe is much closer in character to that predicted by these simulation studies than the pausing observed in the phage T5 studies with dye-labeled DNA, where pauses were mainly observed at specific capsid filling le v els.
Howe v er, at a quantitati v e le v el we do not find good agreement with most of the predictions (Supplementary Table S2). First, almost all the simulation studies predict ejection v elocities or ders of magnitude higher than we measure, e v en after considering predicted scaling laws for the dependence of ejection timescales on DNA length / thickness, initial packing density and viscosity (see Supplementary Data for a discussion). Second, although three studies predict initially increasing velocity, none predict an exponentially incr easing tr end with decr easing packing density like that we observ e. Thir d, although se v eral studies predict pausing, detailed pausing statistics were not reported and predicted pause durations are generally much shorter than we observe (both on an absolute scale and relati v e to ov erall ejection time; Supplementary Table S2). Comparing across all the simulation studies, we do not observe any clear trend suggesting that particular simulation methods or model assumptions result in better agreement with our results (e.g. stochastic rotation dynamics versus Langevin dynamics , different interaction potentials , different initial packing densities and DNA conformations, etc.; Supplementary Tables S1 and S2). One simulation study, by Matsuyama and Yano ( 39 ), does predict both an initially increasing velocity and velocity magnitudes on the same order as those we measure after a ppl ying predicted scaling laws (for this com-parison, the model parameters r equir ed significant extrapola tion to ma tch those of phi29; Supplementary Table S2).
Howe v er, this study assumes an intermediate-distance attracti v e interaction between monomers, which is inconsistent with experimental studies of DN A-DN A interaction forces in our ionic conditions ( 60 , 64 ). The ejection force was also predicted to be independent of packing density, which is inconsistent with experimental studies of phages phi29 and lambda ( 11 , 24 , 26 , 58 ).
Various factors likely contribute to the disagreement between simulation studies and our experimental findings. Many studies modeled DN A lengths / ca psid sizes m uch smaller than phi29 and some modeled polymer properties different from those of DNA (Supplementary Table S1). The predicted scaling laws used to extrapolate these predictions for comparison have not yet been experimentally verified. More importantly, our evidence for DNA-DNA sliding friction suggests that coarse-grained simulation studies lik ely w ould not accurately model such friction since they do not model specific nanoscale structural features and electrostatic interactions of DNA. Since we find that the initial exit velocity is exponentially dependent on packing density, another issue is that most simulation studies assumed lower initial packing densities than that inferred by the latest X-ray studies on phage phi29 (Supplementary Tab le S1) ( 67 ). Moreov er, Mahalik et al. sim ulated DN A packaging prior to ejection using driving forces ∼2-fold larger than the experimentally determined internal force in phi29, yet predicted a ∼2-fold lower maximum packing density ( 45 ). This raises a question of whether packing densities in coarse-grained simulation models can be accurately related to those in experiments.
Since systems with sliding friction sometimes exhibit 'slip-stick' dynamics ( 70 , 71 ), we considered whether this could explain the pausing we observe during DNA exit. Within the Frenk el-Kontoro va model, stick-slip dynamics can occur if the interaction potential is sufficiently large compared to the thermal energy and work done by driving forces. In this case, the distance between pauses during ejection would be predicted to be on the scale of the periodicity of the interaction potential, or ∼0.34 nm for DNA, and the pause durations exponentially distributed. The pauses we observ e, howe v er, hav e much larger distances between them ( ∼10-100 bp; Figure 4 A) and their durations are not exponentially distributed (Figure 4 B). Thus, our results do not support slip-stick friction as a mechanism for pausing.
A second possibility to consider is that pauses might be caused by knots in the DNA that impede DNA exit. It has been found that DNA extracted from phages P2 / P4 is frequently knotted and some simulation studies have also predicted that DNA can become knotted during motordri v en pha ge DNA packa ging ( 44 , 72-74 ). It is also notable that some experimental and simulation studies of the electrophoretic translocation of DNA through nanochannels found evidence that knots can cause pauses (75)(76)(77). One featur e pr edicted by simulations, howe v er, is that increased driving force increases pausing ( 75,76 , 78 ), whereas we find that increased force decreases pausing. Some simulation studies of viral DNA ejection have also specifically investigated the effect of knots ( 44 , 79 , 80 ). These predicted that knots could slow down ejection but did not conclude that they would tend to cause pauses. A caveat of these simulations, as we discussed above, is that none make predictions in quantitati v e agr eement with our findings. Ther efor e, although it is possible that knots could cause pauses during ejection, it seems that additional studies would be needed to further investigate this question.
Another possib le e xplanation we propose, which is consistent with se v eral fea tures of the d ynamics we observe, is that the pausing may be related to a phenomenon in soft matter physics termed 'clogging' (81)(82)(83)(84)(85)(86). This occurs when nonequilibrium materials such as colloid solutions or granular materials are forced to flow through a constriction. Clogging e v ents that temporarily arrest the flow occur due to spontaneous formation of metastable arrangements of particles. One example is in gravity-driven flow of agitated granular material through a hopper, where particles spontaneously form arch-like structures that span the constriction and block the flow until external agitation breaks them apart (81)(82)(83). Another example is in flowing colloid solutions, where Brownian fluctuations play a role in driving clo gging / unclo gging e v ents ( 84 , 85 ). Clogging e v ents hav e varying durations and occur over a wide range of particle densities for a gi v en set of system parameters (e.g. particle and constriction size ra tio, agita tion intensity, driving force, etc.).
Here, we envision that the 'particles' that clog are short DNA segments that approximately behave as independent particles on scales much larger than the persistence length ( P ∼ = 150 bp). Studies of clogging also find that its probability increases when there is greater friction between the particles ( 83 , 86 ). Thus, the DN A-DN A sliding friction we find evidence for would promote clogging. A full investigation of the potential connection between pausing and the phenomenon of clogging would r equir e determining the arrangements of DNA segments in individual complexes that cause pausing e v ents, w hich is not currentl y possible. Howe v er, improv ed simulation studies guided by our present findings could shed light on DNA conformations that cause pausing. Here, we provide evidence that the statistical properties of the pausing are consistent with clogging.
Experimental and theoretical studies of a wide variety of soft matter systems that exhibit clogging find that the amounts of material that flow between clogging e v ents follow an exponential distribution, consistent with onset of clogging being a Poisson process, while distributions of clog durations have power-law tails ( 83 , 87-91 ). The pauses we measure have similar features. First, the distribution of lengths of DNA that exit between pauses at high filling follows an exponential distribution (Figure 4 A). Second, the distribution of pause durations (Figure 4 B) is not exponential but has a power-law tail. Third, the fitted power-law exponent of 2.3 falls in the range of those measured for other soft matter systems that exhibit clogging ( 81,82 , 87-89 ). Fourth, increasing the pulling force or decreasing the ionic screening decreases the average lifetime of pauses, which is consistent with studies showing that clogging e v ents decrease in duration when the dri ving force is increased ( 87 , 92 ). Fifth, the pausing frequency increases at high filling le v els, consistent with studies showing that the probability of clogging increases with increasing particle density ( 91 , 93 ).

CONCLUSIONS
In summary, we introduce a method for probing the mobility of the tightly packed DNA in viral capsids and shed light on the nature of the friction forces that limit the speed of DNA exit. The initial exit velocity for phi29 is much lower than those reported for other phages using dye-labeled DNA and those predicted by theory / simulation studies. We provide evidence that the kinetics of ejection are dominated by DN A-DN A sliding friction during the initial 20% of DNA exit and by stochastic pauses that are different in character from those observed previously with phage T5 and different from those predicted in simulation studies. We present evidence suggesting that the pausing is connected to the phenomenon of 'clogging' observed in nonequilibrium soft matter systems.

DA T A A V AILABILITY
All data presented in this manuscript can be made available upon reasonable request to the corresponding author.

SUPPLEMENT ARY DA T A
Supplementary Data are available at NAR Online.