Investigation of viral DNA packaging using molecular mechanics models

The structure and physical properties of a packaged bacteriophage particle

A string of nucleotides confined within a protein capsid contains all the instructions necessary to make a functional virus particle, a virion. Although the structure of the protein capsid is known for many virus species1,2, the three-dimensional organization of viral genomes has mostly eluded experimental probes3,4. Here we report all-atom structural models of an HK97 virion5, including its entire 39,732 base pair genome, obtained through multiresolution simulations. Mimicking the action of a packaging motor6, the genome was gradually loaded into the capsid. The structure of the packaged capsid was then refined through simulations of increasing resolution, which produced a 26 million atom model of the complete virion, including water and ions confined within the capsid. DNA packaging occurs through a loop extrusion mechanism7 that produces globally different configurations of the packaged genome and gives each viral particle individual traits. Multiple microsecond-long all-atom simulations characterized the effect of the packaged genome on capsid structure, internal pressure, electrostatics and diffusion of water, ions and DNA, and revealed the structural imprints of the capsid onto the genome. Our approach can be generalized to obtain complete all-atom structural models of other virus species, thereby potentially revealing new drug targets at the genome-capsid interface.

Are kuravirus capsid diameters quantized? The first all-atom genome tracing method for double-stranded DNA viruses

The revolution in cryo-electron microscopy has resulted in unprecedented power to resolve large macromolecular complexes including viruses. Many methods exist to explain density corresponding to proteins and thus entire protein capsids have been solved at the all-atom level. However methods for nucleic acids lag behind, and no all-atom viral double-stranded DNA genomes have been published at all. We here present a method which exploits the spiral winding patterns of DNA in icosahedral capsids. The method quickly generates shells of DNA wound in user-specified, idealized spherical or cylindrical spirals. For transition regions, the method allows guided semiflexible fitting. For the kuravirus SU10, our method explains most of the density in a semiautomated fashion. The results suggest rules for DNA turns in the end caps under which two discrete parameters determine the capsid inner diameter. We suggest that other kuraviruses viruses may follow the same winding scheme, producing a discrete rather than continuous spectrum of capsid inner diameters. Our software may be used to explain the published density maps of other double-stranded DNA viruses and uncover their genome packaging principles.

Ion-dependent DNA configuration in bacteriophage capsids

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Chromonic liquid crystals and packing configurations of bacteriophage viruses

We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

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.

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.

Quantitative Study of the Chiral Organization of the Phage Genome Induced by the Packaging Motor

Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of double-stranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the three-dimensional geometry of the packaged genome, but very little is known of the signature of the molecular packaging motor. For instance, biophysical experiments show that in some systems, DNA rotates during the packaging reaction, but most current biophysical models fail to incorporate this property. Furthermore, studies including rotation mechanisms have reached contradictory conclusions. In this study, we compare the geometrical signatures imposed by different possible mechanisms for the packaging motors: rotation, revolution, and rotation with revolution. We used a previously proposed kinetic Monte Carlo model of the motor, combined with Brownian dynamics simulations of DNA to simulate deterministic and stochastic motor models. We find that rotation is necessary for the accumulation of DNA writhe and for the chiral organization of the genome. We observe that although in the initial steps of the packaging reaction, the torsional strain of the genome is released by rotation of the molecule, in the later stages, it is released by the accumulation of writhe. We suggest that the molecular motor plays a key role in determining the final structure of the encapsidated genome in bacteriophages.

Fine structure of viral dsDNA encapsidation

Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plank-shaped molecular compounds, we develop a first-principles effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses available data for a collection of viruses, aimed at applications to viral design. The outcome of the work is a mathematical model and its numerical algorithm, based on the method of finite elements, and computer simulations to identify and label the ordered and disordered regions of the capsid and calculate the inner pressure. It also presents the tools for the local reconstruction of the DNA "scaffolding" and the center curve of the filament within the capsid.

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.

Orientationally ordered states of a wormlike chain in spherical confinement

One of the basic characteristics of a linear dsDNA molecule is its persistence length, typically of order 50 nm. The DNA chain inflicts a large energy penalty if it is bent sharply at that length scale. Viruses of bacteria, known as bacteriophages, typically have a dimension of a few tens of nanometers. Yet, it is known that a bacteriophage actively packages viral DNA inside the capsid and ejects it afterwards. Here, adopting a commonly used polymer model known as the wormlike chain, we answer an idealized question: Placing a linear DNA molecule inside a spherical cavity, what ordered states can we derive from known tools in statistical physics? Solving the model in a rigorous field-theory framework, we report a universal phase diagram for four orientationally ordered and disordered states, in terms of two relevant physical parameters.

Effects of spherical confinement and backbone stiffness on flexible polymer jamming

We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but with lower amplitude for polymers. Polymers have fewer boundary contacts, and this low-density surface layer strongly reduces the global bulk modulus. We further show that bulk-modulus dependence on backbone stiffness can be described by a model of stiffnesses in series and discuss potential experimental and biological applications.

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.

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.

Gene overlapping and size constraints in the viral world

Background

Viruses are the simplest replicating units, characterized by a limited number of coding genes and an exceptionally high rate of overlapping genes. We sought a unified evolutionary explanation that accounts for their genome sizes, gene overlapping and capsid properties.

Results

We performed an unbiased statistical analysis of ~100 families within ~400 genera that comprise the currently known viral world. We found that the volume utilization of capsids is often low, and greatly varies among viral families. Furthermore, although viruses span three orders of magnitude in genome length, they almost never have over 1500 overlapping nucleotides, or over four significantly overlapping genes per virus.

Conclusions

Our findings undermine the generality of the compression theory, which emphasizes optimal packing and length dependency to explain overlapping genes and capsid size in viral genomes. Instead, we propose that gene novelty and evolution exploration offer better explanations to size constraints and gene overlapping in all viruses.

Reviewers

This article was reviewed by Arne Elofsson and David Kreil.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-016-0128-3) contains supplementary material, which is available to authorized users.

Twist-induced defects of the P-SSP7 genome revealed by modeling the cryo-EM density

We consider the consequences of assuming that DNA inside of phages can be approximated as a strongly nonlinear persistence length polymer. Recent cryo-EM experiments find a hole in the density map of P-SSP7 phage, located in the DNA segment filling the portal channel of the phage. We use experimentally derived structural constraints with coarse-grained simulation techniques to consider contrasting model interpretations of reconstructed density in the portal channel. The coarse-grained DNA models used are designed to capture the effects of torsional strain and electrostatic environment. Our simulation results are consistent with the interpretation that the vacancy or hole in the experimental density map is due to DNA strain leading to strand separation. We further demonstrate that a moderate negative twisting strain is able to account for the strand separation. This effect of nonlinear persistence length may be important in other aspects of phage DNA packing.

Morphogenesis of filaments growing in flexible confinements

Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside deformable vesicles or soft tissue-like cell walls, chorions and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements--perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.

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.

Comment on the letter by A. Ben-Shaul: "entropy, energy, and bending of DNA in viral capsids"

The conformational entropic penalty associated with packaging double-stranded DNA into viral capsids remains an issue of contention. So far, models based on a continuum approximation for DNA have either left the question unexamined, or they have assumed that the entropic penalty is negligible, following an early analysis by Riemer and Bloomfield. In contrast, molecular-dynamics (MD) simulations using bead-and-spring models consistently show a large penalty. A recent letter from Ben-Shaul attempts to reconcile the differences. While the letter makes some valid points, the issue of how to include conformational entropy in the continuum models remains unresolved. In this Comment, I show that the free energy decomposition from continuum models could be brought into line with the decomposition from the MD simulations with two adjustments. First, the entropy from Flory-Huggins theory should be replaced by the estimate of the entropic penalty given in Ben-Shaul's letter, which corresponds closely to that from the MD simulations. Second, the DNA-DNA repulsions are well described by the empirical relationship given by the Cal Tech group, but the strength of these should be reduced by about half, using parameters based on the Rau-Parsegian experiments, rather than treating them as "fitting parameters (tuned) to fit the data from (single molecule pulling) experiments."

Influence of chain stiffness on knottedness in single polymers

In the present article, we investigate and review the influence of chain stiffness on self-entanglements and knots in a single polymer chain with Monte Carlo simulations spanning good solvent, theta and globular phases. The last-named are of particular importance as a model system for DNA in viral capsids. Intriguingly, the dependence of knot occurrence and complexity with increasing stiffness is non-trivial, but can be understood with a few simple concepts outlined in the present article.

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.

Knotting of linear DNA in nano-slits and nano-channels: a numerical study

The amount and type of self-entanglement of DNA filaments is significantly affected by spatial confinement, which is ubiquitous in biological systems. Motivated by recent advancements in single DNA molecule experiments based on nanofluidic devices and by the introduction of algorithms capable of detecting knots in open chains, we investigate numerically the entanglement of linear, open DNA chains confined inside nano-slits. The results regard the abundance, type, and length of occurring knots and are compared with recent findings for DNA inside nano-channels. In both cases, the width of the confining region, D, spans the 30 nm-1 μm range and the confined DNA chains are 1-4 μm long. It is found that the knotting probability is maximum for slit widths in the 70-100 nm range. However, over the considered DNA contour lengths, the maximum incidence of knots remains below 20%, while for channel confinement it tops 50%. Further differences of the entanglement are seen for the average contour length of the knotted region, which drops significantly below D ~100 nm for channel-confinement, while it stays approximately constant for slit-like confinement. These properties ought to reverberate in different kinetic properties of linear DNA depending on confinement and could be detectable experimentally or exploitable in nano-technological applications.

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.

Bending and elongation effects on the random packing of curved spherocylinders

Studies on the macroscopic and microscopic packing properties of nonconvex particles are scarce. As a common concave form, the curved spherocylinder is used in the simulations, and its bending and elongation effects on the random packings are investigated numerically with sphere assembly models and a relaxation algorithm. The aspect ratio is demonstrated to be the main factor regarding the packing density. However, at certain aspect ratios of low densities around 0.3-0.4, the density of curved spherocylinders may increase by 15% more than that of the straight ones, indicating that bending is also a contributor to the packing density. The excluded volume of the curved spherocylinder decreases with the increase of the bending angle, indicating that the excluded volume is applicable in explaining the bending effect on the packing density variation of nonconvex particles. The packings are verified to be randomly distributed in orientation with no significant layering or in-plane order. The local arrangements are further analyzed from the radial distribution function and contact results. The results show that the random packings of nonconvex particles have significant differences and richer characteristics on both the macroscopic and microscopic properties compared with convex objects.

Phase diagrams of knotted and unknotted ring polymers

The phase diagram for a lattice ring polymer under applied force, with variable solvent quality, for different topological knot states, is determined for the first time. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that nontrivial knots result in additional pseudophases under tensile force conditions.

Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots

Observation that DNA molecules in bacteriophage capsids preferentially form torus type of knots provided a sensitive gauge to evaluate various models of DNA arrangement in phage heads. Only models resulting in a preponderance of torus knots could be considered as close to reality. Recent studies revealed that experimentally observed enrichment of torus knots can be qualitatively reproduced in numerical simulations that include a potential inducing nematic arrangement of tightly packed DNA molecules within phage capsids. Here, we investigate what aspects of the nematic arrangement are crucial for inducing formation of torus knots. Our results indicate that the effective stiffening of DNA by the nematic arrangement not only promotes knotting in general but is also the decisive factor in promoting formation of DNA torus knots in phage capsids.

Wavelet analysis of human DNA

This paper studies the human DNA in the perspective of signal processing. Six wavelets are tested for analyzing the information content of the human DNA. By adopting real Shannon wavelet several fundamental properties of the code are revealed. A quantitative comparison of the chromosomes and visualization through multidimensional and dendograms is developed.

Nematic ordering of polymers in confined geometry applied to DNA packaging in viral capsids

A density functional theory of the spatial distribution and biaxial nematic order of polymers of arbitrary length and rigidity inside a spherical cavity is proposed. The local order of different chain segments is considered as an alignment to a spatially varying director field of cylindrical symmetry. The steric interactions are taken into account in the second virial approximation. Polymer density and orientational order distributions inside the spherically cavity are the principal results. It was found that short and flexible polymers were located at the center of the sphere and were orientationaly disordered. Upon increasing polymer length and/or polymer rigidity, the location of the polymer was continuously shifted toward the surface of the spherical cavity and the polymer segments became gradually more aligned. Parameters have been selected to model the behavior of genomes in spherical viral capsids.

Role of DNA-DNA interactions on the structure and thermodynamics of bacteriophages Lambda and P4

Electrostatic interactions play an important role in both packaging of DNA inside bacteriophages and its release into bacterial cells. While at physiological conditions DNA strands repel each other, the presence of polyvalent cations such as spermine and spermidine in solutions leads to the formation of DNA condensates. In this study, we discuss packaging of DNA into bacteriophages P4 and Lambda under repulsive and attractive conditions using a coarse-grained model of DNA and capsids. Packaging under repulsive conditions leads to the appearance of the coaxial spooling conformations; DNA occupies all available space inside the capsid. Under the attractive potential both packed systems reveal toroidal conformations, leaving the central part of the capsids empty. We also present a detailed thermodynamic analysis of packaging and show that the forces required to pack the genomes in the presence of polyamines are significantly lower than those observed under repulsive conditions. The analysis reveals that in both the repulsive and attractive regimes the entropic penalty of DNA confinement has a significant non-negligible contribution into the total energy of packaging. Additionally we report the results of simulations of DNA condensation inside partially packed Lambda. We found that at low densities DNA behaves as free unconfined polymer and condenses into the toroidal structures; at higher densities rearrangement of the genome into toroids becomes hindered, and condensation results in the formation of non-equilibrium structures. In all cases packaging in a specific conformation occurs as a result of interplay between bending stresses experienced by the confined polymer and interactions between the strands.

Biopolymer organization upon confinement

Biopolymers in vivo are typically subject to spatial restraints, either as a result of molecular crowding in the cellular medium or of direct spatial confinement. DNA in living organisms provides a prototypical example of a confined biopolymer. Confinement prompts a number of biophysics questions. For instance, how can the high level of packing be compatible with the necessity to access and process the genomic material? What mechanisms can be adopted in vivo to avoid the excessive geometrical and topological entanglement of dense phases of biopolymers? These and other fundamental questions have been addressed in recent years by both experimental and theoretical means. A review of the results, particularly of those obtained by numerical studies, is presented here. The review is mostly devoted to DNA packaging inside bacteriophages, which is the best studied example both experimentally and theoretically. Recent selected biophysical studies of the bacterial genome organization and of chromosome segregation in eukaryotes are also covered.

Polyelectrolyte condensation in bulk, at surfaces, and under confinement

In this review we discuss recent results from computer simulations based on coarse-grained polyion models representing aqueous solutions of polyelectrolytes. The focus will be directed to the conformation of the polyions and, in particular, their condensation in bulk, induced by multivalent ions and oppositely charged polyelectrolytes, at responsive surfaces and under confinement.

Confined nematic polymers: order and packing in a nematic drop

We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer via the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy ansatz is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and density field and investigate the orientation and density profile within a sphere. Two important parameters of the solution are the exact locations of the beginning and the end of the polymer chain. Pending on their spatial distribution and the actual size of the hard sphere enclosure we can get a plethora of various configurations of the chain exhibiting different defect geometry.

DNA-DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting

Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What is the physical basis of this organization? Here we show evidence from stochastic simulation techniques that suggests that a key element is the tendency of contacting DNA strands to order, as in cholesteric liquid crystals. This interaction favors their preferential juxtaposition at a small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect dramatically impacts the geometry and topology of DNA inside phages. Accounting for this local potential allows us to reproduce the main experimental data on DNA organization in phages, including the cryo-EM observations and detailed features of the spectrum of DNA knots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage.

Viral assembly: a molecular modeling perspective

Icosahedral viruses are among the smallest and simplest of biological systems. The investigation of their structures represented the first step toward the establishment of molecular biophysics, over half a century ago. Many research groups are now pursuing investigations of viral assembly, a process that could offer new opportunities for the design of antiviral drugs and novel nanoparticles. A variety of experimental, theoretical and computational methods have been brought to bear on the study of virus structure and assembly. In this Perspective we review the contributions of theoretical and computational approaches to our understanding of the structure, energetics, thermodynamics and assembly of DNA bacteriophage and single-stranded icosahedral RNA viruses.

Characterization of DNA conformation inside bacterial viruses

In this study we develop a formalism to describe the organization of DNA inside bacteriophage capsids during genome packaging. We have previously shown that DNA inside bacteriophage phi29 (phi29) is organized into folded toroids [A. S. Petrov and S. C. Harvey, Structure 15, 21 (2007)], whereas epsilon15 (epsilon15) reveals the coaxial organization of the genetic material [A. S. Petrov, K. Lim-Hing, and S. C. Harvey, Structure 15, 807 (2007)]. We now show that each system undergoes two consecutive transitions. The first transition corresponds to the formation of global conformations and is analogous to a disorder-order conformational transition. The second transition is characterized by a significant loss of DNA mobility at the local level leading to glasslike dynamic behavior. Packing genetic material inside bacteriophages can be used as a general model to study the behavior of semiflexible chains inside confined spaces, and the proposed formalism developed here can be used to study other systems of linear polymer chains confined to closed spaces.

Simulations of knotting in confined circular DNA

The packing of DNA inside bacteriophages arguably yields the simplest example of genome organization in living organisms. As an assay of packing geometry, the DNA knot spectrum produced upon release of viral DNA from the P4 phage capsid has been analyzed, and compared to results of simulation of knots in confined volumes. We present new results from extensive stochastic sampling of confined self-avoiding and semiflexible circular chains with volume exclusion. The physical parameters of the chains (contour length, cross section, and bending rigidity) have been set to match those of P4 bacteriophage DNA. By using advanced sampling techniques, involving multiple Markov chain pressure-driven confinement combined with a thermodynamic reweighting technique, we establish the knot spectrum of the circular chains for increasing confinement up to the highest densities for which available algorithms can exactly classify the knots. Compactified configurations have an enclosing hull diameter approximately 2.5 times larger than the P4 caliper size. The results are discussed in relation to the recent experiments on DNA knotting inside the capsid of a P4 tailless mutant. Our investigation indicates that confinement favors chiral knots over achiral ones, as found in the experiments. However, no significant bias of torus over twist knots is found, contrary to the P4 results. The result poses a crucial question for future studies of DNA packaging in P4: is the discrepancy due to the insufficient confinement of the equilibrium simulation or does it indicate that out-of-equilibrium mechanisms (such as rotation by packaging motors) affect the genome organization, hence its knot spectrum in P4?

Biophysics of viral infectivity: matching genome length with capsid size

In this review, we discuss recent advances in biophysical virology, presenting experimental and theoretical studies on the physical properties of viruses. We focus on the double-stranded (ds) DNA bacteriophages as model systems for all of the dsDNA viruses both prokaryotic and eukaryotic. Recent studies demonstrate that the DNA packaged into a viral capsid is highly pressurized, which provides a force for the first step of passive injection of viral DNA into a bacterial cell. Moreover, specific studies on capsid strength show a strong correlation between genome length, and capsid size and robustness. The implications of these newly appreciated physical properties of a viral particle with respect to the infection process are discussed.

Packing nanomechanics of viral genomes

We investigate the osmotic equilibrium between a bulk polyethylene glycol (PEG) solution and DNA tightly packed in a spherical capsid. We base our analysis on the equations of thermodynamic equilibrium in terms of osmotic pressure. The equality between external osmotic pressure of PEG and osmotic pressure of tightly packed DNA gives us the DNA encapsidation curves. In this way we directly connect the wealth of existing osmotic pressure data for DNA in the bulk with the DNA encapsidation curves within small viral capsids. Specific calculations are made for a monovalent salt, Na(+) -DNA and a divalent salt, Mn(2+) -DNA that have quite different DNA encapsidation behaviors. The main conclusion of our work is that bending energy of DNA is of minor importance regarding the encapsidated DNA length, but has a non-negligible influence on the density distribution of DNA within the capsid.

Packaging double-helical DNA into viral capsids: structures, forces, and energetics

Small, icosahedral double-stranded DNA bacteriophage pack their genomes tightly into preformed protein capsids using an ATP-driven motor. Coarse-grain molecular-mechanics models provide a detailed picture of DNA packaging in bacteriophage, revealing how conformation depends on capsid size and shape, and the presence or absence of a protein core. The forces that oppose packaging have large contributions from both electrostatic repulsions and the entropic penalty of confining the DNA into the capsid, whereas elastic deformations make only a modest contribution. The elastic deformation energy is very sensitive to the final conformation, whereas the electrostatic and entropic penalties are not, so the packaged DNA favors conformations that minimize the bending energy.

The role of DNA twist in the packaging of viral genomes

We performed molecular dynamics simulations of the genome packaging of bacteriophage P4 using two coarse-grained models of DNA. The first model, 1DNA6 (one pseudo-atom per six DNA basepairs), represents DNA as a string of beads, for which DNA torsions are undefined. The second model, 3DNA6 (three pseudo-atoms per six DNA basepairs), represents DNA as a series of base planes with torsions defined by the angles between successive planes. Bacteriophage P4 was packaged with 1DNA6, 3DNA6 in a torsionally relaxed state, and 3DNA6 in a torsionally strained state. We observed good agreement between the packed conformation of 1DNA6 and the packed conformations of 3DNA6. The free energies of packaging were in agreement, as well. Our results suggest that DNA torsions can be omitted from coarse-grained bacteriophage packaging simulations without significantly altering the DNA conformations or free energies of packaging that the simulations predict.