Applying molecular crowding models to simulations of virus capsid assembly in vitro

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.

Structure of the HIV immature lattice allows for essential lattice remodeling within budded virions

For HIV virions to become infectious, the immature lattice of Gag polyproteins attached to the virion membrane must be cleaved. Cleavage cannot initiate without the protease formed by the homo-dimerization of domains linked to Gag. However, only 5% of the Gag polyproteins, termed Gag-Pol, carry this protease domain, and they are embedded within the structured lattice. The mechanism of Gag-Pol dimerization is unknown. Here, we use spatial stochastic computer simulations of the immature Gag lattice as derived from experimental structures, showing that dynamics of the lattice on the membrane is unavoidable due to the missing 1/3 of the spherical protein coat. These dynamics allow for Gag-Pol molecules carrying the protease domains to detach and reattach at new places within the lattice. Surprisingly, dimerization timescales of minutes or less are achievable for realistic binding energies and rates despite retaining most of the large-scale lattice structure. We derive a formula allowing extrapolation of timescales as a function of interaction free energy and binding rate, thus predicting how additional stabilization of the lattice would impact dimerization times. We further show that during assembly, dimerization of Gag-Pol is highly likely and therefore must be actively suppressed to prevent early activation. By direct comparison to recent biochemical measurements within budded virions, we find that only moderately stable hexamer contacts (-12kBT<∆G<-8kBT) retain both the dynamics and lattice structures that are consistent with experiment. These dynamics are likely essential for proper maturation, and our models quantify and predict lattice dynamics and protease dimerization timescales that define a key step in understanding formation of infectious viruses.

Virus Mechanics under Molecular Crowding

Viruses avoid exposure of the viral genome to harmful agents with the help of a protective protein shell known as the capsid. A secondary effect of this protective barrier is that macromolecules that may be in high concentration on the outside cannot freely diffuse across it. Therefore, inside the cell and possibly even outside, the intact virus is generally under a state of osmotic stress. Viruses deal with this type of stress in various ways. In some cases, they might harness it for infection. However, the magnitude and influence of osmotic stress on virus physical properties remains virtually unexplored for single-stranded RNA viruses-the most abundant class of viruses. Here, we report on how a model system for the positive-sense RNA icosahedral viruses, brome mosaic virus (BMV), responds to osmotic pressure. Specifically, we study the mechanical properties and structural stability of BMV under controlled molecular crowding conditions. We show that BMV is mechanically reinforced under a small external osmotic pressure but starts to yield after a threshold pressure is reached. We explain this mechanochemical behavior as an effect of the molecular crowding on the entropy of the "breathing" fluctuation modes of the virus shell. The experimental results are consistent with the viral RNA imposing a small negative internal osmotic pressure that prestresses the capsid. Our findings add a new line of inquiry to be considered when addressing the mechanisms of viral disassembly inside the crowded environment of the cell.

Crystal structure of tomato spotted wilt virus GN reveals a dimer complex formation and evolutionary link to animal-infecting viruses

Tospoviridae is a family of enveloped RNA plant viruses that infect many field crops, inflicting a heavy global economic burden. These tripartite, single-stranded, negative-sense RNA viruses are transmitted from plant to plant by thrips as the insect vector. The medium (M) segment of the viral genome encodes two envelope glycoproteins, GN and GC, which together form the envelope spikes. GC is considered the virus fusogen, while the accompanying GN protein serves as an attachment protein that binds to a yet unknown receptor, mediating the virus acquisition by the thrips carrier. Here we present the crystal structure of glycoprotein N (GN) from the tomato spotted wilt virus (TSWV), a representative member of the Tospoviridae family. The structure suggests that GN is organized as dimers on TSWV's outer shell. Our structural data also suggest that this dimerization is required for maintaining GN structural integrity. Although the structure of the TSWV GN is different from other bunyavirus GN proteins, they all share similar domain connectivity that resembles glycoproteins from unrelated animal-infecting viruses, suggesting a common ancestor for these accompanying proteins.

Modeling the Self-Assembly of Protein Complexes through a Rigid-Body Rotational Reaction-Diffusion Algorithm

The reaction-diffusion equations provide a powerful framework for modeling nonequilibrium, cell-scale dynamics over the long time scales that are inaccessible by traditional molecular modeling approaches. Single-particle reaction-diffusion offers the highest resolution technique for tracking such dynamics, but it has not been applied to the study of protein self-assembly due to its treatment of reactive species as single-point particles. Here, we develop a relatively simple but accurate approach for building rigid structure and rotation into single-particle reaction-diffusion methods, providing a rate-based method for studying protein self-assembly. Our simplifying assumption is that reactive collisions can be evaluated purely on the basis of the separations between the sites, and not their orientations. The challenge of evaluating reaction probabilities can then be performed using well-known equations based on translational diffusion in both 3D and 2D, by employing an effective diffusion constant we derive here. We show how our approach reproduces both the kinetics of association, which is altered by rotational diffusion, and the equilibrium of reversible association, which is not. Importantly, the macroscopic kinetics of association can be predicted on the basis of the microscopic parameters of our structurally resolved model, allowing for critical comparisons with theory and other rate-based simulations. We demonstrate this method for efficient, rate-based simulations of self-assembly of clathrin trimers, highlighting how formation of regular lattices impacts the kinetics of association.

A method for efficient Bayesian optimization of self-assembly systems from scattering data

BACKGROUND

The ability of collections of molecules to spontaneously assemble into large functional complexes is central to all cellular processes. Using the viral capsid as a model system for complicated macro-molecular assembly, we develop methods for probing fine details of the process by learning kinetic rate parameters consistent with experimental measures of assembly. We have previously shown that local rule based stochastic simulation methods in conjunction with bulk indirect experimental data can meaningfully constrain the space of possible assembly trajectories and allow inference of experimentally unobservable features of the real system.

RESULTS

In the present work, we introduce a new Bayesian optimization framework using multi-Gaussian process model regression. We also extend our prior work to encompass small-angle X-ray/neutron scattering (SAXS/SANS) as a possibly richer experimental data source than the previously used static light scattering (SLS). Method validation is based on synthetic experiments generated using protein data bank (PDB) structures of cowpea chlorotic mottle virus. We also apply the same approach to computationally cheaper differential equation based simulation models.

CONCLUSIONS

We present a flexible approach for the global optimization of computationally costly objective functions associated with dynamic, multidimensional models. When applied to the stochastic viral capsid system, our method outperforms a current state of the art black box solver tailored for use with noisy objectives. Our approach also has wide applicability to general stochastic optimization problems.

Cell-free TXTL synthesis of infectious bacteriophage T4 in a single test tube reaction

The bottom-up construction of biological entities from genetic information provides a broad range of opportunities to better understand fundamental processes within living cells, as well as holding great promise for the development of novel biomedical applications. Cell-free transcription–translation (TXTL) systems have become suitable platforms to tackle such topics because they recapitulate the process of gene expression. TXTL systems have advanced to where the in vitro construction of viable, complex, self-assembling deoxyribonucleic acid-programmed biological entities is now possible. Previously, we demonstrated the cell-free synthesis of three bacteriophages from their genomes: MS2, ΦX174, T7. In this work, we present the complete synthesis of the phage T4 from its 169-kbp genome in one-pot TXTL reactions. This achievement, for one of the largest coliphages, demonstrates the integration of complex gene regulation, metabolism and self-assembly, and brings the bottom-up synthesis of biological systems to a new level.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Making microenvironments: A look into incorporating macromolecular crowding into in vitro experiments, to generate biomimetic microenvironments which are capable of directing cell function for tissue engineering applications

Biomimetic microenvironments are key components to successful cell culture and tissue engineering in vitro. One of the most accurate biomimetic microenvironments is that made by the cells themselves. Cell-made microenvironments are most similar to the in vivo state as they are cell-specific and produced by the actual cells which reside in that specific microenvironment. However, cell-made microenvironments have been challenging to re-create in vitro due to the lack of extracellular matrix composition, volume and complexity which are required. By applying macromolecular crowding to current cell culture protocols, cell-made microenvironments, or cell-derived matrices, can be generated at significant rates in vitro. In this review, we will examine the causes and effects of macromolecular crowding and how it has been applied in several in vitro systems including tissue engineering.

Kinetic constraints on self-assembly into closed supramolecular structures

Many biological and synthetic systems exploit self-assembly to generate highly intricate closed supramolecular architectures, ranging from self-assembling cages to viral capsids. The fundamental design principles that control the structural determinants of the resulting assemblies are increasingly well-understood, but much less is known about the kinetics of such assembly phenomena and it remains a key challenge to elucidate how these systems can be engineered to assemble in an efficient manner and avoid kinetic trapping. We show here that simple scaling laws emerge from a set of kinetic equations describing the self-assembly of identical building blocks into closed supramolecular structures and that this scaling behavior provides general rules that determine efficient assembly in these systems. Using this framework, we uncover the existence of a narrow range of parameter space that supports efficient self-assembly and reveal that nature capitalizes on this behavior to direct the reliable assembly of viral capsids on biologically relevant timescales.

Multiscale Modeling of Diffusion in a Crowded Environment

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

Derivative-Free Optimization of Rate Parameters of Capsid Assembly Models from Bulk in Vitro Data

The assembly of virus capsids proceeds by a complicated cascade of association and dissociation steps, the great majority of which cannot be directly experimentally observed. This has made capsid assembly a rich field for computational models, but there are substantial obstacles to model inference for such systems. Here, we describe progress on fitting kinetic rate constants defining capsid assembly models to experimental data, a difficult data-fitting problem because of the high computational cost of simulating assembly trajectories, the stochastic noise inherent to the models, and the limited and noisy data available for fitting. We evaluate the merits of data-fitting methods based on derivative-free optimization (DFO) relative to gradient-based methods used in prior work. We further explore the advantages of alternative data sources through simulation of a model of time-resolved mass spectrometry data, a technology for monitoring bulk capsid assembly that can be expected to provide much richer data than previously used static light scattering approaches. The results show that advances in both the data and the algorithms can improve model inference. More informative data sources lead to high-quality fits for all methods, but DFO methods show substantial advantages on less informative data sources that better represent current experimental practice.

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.

Viruses, Artificial Viruses and Virus-Based Structures for Biomedical Applications

Nanobiomaterials such as virus particles and artificial virus particles offer tremendous opportunities to develop new biomedical applications such as drug- or gene-delivery, imaging and sensing but also improve understanding of biological mechanisms. Recent advances within the field of virus-based systems give insights in how to mimic viral structures and virus assembly processes as well as understanding biodistribution, cell/tissue targeting, controlled and triggered disassembly or release and circulation times. All these factors are of high importance for virus-based functional systems. This review illustrates advances in mimicking and enhancing or controlling these aspects to a high degree toward delivery and imaging applications.

Modeling Effects of RNA on Capsid Assembly Pathways via Coarse-Grained Stochastic Simulation

The environment of a living cell is vastly different from that of an in vitro reaction system, an issue that presents great challenges to the use of in vitro models, or computer simulations based on them, for understanding biochemistry in vivo. Virus capsids make an excellent model system for such questions because they typically have few distinct components, making them amenable to in vitro and modeling studies, yet their assembly can involve complex networks of possible reactions that cannot be resolved in detail by any current experimental technology. We previously fit kinetic simulation parameters to bulk in vitro assembly data to yield a close match between simulated and real data, and then used the simulations to study features of assembly that cannot be monitored experimentally. The present work seeks to project how assembly in these simulations fit to in vitro data would be altered by computationally adding features of the cellular environment to the system, specifically the presence of nucleic acid about which many capsids assemble. The major challenge of such work is computational: simulating fine-scale assembly pathways on the scale and in the parameter domains of real viruses is far too computationally costly to allow for explicit models of nucleic acid interaction. We bypass that limitation by applying analytical models of nucleic acid effects to adjust kinetic rate parameters learned from in vitro data to see how these adjustments, singly or in combination, might affect fine-scale assembly progress. The resulting simulations exhibit surprising behavioral complexity, with distinct effects often acting synergistically to drive efficient assembly and alter pathways relative to the in vitro model. The work demonstrates how computer simulations can help us understand how assembly might differ between the in vitro and in vivo environments and what features of the cellular environment account for these differences.

Coarse-grained simulation reveals key features of HIV-1 capsid self-assembly

The maturation of HIV-1 viral particles is essential for viral infectivity. During maturation, many copies of the capsid protein (CA) self-assemble into a capsid shell to enclose the viral RNA. The mechanistic details of the initiation and early stages of capsid assembly remain to be delineated. We present coarse-grained simulations of capsid assembly under various conditions, considering not only capsid lattice self-assembly but also the potential disassembly of capsid upon delivery to the cytoplasm of a target cell. The effects of CA concentration, molecular crowding, and the conformational variability of CA are described, with results indicating that capsid nucleation and growth is a multi-stage process requiring well-defined metastable intermediates. Generation of the mature capsid lattice is sensitive to local conditions, with relatively subtle changes in CA concentration and molecular crowding influencing self-assembly and the ensemble of structural morphologies.

Significant morphological changes occur during the conversion of the immature HIV virion into a mature infectious form. Here the authors use coarse-grained molecular dynamics simulations to model HIV-1 capsid self-assembly and disassembly events that suggests several metastable capsid intermediates sensitive to local conditions.

Allosteric Control of Icosahedral Capsid Assembly

During the life cycle of a virus, viral proteins and other components self-assemble to form an ordered protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article, we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly and thus should be taken into account in models that are used to estimate interaction parameters from experimental data.

Reconstruction of the Disassembly Pathway of an Icosahedral Viral Capsid and Shape Determination of Two Successive Intermediates

Viral capsids derived from an icosahedral plant virus widely used in physical and nanotechnological investigations were fully dissociated into dimers by a rapid change of pH. The process was probed in vitro at high spatiotemporal resolution by time-resolved small-angle X-ray scattering using a high brilliance synchrotron source. A powerful custom-made global fitting algorithm allowed us to reconstruct the most likely pathway parametrized by a set of stoichiometric coefficients and to determine the shape of two successive intermediates by ab initio calculations. None of these two unexpected intermediates was previously identified in self-assembly experiments, which suggests that the disassembly pathway is not a mirror image of the assembly pathway. These findings shed new light on the mechanisms and the reversibility of the assembly/disassembly of natural and synthetic virus-based systems. They also demonstrate that both the structure and dynamics of an increasing number of intermediate species become accessible to experiments.

Mechanisms of virus assembly

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.

Biomolecular engineering of virus-like particles aided by computational chemistry methods

Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.

Using Markov state models to study self-assembly

Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude.