During the lifecycle of many single-stranded RNA viruses, including many human pathogens, a protein shell called the capsid spontaneously assembles around the viral genome. Understanding the mechanisms by which capsid proteins selectively assemble around the viral RNA amidst diverse host RNAs is a key question in virology. In one proposed mechanism, sequence elements (packaging sites) within the genomic RNA promote rapid and efficient assembly through specific interactions with the capsid proteins. In this work we develop a coarse-grained particle-based computational model for capsid proteins and RNA which represents protein-RNA interactions arising both from non-specific electrostatics and specific packaging sites interactions. Using Brownian dynamics simulations, we explore how the efficiency and specificity of assembly depend on solution conditions (which control protein-protein and nonspecific protein-RNA interactions) as well as the strength and number of packaging sites. We identify distinct regions in parameter space in which packaging sites lead to highly specific assembly via different mechanisms, and others in which packaging sites lead to kinetic traps. We relate these computational predictions to in vitro assays for specificity in which cognate viral RNAs are compete against non-cognate RNAs for assembly by capsid proteins.
Efficient replication and assembly of virus particles are integral to the establishment of infection. In addition to the primary role of the capsid protein (CP) in encapsidating the RNA progeny, experimental evidence on positive sense single-stranded RNA viruses suggests that the CP also regulates RNA synthesis. Here, we demonstrate that replication of Satellite tobacco mosaic virus (STMV) is controlled by the cooperative interaction between STMV CP and the helper virus (HV) Tobacco mosaic virus (TMV) replicase. We identified that the STMV CP-HV replicase interaction requires a positively char…
The assembly and maturation of viruses with icosahedral capsids must be coordinated with icosahedral symmetry. The icosahedral symmetry imposes also the restrictions on the cooperative specific interactions between genomic RNA/DNA and coat proteins that should be reflected in quasi-regular segmentation of viral genomic sequences. Combining discrete direct and double Fourier transforms, we studied the quasi-regular large-scale segmentation in genomic sequences of different ssRNA, ssDNA, and dsDNA viruses. The particular representatives included satellite tobacco mosaic virus and the strains of …
Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid, and in some cases surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assembles within their host cells and in vitro. We describe the thermodynamics and kinetics for assembly of protein subunits into icosahedral capsid shells, and how these are modified in cases where the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques that have been used to characterize caps…
We model the spontaneous assembly of a capsid (a virus's closed outer shell) from many copies of identical units, using entirely irreversible steps and only information local to the growing edge. Our model is formulated in terms of (i) an elastic Hamiltonian with stretching and bending stiffness and a spontaneous curvature, and (ii) a set of rate constants for addition of new units or bonds. An ensemble of highly irregular capsids is generated, unlike the well-known icosahedrally symmetric viruses, but (we argue) plausible as a way to model the irregular capsids of retroviruses such as HIV. We…
Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer interaction in icosahedral capsids fix the form of the shortest and universal truncated multipolar expansion of the two-body interaction between capsomers. The structures of many of the icosahedral and related virus capsids are located as single lowest energy states of this potential energy surface. Our approach unveils relevant features of the natural design of th…
We extend our previously developed general approach (1) to study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation approach combines the traditional Monte Carlo method with the method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we study the assembly and structural origin of non-icosahedral, elongated virus capsids, such as two aberrant flock house virus (FH…
Electrostatic interactions play a central role in the assembly of single-stranded RNA viruses. Under physiological conditions of salinity and acidity, virus capsid assembly requires the presence of genomic material that is oppositely charged to the core proteins. In this paper we apply basic polymer physics and statistical mechanics methods to the self-assembly of a synthetic virus encapsidating generic polyelectrolyte molecules. We find that (i) the mean concentration of the encapsidated polyelectrolyte material depends on the surface charge density, the radius of the capsid, and the linear c…
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. Fu…
In many virus families, tens to thousands of proteins assemble spontaneously into a capsid (protein shell) while packaging the genomic nucleic acid. This review summarizes recent advances in computational modeling of these dynamical processes. We present an overview of recent technological and algorithmic developments, which are enabling simulations to describe the large ranges of length-and time-scales relevant to assembly, under conditions more closely matched to experiments than in earlier work. We then describe two examples in which computational modeling has recently provided an important…
We use computer simulations to study a model, first proposed by Wales [1], for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of thermodynamic and geometric factors can be qualitatively related to the potential energy landscape structure of the assembling system. Even though the model is strongly coarse-grained, it exhibits a number of features also observed in experiments, such as sigmoidal assembly dynamics, hysteresis in capsid formation and numerous kinetic traps. We also investigate the effe…
Viruses self-assemble from identical capsid proteins and their genome consisting, for example, of a long single stranded (ss) RNA. For a big class of T = 3 viruses capsid proteins have long positive N-terminal tails. We explore the role played by the Coulomb interaction between the brush of positive N-terminal tails rooted at the inner surface of the capsid and the negative ss RNA molecule. We show that viruses are most stable when the total contour length of ss RNA is close to the total length of the tails. For such a structure the absolute value of the total RNA charge is approximately twice…
We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions. Previous studies of the capsid self-assembly involved solid objects of a supramolecular scale, e.g. corresponding to capsomeres, with engineered couplings and stochastic movements. In our approach, a single capsid is dissociated by an application of a high temperature for a v…
A big class of viruses self-assemble from a large number of identical capsid proteins with long flexible N-terminal tails and ss RNA. We study the role of the strong Coulomb interaction of positive N-terminal tails with ss RNA in the kinetics of the in vitro virus self-assembly. Capsid proteins stick to unassembled chain of ss RNA (which we call "antenna") and slide on it towards the assembly site. We show that at excess of capsid proteins such one-dimensional diffusion accelerates self-assembly more than ten times. On the other hand at excess of ss RNA, antenna slows self-assembly down. Sever…
Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous co-assembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively charged RNA and the positively charged inner capsid wall. Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.
York St John University（约克圣约翰大学）；University of York（约克大学）；City, University of London（伦敦大学城市学院）；Merton College, University of Oxford（牛津大学默顿学院）；NanKai University（南开大学）
Realistic evolutionary fitness landscapes are notoriously difficult to construct. A recent cutting-edge model of virus assembly consists of a dodecahedral capsid with $12$ corresponding packaging signals in three affinity bands. This whole genome/phenotype space consisting of $3^{12}$ genomes has been explored via computationally expensive stochastic assembly models, giving a fitness landscape in terms of the assembly efficiency. Using latest machine-learning techniques by establishing a neural network, we show that the intensive computation can be short-circuited in a matter of minutes to ast…
Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between a ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. …
Understanding how virus capsids assemble around their nucleic acid (NA) genomes could promote efforts to block viral propagation or to reengineer capsids for gene therapy applications. We develop a coarse-grained model of capsid proteins and NAs with which we investigate assembly dynamics and thermodynamics. In contrast to recent theoretical models, we find that capsids spontaneously `overcharge'; i.e., the negative charge of the NA exceeds the positive charge on capsid. When applied to specific viruses, the optimal NA lengths closely correspond to the natural genome lengths. Calculations base…
A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms. The fact that different viruses adopt similar structural forms is an indication of a common underlying design, motivating the use of simplified, low-resolution models in exploring the assembly process. Several versions of a molecular dynamics approach are described. Polyhedral shells of different sizes are involved, the assembly pathways are either irreversibl…
Icosahedral viruses have their infectious genome encapsulated by a shell assembled by a multiscale process, starting from an integer multiple of 60 viral capsid or coat protein (VP) monomers. We predict and validate inter-atomic hotspot interactions between VP monomers that are important for the assembly of 3 icosahedral viral capsids: Adeno Associated Virus serotype 2 (AAV2) and Minute Virus of Mice (MVM), both T=1 single stranded DNA viruses, and Bromo Mosaic Virus (BMV), a T=3 single stranded RNA virus. Experimental validation is by in-vitro, site-directed mutagenesis data found in literatu…
Understanding protein self-assembly is important for many biological and industrial processes. Proteins can self-assemble into crystals, filaments, gels, and other amorphous aggregates. The final forms include virus capsids and condensed phases associated with diseases, such as amyloid fibrils. Although seemingly different, these assemblies all originate from fundamental protein interactions and are driven by similar thermodynamic and kinetic factors. Here we review recent advances in understanding protein self-assembly through a soft condensed matter perspective with an emphasis on three spec…
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 mec…
Many single-stranded (ss) RNA viruses self assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean field theory to investigate how the secondary structure of the R…
Most of the existing research in assembly pathway prediction/analysis of virus cap- sids makes the simplifying assumption that the configuration of the intermediate states can be extracted directly from the final configuration of the entire capsid. This assump- tion does not take into account the conformational changes of the constituent proteins as well as minor changes to the binding interfaces that continues throughout the assembly process until stabilization. This paper presents a statistical-ensemble based approach which provides sufficient samples of the configurational space for each mo…
A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Assembly models are developed for viral capsids built from protein building blocks that can assume different local bonding structures in the capsid. This situation occurs, for example, for viruses in the family of Papovaviridae, which are linked to cancer and are hence of particular interest for the health sector. More specifically, the viral capsids of the (pseudo-) T=7 particles in this family consist of pentamers that exhibit two different types…
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 …
Many viruses rely on the self-assembly of their capsids to protect and transport their genomic material. For many viral systems, in particular for human viruses like hepatitis B, adeno or human immunodeficiency virus, that lead to persistent infections, capsomeres are continuously produced in the cytoplasm of the host cell while completed capsids exit the cell for a new round of infection. Here we use coarse-grained Brownian dynamics simulations of a generic patchy particle model to elucidate the role of the dynamic supply of capsomeres for the reversible self-assembly of empty T1 icosahedral …
The COVID-19 pandemic caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has spurred unprecedented and concerted worldwide research to curtail and eradicate this pathogen. SARS-CoV-2 has four structural proteins: Envelope (E), Membrane (M), Nucleocapsid (N), and Spike (S), which self-assemble along with its RNA into the infectious virus by budding from intracellular lipid membranes. In this paper, we develop a model to explore the mechanisms of RNA condensation by structural proteins, protein oligomerization and cellular membrane-protein interactions that control the bu…
The distribution of inequivalent geometries occurring during self-assembly of the major capsid protein in thermodynamic equilibrium is determined based on a master equation approach. These results are implemented to characterize the assembly of SV40 virus and to obtain information on the putative pathways controlling the progressive build-up of the SV40 capsid. The experimental testability of the predictions is assessed and an analysis of the geometries of the assembly intermediates on the dominant pathways is used to identify targets for antiviral drug design.
We simulate the assembly dynamics of icosahedral capsids from subunits that interconvert between different conformations (or quasi-equivalent states). The simulations identify mechanisms by which subunits form empty capsids with only one morphology but adaptively assemble into different icosahedral morphologies around nanoparticle cargoes with varying sizes, as seen in recent experiments with brome mosaic virus (BMV) capsid proteins. Adaptive cargo encapsidation requires moderate cargo-subunit interaction strengths; stronger interactions frustrate assembly by stabilizing intermediates with inc…
A major part of the interactions involved in the assembly and stability of icosahedral, positive-sense single-stranded RNA (ssRNA+) viruses is electrostatic in nature, as can be inferred from the strong $pH$- and salt-dependence of their assembly phase diagrams. Electrostatic interactions do not act only between the capsid coat proteins (CPs), but just as often provide a significant contribution to the interactions of the CPs with the genomic RNA, mediated to a large extent by positively charged, flexible N-terminal tails of the CPs. In this work, we provide two clear and complementary definit…
The use of reduced models for investigating the self-assembly dynamics underlying protein shell formation in spherical viruses is described. The spontaneous self-assembly of these polyhedral, supramolecular structures, in which icosahedral symmetry is a conspicuous feature, is a phenomenon whose dynamics remain unexplored; studying the growth process by means of computer simulation provides access to the mechanisms underlying assembly. In order to capture the more universal aspects of self-assembly, namely the manner in which component shapes influence structure and assembly pathway, in this e…
Electrostatic interaction is the driving force for the encapsulation by virus coat proteins of nanoparticles such as quantum dots, gold particles and magnetic beads for, e.g., imaging and therapeutic purposes. In recent experimental work, Daniel et al. [ACS Nano 4 (2010), 3853-3860] found the encapsulation efficiency to sensitively depend on the interplay between the surface charge density of negatively charged gold nanoparticles and the number of positive charges on the RNA binding domains of the proteins. Surprisingly, these experiments reveal that despite the highly cooperative nature of th…
Molecular dynamics simulation is used to model the self-assembly of polyhedral shells containing 180 trapezoidal particles that correspond to the T=3 virus capsid. Three kinds of particle, differing only slightly in shape, are used to account for the effect of quasi-equivalence. Bond formation between particles is reversible and an explicit atomistic solvent is included. Under suitable conditions the simulations are able to produce complete shells, with the majority of unused particles remaining as monomers, and practically no other clusters. There are also no incorrectly assembled clusters. T…
A coarse-grained computational model is used to investigate the effect of a fluctuating fluid membrane on the dynamics of patchy-particle assembly into virus capsid-like cores. Results from simulations for a broad range of parameters are presented, showing the effect of varying interaction strength, membrane stiffness and membrane viscosity. Furthermore, the effect of hydrodynamic interactions is investigated. Attraction to a membrane may promote assembly, including for sub-unit interaction strengths for which it does not occur in the bulk, and may also decrease single-core assembly time. The …
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; significantly longer than optimal polymers often lead…
Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex or the actin cytoskeleton is strongly determined by their spatial structure. Moreover it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positio…
Physical properties of capsids of plant and animal viruses are important factors in capsid self-assembly, survival of viruses in the extracellular environment, and their cell infectivity. Virus shells can have applications as nanocontainers and delivery vehicles in biotechnology and medicine. Combined AFM experiments and computational modeling on sub-second timescales of the indentation nanomechanics of Cowpea Chlorotic Mottle Virus (CCMV) capsid show that the capsid's physical properties are dynamic and local characteristics of the structure, which depend on the magnitude and geometry of mech…
Previous self-assembly experiments on a model icosahedral plant virus have shown that, under physiological conditions, capsid proteins initially bind to the genome through an en masse mechanism and form nucleoprotein complexes in a disordered state, which raises the questions as to how virions are assembled into a highly ordered structure in the host cell. Using small-angle X-ray scattering, we find out that a disorder-order transition occurs under physiological conditions upon an increase in capsid protein concentrations. Our cryo-transmission electron microscopy reveals closed spherical shel…
A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Viral capsids are usually spherical, and for a significant number of viruses exhibit overall icosahedral symmetry. The corresponding surface lattices, that encode the locations of the capsid proteins and intersubunit bonds, can be modelled by Viral Tiling Theory. It has been shown in vitro that under a variation of the experimental boundary conditions, such as the pH value and salt concentration, tubular particles may appear instead of, or in addit…
We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse grained description of protein oligomers based on graph rigidity. These reduced protein descriptions are used in an extended Gillespie algorithm to investigate the stochastic kinetics of the assembly process. The association rates are obtained from a diffusive Smoluchowski equation for rapid coagulation, modified to account for water shielding and protein structure. The dissociation rate…
Classifying the Stoichiometry of Virus-like Particles with Interpretable Machine Learning
University of Sheffield（谢菲尔德大学）；School of Computer Science, University of Sheffield（谢菲尔德大学计算机科学学院）；School of Chemical, Materials and Biological Engineering, University of Sheffield（谢菲尔德大学化学、材料与生物工程学院）
We develop equilibrium and kinetic theories that describe the assembly of viral capsid proteins on a charged central core, as seen in recent experiments in which brome mosaic virus (BMV) capsids assemble around nanoparticles functionalized with polyelectrolyte. We model interactions between capsid proteins and nanoparticle surfaces as the interaction of polyelectrolyte brushes with opposite charge, using the nonlinear Poisson Boltzmann equation. The models predict that there is a threshold density of functionalized charge, above which capsids efficiently assemble around nanoparticles, and that…
In this article we use all-atom simulations to elucidate the mechanisms underlying conformational switching and allostery within the coat protein of the bacteriophage MS2. Assembly of most icosahedral virus capsids requires that the capsid protein adopt different conformations at precise locations within the capsid. It has been shown that a 19 nucleotide stem loop (TR) from the MS2 genome acts as an allosteric effector, guiding conformational switching of the coat protein during capsid assembly. Since the principal conformational changes occur far from the TR binding site, it is important to u…
The functions of RNA pseudoknots (PKs), which are minimal tertiary structural motifs and an integral part of several ribozymes and ribonucleoprotein complexes, are determined by their structure, stability and dynamics. Therefore, it is important to elucidate the general principles governing their thermodynamics/folding mechanisms. Here, we combine experiments and simulations to examine the folding/unfolding pathways of the VPK pseudoknot, a variant of the Mouse Mammary Tumor Virus (MMTV) PK involved in ribosomal frameshifting. Fluorescent nucleotide analogs (2-aminopurine and pyrrolocytidine) …
Recent work has shown that the hydrophobic protein surfaces in aqueous solution sit near a drying transition. The tendency for these surfaces to expel water from their vicinity leads to self assembly of macromolecular complexes. In this article we show with a realistic model for a biologically pertinent system how this phenomenon appears at the molecular level. We focus on the association of the C-terminal domain (CA-C) of the human immunodeficiency virus (HIV) capsid protein. By combining all-atom simulations with specialized sampling techniques we measure the water density distribution durin…
