Polymer packaging and ejection in viral capsids: shape matters

Effects of self-avoidance on the packing of stiff rods on ellipsoids

Using a statistical-mechanics approach, we study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. Within a mean-field approximation, we show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. We find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. We compute the critical surface describing the transition between azimuthal and polar ordering in the three-dimensional parameter space (persistence length, eccentricity, and self-avoidance) and show that the critical behavior of this system is in fact related to the butterfly catastrophe model. We calculate the pressure and shear stress applied by the filament on the surface, and the injection force needed to be applied on the filament in order to insert it into the volume. We compare these results to the pure mechanical study where self-avoidance is ignored, and discuss similarities and differences.

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

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.

Compression of a confined semiflexible polymer under direct and oscillating fields

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Role of DNA-DNA sliding friction and non-equilibrium dynamics in viral genome ejection and packaging

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 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.

Influence of solvent quality on depletion potentials in colloid-polymer mixtures

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments sensitively depend on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here, we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard-sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

Smart and Active Food Packaging: Insights in Novel Food Packaging

The demand for more healthy foods with longer shelf life has been growing. Food packaging as one of the main aspects of food industries plays a vital role in meeting this demand. Integration of nanotechnology with food packaging systems (FPSs) revealed promising promotion in foods’ shelf life by introducing novel FPSs. In this paper, common classification, functionalities, employed nanotechnologies, and the used biomaterials are discussed. According to our survey, FPSs are classified as active food packaging (AFP) and smart food packaging (SFP) systems. The functionality of both systems was manipulated by employing nanotechnologies, such as metal nanoparticles and nanoemulsions, and appropriate biomaterials like synthetic polymers and biomass-derived biomaterials. “Degradability and antibacterial” and “Indicating and scavenging” are the well-known functions for AFP and SFP, respectively. The main purpose is to make a multifunctional FPS to increase foods’ shelf life and produce environmentally friendly and smart packaging without any hazard to human life.

Scaling relation between genome length and particle size of viruses provides insights into viral life history

In terms of genome and particle sizes, viruses exhibit great diversity. With the discovery of several nucleocytoplasmic large DNA viruses (NCLDVs) and jumbo phages, the relationship between particle and genome sizes has emerged as an important criterion for understanding virus evolution. We use allometric scaling of capsid volume with the genome length of different groups of viruses to shed light on its relationship with virus life history. The allometric exponents for icosahedral dsDNA bacteriophages and NCDLVs were found to be 1 and 2, respectively, indicating that with increasing capsid size DNA packaging density remains the same in bacteriophages but decreases for NCLDVs. We argue that the exponents are largely shaped by their entry mechanism and capsid mechanical stability. We further show that these allometric size parameters are also intricately linked to the relative energy costs of translation and replication in viruses and can have further implications on viral life history.

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Capsid and genome size allometric exponent gives insights into viral life history

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The allometric exponent of NCLDVs is almost twice that of bacteriophages

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The exponent is largely shaped by the viral entry mechanism and capsid stability

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The relaxed genome size constraint allows large viruses to evolve greater autonomy

Packing of stiff rods on ellipsoids: Geometry

We suggest a geometrical mechanism for the ordering of slender filaments inside nonisotropic containers, using cortical microtubules in plant cells and the packing of viral genetic material inside capsids as concrete examples. We show analytically how the shape of the cell affects the ordering of phantom elastic rods that are not self-avoiding (i.e., self-crossing is allowed). We find that for oblate cells, the preferred orientation is along the equator, while for prolate spheroids with an aspect ratio close to 1, the orientation is along the principal (long axis). Surprisingly, at a high enough aspect ratio, a configurational phase transition occurs and the rods no longer point along the principal axis, but at an angle to it, due to high curvature at the poles. We discuss some of the possible effects of self-avoidance using energy considerations. These results are relevant to other packing problems as well, such as the spooling of filament in the industry or spider silk inside water droplets.

Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space

A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as mz1/(Nx1D3z1) at the confined stage, and it turns to be m−z2 at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be z1=(3ν−1)−1, z2=2ν and x1=1/3, with ν being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and ϕ0 (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.

Effects of Model Shape, Volume, and Softness of the Capsid for DNA Packaging of phi29

Double-stranded DNA is under extreme confinement when packed in phage phi29 with osmotic pressures approaching 60 atm and densities near liquid crystalline. The shape of the capsid determined from experiment is elongated. We consider the effects of the capsid shape and volume on the DNA distribution. We propose simple models for the capsid of phage phi29 to capture volume, shape, and wall flexibility, leading to an accurate DNA density profile. The effect of the packaging motor twisting the DNA on the resulting density distribution has been explored. We find packing motor induced twisting leads to a greater numbers of defects formed. The emergence of defects such as bubbles or large roll angles along the DNA shows a sequence dependence, and the resulting flexibility leads to an inhomogeneous distribution of defects occurring more often at TpA steps and AT-rich regions. In conjunction with capsid elongation, this has effects on the global DNA packing structures.

Function of a viral genome packaging motor from bacteriophage T4 is insensitive to DNA sequence

Many viruses employ ATP-powered motors during assembly to translocate DNA into procapsid shells. Previous reports raise the question if motor function is modulated by substrate DNA sequence: (i) the phage T4 motor exhibits large translocation rate fluctuations and pauses and slips; (ii) evidence suggests that the phage phi29 motor contacts DNA bases during translocation; and (iii) one theoretical model, the 'B-A scrunchworm', predicts that 'A-philic' sequences that transition more easily to A-form would alter motor function. Here, we use single-molecule optical tweezers measurements to compare translocation of phage, plasmid, and synthetic A-philic, GC rich sequences by the T4 motor. We observed no significant differences in motor velocities, even with A-philic sequences predicted to show higher translocation rate at high applied force. We also observed no significant changes in motor pausing and only modest changes in slipping. To more generally test for sequence dependence, we conducted correlation analyses across pairs of packaging events. No significant correlations in packaging rate, pausing or slipping versus sequence position were detected across repeated measurements with several different DNA sequences. These studies suggest that viral genome packaging is insensitive to DNA sequence and fluctuations in packaging motor velocity, pausing and slipping are primarily stochastic temporal events.

Structure and the role of filling rate on model dsDNA packed in a phage capsid

The conformation of DNA inside bacteriophages is of paramount importance for understanding packaging and ejection mechanisms. Models describing the structure of the confined macromolecule have depicted highly ordered conformations, such as spooled or toroidal arrangements that focus on reproducing experimental results obtained by averaging over thousands of configurations. However, it has been seen that more disordered states, including DNA kinking and the presence of domains with different DNA orientation can also accurately reproduce many of the structural experiments. In this work we have compared the results obtained through different simulated filling rates. We find a rate dependence for the resulting constrained states showing different anisotropic configurations. We present a quantitative analysis of the density distribution and the DNA orientation across the capsid showing excellent agreement with structural experiments. Second, we have analyzed the correlations within the capsid, finding evidence of the presence of domains characterized by aligned segments of DNA characterized by the structure factor. Finally, we have measured the number and distribution of DNA defects such as the emergence of bubbles and kinks as function of the filling rate. We find the slower the rate the fewer kink defects that appear and they would be unlikely at experimental filling rates with our model parameters. DNA domains of various orientation get larger with slower rates.

Packing of semiflexible polymers into viral capsid in crowded environments

We use coarse-grained Langevin dynamics simulations to study packing of semiflexible polymers into a spherical capsid, with and without a tail, inside a crowded cell. We use neutral and charged, but highly screened, polymers and compare packing rates of the two. Such packing conditions are relevant, for example, to λ DNA packing inside Escherichia coli bacterial cells, where the crowd particles are proteins, bacterial DNA, and salts. For a neutral polymer packing into a capsid with a tail, attractive interactions with the crowd particles make packing slightly harder at higher crowd densities, but repulsive interactions make it easier. Our results indicate that packing into a tailless capsid is less efficient at low crowd densities than into one with a long tail. However, this trend becomes opposite at higher densities. In addition, packing into a capsid with a long tail shows a highly variable waiting time before packing initiates, a feature absent for a tailless capsid. Electrical interactions at physiological conditions do not have much effect. Some bacterial cells, such as Pseudomonas chlororaphis, form a nucleuslike structure encapsulating the phage 201ϕ2-1 DNA. We also study here the packing dynamics with the nucleus present. We find packing is faster compared to the case of no-nucleus packing. We also observe knot formations but these knots untangle quickly while the polymer translocates. This knot formation is independent of polymer charge and presence of crowd particles.

Polymer translocation into cavities: Effects of confinement geometry, crowding, and bending rigidity on the free energy

Monte Carlo simulations are used to study the translocation of a polymer into a cavity. Modeling the polymer as a hard-sphere chain with a length up to N=601 monomers, we use a multiple-histogram method to measure the variation of the conformational free energy of the polymer with respect to the number of translocated monomers. The resulting free-energy functions are then used to obtain the confinement free energy for the translocated portion of the polymer. We characterize the confinement free energy for a flexible polymer in cavities with constant cross-sectional area A for various cavity shapes (cylindrical, rectangular, and triangular) as well as for tapered cavities with pyramidal and conical shape. The scaling of the free energy with cavity volume and translocated polymer subchain length is generally consistent with predictions from simple scaling arguments, with small deviations in the scaling exponents likely due to finite-size effects. The confinement free energy depends strongly on cavity shape anisometry and is a minimum for an isometric cavity shape with a length-to-width ratio of unity. Entropic depletion at the edges or vertices of the confining cavity are evident in the results for constant-A and pyramidal cavities. For translocation into infinitely long cones, the scaling of the free energy with taper angle is consistent with a theoretical prediction employing the blob model. We also examine the effects of polymer bending rigidity on the translocation free energy for cylindrical cavities. For isometric cavities, the observed scaling behavior is in partial agreement with theoretical predictions, with discrepancies arising from finite-size effects that prevent the emergence of well-defined scaling regimes. In addition, translocation into highly anisometric cylindrical cavities leads to a multistage folding process for stiff polymers. Finally, we examine the effects of crowding agents inside the cavity. We find that the confinement free energy increases with crowder density. At constant packing fraction the magnitude of this effect lessens with increasing crowder size for a crowder-to-monomer size ratio ≥1.

The breakdown of the local thermal equilibrium approximation for a polymer chain during packaging

The conformational relaxation of a polymer chain often slows down in various biological and engineering processes. The polymer, then, may stay in nonequilibrium states throughout the process such that one may not invoke the local thermal equilibrium (LTE) approximation, which has been usually employed to describe the kinetics of various processes. In this work, motivated by recent single-molecule experiments on DNA packaging into a viral capsid, we investigate how the nonequilibrium conformations and the LTE approximation would affect the packaging of a polymer chain into small confinement. We employ a simple but generic coarse-grained model and Langevin dynamics simulations to investigate the packaging kinetics. The polymer segments (both inside and outside the confinement) stay away from equilibrium under strong external force. We devise a simulation scheme to invoke the LTE approximation during packaging and find that the relaxation of nonequilibrium conformations plays a critical role in regulating the packaging rate.

Slow and steady wins the race: physical limits on the rate of viral DNA packaging

During the assembly of dsDNA viruses such as the tailed bacteriophages and herpesviruses, the viral chromosome is compacted to near crystalline density inside a preformed head shell. DNA translocation is driven by powerful ring ATPase motors that couple ATP binding, hydrolysis, and release to force generation and movement. Studies of the motor of the bacteriophage phi29 have revealed a complex mechanochemistry behind this process that slows as the head fills. Recent studies of the physical behavior of packaging DNA suggest that surprisingly long-time scales of relaxation of DNA inside the head and jamming phenomena during packaging create the physical need for regulation of the rate of packaging. Studies of DNA packaging in viral systems have, therefore, revealed fundamental insight into the complex behavior of DNA and the need for biological systems to accommodate these physical constraints.

Self-assembly of semiflexible polymers confined to thin spherical shells

Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to elucidate the nature of orientational ordering in different parameter regimes. Previous simulations have revealed the emergence of bipolar and quadrupolar topological defects on the surface when the entire cavity was filled with a concentrated polymer solution [Phys. Rev. Lett., 2017, 118, 217803]. In contrast, spherical shell confinement restricts the appearance of a bipolar order. Instead, only the extent of the quadrupolar order changes with chain stiffness, as evidenced by the relative motion of topological defects. In the case of monolayers, we observe a nematic to smectic transition accompanied by a change in the nematic grain-size distribution as the contour length was decreased.

Rigidity-induced scale invariance in polymer ejection from capsid

While the dynamics of a fully flexible polymer ejecting a capsid through a nanopore has been extensively studied, the ejection dynamics of semiflexible polymers has not been properly characterized. Here we report results from simulations of ejection dynamics of semiflexible polymers ejecting from spherical capsids. Ejections start from strongly confined polymer conformations of constant initial monomer density. We find that, unlike for fully flexible polymers, for semiflexible polymers the force measured at the pore does not show a direct relation to the instantaneous ejection velocity. The cumulative waiting time t(s), that is, the time at which a monomer s exits the capsid the last time, shows a clear change when increasing the polymer rigidity κ. The major part of an ejecting polymer is driven out of the capsid by internal pressure. At the final stage the polymer escapes the capsid by diffusion. For the driven part there is a crossover from essentially exponential growth of t with s of the fully flexible polymers to a scale-invariant form. In addition, a clear dependence of t on polymer length N_{0} was found. These findings combined give the dependence t(s)∝N_{0}^{0.55}s^{1.33} for the strongly rigid polymers. This crossover in dynamics where κ acts as a control parameter is reminiscent of a phase transition. This analogy is further enhanced by our finding a perfect data collapse of t for polymers of different N_{0} and any constant κ.

Compaction of quasi-one-dimensional elastoplastic materials

Insight into crumpling or compaction of one-dimensional objects is important for understanding biopolymer packaging and designing innovative technological devices. By compacting various types of wires in rigid confinements and characterizing the morphology of the resulting crumpled structures, here, we report how friction, plasticity and torsion enhance disorder, leading to a transition from coiled to folded morphologies. In the latter case, where folding dominates the crumpling process, we find that reducing the relative wire thickness counter-intuitively causes the maximum packing density to decrease. The segment size distribution gradually becomes more asymmetric during compaction, reflecting an increase of spatial correlations. We introduce a self-avoiding random walk model and verify that the cumulative injected wire length follows a universal dependence on segment size, allowing for the prediction of the efficiency of compaction as a function of material properties, container size and injection force.

Principles underlying crumpling of one-dimensional objects may be relevant to both biomolecular processes and to design of mechanical devices. By compacting various wires under rigid confinement and modelling observed geometric features, the authors show how friction, plasticity and torsion enhance disorder and lead to a transition from coiled to folded geometries.

Experimental comparison of forces resisting viral DNA packaging and driving DNA ejection

We compare forces resisting DNA packaging and forces driving DNA ejection in bacteriophage phi29 with theoretical predictions. Ejection of DNA from prohead-motor complexes is triggered by heating complexes after in vitro packaging and force is inferred from the suppression of ejection by applied osmotic pressure. Ejection force from 0% to 80% filling is found to be in quantitative agreement with predictions of a continuum mechanics model that assumes a repulsive DNA-DNA interaction potential based on DNA condensation studies and predicts an inverse-spool conformation. Force resisting DNA packaging from ∼80% to 100% filling inferred from optical tweezers studies is also consistent with the predictions of this model. The striking agreement with these two different measurements suggests that the overall energetics of DNA packaging is well described by the model. However, since electron microscopy studies of phi29 do not reveal a spool conformation, our findings suggest that the spool model overestimates the role of bending rigidity and underestimates the role of intrastrand repulsion. Below ∼80% filling the inferred forces resisting packaging are unexpectedly lower than the inferred ejection forces, suggesting that in this filling range the forces are less accurately determined or strongly temperature dependent.

Uniform description of polymer ejection dynamics from capsid with and without hydrodynamics

We use stochastic rotation dynamics (SRD) to examine the dynamics of the ejection of an initially strongly confined flexible polymer from a spherical capsid with and without hydrodynamics. The results obtained using stochastic rotation dynamics (SRD) are compared to similar Langevin simulations. Inclusion of hydrodynamic modes speeds up the ejection but also allows the part of the polymer outside the capsid to expand closer to equilibrium. This shows as higher values of radius of gyration when hydrodynamics are enabled. By examining the waiting times of individual polymer beads, we find that the waiting time t_{w} grows with the number of ejected monomers s as a sum of two exponents. When ≈63% of the polymer has ejected, the ejection enters the regime of slower dynamics. The functional form of t_{w} versus s is universal for all ejection processes starting from the same initial monomer densities. Inclusion of hydrodynamics only reduces its magnitude. Consequently, we define a universal scaling function h such that the cumulative waiting time t=N_{0}h(s/N_{0}) for large N_{0}. Our unprecedentedly precise measurements of force indicate that this form for t_{w}(s) originates from the corresponding force toward the pore decreasing superexponentially at the end of the ejection. Our measured t_{w}(s) explains the apparent superlinear scaling of the ejection time with the polymer length for short polymers. However, for asymptotically long polymers, t_{w}(s) predicts linear scaling.

A Molecular View of the Dynamics of dsDNA Packing Inside Viral Capsids in the Presence of Ions

Genome packing in viruses and prokaryotes relies on positively charged ions to reduce electrostatic repulsions, and induce attractions that can facilitate DNA condensation. Here we present molecular dynamics simulations spanning several microseconds of dsDNA packing inside nanometer-sized viral capsids. We use a detailed molecular model of DNA that accounts for molecular structure, basepairing, and explicit counterions. The size and shape of the capsids studied here are based on the 30-nanometer-diameter gene transfer agents of bacterium Rhodobacter capsulatus that transfer random 4.5-kbp (1.5 μm) DNA segments between bacterial cells. Multivalent cations such as spermidine and magnesium induce attraction between packaged DNA sites that can lead to DNA condensation. At high concentrations of spermidine, this condensation significantly increases the shear stresses on the packaged DNA while also reducing the pressure inside the capsid. These effects result in an increase in the packing velocity and the total amount of DNA that can be packaged inside the nanometer-sized capsids. In the simulation results presented here, high concentrations of spermidine³⁺ did not produce the premature stalling observed in experiments. However, a small increase in the heterogeneity of packing velocities was observed in the systems with magnesium and spermidine ions compared to the system with only salt. The results presented here indicate that the effect of multivalent cations and of spermidine, in particular, on the dynamics of DNA packing, increases with decreasing packing velocities.

Flow-induced polymer translocation through a nanopore from a confining nanotube

We study the flow-induced polymer translocation through a nanopore from a confining nanotube, using a hybrid simulation method that couples point particles into a fluctuating lattice-Boltzmann fluid. Our simulation illustrates that the critical velocity flux of the polymer linearly decreases with the decrease in the size of the confining nanotube, which corresponds well with our theoretical analysis based on the blob model of the polymer translocation. Moreover, by decreasing the size of the confining nanotube, we find a significantly favorable capture of the polymer near its ends, as well as a longer translocation time. Our results provide the computational and theoretical support for the development of nanotechnologies based on the ultrafiltration and the single-molecule sequencing.

DNA packaging in viral capsids with peptide arms

Strong chain rigidity and electrostatic self-repulsion of packed double-stranded DNA in viruses require a molecular motor to pull the DNA into the capsid. However, what is the role of electrostatic interactions between different charged components in the packaging process? Though various theories and computer simulation models were developed for the understanding of viral assembly and packaging dynamics of the genome, long-range electrostatic interactions and capsid structure have typically been neglected or oversimplified. By means of molecular dynamics simulations, we explore the effects of electrostatic interactions on the packaging dynamics of DNA based on a coarse-grained DNA and capsid model by explicitly including peptide arms (PAs), linked to the inner surface of the capsid, and counterions. Our results indicate that the electrostatic interactions between PAs, DNA, and counterions have a significant influence on the packaging dynamics. We also find that the packed DNA conformations are largely affected by the structure of the PA layer, but the packaging rate is insensitive to the layer structure.

Scaling, crumpled wires, and genome packing in virions

The packing of a genome in virions is a topic of intense current interest in biology and biological physics. The area is dominated by allometric scaling relations that connect, e.g., the length of the encapsulated genome and the size of the corresponding virion capsid. Here we report scaling laws obtained from extensive experiments of packing of a macroscopic wire within rigid three-dimensional spherical and nonspherical cavities that can shed light on the details of the genome packing in virions. We show that these results obtained with crumpled wires are comparable to those from a large compilation of biological data from several classes of virions.

Translocation of a granular chain in a horizontally vibrated saw-tooth channel

We study the translocation mechanism of a granular chain in a horizontally vibrated saw-tooth channel using MD simulations and macro-scale experiments and show that the translocation speed is independent of the chain length as long as the chain length is larger than the spatial period of the saw-tooth. With the help of simulation, we explore the effect of geometry of the container and frequency and amplitude of vibration as well as chain flexibility on the chain drift speed. We observe that the most efficient transport is achieved when one of the channel walls is shifted with respect to the other wall by an amount equal to half the spatial period of the saw-tooth. We define a persistence length for the chain and show that the translocation speed depends on the ratio of persistence length over the spatial period of the saw-tooth. The optimum translocation occurs when this ratio is about 0.4. We also determine the optimum saw-tooth angle for the translocation of the chain as well as the optimum distance between the two walls. Some properties of this system are similar to those of polymer systems.

The Semiflexible Polymer Translocation into Laterally Unbounded Region between Two Parallel Flat Membranes

Using the dynamic Monte Carlo method, we investigate dynamics of semiflexible polymer translocation through a nanopore into laterally unbounded region between two parallel flat membranes with separation R in presence of an electric field inside the pore. The average translocation time τ initially decreases rapidly with increase of R in the range of R < 10 and then almost keeps constant for R ≥ 10, and the decline range increases with increase of dimensionless bending stiffness κ. We mainly study the effect of chain length N, κ and electric field strength E on the translocation process for R = 5. The translocation dynamics is significantly altered in comparison to an unconfined environment. We find τ ~ N^α, where the exponent α increases with increase of E for small κ. α initially increases slowly with increase of E and then keeps constant for moderate κ. α decreases with increase of E for large κ. However, α decreases with increase of κ under various E. In addition, we find τ ~ κ^β. β decreases with increase of N under various E. These behaviors are interpreted in terms of the probability distribution of translocation time and the waiting time of an individual monomer segment passing through the pore during translocation.

Packaging stiff polymers in small containers: A molecular dynamics study

The question of how stiff polymers are able to pack into small containers is particularly relevant to the study of DNA packaging in viruses. A reduced version of the problem based on coarse-grained representations of the main components of the system-the DNA polymer and the spherical viral capsid-has been studied by molecular dynamics simulation. The results, involving longer polymers than in earlier work, show that as polymers become more rigid there is an increasing tendency to self-organize as spools that wrap from the inside out, rather than the inverse direction seen previously. In the final state, a substantial part of the polymer is packed into one or more coaxial spools, concentrically layered with different orientations, a form of packaging achievable without twisting the polymer.

Single DNA molecule jamming and history-dependent dynamics during motor-driven viral packaging

In many viruses molecular motors forcibly pack single DNA molecules to near-crystalline density into ~50-100 nm prohead shells1, 2. Unexpectedly, we found that packaging frequently stalls in conditions that induce net attractive DNA-DNA interactions3. Here, we present findings suggesting that this stalling occurs because the DNA undergoes a nonequilibrium jamming transition analogous to that observed in many soft-matter systems, such as colloidal and granular systems4-8. Experiments in which conditions are changed during packaging to switch DNA-DNA interactions between purely repulsive and net attractive reveal strongly history-dependent dynamics. An abrupt deceleration is usually observed before stalling, indicating that a transition in DNA conformation causes an abrupt increase in resistance. Our findings suggest that the concept of jamming can be extended to a single polymer molecule. However, compared with macroscopic samples of colloidal particles5 we find that single DNA molecules jam over a much larger range of densities. We attribute this difference to the nanoscale system size, consistent with theoretical predictions for jamming of attractive athermal particles.9, 10.

Computational virology: From the inside out

Viruses typically pack their genetic material within a protein capsid. Enveloped viruses also have an outer membrane made up of a lipid bilayer and membrane-spanning glycoproteins. X-ray diffraction and cryoelectron microscopy provide high resolution static views of viral structure. Molecular dynamics (MD) simulations may be used to provide dynamic insights into the structures of viruses and their components. There have been a number of simulations of viral capsids and (in some cases) of the inner core of RNA or DNA packaged within them. These simulations have generally focussed on the structural integrity and stability of the capsid and/or on the influence of the nucleic acid core on capsid stability. More recently there have been a number of simulation studies of enveloped viruses, including HIV-1, influenza A, and dengue virus. These have addressed the dynamic behaviour of the capsid, the matrix, and/or of the outer envelope. Analysis of the dynamics of the lipid bilayer components of the envelopes of influenza A and of dengue virus reveals a degree of biophysical robustness, which may contribute to the stability of virus particles in different environments. Significant computational challenges need to be addressed to aid simulation of complex viruses and their membranes, including the need to integrate structural data from a range of sources to enable us to move towards simulations of intact virions. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Polymer ejection from strong spherical confinement

We examine the ejection of an initially strongly confined flexible polymer from a spherical capsid through a nanoscale pore. We use molecular dynamics for unprecedentedly high initial monomer densities. We show that the time for an individual monomer to eject grows exponentially with the number of ejected monomers. By measurements of the force at the pore we show this dependence to be a consequence of the excess free energy of the polymer due to confinement growing exponentially with the number of monomers initially inside the capsid. This growth relates closely to the divergence of mixing energy in the Flory-Huggins theory at large concentration. We show that the pressure inside the capsid driving the ejection dominates the process that is characterized by the ejection time growing linearly with the lengths of different polymers. Waiting time profiles would indicate that the superlinear dependence obtained for polymers amenable to computer simulations results from a finite-size effect due to the final retraction of polymers' tails from capsids.

Controlling the extent of viral genome release by a combination of osmotic stress and polyvalent cations

While several in vitro experiments on viral genome release have specifically studied the effects of external osmotic pressure and of the presence of polyvalent cations on the ejection of DNA from bacteriophages, few have systematically investigated how the extent of ejection is controlled by a combination of these effects. In this work we quantify the effect of osmotic pressure on the extent of DNA ejection from bacteriophage lambda as a function of polyvalent cation concentration (in particular, the tetravalent polyamine spermine). We find that the pressure required to completely inhibit ejection decreases from 38 to 17 atm as the spermine concentration is increased from 0 to 1.5 mM. Further, incubation of the phage particles in spermine concentrations as low as 0.15 mM--the threshold for DNA condensation in bulk solution-is sufficient to significantly limit the extent of ejection in the absence of osmolyte; for spermine concentrations below this threshold, the ejection is complete. In accord with recent investigations on the packaging of DNA in the presence of a condensing agent, we observe that the self-attraction induced by the polyvalent cation affects the ordering of the genome, causing it to get stuck in a broad range of nonequilibrated structures.

Stripe to slab confinement for the linearization of macromolecules in nanochannels

We investigated the recently suggested advantageous analysis of chain linearization experiments with macromolecules confined in a stripe-like channel (Huang and Battacharya, EPL, 2014, 106, 18004) using Monte Carlo simulations. The enhanced chain extension in a stripe, which is due to the significant excluded volume interactions between the monomers in two dimensions, weakens considerably on transition to an experimentally feasible slit-like channel. Based on the chain extension-confinement strength dependence and the structure factor behavior for a chain in a stripe, we infer the excluded volume regime (de Gennes regime) typical for two-dimensional systems. On widening of the stripe in a direction perpendicular to the stripe plane, i.e. on the transition to the slab geometry, the advantageous chain extension decreases and a Gaussian regime is observed for not very long semiflexible chains. The evidence for pseudo-ideality in confined chains is based on four indicators: the extension curves, variation of the extension with the persistence length P, estimated limits for the regimes in the investigated systems, and the structure factor behavior. The slab behavior can be observed when the two-dimensional stripe (originally of a one-monomer thickness) reaches a reduced thickness D larger than approximately D/P ≈ 0.2 in the third dimension. This maximum height of a slab at which the advantage of a stripe is retained is very low and has implications for DNA linearization experiments.

Polymer translocation: the first two decades and the recent diversification

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.

Dynamics and limitations of spontaneous polyelectrolyte intrusion into a charged nanocavity

We systematically investigate the spontaneous packaging mechanism of a single polyelectrolyte chain into an oppositely charged nanocavity by Langevin molecular dynamics simulations of a generic coarse-grained model. Intrusion dynamics and packaging rate, as well as the self-assembly process inside turn out to depend sensitively on the stiffness of the polyelectrolyte, the surface charge density inside the capsid, and the radius of the cavity. Further analysis shows that, depending on the stiffness, thermal fluctuations and charge inversion can be important factors to overcome barriers that slow down the intrusion and packaging dynamics. These results help advance our understanding of the function of charges on the inner surface of viral capsids and the possibility to design capsids as synthetic nanocarriers.

Repulsive DNA-DNA interactions accelerate viral DNA packaging in phage Phi29

We use optical tweezers to study the effect of attractive versus repulsive DNA-DNA interactions on motor-driven viral packaging. Screening of repulsive interactions accelerates packaging, but induction of attractive interactions by spermidine(3+) causes heterogeneous dynamics. Acceleration is observed in a fraction of complexes, but most exhibit slowing and stalling, suggesting that attractive interactions promote nonequilibrium DNA conformations that impede the motor. Thus, repulsive interactions facilitate packaging despite increasing the energy of the theoretical optimum spooled DNA conformation.

Nonequilibrium dynamics and ultraslow relaxation of confined DNA during viral packaging

Many viruses use molecular motors that generate large forces to package DNA to near-crystalline densities inside preformed viral proheads. Besides being a key step in viral assembly, this process is of interest as a model for understanding the physics of charged polymers under tight 3D confinement. A large number of theoretical studies have modeled DNA packaging, and the nature of the molecular dynamics and the forces resisting the tight confinement is a subject of wide debate. Here, we directly measure the packaging of single DNA molecules in bacteriophage phi29 with optical tweezers. Using a new technique in which we stall the motor and restart it after increasing waiting periods, we show that the DNA undergoes nonequilibrium conformational dynamics during packaging. We show that the relaxation time of the confined DNA is >10 min, which is longer than the time to package the viral genome and 60,000 times longer than that of the unconfined DNA in solution. Thus, the confined DNA molecule becomes kinetically constrained on the timescale of packaging, exhibiting glassy dynamics, which slows the motor, causes significant heterogeneity in packaging rates of individual viruses, and explains the frequent pausing observed in DNA translocation. These results support several recent hypotheses proposed based on polymer dynamics simulations and show that packaging cannot be fully understood by quasistatic thermodynamic models.

Dynamics of polymer ejection from capsid

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the ejection times scale with polymer length, τ ∼ N(α). We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) ρ inside the capsid. For very low densities ρ ≤ 0.002 the polymer is only weakly confined by the capsid, and we measure α = 1.33, which is close to α=1.4 obtained for polymer translocation. At intermediate densities the scaling exponents α = 1.25 and 1.21 for ρ = 0.01 and 0.02, respectively. These scalings are in accord with a crude derivation for the lower limit α = 1.2. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, ρ ⪆ 0.25. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.

Langevin dynamics simulation of DNA ejection from a phage

We have performed Langevin dynamics simulations of a coarse-grained model of ejection of dsDNA from Φ29 phage. Our simulation results show significant variations in the local ejection speed, consistent with experimental observations reported in the literature for both in vivo and in vitro systems. In efforts to understand the origin of such variations in the local speed of ejection, we have investigated the correlations between the local ejection kinetics and the packaged structures created at various motor forces and chain flexibility. At lower motor forces, the packaged DNA length is shorter with better organization. On the other hand, at higher motor forces typical of realistic situations, the DNA organization inside the capsid suffers from significant orientational disorder, but yet with long orientational correlation times. This in turn leads to lack of registry between the direction of the DNA segments just to be ejected and the direction of exit. As a result, a significant amount of momentum transfer is required locally for successful exit. Consequently, the DNA ejection temporarily slows down exhibiting pauses. This slowing down occurs at random times during the ejection process, completely determined by the particular starting conformation created by prescribed motor forces. In order to augment our inference, we have additionally investigated the ejection of chains with deliberately changed persistence length. For less inflexible chains, the demand on the occurrence of large momentum transfer for successful ejection is weaker, resulting in more uniform ejection kinetics. While being consistent with experimental observations, our results show the nonergodic nature of the ejection kinetics and call for better theoretical models to portray the kinetics of genome ejection from phages.

Effects of pulling forces, osmotic pressure, condensing agents and viscosity on the thermodynamics and kinetics of DNA ejection from bacteriophages to bacterial cells: a computational study

In this work, we report on simulations of double-stranded DNA (dsDNA) ejection from bacteriophage φ29 into a bacterial cell. The ejection was studied with a coarse-grained model, in which viral dsDNA was represented by beads on a torsion-less string. The bacteriophage's capsid and the bacterial cell were defined by sets of spherical constraints. To account for the effects of the viscous medium inside the bacterial cell, the simulations were carried out using a Langevin dynamics protocol. Our simplest simulations (involving constant viscosity and no external biasing forces) produced results compatible with the push-pull model of DNA ejection, with an ejection rate significantly higher in the first part of ejection than in the latter parts. Additionally, we performed more complicated simulations, in which we included additional factors such as external forces, osmotic pressure, condensing agents and ejection-dependent viscosity. The effects of these factors (independently and in combination) on the thermodynamics and kinetics of DNA ejection were studied. We found that, in general, the dependence of ejection forces and ejection rates on the amount of DNA ejected becomes more complex if the ejection is modeled with a broader, more realistic set of parameters and influences (such as variation in the solvent's viscosity and the application of an external force). However, certain combinations of factors and numerical parameters led to the opposition of some ejection-driving and ejection-inhibiting influences, ultimately causing an apparent simplification of the ejection profiles.

Effect of temperature and capsid tail on the packing and ejection of viral DNA

We use a simulation technique based on molecular dynamics and stochastic rotation model to present the effect of temperature and capsid tail on the packaging and ejection processes of semiflexible polymers. We consider two types of solvents, a good solvent, where the polymer is neutral and repulsion interactions among its various sections are favored, and one where the polymer is charged, giving rise to extra electrostatic reaction. For tailless capsids, we find that packing a neutral polymer is slightly slower at higher temperatures whereas its ejection is slightly slower at lower temperatures. We find the same trend for a charged polymer but the effect is noticeably larger. At a high enough temperature, we notice that packing a charged polymer can be stopped. On the other hand, at fixed temperature and regardless whether the polymer is charged, packing is much easier for a capsid with a tail whereas ejection is much slower. The effect of including the tail on the dynamics of a charged polymer, in particular, is rather significant: more packing fraction is facilitated at higher temperatures due to more ordered polymer configuration inside the capsid. In contrast, during ejection the tail traps the last remaining beads for quite some time before allowing full ejection. We interpret these results in terms of entropic and electrostatic forces.