Dynamic pathways for viral capsid assembly

Recent advances in the structure and assembly of non-enveloped spherical viruses

Non-enveloped spherical viruses (NSVs) are characterized by their highly symmetrical capsids that serve to protect and encapsulate the genomes. The stability and functionality of the capsids determine their ability for survival and proliferation in harsh environments. Over four decades of structural studies using X-ray crystallography and NMR have provided static, high-resolution snapshots of several viruses. Recently, advances in cryo-electron microscopy, together with AI-based structure predictions and traditional methods, have aided in elucidating not only the structural details of complex NSVs but also the mechanistic processes underlying their assembly. The knowledge thus generated has been instrumental in critical understanding of the conformational changes and interactions associated with the coat proteins, the genome, and the auxiliary factors that regulate the capsid dynamics. This review seeks to summarize current literature regarding the structure and assembly of the NSVs and discusses how the data has facilitated a deeper understanding of their biology and phylogeny.

Nonequilibrium Self-Assembly Control by the Stochastic Landscape Method

Self-assembly of building blocks is a fundamental process in nanotechnology, materials science, and biological systems, offering pathways to the formation of complex and functional structures through local interactions. However, the lack of effective error correction mechanisms often limits the efficiency and precision of assembly, particularly in systems with strong binding energies. Inspired by cellular processes and stochastic resetting, we present a closed-loop feedback control method that employs transient modulations in interaction energies, mimicking, for instance, the global effect of pH changes as nonequilibrium drives to optimize assembly outcomes in real time. By leveraging the stochastic landscape method, a framework using energy trend-based segmentation to predict self-assembly behavior, our approach dynamically analyzes the system's state and energy trends to guide control actions. We show that the transient energy modulation during kinetic trapping conditions substantially enhances assembly yields and reduces assembly times across diverse scenarios. This strategy provides a broadly applicable, data-driven framework for optimizing nonequilibrium assembly processes, with potential implications for precision manufacturing and responsive materials design, while also advancing our understanding of controlled molecular assembly in biological and synthetic contexts.

Disassembly of Virus-Like Particles and the Stabilizing Role of the Nucleic Acid Cargo

In many simple viruses and virus-like particles, the protein capsid self-assembles around a nucleic-acid genome. Although the assembly process has been studied in detail, relatively little is known about how the capsid disassembles, a potentially important step for infection (in viruses) or cargo delivery (in virus-like particles). We investigate capsid disassembly using a coarse-grained molecular dynamics model of a T = 1 dodecahedral capsid and an RNA-like polymer. We alter the interactions between the subunits of the capsid as well as the ionic strength of the solution to induce partial or complete disassembly of self-assembled particles. We find that disassembly follows nucleation-and-growth kinetics, where the nucleation barrier is related to the interaction strengths as well as to the conformation of the polymer. In particular, we find that polymer segments that interact with adjacent subunits reinforce the subunit-subunit contacts. These results have implications for the design of virus-like particles for applications such as drug delivery. A cargo designed with reinforcement in mind might be used to control the stability of such particles and mediate disassembly.

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.

Heterogeneity of HPV16 virus-like particles indicates a complex assembly energy surface

Human Papillomavirus serotype 16 (HPV16) capsid protein (L1) pentamers canonically assemble into T = 7 icosahedral capsids. Such virus-like particles are the basis of the HPV vaccine. We examined assembly of L1 pentamers in response to pH, mild oxidants, and ionic strength and found a mixture of closed, roughly spherical structures from ∼20 to ∼70 nm in diameter, indicating the presence of many kinetically accessible energy minima. Using bulk and single particle techniques we observed that the size distribution changes but does not reach homogeneity. Though heterogenous in size, particles showed uniform responses to low ionic strength dissociation, thermal unfolding, and susceptibility to protease digestion. These assays suggest maturation over time, but at different rates. Cysteine oxidation further stabilized particles at early, but not late, times without changing general characteristics including thermal stability and protease digestion. These data show complex assembly paths to species of different sizes, but with locally similar interactions.

Effect of Pregenomic RNA on the Mechanical Stability of HBV Capsid by Coarse-Grained Molecular Simulations

Hepatitis B virus (HBV) is a double-stranded DNA virus, but its life cycle involves an intermediate stage, during which pregenomic RNA (pgRNA) is encapsulated in the capsid and then reverse-transcribed into the minus DNA strand. These immature HBV virions are the key target for antiviral drug discovery. In this study, we investigate the flexibility and mechanical stability of the HBV capsid containing pgRNA by employing residue-resolved coarse-grained molecular dynamics simulations. The results showed that the presence of pgRNA tends to decrease the overall flexibility of the capsid. In addition, the symmetrically arranged subunits of the capsid show asymmetry in the dominant modes of the conformational fluctuations with or without the presence of pgRNA. Furthermore, the simulations revealed that the presence of pgRNA enhances the overall mechanical stability of the virion particle. Electrostatic interactions between the disordered CTD of capsid and pgRNA were found to play a crucial role in modulating viral mechanical stability. Decreasing the electrostatic interactions by CTD phosphorylation or high salt concentration significantly reduces the mechanical stability of the HBV capsid containing pgRNA. Finally, the 2-fold symmetric sites have been proposed to be the most vulnerable to rupture during the initial stages of capsid disassembly. These findings could enhance our understanding of the physical basis of viral invasion and provide valuable insights into the development of antiviral drugs.

2D capsid formation within an oscillatory energy landscape: orderly self-assembly depends on the interplay between a dynamic potential and intrinsic relaxation times

Multiple dissipative self-assembly protocols designed to create novel structures or to reduce kinetic traps have recently emerged. Specifically, temporal oscillations of particle interactions have been shown effective at both aims, but investigations thus far have focused on systems of simple colloids or their binary mixtures. In this work, we expand our understanding of the effect of temporally oscillating interactions to a two-dimensional coarse-grained viral capsid-like model that undergoes a self-limited assembly. This model includes multiple intrinsic relaxation times due to the internal structure of the capsid subunits and, under certain interaction regimes, proceeds via a two-step nucleation mechanism. We find that oscillations much faster than the local intrinsic relaxation times can be described via a time averaged inter-particle potential across a wide range of interaction strengths, while oscillations much slower than these relaxation times result in structures that adapt to the attraction strength of the current half-cycle. Interestingly, oscillation periods similar to these relaxation times shift the interaction window over which orderly assembly occurs by enabling error correction during the half-cycles with weaker attractions. Our results provide fundamental insights to non-equilibrium self-assembly on temporally variant energy landscapes.

Modeling reveals the strength of weak interactions in stacked-ring assembly

Cells employ many large macromolecular machines for the execution and regulation of processes that are vital for cell and organismal viability. Interestingly, cells cannot synthesize these machines as functioning units. Instead, cells synthesize the molecular parts that must then assemble into the functional complex. Many important machines, including chaperones such as GroEL and proteases such as the proteasome, comprise protein rings that are stacked on top of one another. While there is some experimental data regarding how stacked-ring complexes such as the proteasome self-assemble, a comprehensive understanding of the dynamics of stacked-ring assembly is currently lacking. Here, we developed a mathematical model of stacked-trimer assembly and performed an analysis of the assembly of the stacked homomeric trimer, which is the simplest stacked-ring architecture. We found that stacked rings are particularly susceptible to a form of kinetic trapping that we term "deadlock," in which the system gets stuck in a state where there are many large intermediates that are not the fully assembled structure but that cannot productively react. When interaction affinities are uniformly strong, deadlock severely limits assembly yield. We thus predicted that stacked rings would avoid situations where all interfaces in the structure have high affinity. Analysis of available crystal structures indicated that indeed the majority-if not all-of stacked trimers do not contain uniformly strong interactions. Finally, to better understand the origins of deadlock, we developed a formal pathway analysis and showed that, when all the binding affinities are strong, many of the possible pathways are utilized. In contrast, optimal assembly strategies utilize only a small number of pathways. Our work suggests that deadlock is a critical factor influencing the evolution of macromolecular machines and provides general principles for understanding the self-assembly efficiency of existing machines.

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Affinity chromatography for virus-like particle manufacturing: Challenges, solutions, and perspectives

The increasing medical application of virus-like particles (VLPs), notably vaccines and viral vectors, has increased the demand for commercial VLP production. However, VLP manufacturing has not yet reached the efficiency level achieved for recombinant protein therapeutics, especially in downstream processing. This review provides a comprehensive analysis of the challenges associated with affinity chromatography for VLP purification with respect to the diversity and complexity of VLPs and the associated upstream and downstream processes. The use of engineered affinity ligands and matrices for affinity chromatography is first discussed. Although several representative affinity ligands are currently available for VLP purification, most of them have difficulty in balancing ligand universality, ligand selectivity and mild operation conditions. Then, phage display technology and computer-assisted design are discussed as efficient methods for the rapid discovery of high-affinity peptide ligands. Finally, the VLP purification by affinity chromatography is analyzed. The process is significantly influenced by virus size and variation, ligand type and chromatographic mode. To address the updated regulatory requirements and epidemic outbreaks, technical innovations in affinity chromatography and process intensification and standardization in VLP purification should be promoted to achieve rapid process development and highly efficient VLP manufacturing, and emphasis is given to the discovery of universal ligands, applications of gigaporous matrices and platform technology. It is expected that the information in this review can provide a better understanding of the affinity chromatography methods available for VLP purification and offer useful guidance for the development of affinity chromatography for VLP manufacturing in the decades to come.

Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T = 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.

Virtual indentation of the empty capsid of the minute virus of mice using a minimal coarse-grained model

A minimal coarse-grained model for T=1 viral capsids assembled from 20 protein rigid trimers has been designed by extending a previously proposed form of the interaction energy written as a sum of anisotropic pairwise interactions between the trimeric capsomers. The extension of the model has been performed to properly account for the coupling between two internal coordinates: the one that measures the intercapsomer distance and the other that gives the intercapsomer dihedral angle. The model has been able to fit with less than a 10% error the atomic force microscopy (AFM) indentation experimental data for the empty capsid of the minute virus of mice (MVM), providing in this way an admissible picture of the main mechanisms behind the capsid deformations. In this scenario, the bending of the intercapsomer dihedral angle is the angular internal coordinate that can support larger deformations away from its equilibrium values, determining important features of the AFM indentation experiments as the elastic constants along the three symmetry axes of the capsid and the critical indentations. From the value of one of the parameters of our model, we conclude that trimers in the MVM must be quite oblate tops, in excellent agreement with their known structure. The transition from the linear to the nonlinear regimes sampled in the indentation process appears to be an interesting topic for future research in physical virology.

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.

The role of flow in the self-assembly of dragline spider silk proteins

Hydrodynamic flow in the spider duct induces conformational changes in dragline spider silk proteins (spidroins) and drives their assembly, but the underlying physical mechanisms are still elusive. Here we address this challenging multiscale problem with a complementary strategy of atomistic and coarse-grained molecular dynamics simulations with uniform flow. The conformational changes at the molecular level were analyzed for single-tethered spider silk peptides. Uniform flow leads to coiled-to-stretch transitions and pushes alanine residues into β sheet and poly-proline II conformations. Coarse-grained simulations of the assembly process of multiple semi-flexible block copolymers using multi-particle collision dynamics reveal that the spidroins aggregate faster but into low-order assemblies when they are less extended. At medium-to-large peptide extensions (50%-80%), assembly slows down and becomes reversible with frequent association and dissociation events, whereas spidroin alignment increases and alanine repeats form ordered regions. Our work highlights the role of flow in guiding silk self-assembly into tough fibers by enhancing alignment and kinetic reversibility, a mechanism likely relevant also for other proteins whose function depends on hydrodynamic flow.

Effect of ionic strength on the assembly of simian vacuolating virus capsid protein around poly(styrene sulfonate)

Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent, such as RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with a combinatorial number of intermediates. Hence, the mechanism of the reaction is poorly understood. In this paper, we combined solution small-angle X-ray scattering (SAXS), cryo-transmission electron microscopy (TEM), and computational modeling to determine the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by SAXS and cryo-TEM. To analyze the data, we performed Langevin dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures consistent with the experimental data. We found that close to physiological ionic strength, [Formula: see text] VLPs coexisted with VP1 pentamers. At lower or higher ionic strengths, incomplete particles coexisted with pentamers and [Formula: see text] particles. Including the simulated structures was essential to explain the SAXS data in a manner that is consistent with the cryo-TEM images.

Nonequilibrium design strategies for functional colloidal assemblies

We use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

Molecular Dynamics Simulations of Deformable Viral Capsomers

Most coarse-grained models of individual capsomers associated with viruses employ rigid building blocks that do not exhibit shape adaptation during self-assembly. We develop a coarse-grained general model of viral capsomers that incorporates their stretching and bending energies while retaining many features of the rigid-body models, including an overall trapezoidal shape with attractive interaction sites embedded in the lateral walls to favor icosahedral capsid assembly. Molecular dynamics simulations of deformable capsomers reproduce the rich self-assembly behavior associated with a general T=1 icosahedral virus system in the absence of a genome. Transitions from non-assembled configurations to icosahedral capsids to kinetically-trapped malformed structures are observed as the steric attraction between capsomers is increased. An assembly diagram in the space of capsomer-capsomer steric attraction and capsomer deformability reveals that assembling capsomers of higher deformability into capsids requires increasingly large steric attraction between capsomers. Increasing capsomer deformability can reverse incorrect capsomer-capsomer binding, facilitating transitions from malformed structures to symmetric capsids; however, making capsomers too soft inhibits assembly and yields fluid-like structures.

Understanding Virus Structure and Dynamics through Molecular Simulations

Viral outbreaks remain a serious threat to human and animal populations and motivate the continued development of antiviral drugs and vaccines, which in turn benefits from a detailed understanding of both viral structure and dynamics. While great strides have been made in characterizing these systems experimentally, molecular simulations have proven to be an essential, complementary approach. In this work, we review the contributions of molecular simulations to the understanding of viral structure, functional dynamics, and processes related to the viral life cycle. Approaches ranging from coarse-grained to all-atom representations are discussed, including current efforts at modeling complete viral systems. Overall, this review demonstrates that computational virology plays an essential role in understanding these systems.

Self-assembly coupled to liquid-liquid phase separation

Liquid condensate droplets with distinct compositions of proteins and nucleic acids are widespread in biological cells. While it is known that such droplets, or compartments, can regulate irreversible protein aggregation, their effect on reversible self-assembly remains largely unexplored. In this article, we use kinetic theory and solution thermodynamics to investigate the effect of liquid-liquid phase separation on the reversible self-assembly of structures with well-defined sizes and architectures. We find that, when assembling subunits preferentially partition into liquid compartments, robustness against kinetic traps and maximum achievable assembly rates can be significantly increased. In particular, both the range of solution conditions leading to productive assembly and the corresponding assembly rates can increase by orders of magnitude. We analyze the rate equation predictions using simple scaling estimates to identify effects of liquid-liquid phase separation as a function of relevant control parameters. These results may elucidate self-assembly processes that underlie normal cellular functions or pathogenesis, and suggest strategies for designing efficient bottom-up assembly for nanomaterials applications.

Design strategies for the self-assembly of polyhedral shells

The control over the self-assembly of complex structures is a long-standing challenge of material science, especially at the colloidal scale, as the desired assembly pathway is often kinetically derailed by the formation of amorphous aggregates. Here, we investigate in detail the problem of the self-assembly of the three Archimedean shells with five contact points per vertex, i.e., the icosahedron, the snub cube, and the snub dodecahedron. We use patchy particles with five interaction sites (or patches) as model for the building blocks and recast the assembly problem as a Boolean satisfiability problem (SAT) for the patch-patch interactions. This allows us to find effective designs for all targets and to selectively suppress unwanted structures. By tuning the geometrical arrangement and the specific interactions of the patches, we demonstrate that lowering the symmetry of the building blocks reduces the number of competing structures, which in turn can considerably increase the yield of the target structure. These results cement SAT-assembly as an invaluable tool to solve inverse design problems.

Investigating Fundamental Principles of Nonequilibrium Assembly Using Temperature-Sensitive Copolymers

Both natural biomaterials and synthetic materials benefit from complex energy landscapes that provide the foundation for structure-function relationships and environmental sensitivity. Understanding these nonequilibrium dynamics is important for the development of design principles to harness this behavior. Using a model system of poly(ethylene glycol) methacrylate-based thermoresponsive lower critical solution temperature (LCST) copolymers, we explored the impact of composition and stimulus path on nonequilibrium thermal hysteretic behavior. Through turbidimetry analysis of nonsuperimposable heat-cool cycles, we observe that LCST copolymers show clear hysteresis that varies as a function of pendent side chain length and hydrophobicity. Hysteresis is further impacted by the temperature ramp rate, as insoluble states can be kinetically trapped under optimized temperature protocols. This systematic study brings to light fundamental principles that can enable the harnessing of out-of-equilibrium effects in synthetic soft materials.

Beneficial and detrimental effects of non-specific binding during DNA hybridization

DNA strands have to sample numerous states to find the alignment that maximizes Watson-Crick-Franklin base pairing. This process depends strongly on sequence, which affects the stability of the native duplex as well as the prevalence of non-native inter- and intramolecular helices. We present a theory that describes DNA hybridization as a three-stage process: diffusion, registry search, and zipping. We find that non-specific binding affects each of these stages in different ways. Mis-registered intermolecular binding in the registry search stage helps DNA strands sample different alignments and accelerates the hybridization rate. Non-native intramolecular structure affects all three stages by rendering portions of the molecule inert to intermolecular association, limiting mis-registered alignments to be sampled, and impeding the zipping process. Once in-register base pairs are formed, the stability of the native structure is important to hold the molecules together long enough for non-native contacts to break.

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with the experimental ones. Adsorption onto the surface was simulated by a grand canonical Monte Carlo procedure and random sequential adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that the selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry.

Optimization of non-equilibrium self-assembly protocols using Markov state models

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Heat-induced transitions of an empty minute virus of mice capsid in explicit water: all-atom MD simulation

The capsid-like structure of the virus-based protein nanoparticles (NPs) can serve as bionanomaterials, with applications in biomedicines and nanotechnology. Release of packaged material from these nanocontainers is associated with subtle conformational changes of the NP structure, which in vitro, is readily accomplished by heating. Characterizing the structural changes as a function of temperature may provide fresh insights into nanomaterial/antiviral strategies. Here, we have calculated heat induced changes in the properties of an empty minute virus of mice particle using large-scale ≈ 3.0 × 10⁶ all-atom molecular dynamics simulations. We focus on two heat induced structural changes of the NP, namely, dynamical transition (DT) and breathing transition (BT), both characterized by sudden and sharp change of measured parameters at temperatures, T_DT and T_BT, respectively. While DT is assessed by mean-square fluctuation of hydrogen atoms of the NP, BT is monitored through internal volume and permeation rate of water molecules through the NP. Both the transitions, resulting primarily from collective atomistic motion, are found to occur at temperatures widely separated from one another (T_BT>T_DT). The breathing motions, responsible for the translocation events of the packaged materials through the NP to kick off, are further probed by computing atomic resolution stresses from NVE simulations. Distribution of equilibrium atomistic stresses on the NP reveals a largely asymmetric nature and suggests structural breathing may actually represent large dynamic changes in the hotspot regions, far from the NP pores, which is in remarkable resemblance with recently conducted hydrogen-deuterium exchange coupled to mass spectrometry experiment. Communicated by Ramaswamy H. Sarma.

Hierarchical Coarse-Grained Strategy for Macromolecular Self-Assembly: Application to Hepatitis B Virus-Like Particles

Macromolecular self-assembly is at the basis of many phenomena in material and life sciences that find diverse applications in technology. One example is the formation of virus-like particles (VLPs) that act as stable empty capsids used for drug delivery or vaccine fabrication. Similarly to the capsid of a virus, VLPs are protein assemblies, but their structural formation, stability, and properties are not fully understood, especially as a function of the protein modifications. In this work, we present a data-driven modeling approach for capturing macromolecular self-assembly on scales beyond traditional molecular dynamics (MD), while preserving the chemical specificity. Each macromolecule is abstracted as an anisotropic object and high-dimensional models are formulated to describe interactions between molecules and with the solvent. For this, data-driven protein-protein interaction potentials are derived using a Kriging-based strategy, built on high-throughput MD simulations. Semi-automatic supervised learning is employed in a high performance computing environment and the resulting specialized force-fields enable a significant speed-up to the micrometer and millisecond scale, while maintaining high intermolecular detail. The reported generic framework is applied for the first time to capture the formation of hepatitis B VLPs from the smallest building unit, i.e., the dimer of the core protein HBcAg. Assembly pathways and kinetics are analyzed and compared to the available experimental observations. We demonstrate that VLP self-assembly phenomena and dependencies are now possible to be simulated. The method developed can be used for the parameterization of other macromolecules, enabling a molecular understanding of processes impossible to be attained with other theoretical models.

Engineering Self-Assembling Protein Nanoparticles for Therapeutic Delivery

Despite remarkable advances over the past several decades, many therapeutic nanomaterials fail to overcome major in vivo delivery barriers. Controlling immunogenicity, optimizing biodistribution, and engineering environmental responsiveness are key outstanding delivery problems for most nanotherapeutics. However, notable exceptions exist including some lipid and polymeric nanoparticles, some virus-based nanoparticles, and nanoparticle vaccines where immunogenicity is desired. Self-assembling protein nanoparticles offer a powerful blend of modularity and precise designability to the field, and have the potential to solve many of the major barriers to delivery. In this review, we provide a brief overview of key designable features of protein nanoparticles and their implications for therapeutic delivery applications. We anticipate that protein nanoparticles will rapidly grow in their prevalence and impact as clinically relevant delivery platforms.

Polymorphic self-assembly of helical tubules is kinetically controlled

In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger than the size scale of the individual monomers. In many such cases, the finite dimension is selected by a preferred curvature of the monomers, which leads to self-closure of the assembly. In this article, we study an example class of self-closing assemblies: cylindrical tubules that assemble from triangular monomers. By combining kinetic Monte Carlo simulations, free energy calculations, and simple theoretical models, we show that a range of programmable size scales can be targeted by controlling the intricate balance between the preferred curvature of the monomers and their interaction strengths. However, their assembly is kinetically controlled-the tubule morphology is essentially fixed shortly after closure, resulting in a distribution of tubule widths that is significantly broader than the equilibrium distribution. We develop a simple kinetic model based on this observation and the underlying free-energy landscape of assembling tubules that quantitatively describes the distributions. Our results are consistent with recent experimental observations of tubule assembly from triangular DNA origami monomers. The modeling framework elucidates design principles for assembling self-limited structures from synthetic components, such as artificial microtubules that have a desired width and chirality.

The Dynamics of Viruslike Capsid Assembly and Disassembly

Cowpea chlorotic mottle virus (CCMV) is a widely used model for virus replication studies. A major challenge lies in distinguishing between the roles of the interaction between coat proteins and that between the coat proteins and the viral RNA in assembly and disassembly processes. Here, we report on the spontaneous and reversible size conversion of the empty capsids of a CCMV capsid protein functionalized with a hydrophobic elastin-like polypeptide which occurs following a pH jump. We monitor the concentrations of T = 3 and T = 1 capsids as a function of time and show that the time evolution of the conversion from one T number to another is not symmetric: The conversion from T = 1 to T = 3 is a factor of 10 slower than that of T = 3 to T = 1. We explain our experimental findings using a simple model based on classical nucleation theory applied to virus capsids, in which we account for the change in the free protein concentration, as the different types of shells assemble and disassemble by shedding or absorbing single protein subunits. As far as we are aware, this is the first study confirming that both the assembly and disassembly of viruslike shells can be explained through classical nucleation theory, reproducing quantitatively results from time-resolved experiments

Microcompartment assembly around multicomponent fluid cargoes

This article describes dynamical simulations of the assembly of an icosahedral protein shell around a bicomponent fluid cargo. Our simulations are motivated by bacterial microcompartments, which are protein shells found in bacteria that assemble around a complex of enzymes and other components involved in certain metabolic processes. The simulations demonstrate that the relative interaction strengths among the different cargo species play a key role in determining the amount of each species that is encapsulated, their spatial organization, and the nature of the shell assembly pathways. However, the shell protein–shell protein and shell protein–cargo component interactions that help drive assembly and encapsulation also influence cargo composition within certain parameter regimes. These behaviors are governed by a combination of thermodynamic and kinetic effects. In addition to elucidating how natural microcompartments encapsulate multiple components involved within reaction cascades, these results have implications for efforts in synthetic biology to colocalize alternative sets of molecules within microcompartments to accelerate specific reactions. More broadly, the results suggest that coupling between self-assembly and multicomponent liquid–liquid phase separation may play a role in the organization of the cellular cytoplasm.

Inositol Hexakisphosphate (IP6) Accelerates Immature HIV-1 Gag Protein Assembly toward Kinetically Trapped Morphologies

During the late stages of the HIV-1 lifecycle, immature virions are produced by the concerted activity of Gag polyproteins, primarily mediated by the capsid (CA) and spacer peptide 1 (SP1) domains, which assemble into a spherical lattice, package viral genomic RNA, and deform the plasma membrane. Recently, inositol hexakisphosphate (IP6) has been identified as an essential assembly cofactor that efficiently produces both immature virions in vivo and immature virus-like particles in vitro. To date, however, several distinct mechanistic roles for IP6 have been proposed on the basis of independent functional, structural, and kinetic studies. In this work, we investigate the molecular influence of IP6 on the structural outcomes and dynamics of CA/SP1 assembly using coarse-grained (CG) molecular dynamics (MD) simulations and free energy calculations. Here, we derive a bottom-up, low-resolution, and implicit-solvent CG model of CA/SP1 and IP6, and simulate their assembly under conditions that emulate both in vitro and in vivo systems. Our analysis identifies IP6 as an assembly accelerant that promotes curvature generation and fissure-like defects throughout the lattice. Our findings suggest that IP6 induces kinetically trapped immature morphologies, which may be physiologically important for later stages of viral morphogenesis and potentially useful for virus-like particle technologies.

Protein Cages: From Fundamentals to Advanced Applications

Proteins that self-assemble into polyhedral shell-like structures are useful molecular containers both in nature and in the laboratory. Here we review efforts to repurpose diverse protein cages, including viral capsids, ferritins, bacterial microcompartments, and designed capsules, as vaccines, drug delivery vehicles, targeted imaging agents, nanoreactors, templates for controlled materials synthesis, building blocks for higher-order architectures, and more. A deep understanding of the principles underlying the construction, function, and evolution of natural systems has been key to tailoring selective cargo encapsulation and interactions with both biological systems and synthetic materials through protein engineering and directed evolution. The ability to adapt and design increasingly sophisticated capsid structures and functions stands to benefit the fields of catalysis, materials science, and medicine.

Optimizing thermodynamic trajectories using evolutionary and gradient-based reinforcement learning

Using a model heat engine, we show that neural-network-based reinforcement learning can identify thermodynamic trajectories of maximal efficiency. We consider both gradient and gradient-free reinforcement learning. We use an evolutionary learning algorithm to evolve a population of neural networks, subject to a directive to maximize the efficiency of a trajectory composed of a set of elementary thermodynamic processes; the resulting networks learn to carry out the maximally efficient Carnot, Stirling, or Otto cycles. When given an additional irreversible process, this evolutionary scheme learns a previously unknown thermodynamic cycle. Gradient-based reinforcement learning is able to learn the Stirling cycle, whereas an evolutionary approach achieves the optimal Carnot cycle. Our results show how the reinforcement learning strategies developed for game playing can be applied to solve physical problems conditioned upon path-extensive order parameters.

Predicting a Kind of Unusual Multiple-States Dimerization-Modes Transformation in Protein PD-L1 System by Computational Investigation and a Generalized Rate Theory

The new cancer immunotherapy has been carried out with an almost messianic zeal, but its molecular basis remains unclear due to the complexity of programmed death ligand 1 (PD-L1) dimerization. In this study, a new and integral multiple dimerization-modes transformation process of PD-L1s (with a new PD-L1 dimerization mode and a new transformation path discovered) and the corresponding mechanism are predicted using theoretical and computational methods. The results of the state analysis show that 5 stable binding states exist in system. A generalized inter-state transformation rate (GITR) theory is also proposed in such multiple-states self-assembly system to explore the kinetic characteristics of inter-state transformation. A “drug insertion” path was identified as the dominant path of the PD-L1 dimerization-modes transformation. Above results can provide supports for both the relative drug design and other multiple-states self-assembly system from the theoretical chemistry perspective.

Phase transitions in virology

Viruses have established relationships with almost every other living organism on Earth and at all levels of biological organization: from other viruses up to entire ecosystems. In most cases, they peacefully coexist with their hosts, but in most relevant cases, they parasitize them and induce diseases and pandemics, such as the AIDS and the most recent avian influenza and COVID-19 pandemic events, causing a huge impact on health, society, and economy. Viruses play an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organization, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as occurs with temperature separating phases in a liquid, define sharp qualitative types of behaviour. Thesephase transitionsare very well known in physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing us to better understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known mathematical models of transition phenomena in virology. We suggest that the advantages of abstract, simplified pictures used in physics are also the key to properly understanding the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across scales and their evolutionary and clinical implications are outlined.

Minimal Design Principles for Icosahedral Virus Capsids

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.

Thermodynamic stability versus kinetic accessibility: Pareto fronts for programmable self-assembly

A challenge in designing self-assembling building blocks is to ensure the target state is both thermodynamically stable and kinetically accessible. These two objectives are known to be typically in competition, but it is not known how to simultaneously optimize them. We consider this problem through the lens of multi-objective optimization theory: we develop a genetic algorithm to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies. We use a coarse-grained model for the particles' dynamics that allows us to efficiently search over parameters, for systems small enough to be enumerated. For most target states there is a tradeoff when the number of types of particles is small, with medium-weak bonds favouring fast folding, and strong bonds favouring high equilibrium probability. The tradeoff disappears when the number of particle types reaches a value m*, that is usually much less than the total number of particles. This general approach of computing Pareto fronts allows one to identify the minimum number of design parameters to avoid a thermodynamic-kinetic tradeoff. However, we argue, by contrasting our coarse-grained model's predictions with those of Brownian dynamics simulations, that particles with short-ranged isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. The learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

How Hierarchical Interactions Make Membraneless Organelles Tick Like Clockwork

Biomolecular condensates appear throughout the cell, serving many different biochemical functions. We argue that condensate functionality is optimized when the interactions driving condensation vary widely in affinity. Strong interactions provide structural specificity needed to encode functional properties but carry the risk of kinetic arrest, while weak interactions allow the system to remain dynamic but do not restrict the conformational ensemble enough to sustain specific functional features. To support our opinion, we describe illustrative examples of the interplay of strong and weak interactions that are found in the nucleolus, SPOP/DAXX condensates, polySUMO/polySIM condensates, chromatin, and stress granules. The common feature of these systems is a hierarchical assembly motif in which weak, transient interactions condense structurally defined functional units.

Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Immature HIV-1 assembles from Gag dimers leaving partial hexamers at lattice edges as potential substrates for proteolytic maturation

HIV-1 particle assembly is driven by the viral Gag protein, which oligomerizes into a hexameric array on the inner surface of the viral envelope, forming a truncated spherical lattice containing large and small gaps. Gag is then cut by the viral protease, disassembles, and rearranges to form the mature, infectious virus. Here, we present structures and molecular dynamics simulations of the edges of the immature Gag lattice. Our analysis shows that Gag dimers are the basic assembly unit of the HIV-1 particle, lattice edges are partial hexamers, and partial hexamers are prone to structural changes allowing protease to cut Gag. These findings provide insights into assembly of the immature virus, its structure, and how it disassembles during maturation.

The CA (capsid) domain of immature HIV-1 Gag and the adjacent spacer peptide 1 (SP1) play a key role in viral assembly by forming a lattice of CA hexamers, which adapts to viral envelope curvature by incorporating small lattice defects and a large gap at the site of budding. This lattice is stabilized by intrahexameric and interhexameric CA-CA interactions, which are important in regulating viral assembly and maturation. We applied subtomogram averaging and classification to determine the oligomerization state of CA at lattice edges and found that CA forms partial hexamers. These structures reveal the network of interactions formed by CA-SP1 at the lattice edge. We also performed atomistic molecular dynamics simulations of CA-CA interactions stabilizing the immature lattice and partial CA-SP1 helical bundles. Free energy calculations reveal increased propensity for helix-to-coil transitions in partial hexamers compared to complete six-helix bundles. Taken together, these results suggest that the CA dimer is the basic unit of lattice assembly, partial hexamers exist at lattice edges, these are in a helix-coil dynamic equilibrium, and partial helical bundles are more likely to unfold, representing potential sites for HIV-1 maturation initiation.

Protein nanofibril design via manipulation of hydrogen bonds

The process of amyloid nanofibril formation has broad implications including the generation of the strongest natural materials, namely silk fibers, and their major contribution to the progression of many degenerative diseases. The key question that remains unanswered is whether the amyloidogenic nature, which includes the characteristic H-bonded β-sheet structure and physical characteristics of protein assemblies, can be modified via controlled intervention of the molecular interactions. Here we show that tailored changes in molecular interactions, specifically in the H-bonded network, do not affect the nature of amyloidogenic fibrillation, and even have minimal effect on the initial nucleation events of self-assembly. However, they do trigger changes in networks at a higher hierarchical level, namely enhanced 2D packaging which is rationalized by the 3D hierarchy of β-sheet assembly, leading to variations in fibril morphology, structural composition and, remarkably, nanomechanical properties. These results pave the way to a better understanding of the role of molecular interactions in sculpting the structural and physical properties of protein supramolecular constructs.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control

This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.

Complete and cooperative in vitro assembly of computationally designed self-assembling protein nanomaterials

Recent advances in computational methods have enabled the predictive design of self-assembling protein nanomaterials with atomic-level accuracy. These design strategies focus exclusively on a single target structure, without consideration of the mechanism or dynamics of assembly. However, understanding the assembly process, and in particular its robustness to perturbation, will be critical for translating this class of materials into useful technologies. Here we investigate the assembly of two computationally designed, 120-subunit icosahedral complexes in detail using several complementary biochemical methods. We found that assembly of each material from its two constituent protein building blocks was highly cooperative and yielded exclusively complete, 120-subunit complexes except in one non-stoichiometric regime for one of the materials. Our results suggest that in vitro assembly provides a robust and controllable route for the manufacture of designed protein nanomaterials and confirm that cooperative assembly can be an intrinsic, rather than evolved, feature of hierarchically structured protein complexes.

Recent advances in computational methods have enabled the predictive design of self-assembling protein nanomaterials with atomic-level accuracy. Here authors investigate the assembly of two computationally designed, 120-subunit icosahedral complexes and find that assembly of each material from its two constituent protein building blocks was highly cooperative.

Frustration and Direct-Coupling Analyses to Predict Formation and Function of Adeno-Associated Virus

Adeno-associated virus (AAV) is a promising gene therapy vector because of its efficient gene delivery and relatively mild immunogenicity. To improve delivery target specificity, researchers use combinatorial and rational library design strategies to generate novel AAV capsid variants. These approaches frequently propose high proportions of nonforming or noninfective capsid protein sequences that reduce the effective depth of synthesized vector DNA libraries, thereby raising the discovery cost of novel vectors. We evaluated two computational techniques for their ability to estimate the impact of residue mutations on AAV capsid protein-protein interactions and thus predict changes in vector fitness, reasoning that these approaches might inform the design of functionally enriched AAV libraries and accelerate therapeutic candidate identification. The Frustratometer computes an energy function derived from the energy landscape theory of protein folding. Direct-coupling analysis (DCA) is a statistical framework that captures residue coevolution within proteins. We applied the Frustratometer to select candidate protein residues predicted to favor assembled or disassembled capsid states, then predicted mutation effects at these sites using the Frustratometer and DCA. Capsid mutants were experimentally assessed for changes in virus formation, stability, and transduction ability. The Frustratometer-based metric showed a counterintuitive correlation with viral stability, whereas a DCA-derived metric was highly correlated with virus transduction ability in the small population of residues studied. Our results suggest that coevolutionary models may be able to elucidate complex capsid residue-residue interaction networks essential for viral function, but further study is needed to understand the relationship between protein energy simulations and viral capsid metastability.

The Integrity of the Intradimer Interface of the Hepatitis B Virus Capsid Protein Dimer Regulates Capsid Self-Assembly

During the hepatitis B virus lifecycle, 120 copies of homodimeric capsid protein assemble around a copy of reverse transcriptase and viral RNA and go on to produce an infectious virion. Assembly needs to be tightly regulated by protein conformational change to ensure symmetry, fidelity, and reproducibility. Here, we show that structures at the intradimer interface regulate conformational changes at the distal interdimer interface and so regulate assembly. A pair of interacting charged residues, D78 from each monomer, conspicuously located at the top of a four-helix bundle that forms the intradimer interface, were mutated to serine to disrupt communication between the two monomers. The mutation slowed assembly and destabilized the dimer to thermal and chemical denaturation. Mutant dimers showed evidence of transient partial unfolding based on the appearance of new proteolytically sensitive sites. Though the mutant dimer was less stable, the resulting capsids were as stable as the wildtype, based on assembly and thermal denaturation studies. Cryo-EM image reconstructions of capsid indicated that the subunits adopted an "open" state more usually associated with a free dimer and that the spike tips were either disordered or highly flexible. Molecular dynamics simulations provide mechanistic explanations for these results, suggesting that D78 stabilizes helix 4a, which forms part of the intradimer interface, by capping its N-terminus and hydrogen-bonding to nearby residues, whereas the D78S mutation disrupts these interactions, leading to partial unwinding of helix 4a. This in turn weakens the connection from helix 4 and the intradimer interface to helix 5, which forms the interdimer interface.

Revealing Thermodynamics and Kinetics of Lipid Self-Assembly by Markov State Model Analysis

Self-assembly is ubiquitous in the realm of biology and has become an elegant bottom-up approach to fabricate new materials. Although molecular dynamics (MD) simulations can complement experiments by providing the missing atomic details, it still remains a grand challenge to reveal the thermodynamic and kinetic information on a self-assembly system. In this work, we demonstrate for the first time that the Markov state model analysis can be used to delineate the variation of free energy during the self-assembly process of a typical amphiphilic lipid dipalmitoyl-phosphatidylcholine (DPPC). Free energy profiles against the solvent-accessible surface area and the root-mean-square deviation have been derived from extensive MD results of more than five hundred trajectories, which identified a metastable crossing-cylinder (CC) state and a transition state of the distorted bilayer with a free energy barrier of ∼0.02 kJ mol^-1 per DPPC lipid, clarifying a long-standing speculation for 20 years that there exists a free energy barrier during lipid self-assembly. Our simulations also unearth two mesophase structures at the early stage of self-assembly, discovering two assembling pathways to the CC state that have never been reported before. Further thermodynamic analysis derives the contributions from the enthalpy and the entropy terms to the free energy, demonstrating the critical role played by the enthalpy-entropy compensation. Our strategy opens the door to quantitatively understand the self-assembly processes in general and provides new opportunities for identifying common thermodynamic and kinetic patterns in different self-assembly systems and inspiring new ideas for experiments. It may also contribute to the refinement of force field parameters of various self-assembly systems.