Movement and self-control in protein assemblies. Quasi-equivalence revisited

Hierarchical Self-Organization and Disorganization of Helical Supramolecular Columns Mediated by H-Bonding and Shape Complementarity

H-bonding, shape complementarity, and quasi-equivalence are widely accepted as some of the most influential molecular recognition events mediating biological and synthetic self-organizations. H-bonds are weaker than ionic but stronger than van der Waals forces. However, the directionality of H-bonds makes them the most powerful among all nonbonding interactions. Here, we selected two taper-shaped self-assembling dendrons, one flexible and one rigid, and equipped them with -CO2CH3, -CH2OH, and -COOH at their apex. They demonstrated the hierarchical way in which shape-complementarity in the presence of -CO2CH3 mediated highly ordered helical self-organization for the case of the rigid building block and less ordered helical arrays for the flexible one. Weak H-bonding by -CH2OH unwound the helix from the rigid dendron, yielding a porous column. Due to its quasi-equivalence, the flexible dendron tolerated better the H-bonding by -CH2OH self-organizing a different helical column. The rigid and the flexible dendrons yielded only disorganized nonhelical columns in the presence of -COOH at the apex. This balance between rigidity, flexibility, and tolerance or lack of it to diverse H-bonding architectures indicates that mechanistic elucidation of the self-organization process helps endow it with the same building block, both helical organizations approaching biological precision, and disorganized nonhelical arrangements.

Structure and proposed DNA delivery mechanism of a marine roseophage

Tailed bacteriophages (order, Caudovirales) account for the majority of all phages. However, the long flexible tail of siphophages hinders comprehensive investigation of the mechanism of viral gene delivery. Here, we report the atomic capsid and in-situ structures of the tail machine of the marine siphophage, vB_DshS-R4C (R4C), which infects Roseobacter. The R4C virion, comprising 12 distinct structural protein components, has a unique five-fold vertex of the icosahedral capsid that allows genome delivery. The specific position and interaction pattern of the tail tube proteins determine the atypical long rigid tail of R4C, and further provide negative charge distribution within the tail tube. A ratchet mechanism assists in DNA transmission, which is initiated by an absorption device that structurally resembles the phage-like particle, RcGTA. Overall, these results provide in-depth knowledge into the intact structure and underlining DNA delivery mechanism for the ecologically important siphophages.

Single-particle studies of the effects of RNA-protein interactions on the self-assembly of RNA virus particles

Understanding the pathways by which simple RNA viruses self-assemble from their coat proteins and RNA is of practical and fundamental interest. Although RNA-protein interactions are thought to play a critical role in the assembly, our understanding of their effects is limited because the assembly process is difficult to observe directly. We address this problem by using interferometric scattering microscopy, a sensitive optical technique with high dynamic range, to follow the in vitro assembly kinetics of more than 500 individual particles of brome mosaic virus (BMV)-for which RNA-protein interactions can be controlled by varying the ionic strength of the buffer. We find that when RNA-protein interactions are weak, BMV assembles by a nucleation-and-growth pathway in which a small cluster of RNA-bound proteins must exceed a critical size before additional proteins can bind. As the strength of RNA-protein interactions increases, the nucleation time becomes shorter and more narrowly distributed, but the time to grow a capsid after nucleation is largely unaffected. These results suggest that the nucleation rate is controlled by RNA-protein interactions, while the growth process is driven less by RNA-protein interactions and more by protein-protein interactions and intraprotein forces. The nucleated pathway observed with the plant virus BMV is strikingly similar to that previously observed with bacteriophage MS2, a phylogenetically distinct virus with a different host kingdom. These results raise the possibility that nucleated assembly pathways might be common to other RNA viruses.

A kinetic model for the impact of packaging signal mimics on genome encapsulation

Inspired by recent experiments on the spontaneous assembly of virus-like particles from a solution containing a synthetic coat protein and double-stranded DNA, we put forward a kinetic model that has as main ingredients a stochastic nucleation and a deterministic growth process. The efficiency and rate of DNA packaging strongly increase after tiling the DNA with CRISPR-Cas proteins at predesignated locations, mimicking assembly signals in viruses. Our model shows that treating these proteins as nucleation-inducing diffusion barriers is sufficient to explain the experimentally observed increase in encapsulation efficiency, but only if the nucleation rate is sufficiently high. We find an optimum in the encapsulation kinetics for conditions where the number of packaging signal mimics is equal to the number of nucleation events that can occur during the time required to fully encapsulate the DNA template, presuming that the nucleation events can only take place adjacent to a packaging signal. Our theory is in satisfactory agreement with the available experimental data.

The time complexity of self-assembly

Time efficiency of self-assembly is crucial for many biological processes. Moreover, with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. While structural determinants and the final assembly yield are increasingly well understood, kinetic aspects concerning the time efficiency, however, remain much more elusive. In computer science, the concept of time complexity is used to characterize the efficiency of an algorithm and describes how the algorithm's runtime depends on the size of the input data. Here we characterize the time complexity of nonequilibrium self-assembly processes by exploring how the time required to realize a certain, substantial yield of a given target structure scales with its size. We identify distinct classes of assembly scenarios, i.e., "algorithms" to accomplish this task, and show that they exhibit drastically different degrees of complexity. Our analysis enables us to identify optimal control strategies for nonequilibrium self-assembly processes. Furthermore, we suggest an efficient irreversible scheme for the artificial self-assembly of nanostructures, which complements the state-of-the-art approach using reversible binding reactions and requires no fine-tuning of binding energies.

Shape shifter: redirection of prolate phage capsid assembly by staphylococcal pathogenicity islands

Staphylococcus aureus pathogenicity islands (SaPIs) are molecular parasites that hijack helper phages for their transfer. SaPIbov5, the prototypical member of a family of cos type SaPIs, redirects the assembly of ϕ12 helper capsids from prolate to isometric. This size and shape shift is dependent on the SaPIbov5-encoded protein Ccm, a homolog of the ϕ12 capsid protein (CP). Using cryo-electron microscopy, we have determined structures of prolate ϕ12 procapsids and isometric SaPIbov5 procapsids. ϕ12 procapsids have icosahedral end caps with T_end = 4 architecture and a T_mid = 14 cylindrical midsection, whereas SaPIbov5 procapsids have T = 4 icosahedral architecture. We built atomic models for CP and Ccm, and show that Ccm occupies the pentameric capsomers in the isometric SaPIbov5 procapsids, suggesting that preferential incorporation of Ccm pentamers prevents the cylindrical midsection from forming. Our results highlight that pirate elements have evolved diverse mechanisms to suppress phage multiplication, including the acquisition of phage capsid protein homologs.

Phage-inducible chromosomal islands (PICIs) are a group of mobile genetic elements that hijack the replication and assembly machinery of helper bacteriophages. Here the authors describe a mechanism by which a group of PICIs from Staphylococcus aureus re-direct the assembly pathway of their helpers using a capsid protein homolog.

Quantitative description of a contractile macromolecular machine

Contractile injection systems (CISs) [type VI secretion system (T6SS), phage tails, and tailocins] use a contractile sheath-rigid tube machinery to breach cell walls and lipid membranes. The structures of the pre- and postcontraction states of several CISs are known, but the mechanism of contraction remains poorly understood. Combining structural information of the end states of the 12-megadalton R-type pyocin sheath-tube complex with thermodynamic and force spectroscopy analyses and an original modeling procedure, we describe the mechanism of pyocin contraction. We show that this nanomachine has an activation energy of 160 kilocalories/mole (kcal/mol), and it releases 2160 kcal/mol of heat and develops a force greater than 500 piconewtons. Our combined approach provides a quantitative and experimental description of the membrane penetration process by a CIS.

The Trimeric Major Capsid Protein of Mavirus is stabilized by its Interlocked N-termini Enabling Core Flexibility for Capsid Assembly

Icosahedral viral capsids assemble with high fidelity from a large number of identical buildings blocks. The mechanisms that enable individual capsid proteins to form stable oligomeric units (capsomers) while affording structural adaptability required for further assembly into capsids are mostly unknown. Understanding these mechanisms requires knowledge of the capsomers' dynamics, especially for viruses where no additional helper proteins are needed during capsid assembly like for the Mavirus virophage that despite its complexity (triangulation number T = 27) can assemble from its major capsid protein (MCP) alone. This protein forms the basic building block of the capsid namely a trimer (MCP₃) of double-jelly roll protomers with highly intertwined N-terminal arms of each protomer wrapping around the other two at the base of the capsomer, secured by a clasp that is formed by part of the C-terminus. Probing the dynamics of the capsomer with HDX mass spectrometry we observed differences in conformational flexibility between functional elements of the MCP trimer. While the N-terminal arm and clasp regions show above average deuterium incorporation, the two jelly-roll units in each protomer also differ in their structural plasticity, which might be needed for efficient assembly. Assessing the role of the N-terminal arm in maintaining capsomer stability showed that its detachment is required for capsomer dissociation, constituting a barrier towards capsomer monomerisation. Surprisingly, capsomer dissociation was irreversible since it was followed by a global structural rearrangement of the protomers as indicated by computational studies showing a rearrangement of the N-terminus blocking part of the capsomer forming interface.

The impact of size on particle drainage dynamics and antibody response

Vaccine-induced immune response can be greatly enhanced by mimicking pathogen properties. The size and the repetitive geometric shape of virus-like particles (VLPs) influence their immunogenicity by facilitating drainage to secondary lymphoid organs and enhancing interaction with and activation of B cells and innate humoral immune components. VLPs derived from the plant Bromovirus genus, specifically cowpea chlorotic mottle virus (CCMV), are T = 3 icosahedral particles. (T) is the triangulation number that refers to the number and arrangements of the subunits (pentamers and hexamers) of the VLPs. CCMV-VLPs can be easily expressed in an E. coli host system and package ssRNA during the expression process. Recently, we have engineered CCMV-VLPs by incorporating the universal tetanus toxin (TT) epitope at the N-terminus. The modified CCMV_TT-VLPs successfully form icosahedral particles T = 3, with a diameter of ~30 nm analogous to the parental VLPs. Interestingly, incorporating TT epitope at the C-terminus of CCMV_TT-VLPs results in the formation of Rod-shaped VLPs, ~1 μm in length and ~ 30 nm in width. In this study, we have investigated the draining kinetics and immunogenicity of both engineered forms (termed as Round-shaped CCMV_TT-VLPs and Rod-shaped CCMV_TT-VLPs) as potential B cell immunogens using different in vitro and in vivo assays. Our results reveal that Round-shaped CCMV_TT-VLPs are more efficient in draining to secondary lymphoid organs to charge professional antigen-presenting cells as well as B cells. Furthermore, compared to Rod-shaped CCMV_TT-VLPs, Round-shaped CCMV_TT-VLPs led to more than 100-fold increased systemic IgG and IgA responses accompanied by prominent formation of splenic germinal centers. Round-shaped CCMV_TT-VLPs could also polarize the induced T cell response toward Th1. To our knowledge, this is the first study investigating and comparing the draining kinetics and immunogenicity of one and the same VLP monomer forming nano-sized icosahedra or rods in the micrometer size.

The 3Ds in virus-like particle based-vaccines: "Design, Delivery and Dynamics"

Vaccines need to be rationally designed in order be delivered to the immune system for maximizing induction of dynamic immune responses. Virus‐like particles (VLPs) are ideal platforms for such 3D vaccines, as they allow the display of complex and native antigens in a highly repetitive form on their surface and can easily reach lymphoid organs in intact form for optimal activation of B and T cells. Adjusting size and zeta potential may allow investigators to further fine‐tune delivery to lymphoid organs. An additional way to alter vaccine transfer to lymph nodes and spleen may be the formulation with micron‐sized adjuvants that creates a local depot and results in a slow release of antigen and adjuvant. Ideally, the adjuvant in addition stimulates the innate immune system. The dynamics of the immune response may be further enhanced by inclusion of Toll‐like receptor ligands, which many VLPs naturally package. Hence, considering the 3Ds in vaccine development may allow for enhancement of their attributes to tackle complex diseases, not usually amenable to conventional vaccine strategies.

Icosadeltahedral Geometry of Geodesic Domes, Fullerenes and Viruses: A Tutorial on the T-Number

The Caspar–Klug (CK) classification of viruses is discussed by parallel examination of geometry of icosahedral geodesic domes, fullerenes, and viruses. The underlying symmetry of all structures is explained and thoroughly visually represented. Euler’s theorem on polyhedra is used to calculate the number of vertices, edges, and faces in domes, number of atoms, bonds, and pentagonal and hexagonal rings in fullerenes, and number of proteins and protein–protein contacts in viruses. The T-number, the characteristic for the CK classification, is defined and discussed. The superposition of fullerene and dome designs is used to obtain a representation of a CK virus with all the proteins indicated. Some modifications of the CK classifications are sketched, including elongation of the CK blueprint, fusion of two CK blueprints, dodecahedral view of the CK shapes, and generalized CK designs without a clearly visible geometry of the icosahedron. These are compared to cases of existing viruses.

Hepatitis C Virus Structure: Defined by What It Is Not

Hepatitis C virus (HCV) represents an important and growing public health problem, chronically infecting an estimated 70 million people worldwide. This blood-borne pathogen is generating a new wave of infections in the United States, associated with increasing intravenous drug use over the last decade. In most cases, HCV establishes a chronic infection, sometimes causing cirrhosis, end-stage liver disease, and hepatocellular carcinoma. Although a curative therapy exists, it is extremely expensive and provides no barrier to reinfection; therefore, a vaccine is urgently needed. The virion is asymmetric and heterogeneous with the buoyancy and protein content similar to low-density lipoparticles. Core protein is unstructured, and of the two envelope glycoproteins, E1 and E2, the function of E1 remains enigmatic. E2 is responsible for specifically binding host receptors CD81 and scavenger receptor class B type I (SR-BI). This review will focus on structural progress on HCV virion, core protein, envelope glycoproteins, and specific host receptors.

How the phage T4 injection machinery works including energetics, forces, and dynamic pathway

The virus bacteriophage T4, from the family Myoviridae, employs an intriguing contractile injection machine to inject its genome into the bacterium Escherichia coli Although the atomic structure of phage T4 is largely understood, the dynamics of its injection machinery remains unknown. This study contributes a system-level model describing the nonlinear dynamics of the phage T4 injection machinery interacting with a host cell. The model employs a continuum representation of the contractile sheath using elastic constants inferred from atomistic molecular-dynamics (MD) simulations. Importantly, the sheath model is coupled to component models representing the remaining structures of the virus and the host cell. The resulting system-level model captures virus-cell interactions as well as competing energetic mechanisms that release and dissipate energy during the injection process. Simulations reveal the dynamical pathway of the injection process as a "contraction wave" that propagates along the sheath, the energy that powers the injection machinery, the forces responsible for piercing the host cell membrane, and the energy dissipation that controls the timescale of the injection process. These results from the model compare favorably with the available (but limited) experimental measurements.

Principles for enhancing virus capsid capacity and stability from a thermophilic virus capsid structure

The capsids of double-stranded DNA viruses protect the viral genome from the harsh extracellular environment, while maintaining stability against the high internal pressure of packaged DNA. To elucidate how capsids maintain stability in an extreme environment, we use cryoelectron microscopy to determine the capsid structure of thermostable phage P74-26 to 2.8-Å resolution. We find P74-26 capsids exhibit an overall architecture very similar to those of other tailed bacteriophages, allowing us to directly compare structures to derive the structural basis for enhanced stability. Our structure reveals lasso-like interactions that appear to function like catch bonds. This architecture allows the capsid to expand during genome packaging, yet maintain structural stability. The P74-26 capsid has T = 7 geometry despite being twice as large as mesophilic homologs. Capsid capacity is increased with a larger, flatter major capsid protein. Given these results, we predict decreased icosahedral complexity (i.e. T ≤ 7) leads to a more stable capsid assembly.

Viral capsids need to protect the genome against harsh environmental conditions and cope with high internal pressure from the packaged genome. Here, the authors determine the structure of the thermostable phage P74-26 capsid at 2.8-Å resolution and identify features underlying enhanced capsid capacity and structural stability.

Structural Differences between the Woodchuck Hepatitis Virus Core Protein in the Dimer and Capsid States Are Consistent with Entropic and Conformational Regulation of Assembly

Hepadnaviruses are hepatotropic enveloped DNA viruses with an icosahedral capsid. Hepatitis B virus (HBV) causes chronic infection in an estimated 240 million people; woodchuck hepatitis virus (WHV), an HBV homologue, has been an important model system for drug development. The dimeric capsid protein (Cp) has multiple functions during the viral life cycle and thus has become an important target for a new generation of antivirals. Purified HBV and WHV Cp spontaneously assemble into 120-dimer capsids. Though they have 65% identity, WHV Cp has error-prone assembly with stronger protein-protein association. We have taken advantage of the differences in assemblies to investigate the basis of assembly regulation. We determined the structures of the WHV capsid to 4.5-Å resolution by cryo-electron microscopy (cryo-EM) and of the WHV Cp dimer to 2.9-Å resolution by crystallography and examined the biophysical properties of the dimer. We found, in dimer, that the subdomain that makes protein-protein interactions is partially disordered and rotated 21° from its position in capsid. This subdomain is susceptible to proteolysis, consistent with local disorder. WHV assembly shows similar susceptibility to HBV antiviral molecules, suggesting that HBV assembly follows similar transitions. These data show that there is an entropic cost for assembly that is compensated for by the energetic gain of burying hydrophobic interprotein contacts. We propose a series of stages in assembly that incorporate a disorder-to-order transition and structural shifts. We suggest that a cascade of structural changes may be a common mechanism for regulating high-fidelity capsid assembly in HBV and other viruses.IMPORTANCE Virus capsids assemble spontaneously with surprisingly high fidelity. This requires strict geometry and a narrow range of association energies for these protein-protein interactions. It was hypothesized that requiring subunits to undergo a conformational change to become assembly active could regulate assembly by creating an energetic barrier and attenuating association. We found that woodchuck hepatitis virus capsid protein undergoes structural transitions between its dimeric and its 120-dimer capsid states. It is likely that the closely related hepatitis B virus capsid protein undergoes similar structural changes, which has implications for drug design. Regulation of assembly by structural transition may be a common mechanism for many viruses.

Physical, chemical, and synthetic virology: Reprogramming viruses as controllable nanodevices

The fields of physical, chemical, and synthetic virology work in partnership to reprogram viruses as controllable nanodevices. Physical virology provides the fundamental biophysical understanding of how virus capsids assemble, disassemble, display metastability, and assume various configurations. Chemical virology considers the virus capsid as a chemically addressable structure, providing chemical pathways to modify the capsid exterior, interior, and subunit interfaces. Synthetic virology takes an engineering approach, modifying the virus capsid through rational, combinatorial, and bioinformatics-driven design strategies. Advances in these three subfields of virology aim to develop virus-based materials and tools that can be applied to solve critical problems in biomedicine and biotechnology, including applications in gene therapy and drug delivery, diagnostics, and immunotherapy. Examples discussed include mammalian viruses, such as adeno-associated virus (AAV), plant viruses, such as cowpea mosaic virus (CPMV), and bacterial viruses, such as Qβ bacteriophage. Importantly, research efforts in physical, chemical, and synthetic virology have further unraveled the design principles foundational to the form and function of viruses. This article is categorized under: Diagnostic Tools > Diagnostic Nanodevices Biology-Inspired Nanomaterials > Protein and Virus-Based Structures.

A New Model System for Exploring Assembly Mechanisms of the HIV-1 Immature Capsid In Vivo

The assembly of the HIV-1 immature capsid (HIC) is an essential step in the virus life cycle. In vivo, the HIC is composed of [Formula: see text] hexameric building blocks, and it takes 5-6 min to complete the assembly process. The involvement of numerous building blocks and the rapid timecourse makes it difficult to understand the HIC assembly process. In this work, we study HIC assembly in vivo by using differential equations. We first obtain a full model with 420 differential equations. Then, we reduce six addition reactions for separate building blocks to a single complex reaction. This strategy reduces the full model to 70 equations. Subsequently, the theoretical analysis of the reduced model shows that it might not be an effective way to decrease the HIC concentration at the equilibrium state by decreasing the microscopic on-rate constants. Based on experimental data, we estimate that the nucleating structure is much smaller than the HIC. We also estimate that the microscopic on-rate constant for nucleation reactions is far less than that for elongation reactions. The parametric collinearity investigation testifies the reliability of these two characteristics, which might explain why free building blocks do not readily polymerize into higher-order polymers until their concentration reaches a threshold value. These results can provide further insight into the assembly mechanisms of the HIC in vivo.

Molecular dynamics study of T = 3 capsid assembly

Molecular dynamics simulation is used to model the self-assembly of polyhedral shells containing 180 trapezoidal particles that correspond to the T = 3 virus capsid. Three kinds of particle, differing only slightly in shape, are used to account for the effect of quasi-equivalence. Bond formation between particles is reversible and an explicit atomistic solvent is included. Under suitable conditions the simulations are able to produce complete shells, with the majority of unused particles remaining as monomers, and practically no other clusters. There are also no incorrectly assembled clusters. The simulations reveal details of intermediate structures along the growth pathway, information that is relevant for interpreting experiment.

Commensurability between protein nanotubes in contractile ejection nanomachines

Contractile ejection nanomachines being sheath-tube assemblies create an opening in the cell membrane to translocate molecules or ions across it. Here, on the most structurally investigated examples of the bacteriophage T4 tail and pyocin R2, we show that the rearrangement of the sheath structure resulting in its contraction and twist occurs in such a way that the contracted sheath becomes commensurate with the inner tube. This fact dictates the previously unknown simple geometrical relationship between the nanotube symmetries. Using the Frank and van der Merwe classical theory of commensurability, we study an interaction between two protein nanotubes forming such nanomachines and obtain an expression for the corresponding energy, which depends on the tube structures and their mutual arrangement. The appearance of commensurability between the contracted sheath and the inner tube decreases both the interaction energy and the total energy of the system. It improves the nanomachine efficiency, since the energy gain obtained increases the torque of the inner tube piercing the cell membrane.

Losing supramolecular orientational memory via self-organization of a misfolded secondary structure

Comparing the self-organization of two dendronized perylene bisimides reveals how structurally defective primary structure eliminates memory function via hierarchical self-organization.

Mathematical modeling of HIV-like particle assembly in vitro

In vitro, the recombinant HIV-1 Gag protein can generate spherical particles with a diameter of 25-30 nm in a fully defined system. It has approximately 80 building blocks, and its intermediates for assembly are abundant in geometry. Accordingly, there are a large number of nonlinear equations in the classical model. Therefore, it is difficult to compute values of geometry parameters for intermediates and make the mathematical analysis using the model. In this work, we develop a new model of HIV-like particle assembly in vitro by using six-fold symmetry of HIV-like particle assembly to decrease the number of geometry parameters. This method will greatly reduce computational costs and facilitate the application of the model. Then, we prove the existence and uniqueness of the positive equilibrium solution for this model with 79 nonlinear equations. Based on this model, we derive the interesting result that concentrations of all intermediates at equilibrium are independent of three important parameters, including two microscopic on-rate constants and the size of nucleating structure. Before equilibrium, these three parameters influence the concentration variation rates of all intermediates. We also analyze the relationship between the initial concentration of building blocks and concentrations of all intermediates. Furthermore, the bounds of concentrations of free building blocks and HIV-like particles are estimated. These results will be helpful to guide HIV-like particle assembly experiments and improve our understanding of the assembly dynamics of HIV-like particles in vitro.

Molecular assembly and structure of the bacteriophage T4 tail

The tail of bacteriophage T4 undergoes large structural changes upon infection while delivering the phage genome into the host cell. The baseplate is located at the distal end of the contractile tail and plays a central role in transmitting the signal to the tail sheath that the tailfibers have been adsorbed by a host bacterium. This then triggers the sheath contraction. In order to understand the mechanism of assembly and conformational changes of the baseplate upon infection, we have determined the structure of an in vitro assembled baseplate through the three-dimensional reconstruction of cryo-electron microscopy images to a resolution of 3.8 Å from electron micrographs. The atomic structure was fitted to the baseplate structure before and after sheath contraction in order to elucidate the conformational changes that occur after bacteriophage T4 has attached itself to a cell surface. The structure was also used to investigate the protease digestion of the assembly intermediates and the mutation sites of the tail genes, resulting in a number of phenotypes.

The Structural Biology of Hepatitis B Virus: Form and Function

Hepatitis B virus is one of the smallest human pathogens, encoded by a 3,200-bp genome with only four open reading frames. Yet the virus shows a remarkable diversity in structural features, often with the same proteins adopting several conformations. In part, this is the parsimony of viruses, where a minimal number of proteins perform a wide variety of functions. However, a more important theme is that weak interactions between components as well as components with multiple conformations that have similar stabilities lead to a highly dynamic system. In hepatitis B virus, this is manifested as a virion where the envelope proteins have multiple structures, the envelope-capsid interaction is irregular, and the capsid is a dynamic compartment that actively participates in metabolism of the encapsidated genome and carries regulated signals for intracellular trafficking.

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.

Self-crowding induced phase separation in protein dispersions

The coupling between protein conformation, molecular volume, and solution phase behaviour is studied theoretically for a two-state, coarse-grained protein model in which protein molecules can reversibly switch between a native and a non-native excited state. In the model, native and non-native conformers are represented by perfect spheres with different hard-core diameters. We presume the larger, non-native species to attract each other through some unspecified potential. We find that at low concentrations the native state is stabilised energetically and that at high concentrations the native state is again stabilised but this time by self-crowding, i.e., a lack of free volume. These two regimes are separated by two first-order transitions from a region where the non-native conformational state is prevalent, stabilised by attractive interactions between the proteins. The calculated phase diagram is very sensitive to even quite small differences in particle volumes and has unusual features, including the loss of a critical point if the size difference is sufficiently large.

Assembly and Release of Hepatitis B Virus

The hepatitis B virus (HBV) core protein is a dynamic and versatile protein that directs many viral processes. During capsid assembly, core protein allosteric changes ensure efficient formation of a stable capsid that assembles while packaging viral RNA-polymerase complex. Reverse transcription of the RNA genome as well as transport of the capsid to multiple cellular compartments are directed by dynamic phosphorylation and structural changes of core protein. Subsequently, interactions of the capsid with the surface proteins and/or host proteins trigger envelopment and release of the viral capsids or the transport to the nucleus. Held together by many weak protein-protein interactions, the viral capsid is an extraordinary metastable machine that is stable enough to persist in the cellular and extracellular environment but dissociates to allow release of the viral genome at the right time during infection.

Protein-Protein Interfaces in Viral Capsids Are Structurally Unique

Viral capsids exhibit elaborate and symmetrical architectures of defined sizes and remarkable mechanical properties not seen with cellular macromolecular complexes. Given the uniqueness of the higher-order organization of viral capsid proteins in the virosphere, we explored the question of whether the patterns of protein-protein interactions within viral capsids are distinct from those in generic protein complexes. Our comparative analysis involving a non-redundant set of 551 inter-subunit interfaces in viral capsids from VIPERdb and 20,014 protein-protein interfaces in non-capsid protein complexes from the Protein Data Bank found 418 generic protein-protein interfaces that share similar physicochemical patterns with some protein-protein interfaces in the capsid set, using the program PCalign we developed for comparing protein-protein interfaces. This overlap in the structural space of protein-protein interfaces is significantly small, with a p-value <0.0001, based on a permutation test on the total set of protein-protein interfaces. Furthermore, the generic protein-protein interfaces that bear similarity in their spatial and chemical arrangement with capsid ones are mostly small in size with fewer than 20 interfacial residues, which results from the relatively limited choices of natural design for small interfaces rather than having significant biological implications in terms of functional relationships. We conclude based on this study that protein-protein interfaces in viral capsids are non-representative of patterns in the smaller, more compact cellular protein complexes. Our finding highlights the design principle of building large biological containers from repeated, self-assembling units and provides insights into specific targets for antiviral drug design for improved efficacy.

Molecular dynamics simulation: a tool for exploration and discovery using simple models

Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome is not always a foregone conclusion. The present survey focuses on several simple model systems that exhibit surprisingly rich emergent behavior, all studied by molecular dynamics (MD) simulation.The examples are taken from the disparate fields of fluid dynamics, granular matter and supramolecular self-assembly. In studies of fluids modeled at the detailed microscopic level using discrete particles, the simulations demonstrate that complex hydrodynamic phenomena in rotating and convecting fluids—the Taylor–Couette and Rayleigh–Bénard instabilities—cannot only be observed within the limited length and time scales accessible to MD, but even allow quantitative agreement to be achieved. Simulation of highly counter-intuitive segregation phenomena in granular mixtures, again using MD methods, but now augmented by forces producing damping and friction, leads to results that resemble experimentally observed axial and radial segregation in the case of a rotating cylinder and to a novel form of horizontal segregation in a vertically vibrated layer. Finally, when modeling self-assembly processes analogous to the formation of the polyhedral shells that package spherical viruses, simulation of suitably shaped particles reveals the ability to produce complete, error-free assembly and leads to the important general observation that reversible growth steps contribute to the high yield. While there are limitations to the MD approach, both computational and conceptual, the results offer a tantalizing hint of the kinds of phenomena that can be explored and what might be discovered when sufficient resources are brought to bear on a problem.

The hepatitis B virus core protein intradimer interface modulates capsid assembly and stability

During the hepatitis B virus (HBV) life cycle, capsid assembly and disassembly must ensure correct packaging and release of the viral genome. Here we show that changes in the dynamics of the core protein play an important role in regulating these processes. The HBV capsid assembles from 120 copies of the core protein homodimer. Each monomer contains a conserved cysteine at position 61 that can form an intradimer disulfide that we use as a marker for dimer conformational states. We show that dimers in the context of capsids form intradimer disulfides relatively rapidly. Surprisingly, compared to reduced dimers, fully oxidized dimers assembled slower and into capsids that were morphologically similar but less stable. We hypothesize that oxidized protein adopts a geometry (or constellation of geometries) that is unfavorable for capsid assembly, resulting in weaker dimer-dimer interactions as well as slower assembly kinetics. Our results suggest that structural flexibility at the core protein intradimer interface is essential for regulating capsid assembly and stability. We further suggest that capsid destabilization by the C61-C61 disulfide has a regulatory function to support capsid disassembly and release of the viral genome.

Prediction of the structure of a silk-like protein in oligomeric states using explicit and implicit solvent models

We perform Replica Exchange Molecular Dynamics (REMD) simulations on a silk-like protein design with amino-acid sequence [(Gly-Ala)3-Gly-Glu]5 to investigate the stability of a single protein, a dimer, a trimer and a tetramer made up of these proteins starting from β-roll and β-sheet structures in both explicit (TIP3P) and implicit (GBSA) solvent models. Our simulation results for the implicit solvent model agree with those for the explicit solvent model for simulation times up to the longest tested, being 30 ns per replica. From this we infer that the implicit solvent model that we use is reliable, allowing us to reach much longer time scales (up to 200 ns per replica). We find that the self-assembly of fibers of these proteins in solution must be a nucleated process, involving nuclei made up of at least three monomers. We also find that the conformation of the protein changes upon assembly, i.e., there is a transition from a disordered globular state to an ordered β-sheet structure in the self-assembled state of aggregates containing more than two monomers. This indicates that autosteric effects must be important in the polymerization of this protein, reminiscent of what is observed for β-amyloids. Our findings are consistent with recent experimental results on a protein with an amino acid sequence similar to that of the protein we study.

Pathways for virus assembly around nucleic acids

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

A minimal representation of the self-assembly of virus capsids

Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer interaction in icosahedral capsids and the requirement of low frustration fix the form of the shortest and universal truncated multipolar expansion of the two-body interaction between capsomers. The structures of many of the icosahedral and related virus capsids are located as single lowest energy states of a potential energy surface built from this interaction. Our minimalist representation is consistent with other models known to produce a controllable and efficient self-assembly, and unveils relevant features of the natural design of the capsids. It promises to be very useful in physical virology and may also be of interest in fields of nanoscience and nanotechnology where similar hollow convex structures are relevant.

Tensegrity, cellular biophysics, and the mechanics of living systems

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life—from individual molecules to whole living organisms—to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

Architecture of a dsDNA viral capsid in complex with its maturation protease

Most double-stranded DNA (dsDNA) viruses, including bacteriophages and herpesviruses, rely on a staged assembly process of capsid formation. A viral protease is required for many of them to disconnect scaffolding domains/proteins from the capsid shell, therefore priming the maturation process. We used the bacteriophage HK97 as a model system to decipher the molecular mechanisms underlying the recruitment of the maturation protease by the assembling procapsid and the influence exerted onto the latter. Comparisons of the procapsid with and without protease using single-particle cryoelectron microscopy reconstructions, hydrogen/deuterium exchange coupled to mass spectrometry, and native mass spectrometry demonstrated that the protease interacts with the scaffolding domains within the procapsid interior and stabilizes them as well as the whole particle. The results suggest that the thermodynamic consequences of protease packaging are to shift the equilibrium between isolated coat subunit capsomers and procapsid in favor of the latter by stabilizing the assembled particle before making the process irreversible through proteolysis of the scaffolding domains.

Self-organization of the vesicular stomatitis virus nucleocapsid into a bullet shape

The typical bullet shape of Rhabdoviruses is thought to rely on the matrix protein for stabilizing the nucleocapsid coil. Here we scrutinize the morphology of purified and recombinant nucleocapsids of vesicular stomatitis virus in vitro. We elucidate pH and ionic strength conditions for their folding into conical tips and further growth into whole bullets, and provide cryo-electron microscopy reconstructions of the bullet tip and the helical trunk. We address conformational variability of the reconstituted nucleocapsids and the issue of constraints imposed by the binding of matrix protein. Our findings bridge the gap between the isolated nucleoprotein-RNA string in its form of an undulating ribbon, and the tight bullet-shaped virion skeleton.

Virus assembly and maturation: auto-regulation through allosteric molecular switches

We generalize the concept of allostery from the traditional non-active-site control of enzymes to virus maturation. Virtually, all animal viruses transition from a procapsid noninfectious state to a mature infectious state. The procapsid contains an encoded chemical program that is executed following an environmental cue. We developed an exceptionally accessible virus system for the study of the activators of maturation and the downstream consequences that result in particle stability and infectivity. Nudaurelia capensis omega virus (NωV) is a T=4 icosahedral virus that undergoes a dramatic maturation in which the 490-Å spherical procapsid condenses to a 400-Å icosahedral-shaped capsid with associated specific auto-proteolysis and stabilization. Employing X-ray crystallography, time-resolved electron cryo-microscopy and hydrogen/deuterium exchange as well as biochemistry, it was possible to define the mechanisms of allosteric communication among the four quasi-equivalent subunits in the icosahedral asymmetric unit. These gene products undergo proteolysis at different rates, dependent on quaternary structure environment, while particle stability is conferred globally following only a few local subunit transitions. We show that there is a close similarity between the concepts of tensegrity (associated with geodesic domes and mechanical engineering) and allostery (associated with biochemical control mechanisms).

Molecular dynamics simulation of reversibly self-assembling shells in solution using trapezoidal particles

The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the capsid of a T=1 virus. Growth occurs in the presence of an atomistic solvent and, under suitable conditions, achieves a high yield of complete shells. The simulations provide details of the structure and lifetime of the particle clusters that appear as intermediate states along the growth pathway, and the nature of the transitions between them. In certain respects the growth of size-60 shells from trapezoidal particles resembles the growth of icosahedral shells from triangular particles studied previously, with reversible bonding playing a major role in avoiding incorrect assembly, although the details differ due to particle shape and bond organization. The strong preference for maximal bonding exhibited by the triangular particle clusters is also apparent for trapezoidal particles, but this is now confined to early growth and is less pronounced as shells approach completion along a variety of pathways.

Protein nanotubes, channels and cages

Proteins are the work-horses of life and excute the essential processes involved in the growth and repair of cells. These roles include all aspects of cell signalling, metabolism and repair that allow living things to exist. They are not only chemical catalysts and machine components, they are also structural components of the cell or organism, capable of self-organisation into strong supramolecular cages, fibres and meshes. How proteins are encoded genetically and how they are sythesised in vivo is now well understood, and for an increasing number of proteins, the relationship between structure and function is known in exquisite detail. The next challenge in bionanoscience is to adapt useful protein systems to build new functional structures. Well-defined natural structures with potential useful shapes are a good starting point. With this in mind, in this chapter we discuss the properties of natural and artificial protein channels, nanotubes and cages with regard to recent progress and potential future applications. Chemistries for attaching together different proteins to form superstructures are considered as well as the difficulties associated with designing complex protein structures ab initio.

Properties of the adeno-associated virus assembly-activating protein

Adeno-associated virus (AAV) capsid assembly requires expression of the assembly-activating protein (AAP) together with capsid proteins VP1, VP2, and VP3. AAP is encoded by an alternative open reading frame of the cap gene. Sequence analysis and site-directed mutagenesis revealed that AAP contains two hydrophobic domains in the N-terminal part of the molecule that are essential for its assembly-promoting activity. Mutation of these sequences reduced the interaction of AAP with the capsid proteins. Deletions and a point mutation in the capsid protein C terminus also abolished capsid assembly and strongly reduced the interaction with AAP. Interpretation of these observations on a structural basis suggests an interaction of AAP with the VP C terminus, which forms the capsid protein interface at the 2-fold symmetry axis. This interpretation is supported by a decrease in the interaction of monoclonal antibody B1 with VP3 under nondenaturing conditions in the presence of AAP, indicative of steric hindrance of B1 binding to its C-terminal epitope by AAP. In addition, AAP forms high-molecular-weight oligomers and changes the conformation of nonassembled VP molecules as detected by conformation-sensitive monoclonal antibodies A20 and C37. Combined, these observations suggest a possible scaffolding activity of AAP in the AAV capsid assembly reaction.

Probing, by self-assembly, the number of potential binding sites for minor protein subunits in the procapsid of double-stranded RNA bacteriophage Φ6

The double-stranded RNA bacteriophage Φ6 is an extensively studied prokaryotic model system for virus assembly. There are established in vitro assembly protocols available for the Φ6 system for obtaining infectious particles from purified protein and RNA constituents. The polymerase complex is a multifunctional nanomachine that replicates, transcribes, and translocates viral RNA molecules in a highly specific manner. The complex is composed of (i) the major structural protein (P1), forming a T=1 icosahedral lattice with two protein subunits in the icosahedral asymmetric unit; (ii) the RNA-dependent RNA polymerase (P2); (iii) the hexameric packaging nucleoside triphosphatase (NTPase) (P4); and (iv) the assembly cofactor (P7). In this study, we analyzed several Φ6 virions and recombinant polymerase complexes to investigate the relative copy numbers of P2, P4, and P7, and we applied saturated concentrations of these proteins in the self-assembly system to probe their maximal numbers of binding sites in the P1 shell. Biochemical quantitation confirmed that the composition of the recombinant particles was similar to that of the virion cores. By including a high concentration of P2 or P7 in the self-assembly reaction mix, we observed that the numbers of these proteins in the resulting particles could be increased beyond those observed in the virion. Our results also suggest a previously unidentified P2-P7 dependency in the assembly reaction. Furthermore, it appeared that P4 must initially be incorporated at each, or a majority, of the 5-fold symmetry positions of the P1 shell for particle assembly. Although required for nucleation, excess P4 resulted in slower assembly kinetics.

Quantitation of ten 30S ribosomal assembly intermediates using fluorescence triple correlation spectroscopy

The self-assembly of bacterial 30S ribosomes involves a large number of RNA folding and RNA-protein binding steps. The sequence of steps determines the overall assembly mechanism and the structure of the mechanism has ramifications for the robustness of biogenesis and resilience against kinetic traps. Thermodynamic interdependencies of protein binding inferred from omission-reconstitution experiments are thought to preclude certain assembly pathways and thus enforce ordered assembly, but this concept is at odds with kinetic data suggesting a more parallel assembly landscape. A major challenge is deconvolution of the statistical distribution of intermediates that are populated during assembly at high concentrations approaching in vivo assembly conditions. To specifically resolve the intermediates formed by binding of three ribosomal proteins to the full length 16S rRNA, we introduce Fluorescence Triple-Correlation Spectroscopy (F3CS). F3CS identifies specific ternary complexes by detecting coincident fluctuations in three-color fluorescence data. Triple correlation integrals quantify concentrations and diffusion kinetics of triply labeled species, and F3CS data can be fit alongside auto-correlation and cross-correlation data to quantify the populations of 10 specific ribosome assembly intermediates. The distribution of intermediates generated by binding three ribosomal proteins to the entire native 16S rRNA included significant populations of species that were not previously thought to be thermodynamically accessible, questioning the current interpretation of the classic omission-reconstitution experiments. F3CS is a general approach for analyzing assembly and function of macromolecular complexes, especially those too large for traditional biophysical methods.