Viral assembly: a molecular modeling perspective

Single-molecule measurements of bacteriophage lambda DNA packaging using purified terminase motor proteins and E. coli integration host factor

Biomotor-driven DNA packaging is a key step in the life cycle of many viruses. We previously developed single-molecule methods using optical tweezers to measure packaging dynamics of the bacteriophage lambda motor. The lambda system is more complex than others examined via single-molecule assays with respect to the packaging substrate and ancillary proteins required. Because of this, previous studies which efficiently detected packaging events used crude E. coli cell extracts containing host factors and the terminase packaging enzyme. However, use of extracts is suboptimal for biochemical manipulation and obfuscates interrogation of additional factors that affect the process. Here we describe an optical tweezers assay using purified lambda terminase holoenzyme. Packaging events are as efficient as with crude extracts, but only if purified E. coli integration host factor (IHF) is included in the motor assembly reactions. We find that the ATP-driven DNA translocation dynamics, motor force generation, and motor-DNA interactions without nucleotide are virtually identical to those measured with extracts. Thus, single-molecule packaging activity can be fully recapitulated in a minimal system containing only purified lambda procapsids, purified terminase, IHF, and ATP. This sets the stage for single-molecule studies to investigate additional phage proteins known to play essential roles in the packaging reaction.

Modeling Viral Capsid Assembly: A Review of Computational Strategies and Applications

Viral capsid assembly is a complex and critical process, essential for understanding viral behavior, evolution, and the development of antiviral treatments, vaccines, and nanotechnology. Significant progress in studying viral capsid assembly has been achieved through various computational approaches, including molecular dynamics (MD) simulations, stochastic dynamics simulations, coarse-grained (CG) models, electrostatic analyses, lattice models, hybrid techniques, machine learning methods, and kinetic models. Each of these techniques offers unique advantages, and by integrating these diverse computational strategies, researchers can more accurately model the dynamic behaviors and structural features of viral capsids, deepening our understanding of the assembly process. This review provides a comprehensive overview of studies on viral capsid assembly, emphasizing their critical role in advancing our knowledge. It examines the contributions, strengths, and limitations of different computational methods, presents key computational works in the field, and analyzes milestone studies that have shaped current research.

Theoretical Studies on Assembly, Physical Stability, and Dynamics of Viruses

All matter must obey the general laws of physics and living matter is not an exception. Viruses have not only learnt how to cope with them but have managed to use them for their own survival. In this chapter, we will review some of the exciting physics that are behind viruses and discuss simple physical models that can shed some light on different aspects of the viral life cycle and viral properties. In particular, we will focus on how the structure and shape of the viral capsid, its assembly and stability, and the entry and exit of viral particles and their genomes can be explained using fundamental physics theories.

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.

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.

Nucleotide-dependent DNA gripping and an end-clamp mechanism regulate the bacteriophage T4 viral packaging motor

ATP-powered viral packaging motors are among the most powerful biomotors known. Motor subunits arranged in a ring repeatedly grip and translocate the DNA to package viral genomes into capsids. Here, we use single DNA manipulation and rapid solution exchange to quantify how nucleotide binding regulates interactions between the bacteriophage T4 motor and DNA substrate. With no nucleotides, there is virtually no gripping and rapid slipping occurs with only minimal friction resisting. In contrast, binding of an ATP analog engages nearly continuous gripping. Occasional slips occur due to dissociation of the analog from a gripping motor subunit, or force-induced rupture of grip, but multiple other analog-bound subunits exert high friction that limits slipping. ADP induces comparably infrequent gripping and variable friction. Independent of nucleotides, slipping arrests when the end of the DNA is about to exit the capsid. This end-clamp mechanism increases the efficiency of packaging by making it essentially irreversible.

Packaging of viral DNA depends on strong molecular motors that are powered by ATP hydrolysis. Here, the authors develop a single-molecule assay to monitor how nucleotide binding regulates motor-DNA interactions and reveal a generic mechanism that prevents exit of the whole DNA from the viral capsid during packaging.

States of phage T3/T7 capsids: buoyant density centrifugation and cryo-EM

Mature double-stranded DNA bacteriophages have capsids with symmetrical shells that typically resist disruption, as they must to survive in the wild. However, flexibility and associated dynamism assist function. We describe biochemistry-oriented procedures used to find previously obscure flexibility for capsids of the related phages, T3 and T7. The primary procedures are hydration-based buoyant density ultracentrifugation and purified particle-based cryo-electron microscopy (cryo-EM). We review the buoyant density centrifugation in detail. The mature, stable T3/T7 capsid is a shell flexibility-derived conversion product of an initially assembled procapsid (capsid I). During DNA packaging, capsid I expands and loses a scaffolding protein to form capsid II. The following are observations made with capsid II. (1) The in vivo DNA packaging of wild type T3 generates capsid II that has a slight (1.4%), cryo-EM-detected hyper-expansion relative to the mature phage capsid. (2) DNA packaging in some altered conditions generates more extensive hyper-expansion of capsid II, initially detected by hydration-based preparative buoyant density centrifugation in Nycodenz density gradients. (3) Capsid contraction sometimes occurs, e.g., during quantized leakage of DNA from mature T3 capsids without a tail.

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.

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.

Continuous allosteric regulation of a viral packaging motor by a sensor that detects the density and conformation of packaged DNA

We report evidence for an unconventional type of allosteric regulation of a biomotor. We show that the genome-packaging motor of phage ϕ29 is regulated by a sensor that detects the density and conformation of the DNA packaged inside the viral capsid, and slows the motor by a mechanism distinct from the effect of a direct load force on the motor. Specifically, we show that motor-ATP interactions are regulated by a signal that is propagated allosterically from inside the viral shell to the motor mounted on the outside. This signal continuously regulates the motor speed and pausing in response to changes in either density or conformation of the packaged DNA, and slows the motor before the buildup of large forces resisting DNA confinement. Analysis of motor slipping reveals that the force resisting packaging remains low (<1 pN) until ∼ 70% and then rises sharply to ∼ 23 pN at high filling, which is a several-fold lower value than was previously estimated under the assumption that force alone slows the motor. These findings are consistent with recent studies of the stepping kinetics of the motor. The allosteric regulatory mechanism we report allows double-stranded DNA viruses to achieve rapid, high-density packing of their genomes by limiting the buildup of nonequilibrium load forces on the motor.

Modeling Viral Capsid Assembly

I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.

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.

Molecular interactions and residues involved in force generation in the T4 viral DNA packaging motor

Many viruses utilize molecular motors to package their genomes into preformed capsids. A striking feature of these motors is their ability to generate large forces to drive DNA translocation against entropic, electrostatic, and bending forces resisting DNA confinement. A model based on recently resolved structures of the bacteriophage T4 motor protein gp17 suggests that this motor generates large forces by undergoing a conformational change from an extended to a compact state. This transition is proposed to be driven by electrostatic interactions between complementarily charged residues across the interface between the N- and C-terminal domains of gp17. Here we use atomistic molecular dynamics simulations to investigate in detail the molecular interactions and residues involved in such a compaction transition of gp17. We find that although electrostatic interactions between charged residues contribute significantly to the overall free energy change of compaction, interactions mediated by the uncharged residues are equally if not more important. We identify five charged residues and six uncharged residues at the interface that play a dominant role in the compaction transition and also reveal salt bridging, van der Waals, and solvent hydrogen-bonding interactions mediated by these residues in stabilizing the compact form of gp17. The formation of a salt bridge between Glu309 and Arg494 is found to be particularly crucial, consistent with experiments showing complete abrogation in packaging upon Glu309Lys mutation. The computed contributions of several other residues are also found to correlate well with single-molecule measurements of impairments in DNA translocation activity caused by site-directed mutations.

Pathways for virus assembly around nucleic acids

Understanding the pathways by which viral capsid proteins assemble around their genomes could identify key intermediates as potential drug targets. In this work, we use computer simulations to characterize assembly over a wide range of capsid protein-protein interaction strengths and solution ionic strengths. We find that assembly pathways can be categorized into two classes, in which intermediates are either predominantly ordered or disordered. Our results suggest that estimating the protein-protein and the protein-genome binding affinities may be sufficient to predict which pathway occurs. Furthermore, the calculated phase diagrams suggest that knowledge of the dominant assembly pathway and its relationship to control parameters could identify optimal strategies to thwart or redirect assembly to block infection. Finally, analysis of simulation trajectories suggests that the two classes of assembly pathways can be distinguished in single-molecule fluorescence correlation spectroscopy or bulk time-resolved small-angle X-ray scattering experiments.

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.

Evidence for an electrostatic mechanism of force generation by the bacteriophage T4 DNA packaging motor

How viral packaging motors generate enormous forces to translocate DNA into viral capsids remains unknown. Recent structural studies of the bacteriophage T4 packaging motor have led to a proposed mechanism wherein the gp17 motor protein translocates DNA by transitioning between extended and compact states, orchestrated by electrostatic interactions between complimentarily charged residues across the interface between the N- and C-terminal subdomains. Here we show that site-directed alterations in these residues cause force dependent impairments of motor function including lower translocation velocity, lower stall force and higher frequency of pauses and slips. We further show that the measured impairments correlate with computed changes in free-energy differences between the two states. These findings support the proposed structural mechanism and further suggest an energy landscape model of motor activity that couples the free-energy profile of motor conformational states with that of the ATP hydrolysis cycle.

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."

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.

The entropic cost of polymer confinement

The confinement of a polymer into a small space is thermodynamically unfavorable because of the reduction in the number of conformational states. The entropic penalty affects a variety of biological processes, and it plays an important role in polymer transport properties and in microfluidic devices. We determine the entropic penalty for the confinement of elastic polymer of persistence length P in the long-chain limit. We examine three geometries: (1) parallel planes separated by a distance d (a slit); (2) a circular tube of diameter d; and (3) a sphere of diameter d. We first consider infinitely thin (ideal) chains. As d/P drops from 100 to 0.01, TΔS rises from ∼5 × 10(-4) kT to ∼30 kT per persistence length for cases (1) and (2), with the entropic penalty for case (2) being consistently about twice that for case (1). TΔS is ∼5 kT per persistence length for confinement to a sphere when d = P, about twice the value predicted by mean field theory. For all three geometries, in the limit d/P ≫ 1, the asymptotic behavior of ΔS vs d is consistent with the d(-2) behavior predicted by theory. In the limit d/P ≪ 1, the scaling of ΔS for slits and tubes is also consistent with earlier predictions (d(-2/3)). Finally, we treat volume exclusion effects, examining chains of diameter D > 0. Confinement to a narrow slit or tube (d/P ≪ 1) has the same entropic penalty as that for an ideal chain in a slit or tube with d' = d - D; in the weak confinement regime (d/P ≫ 1), the entropic penalties are significantly larger than those for infinitely thin chains. When a chain of finite diameter is forced into a sphere or other closed cavity, the entropic confinement penalty rises without limit because there are no configurations available to the chain once its volume exceeds that of the cavity.

Density functional theory for encapsidated polyelectrolytes: a comparison with Monte Carlo simulation

Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.

A model for the structure of satellite tobacco mosaic virus

Satellite tobacco mosaic virus (STMV) is an icosahedral T=1 single-stranded RNA virus with a genome containing 1058 nucleotides. X-ray crystallography revealed a structure containing 30 double-helical RNA segments, with each helix having nine base pairs and an unpaired nucleotide at the 3' end of each strand. Based on this structure, Larson and McPherson proposed a model of 30 hairpin-loop elements occupying the edges of the icosahedron and connected by single-stranded regions. More recently, Schroeder et al. have combined the results of chemical probing with a novel helix searching algorithm to propose a specific secondary structure for the STMV genome, compatible with the Larson-McPherson model. Here we report an all-atom model of STMV, using the complete protein and RNA sequences and the Schroeder RNA secondary structure. As far as we know, this is the first all-atom model for the complete structure of any virus (100% of the atoms) using the natural genomic sequence.

Screening for the Location of RNA using the Chloride Ion Distribution in Simulations of Virus Capsids

The complete structure of the genomic material inside a virus capsid remains elusive, although a limited amount of symmetric nucleic acid can be resolved in the crystal structure of 17 icosahedral viruses. The negatively charged sugar-phosphate backbone of RNA and DNA as well as the large positive charge of the interior surface of the virus capsids suggest that electrostatic complementarity is an important factor in the packaging of the genomes in these viruses. To test how much packing information is encoded by the electrostatic and steric envelope of the capsid interior, we performed extensive all-atom molecular dynamics (MD) simulations of virus capsids with explicit water molecules and solvent ions. The model systems were two small plant viruses in which significant amounts of RNA has been observed by X-ray crystallography: satellite tobacco mosaic virus (STMV, 62% RNA visible) and satellite tobacco necrosis virus (STNV, 34% RNA visible). Simulations of half-capsids of these viruses with no RNA present revealed that the binding sites of RNA correlated well with regions populated by chloride ions, suggesting that it is possible to screen for the binding sites of nucleic acids by determining the equilibrium distribution of negative ions. By including the crystallographically resolved RNA in addition to ions, we predicted the localization of the unresolved RNA in the viruses. Both viruses showed a hot-spot for RNA binding at the 5-fold symmetry axis. The MD simulations were compared to predictions of the chloride density based on nonlinear Poisson-Boltzmann equation (PBE) calculations with mobile ions. Although the predictions are superficially similar, the PBE calculations overestimate the ion concentration close to the capsid surface and underestimate it far away, mainly because protein dynamics is not taken into account. Density maps from chloride screening can be used to aid in building atomic models of packaged virus genomes. Knowledge of the principles of genome packaging might be exploited for both antiviral therapy and technological applications.

Single-molecule studies of viral DNA packaging

Many double-stranded DNA bacteriophages and viruses use specialized ATP-driven molecular machines to package their genomes into tightly confined procapsid shells. Over the last decade, single-molecule approaches - and in particular, optical tweezers - have made key contributions to our understanding of this remarkable process. In this chapter, we review these advances and the insights they have provided on the packaging mechanisms of three bacteriophages: φ 29, λ, and T4.

[Bioinformatics studies on drug resistance against anti-HIV-1 drugs]

More than 20 drugs have been available for anti-HIV-1 treatment in Japan. Combination therapy with these drugs dramatically decreases in morbidity and mortality of AIDS. However, due to high mutation rate of HIV-1, treatment with ineffective drugs toward patients infected with HIV-1 causes accumulation of mutations in the virus, and emergence of drug resistant viruses. Thus, to achieve appropriate application of the drugs toward the respective patients living with HIV-1, methods for predicting the level of drug-resistance using viral sequence information has been developed on the basis of bioinformatics. Furthermore, ultra-deep sequencing by next-generation sequencer whose data analysis is also based on bioinformatics, or in silico structural modeling have been achieved to understand drug resistant mechanisms. In this review, I overview the bioinformatics studies about drug resistance against anti-HIV-1 drugs.

Bacteriophage assembly

Bacteriophages have been a model system to study assembly processes for over half a century. Formation of infectious phage particles involves specific protein-protein and protein-nucleic acid interactions, as well as large conformational changes of assembly precursors. The sequence and molecular mechanisms of phage assembly have been elucidated by a variety of methods. Differences and similarities of assembly processes in several different groups of bacteriophages are discussed in this review. The general principles of phage assembly are applicable to many macromolecular complexes.

Encapsulation of a polymer by an icosahedral virus

The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus 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.

Mechanisms of capsid assembly around a polymer

Capsids of many viruses assemble around nucleic acids or other polymers. Understanding how the properties of the packaged polymer affect the assembly process could promote biomedical efforts to prevent viral assembly or nanomaterials applications that exploit assembly. To this end, we simulate on a lattice the dynamical assembly of closed, hollow shells composed of several hundred to 1000 subunits, around a flexible polymer. We find that assembly is most efficient at an optimum polymer length that scales with the surface area of the capsid; polymers that are significantly longer than optimal often lead to partial-capsids with unpackaged polymer "tails" or a competition between multiple partial-capsids attached to a single polymer. These predictions can be tested with bulk experiments in which capsid proteins assemble around homopolymeric RNA or synthetic polyelectrolytes. We also find that the polymer can increase the net rate of subunit accretion to a growing capsid both by stabilizing the addition of new subunits and by enhancing the incoming flux of subunits; the effects of these processes may be distinguishable with experiments that monitor the assembly of individual capsids.

Hydration effect on the optical property of a DNA fiber: first-principles and molecular dynamics studies

We have studied the theoretical hydration effect on the optical property of a deoxyribonucleic acid (DNA) double helix fiber. First-principles electronic structure and molecular dynamics simulations reveal that the electronic structure of the DNA fiber varies according to the amount of hydration or the relative humidity. We show that ultraviolet optical conductivity is influenced by hydration structure and DNA deformation, and our findings agree with other theoretical results and experimental observations. Infrared (IR) optical conductivity is estimated by the molecular dynamics approach. The humidity dependence of optical conductivity due to dipole relaxation of water is in close agreement with experimental observations. The theoretical IR absorption spectrum due to DNA vibrations agrees with the experimental spectrum. We discuss deformation and screening effects of the DNA fiber on humidity dependence of the optical spectra.