Nucleation and growth phases in the polymerization of coat and scaffolding subunits into icosahedral procapsid shells

Studies of reversible capsid shell growth

Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit solvent and the nature of the events along their growth pathways; the results provide further evidence of the importance of reversibility in the assembly process. The underlying goal of this approach is the modeling of virus capsid growth, a phenomenon at the submicroscopic scale that, despite its importance, is little understood.

P22 coat protein structures reveal a novel mechanism for capsid maturation: stability without auxiliary proteins or chemical crosslinks

Viral capsid assembly and stability in tailed, dsDNA phage and Herpesviridae are achieved by various means including chemical crosslinks (unique to HK97), or auxiliary proteins (lambda, T4, phi29, and herpesviruses). All these viruses have coat proteins (CP) with a conserved, HK97-like core structure. We used a combination of trypsin digestion, gold labeling, cryo-electron microscopy, 3D image reconstruction, and comparative modeling to derive two independent, pseudoatomic models of bacteriophage P22 CP: before and after maturation. P22 capsid stabilization results from intersubunit interactions among N-terminal helices and an extensive "P loop," which obviate the need for crosslinks or auxiliary proteins. P22 CP also has a telokin-like Ig domain that likely stabilizes the monomer fold so that assembly may proceed via individual subunit addition rather than via preformed capsomers as occurs in HK97. Hence, the P22 CP structure may be a paradigm for understanding how monomers assemble in viruses like phi29 and HSV-1.

Spontaneous curvature as a regulator of the size of virus capsids

We investigate the physical reasons underlying the high monodispersity of empty virus capsids assembled in thermodynamical equilibrium in conditions of favorable pH and ionic strength. We propose that the high fidelity of the assembly results from the effective spontaneous curvature of the viral protein assemblies and the corresponding bending rigidity that penalizes curvatures which are larger and smaller from the spontaneous one. On the example of hepatitis B virus, which has been thoroughly studied experimentally in the context of interest to us, we estimate the magnitude of bending rigidity that is needed to suppress the appearance of aberrant capsid structures (approximately 60k(B)T). Our approach also demonstrates that the aberrant capsids that can be classified within the Caspar-Klug framework are in most circumstances likely to be smaller from the regular ones, in agreement with the experimental findings.

Retroviral capsid assembly: a role for the CA dimer in initiation

In maturing retroviral virions, CA protein assembles to form a capsid shell that is essential for infectivity. The structure of the two folded domains [N-terminal domain (NTD) and C-terminal domain (CTD)] of CA is highly conserved among various retroviruses, and the capsid assembly pathway, although poorly understood, is thought to be conserved as well. In vitro assembly reactions with purified CA proteins of the Rous sarcoma virus (RSV) were used to define factors that influence the kinetics of capsid assembly and provide insights into underlying mechanisms. CA multimerization was triggered by multivalent anions providing evidence that in vitro assembly is an electrostatically controlled process. In the case of RSV, in vitro assembly was a well-behaved nucleation-driven process that led to the formation of structures with morphologies similar to those found in virions. Isolated RSV dimers, when mixed with monomeric protein, acted as efficient seeds for assembly, eliminating the lag phase characteristic of a monomer-only reaction. This demonstrates for the first time the purification of an intermediate on the assembly pathway. Differences in the intrinsic tryptophan fluorescence of monomeric protein and the assembly-competent dimer fraction suggest the involvement of the NTD in the formation of the functional dimer. Furthermore, in vitro analysis of well-characterized CTD mutants provides evidence for assembly dependence on the second domain and suggests that the establishment of an NTD-CTD interface is a critical step in capsid assembly initiation. Overall, the data provide clear support for a model whereby capsid assembly within the maturing virion is dependent on the formation of a specific nucleating complex that involves a CA dimer and is directed by additional virion constituents.

N-terminal deletions of the phiX174 external scaffolding protein affect the timing and fidelity of assembly

The first alpha-helices of Microviridae external scaffolding proteins function as coat protein substrate specificity domains. Mutations in this helix can lengthen the lag phase before progeny production. 5' deletion genes, encoding N-terminal deletion proteins, were constructed on plasmids and in the øX174 genome. Proteins lacking the first seven amino acids were able to rescue a nullD mutant when expressed from a plasmid. However, the lag phase before progeny production was lengthened. The øX174 mutant with the corresponding genomic gene grew very poorly. The molecular basis of the defective phenotype was complex. External scaffolding protein levels were reduced compared to wild-type and most of the viral coat protein in mutant infected cells appears to be siphoned off the assembly pathway. Second-site suppressors of the growth defects were isolated and appear to act via two different mechanisms. One class of suppressors most likely acts by altering mutant external scaffolding protein expression while the second class of suppressors appears to act on the level of protein-protein interactions.

Energy landscapes for shells assembled from pentagonal and hexagonal pyramids

We present new rigid body potentials that should favour efficient self-assembly of pentagonal and hexagonal pyramids into icosahedral shells over a wide range of temperature. By adding an extra repulsive site opposite the existing apex sites of the pyramids considered in a previously published model, frustrated energy landscapes are transformed into systems identified with self-assembling properties. The extra interaction may be considered analogous to a hydrophobic-hydrophilic repulsion, as in micelle formation.

Role of reversibility in viral capsid growth: a paradigm for self-assembly

Self-assembly at submicroscopic scales is an important but little understood phenomenon. A prominent example is virus capsid growth, whose underlying behavior can be modeled using simple particles that assemble into polyhedral shells. Molecular dynamics simulation of shell formation in the presence of an atomistic solvent provides new insight into the self-assembly mechanism, notably that growth proceeds via a cascade of strongly reversible steps and, despite the large variety of possible intermediates, only a small fraction of highly bonded forms appear on the pathway.

Self-assembly of brome mosaic virus capsids: insights from shorter time-scale experiments

An amended kinetic model for the self-assembly of empty capsids of brome mosaic virus is proposed. The model has been modified to account for a new feature in the assembly kinetics revealed by time-course light scattering experiments at higher temporal resolution than previously attempted. To be able to simulate the sharp takeoff from the initial lag phase to the growth phase in the kinetic curves, a monomer activation step was proposed.

Protein–protein interaction and quaternary structure

Protein–protein recognition plays an essential role in structure and function. Specific non-covalent interactions stabilize the structure of macromolecular assemblies, exemplified in this review by oligomeric proteins and the capsids of icosahedral viruses. They also allow proteins to form complexes that have a very wide range of stability and lifetimes and are involved in all cellular processes. We present some of the structure-based computational methods that have been developed to characterize the quaternary structure of oligomeric proteins and other molecular assemblies and analyze the properties of the interfaces between the subunits. We compare the size, the chemical and amino acid compositions and the atomic packing of the subunit interfaces of protein–protein complexes, oligomeric proteins, viral capsids and protein–nucleic acid complexes. These biologically significant interfaces are generally close-packed, whereas the non-specific interfaces between molecules in protein crystals are loosely packed, an observation that gives a structural basis to specific recognition. A distinction is made within each interface between a core that contains buried atoms and a solvent accessible rim. The core and the rim differ in their amino acid composition and their conservation in evolution, and the distinction helps correlating the structural data with the results of site-directed mutagenesis and in vitro studies of self-assembly.

Detection of intermediates and kinetic control during assembly of bacteriophage P22 procapsid

Bacteriophage P22 serves as a model for the assembly and maturation of other icosahedral double-stranded DNA viruses. P22 coat and scaffolding proteins assemble in vitro into an icosahedral procapsid, which then expands during DNA packaging (maturation). Efficient in vitro assembly makes this system suitable for design and production of monodisperse spherical nanoparticles (diameter approximately 50 nm). In this work, we explore the possibility of controlling the outcome of assembly by scaffolding protein engineering. The scaffolding protein exists in monomer-dimer-tetramer equilibrium. We address the role of monomers and dimers in assembly by using three different scaffolding proteins with altered monomer-dimer equilibrium (weak dimer, covalent dimer, monomer). The progress and outcome of assembly was monitored by time-resolved X-ray scattering, which allowed us to distinguish between closed shells and incomplete assembly intermediates. Binding of scaffolding monomer activates the coat protein for assembly. Excess dimeric scaffolding protein resulted in rapid nucleation and kinetic trapping yielding incomplete shells. Addition of monomeric wild-type scaffold with excess coat protein completed these metastable shells. Thus, the monomeric scaffolding protein plays an essential role in the elongation phase by activating the coat and effectively lowering its critical concentration for assembly.

Critical role of conserved hydrophobic residues within the major homology region in mature retroviral capsid assembly

During retroviral maturation, the CA protein undergoes dramatic structural changes and establishes unique intermolecular interfaces in the mature capsid shell that are different from those that existed in the immature precursor. The most conserved region of CA, the major homology region (MHR), has been implicated in both immature and mature assembly, although the precise contribution of the MHR residues to each event has been largely undefined. To test the roles of specific MHR residues in mature capsid assembly, an in vitro system was developed that allowed for the first-time formation of Rous sarcoma virus CA into structures resembling authentic capsids. The ability of CA to assemble organized structures was destroyed by substitutions of two conserved hydrophobic MHR residues and restored by second-site suppressors, demonstrating that these MHR residues are required for the proper assembly of mature capsids in addition to any role that these amino acids may play in immature particle assembly. The defect caused by the MHR mutations was identified as an early step in the capsid assembly process. The results provide strong evidence for a model in which the hydrophobic residues of the MHR control a conformational reorganization of CA that is needed to initiate capsid assembly and suggest that the formation of an interdomain interaction occurs early during maturation.

Controlling viral capsid assembly with templating

We develop coarse-grained models that describe the dynamic encapsidation of functionalized nanoparticles by viral capsid proteins. We find that some forms of cooperative interactions between protein subunits and nanoparticles can dramatically enhance rates and robustness of assembly, as compared to the spontaneous assembly of subunits into empty capsids. For large core-subunit interactions, subunits adsorb onto core surfaces en masse in a disordered manner, and then undergo a cooperative rearrangement into an ordered capsid structure. These assembly pathways are unlike any identified for empty capsid formation. Our models can be directly applied to recent experiments in which viral capsid proteins assemble around functionalized inorganic nanoparticles [Sun, Proc. Natl. Acad. Sci. U.S.A. 104, 1354 (2007)]. In addition, we discuss broader implications for understanding the dynamic encapsidation of single-stranded genomic molecules during viral replication and for developing multicomponent nanostructured materials.

Oligomerization of the SPP1 scaffolding protein

Viral scaffolding proteins direct polymerization of major capsid protein subunits into icosahedral procapsid structures. The scaffolding protein of bacteriophage SPP1 was engineered with a C-terminal hexahistidine tag (gp11-His(6)) and purified. The protein is an alpha-helical-rich molecule with a very elongated shape as found for internal scaffolding proteins from other phages. It is a 3.3 S tetramer of 93.6 kDa at micromolar concentrations. Intersubunit cross-linking of these tetramers generated preferentially covalently bound dimers, revealing that gp11-His(6) is structurally a dimer of dimers. Incubation at temperatures above 37 degrees C correlated with a reduction of its alpha-helical content and a less effective intersubunit cross-linking. Complete loss of secondary structure was observed at temperatures above 60 degrees C. Refolding of gp11-His(6) thermally denatured at 65 degrees C led to reacquisition of the protein native ellipticity spectrum but the resulting population of molecules was heterogeneous. Its hydrodynamic behavior was compatible with a mix of 3.3 S elongated tetramers (approximately 90%) and a smaller fraction of 2.4 S dimers (approximately 10%). This population of gp11-His(6) was competent to direct polymerization of the SPP1 major capsid protein gp13 into procapsid-like structures in a newly developed assembly assay in vitro. Although native tetramers were active in assembly, refolded gp11-His(6) showed enhanced binding to gp13 revealing a more active species for interaction with the major capsid protein than native gp11-His(6).

Kinetic theory of virus capsid assembly

A phenomenological theory is presented for the kinetics of the in vitro assembly and disassembly of icosahedral virus capsids in solutions of coat proteins. The focus is on conditions where nucleation-type processes can be ignored. We find that the kinetics of assembly is strongly concentration dependent and that the late-stage relaxation time varies as the inverse of the square of the concentration. These findings are corroborated by experimental observations on a number of viruses. Further, our theory shows that hysteresis observed in some experiments could be a direct effect of the kinetics of a high-order mass action law, not necessarily the result of a free energy barrier between assembled and disassembled states.

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-to-gas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.

Exploring the parameter space of complex self-assembly through virus capsid models

We use discrete event stochastic simulations to characterize the parameter space of a model of icosahedral viral capsid assembly as functions of monomer-monomer binding rates. The simulations reveal a parameter space characterized by three major assembly mechanisms, a standard nucleation-limited monomer-accretion pathway and two distinct hierarchical assembly pathways, as well as unproductive regions characterized by kinetically trapped species. Much of the productive parameter space also consists of border regions between these domains where hybrid pathways are likely to operate. A simpler octamer system studied for comparison reveals three analogous pathways, but is characterized by much lesser sensitivity to parameter variations in contrast to the sharp changes visible in the icosahedral model. The model suggests that modest changes in assembly conditions, consistent with expected differences between in vitro and in vivo assembly environments, could produce substantial shifts in assembly pathways. These results suggest that we must be cautious in drawing conclusions about in vivo capsid self-assembly dynamics from theoretical or in vitro models, as the nature of the basic assembly mechanisms accessible to a system can substantially differ between simple and complex model systems, between theoretical models and simulation results, and between in vitro and in vivo assembly conditions.

Polyhead formation in phage P22 pinpoints a region in coat protein required for conformational switching

Eighteen single amino acid substitutions in phage P22 coat protein cause temperature-sensitive folding defects (tsf). Three intragenic global suppressor (su) substitutions (D163G, T166I and F170L), localized to a flexible loop, rescue the folding of several tsf coat proteins. Here we investigate the su substitutions in the absence of the original tsf substitutions. None of the su variant coat proteins displayed protein folding defects. Individual su substitutions had little effect on phage production in vivo; yet double and triple combinations resulted in a cold-sensitive (cs) phenotype, consistent with a defect in assembly. During virus assembly and maturation, conformational switching of capsid subunits is required when chemically identical capsid subunits form an icosahedron. Analysis of double- and triple-su phage-infected cell lysates by negative-stain electron microscopy reveals an increase in aberrant structures at the cs temperature. In vitro assembly of F170L coat protein causes production of polyheads, never seen before in phage P22. Purified procapsids composed of all of the su coat proteins showed defects in expansion, which mimics maturation in vitro. Our results suggest that a previously identified surface-exposed loop in coat protein is critical in conformational switching of subunits during both procapsid assembly and maturation.

Computational models of molecular self-organization in cellular environments

The cellular environment creates numerous obstacles to efficient chemistry, as molecular components must navigate through a complex, densely crowded, heterogeneous, and constantly changing landscape in order to function at the appropriate times and places. Such obstacles are especially challenging to self-organizing or self-assembling molecular systems, which often need to build large structures in confined environments and typically have high-order kinetics that should make them exquisitely sensitive to concentration gradients, stochastic noise, and other non-ideal reaction conditions. Yet cells nonetheless manage to maintain a finely tuned network of countless molecular assemblies constantly forming and dissolving with a robustness and efficiency generally beyond what human engineers currently can achieve under even carefully controlled conditions. Significant advances in high-throughput biochemistry and genetics have made it possible to identify many of the components and interactions of this network, but its scale and complexity will likely make it impossible to understand at a global, systems level without predictive computational models. It is thus necessary to develop a clear understanding of how the reality of cellular biochemistry differs from the ideal models classically assumed by simulation approaches and how simulation methods can be adapted to accurately reflect biochemistry in the cell, particularly for the self-organizing systems that are most sensitive to these factors. In this review, we present approaches that have been undertaken from the modeling perspective to address various ways in which self-organization in the cell differs from idealized models.

Characterization and function of putative substrate specificity domain in microvirus external scaffolding proteins

Microviruses (canonical members are bacteriophages phiX174, G4, and alpha3) are T=1 icosahedral virions with an assembly pathway mediated by two scaffolding proteins. The external scaffolding protein D plays a major role during morphogenesis, particularly in icosahedral shell formation. The results of previous studies, conducted with a cloned chimeric external scaffolding gene, suggest that the first alpha-helix acts as a substrate specificity domain, perhaps mediating the initial coat-external scaffolding protein interaction. However, the expression of a cloned gene could lead to protein concentrations higher than those found in typical infections. Moreover, its induction before infection could alter the timing of the protein's accumulation. Both of these factors could drive or facilitate reactions that may not occur under physiological conditions or before programmed cell lysis. In order to elucidate a more detailed mechanistic model, a chimeric external scaffolding gene was placed directly in the phiX174 genome under wild-type transcriptional and translational control, and the chimeric virus, which was not viable on the level of plaque formation, was characterized. The results of the genetic and biochemical analyses indicate that alpha-helix 1 most likely mediates the nucleation reaction for the formation of the first assembly intermediate containing the external scaffolding protein. Mutants that can more efficiently use the chimeric scaffolding protein were isolated. These second-site mutations appear to act on a kinetic level, shortening the lag phase before virion production, perhaps lowering the critical concentration of the chimeric protein required for a nucleation reaction.

A Dissection of the Protein–Protein Interfaces in Icosahedral Virus Capsids

We selected 49 icosahedral virus capsids whose crystal structures are reported in the Protein Data Bank. They belong to the T=1, T=3, pseudo T=3 and other lattice types. We identified in them 779 unique interfaces between pairs of subunits, all repeated by icosahedral symmetry. We analyzed the geometric and physical chemical properties of these interfaces and compared with interfaces in protein-protein complexes and homodimeric proteins, and with crystal packing contacts. The capsids contain one to 16 subunits implicated in three to 66 unique interfaces. Each subunit loses 40-60% of its accessible surface in contacts with an average of 8.5 neighbors. Many of the interfaces are very large with a buried surface area (BSA) that can exceed 10,000 A(2), yet 39% are small with a BSA<800 A(2) comparable to crystal packing contacts. Pairwise capsid interfaces overlap, so that one-third of the residues are part of more than one interface. Those with a BSA>800 A(2) resemble homodimer interfaces in their chemical composition. Relative to the protein surface, they are non-polar, enriched in aliphatic residues and depleted of charged residues, but not of neutral polar residues. They contain one H-bond per about 200 A(2) BSA. Small capsid interfaces (BSA<800 A(2)) are only slightly more polar. They have a similar amino acid composition, but they bury fewer atoms and contain fewer H-bonds for their size. Geometric parameters that estimate the quality of the atomic packing suggest that the small capsid interfaces are loosely packed like crystal packing contacts, whereas the larger interfaces are close-packed as in protein-protein complexes and homodimers. We discuss implications of these findings on the mechanism of capsid assembly, assuming that the larger interfaces form first to yield stable oligomeric species (capsomeres), and that medium-size interfaces allow the stepwise addition of capsomeres to build larger intermediates.

Deciphering the kinetic mechanism of spontaneous self-assembly of icosahedral capsids

Self-assembly of viral proteins into icosahedral capsids is an interesting yet poorly understood phenomenon of which elucidation may aid the exploration of beneficial applications of capsids in materials science and medicine. Using molecular dynamics simulations of coarse-grained models for capsid proteins, we show that the competition between the formation of full capsids and nonidealized structures is strongly dependent upon the protein concentration and temperature, occurring kinetically as a cascade of elementary reactions in which free monomers are added to the growing oligomers on a downhill free-energy landscape. However, the insertion of the final subunits is the rate-limiting, energetically unfavorable step in viral capsid assembly. A phase diagram has been constructed to show the regions where capsids or nonidealized structures are stable at each concentration and temperature. We anticipate that our findings will provide guidance in identifying suitable conditions required for in vitro viral capsid assembly experiments.

Mathematical virology: a novel approach to the structure and assembly of viruses

Understanding the structure and life cycle of viruses is a fascinating challenge with a crucial impact on the public health sector. In the early 1960s, Caspar & Klug (Caspar & Klug 1962 Cold Spring Harbor Symp. Quant. Biol. 27, 1-24) established a theory for the prediction of the surface structures of the protein shells, called viral capsids, which encapsulate and hence provide protection for the viral genome. It is of fundamental importance in virology, with a broad spectrum of applications ranging from the image analysis and classification of experimental data to the construction of assembly models. However, experimental results have provided evidence for the fact that it is incomplete and, in particular, cannot account for the structures of Papovaviridae, which are of particular interest because they contain cancer-causing viruses. This gap has recently been closed by the viral tiling theory, which describes the locations of the protein subunits and inter-subunit bonds in viral capsids based on mathematical tools from the area of quasicrystals. The predictions and various recent applications of the new theory are presented, and it is discussed how further research along these lines may lead to new insights in virology and the design of anti-viral therapeutics.

Molecular dissection of ø29 scaffolding protein function in an in vitro assembly system

An in vitro assembly system was developed to study prolate capsid assembly of phage ø29 biochemically, and to identify regions of scaffolding protein required for its functions. The crowding agent polyethylene glycol can induce bacteriophage ø29 monomeric capsid protein and dimeric scaffolding protein to co-assemble to form particles which have the same geometry as either prolate T=3 Q=5 procapsids formed in vivo or previously observed isometric particles. The formation of particles is a scaffolding-dependent reaction. The balance between the fidelity and efficiency of assembly is controlled by the concentration of crowding agent and temperature. The assembly process is salt sensitive, suggesting that the interactions between the scaffolding and coat proteins are electrostatic. Three N-terminal ø29 scaffolding protein deletion mutants, Delta 1-9, Delta 1-15 and Delta 1-22, abolish the assembly activity. Circular dichroism spectra indicate that these N-terminal deletions are accompanied by a loss of helicity. The inability of these proteins to dimerize suggests that the N-terminal region of the scaffolding protein contributes to the dimer interface and maintains the structural integrity of the dimeric protein. Two C-terminal scaffolding protein deletion mutants, Delta 79-97 and Delta 62-97, also fail to promote assembly. However, the secondary structure and the dimerization ability of these mutants are unchanged relative to wild-type, which suggests that the C terminus is the likely site of interaction with the capsid protein.

Specific short hairpin RNA-mediated inhibition of viral DNA packaging of human cytomegalovirus

To clearly demonstrate the role of the human cytomegalovirus (HCMV) portal protein pUL104 RNA interference was applied. Expressing cell lines were constructed by transduction of shRNAs via the infection with retroviral vectors. After infection of these cells with HCMV AD169 the expression of pUL104 was reduced up to 80% for shRNA S1 and 54% for shRNA S2 at late times of infection compared to controls. In addition, the inhibitory effect was corresponding with a decrease in viral mRNA and plaque formations. Electron microscopic analysis demonstrated that infection of cells expressing pUL104-specific shRNAs resulted in the inhibition of formation of replicative particles.

Phage P22 procapsids equilibrate with free coat protein subunits

Assembly of bacteriophage P22 procapsids has long served as a model for assembly of spherical viruses. Historically, assembly of viruses has been viewed as a non-equilibrium process. Recently alternative models have been developed that treat spherical virus assembly as an equilibrium process. Here we have investigated whether P22 procapsid assembly reactions achieve equilibrium or are irreversibly trapped. To assemble a procapsid-like particle in vitro, pure coat protein monomers are mixed with scaffolding protein. We show that free subunits can exchange with assembled structures, indicating that assembly is a reversible, equilibrium process. When empty procapsid shells (procapsids with the scaffolding protein stripped out) were diluted so that the concentration was below the dissociation constant ( approximately 5 microM) for coat protein monomers, free monomers were detected. The released monomers were assembly-competent; when NaCl was added to metastable partial capsids that were aged for an extended period, the released coat subunits were able to rapidly re-distribute from the partial capsids and form whole procapsids. Lastly, radioactive monomeric coat subunits were able to exchange with the subunits from empty procapsid shells. The data presented illustrate that coat protein monomers are able to dissociate from procapsids in an active state, that assembly of procapsids is consistent with reactions at equilibrium and that the reaction follows the law of mass action.

Quantitative analysis of a virulent bacteriophage transcription strategy

An increasingly large number of bacteriophage genomes are being sequenced each year. What is an efficient experimental and computational procedure to analyze transcription strategies of newly sequenced novel bacteriophages? We address this issue using an example of bacteriophage Xp10, which infects rice pathogen Xanthomonas oryzae. This phage is particularly challenging for analysis, since part of its genome is jointly transcribed by two (host and viral) RNA polymerases. To understand the roles played by the two RNA polymerases, we developed a novel method of data analysis which combines quantitative analysis of Xp10 global gene expression data and kinetic modeling of the infection process. To generalize our approach, we discuss how our method can be applied to other systems and argue that genomic array experiments combined with the methods of data analysis that we present provide an efficient way to analyze gene expression strategies of novel bacteriophages.

Quantitative Analysis of Multi-component Spherical Virus Assembly: Scaffolding Protein Contributes to the Global Stability of Phage P22 Procapsids

Assembly of the hundreds of subunits required to form an icosahedral virus must proceed with exquisite fidelity, and is a paradigm for the self-organization of complex macromolecular structures. However, the mechanism for capsid assembly is not completely understood for any virus. Here we have investigated the in vitro assembly of phage P22 procapsids using a quantitative model specifically developed to analyze assembly of spherical viruses. Phage P22 procapsids are the product of the co-assembly of 420 molecules of coat protein and approximately 100-300 molecules of scaffolding protein. Scaffolding protein serves as an assembly chaperone and is not part of the final mature capsid, but is essential for proper procapsid assembly. Here we show that scaffolding protein also affects the thermodynamics of assembly, and for the first time this quantitative analysis has been performed on a virus composed of more than one type of protein subunit. Purified coat and scaffolding proteins were mixed in varying ratios in vitro to form procapsids. The reactions were allowed to reach equilibrium and the proportion of the input protein assembled into procapsids or remaining as free subunits was determined by size exclusion chromatography and SDS-PAGE. The results were used to calculate the free energy contributions for individual coat and scaffolding proteins. Each coat protein subunit was found to contribute -7.2(+/-0.1)kcal/mol and each scaffolding protein -6.1(+/-0.2)kcal/mol to the stability of the procapsid. Because each protein interacts with two or more neighbors, the pair-wise energies are even less. The weak protein interactions observed in the assembly of procapsids are likely important in the control of nucleation, since an increase in affinity between coat and scaffolding proteins can lead to kinetic traps caused by the formation of too many nuclei. In addition, we find that adjusting the molar ratio of scaffolding to coat protein can alter the assembly product. When the scaffolding protein concentration is low relative to coat protein, there is a correspondingly low yield of proper procapsids. When the relative concentration is very high, too many nuclei form, leading to kinetically trapped assembly intermediates.

Dynamic motions of free and bound O29 scaffolding protein identified by hydrogen deuterium exchange mass spectrometry

In the double-stranded DNA containing bacteriophages, hundreds of copies of capsid protein subunits polymerize to form icosahedral shells, called procapsids, into which the viral genome is subsequently packaged to form infectious virions. High assembly fidelity requires the assistance of scaffolding protein molecules, which interact with the capsid proteins to insure proper geometrical incorporation of subunits into the growing icosahedral lattices. The interactions between the scaffolding and capsid proteins are transient and are subsequently disrupted during DNA packaging. Removal of scaffolding protein is achieved either by proteolysis or alternatively by some form of conformational switch that allows it to dissociate from the capsid. To identify the switch controlling scaffolding protein association and release, hydrogen deuterium exchange was applied to Bacillus subtilis phage Ø29 scaffolding protein gp7 in both free and procapsid-bound forms. The H/D exchange experiments revealed highly dynamic and cooperative opening motions of scaffolding molecules in the N-terminal helix-loop-helix (H-L-H) region. The motions can be promoted by destabilizing the hydrophobic contact between two helices. At low temperature where high energy motions were damped, or in a mutant in which the helices were tethered through the introduction of a disulfide bond, this region displayed restricted cooperative opening motions as demonstrated by a switch in the exchange kinetics from correlated EX1 exchange to uncorrelated EX2 exchange. The cooperative opening rate was increased in the procapsid-bound form, suggesting this region might interact with the capsid protein. Its dynamic nature might play a role in the assembly and release mechanism.

Symmetry, equivalence, and molecular self-assembly

Molecular self-assembly at equilibrium is fundamental to the fields of biological self-organization, the development of novel environmentally responsive polymeric materials, and nanofabrication. Our approach to understanding the principles governing this process is inspired by existing models and measurements for the self-assembly of actin, tubulin, and the ubiquitous icosahedral shell structures of viral capsids. We introduce a family of simple potentials that give rise to the self-assembly of linear polymeric, random surface ("membrane"), tubular ("nanotube"), and hollow icosahedral structures that are similar in many respects to their biological counterparts. The potentials involve equivalent particles and an interplay between directional (dipolar, multipolar) and short-range (van der Waals) interactions. Specifically, we find that the dipolar potential, having a continuous rotational symmetry about the dipolar axis, gives rise to chain formation, while particles with multipolar potentials, having discrete rotational symmetries (square quadrupole or triangular ring of dipoles or "hexapole"), lead to the self-assembly of open sheet, nanotube, and hollow icosahedral geometries. These changes in the geometry of self-assembly are accompanied by significant changes in the kinetics of the organization.

Classical nucleation theory of virus capsids

A fundamental step in the replication of a viral particle is the self-assembly of its rigid shell (capsid) from its constituent proteins. Capsids play a vital role in genome replication and intercellular movement of viruses, and as such, understanding viral assembly has great potential in the development of new antiviral therapies and a systematic treatment of viral infection. In this article, we assume that nucleation is the underlying mechanism for self-assembly and combine the theoretical methods of the physics of equilibrium polymerization with those of the classical nucleation to develop a theory for the kinetics of virus self-assembly. We find expressions for the size of the critical capsid, the lag time, and the steady-state nucleation rate of capsids, and how they depend on both protein concentration and binding energy. The latter is a function of the acidity of the solution, the ionic strength, and the temperature, explaining why capsid nucleation is a sensitive function of the ambient conditions.

Electrostatic interactions govern both nucleation and elongation during phage P22 procapsid assembly

Icosahedral capsid assembly is an example of a reaction controlled solely by the interactions of the proteins involved. Bacteriophage P22 procapsids can be assembled in vitro by mixing coat and scaffolding proteins in a nucleation-limited reaction, where scaffolding protein directs the proper assembly of coat protein. Here, we investigated the effect of the buffer composition on the interactions necessary for capsid assembly. Different concentrations of various salts, chosen to follow the electroselectivity series for anions, were added to the assembly reaction. The concentration and type of salt was found to be crucial for proper nucleation of procapsids. Nucleation in low salt concentrations readily occurred but led to bowl-like partial procapsids, as visualized by negative stain electron microscopy. The edge of the partial capsids remained assembly-competent since coat protein addition triggered procapsid completion. The addition of salt to the partial capsids also caused procapsid completion. In addition, each salt affected both assembly rates and the extent of procapsid formation. We hypothesize that low salt conditions increase the coat protein:scaffolding protein affinity, causing excessive nuclei to form, which decreases coat protein levels leading to incomplete assembly.

Simulation study of the contribution of oligomer/oligomer binding to capsid assembly kinetics

The process by which hundreds of identical capsid proteins self-assemble into icosahedral structures is complex and poorly understood. Establishing constraints on the assembly pathways is crucial to building reliable theoretical models. For example, it is currently an open question to what degree overall assembly kinetics are dominated by one or a few most efficient pathways versus the enormous number theoretically possible. The importance of this question, however, is often overlooked due to the difficulties of addressing it in either theoretical or experimental practice. We apply a computer model based on a discrete-event simulation method to evaluate the contributions of nondominant pathways to overall assembly kinetics. This is accomplished by comparing two possible assembly models: one allowing growth to proceed only by the accretion of individual assembly subunits and the other allowing the binding of sterically compatible assembly intermediates any sizes. Simulations show that the two models perform almost identically under low binding rate conditions, where growth is strongly nucleation-limited, but sharply diverge under conditions of higher association rates or coat protein concentrations. The results suggest the importance of identifying the actual binding pattern if one is to build reliable models of capsid assembly or other complex self-assembly processes.

A reaction landscape identifies the intermediates critical for self-assembly of virus capsids and other polyhedral structures

The capsids of spherical viruses may contain from tens to hundreds of copies of the capsid protein(s). Despite their complexity, these particles assemble rapidly and with high fidelity. Subunit and capsid represent unique end states. However, the number of intermediate states in these reactions can be enormous-a situation analogous to the protein folding problem. Approaches to accurately model capsid assembly are still in their infancy. In this paper, we describe a sail-shaped reaction landscape, defined by the number of subunits in each species, the predicted prevalence of each species, and species stability. Prevalence can be calculated from the probability of synthesis of a given intermediate and correlates well with the appearance of intermediates in kinetics simulations. In these landscapes, we find that only those intermediates along the leading edge make a significant contribution to assembly. Although the total number of intermediates grows exponentially with capsid size, the number of leading-edge intermediates grows at a much slower rate. This result suggests that only a minute fraction of intermediates needs to be considered when describing capsid assembly.

A second-site suppressor of a folding defect functions via interactions with a chaperone network to improve folding and assembly in vivo

Single amino acid substitutions in a protein can cause misfolding and aggregation to occur. Protein misfolding can be rescued by second-site amino acid substitutions called suppressor substitutions (su), commonly through stabilizing the native state of the protein or by increasing the rate of folding. Here we report evidence that su substitutions that rescue bacteriophage P22 temperature-sensitive-folding (tsf) coat protein variants function in a novel way. The ability of tsf:su coat proteins to fold and assemble under a variety of cellular conditions was determined by monitoring levels of phage production. The tsf:su coat proteins were found to more effectively utilize P22 scaffolding protein, an assembly chaperone, as compared with their tsf parents. Phage-infected cells were radioactively labelled to quantify the associations between coat protein variants and folding and assembly chaperones. Phage carrying the tsf:su coat proteins induced more GroEL and GroES, and increased formation of protein:chaperone complexes as compared with their tsf parents. We propose that the su substitutions result in coat proteins that are more assembly competent in vivo because of a chaperone-driven kinetic partitioning between aggregation-prone intermediates and the final assembled state. Through more proficient use of this chaperone network, the su substitutions exhibit a novel means of suppression of a folding defect.

Control of virus assembly: HK97 "Whiffleball" mutant capsids without pentons

The capsid of Escherichia coli bacteriophage HK97 assembles as a 420 subunit icosahedral shell called Prohead I which undergoes a series of maturation steps, including proteolytic cleavage, conformational rearrangements, and covalent cross-linking among all the subunits to yield the highly stable mature Head II shell. Prohead I have been shown to assemble from pre-formed hexamers and pentamers of the capsid protein subunit. We report here the properties of a mutant of the capsid protein, E219K, which illuminate the assembly of Prohead I. The mutant capsid protein is capable of going through all of the biochemically and morphologically defined steps of capsid maturation, and when it is expressed by itself from a plasmid it assembles efficiently into a Prohead I that is morphologically indistinguishable from the wild-type Prohead I, with a full complement of both hexamers and pentamers. Unlike the wild-type Prohead I, when the mutant structure is dissociated into capsomers in vitro, only hexamers are found. When such preparations are put under assembly conditions, these mutant hexamers assemble into "Whiffleballs", particles that are identical with Prohead I except that they are missing the 12 pentamers. These Whiffleballs can even be converted to Prohead I by specifically binding wild-type pentamers. We argue that the ability of the mutant hexamers to assemble in the absence of pentamers implies that they retain a memory of their earlier assembled state, most likely as a conformational difference relative to assembly-naive hexamers. The data therefore favor a model in which Prohead I assembly is regulated by conformational switching of the hexamer.

Regulating self-assembly of spherical oligomers

In multistep reactions, stability of intermediates is critical to the rate of product formation and a significant factor in generating kinetic traps. The capsid protein of cowpea chlorotic mottle virus (CCMV) can be induced to assemble into spherical particles of 30, 60, and 90 dimers. Based on examining assembly kinetics and reaction end points, we find that formation of uniform, ordered structures is not always a result of reactions that reach equilibrium. Equilibration or, alternatively, kinetic trapping can be identified by a straightforward analysis. Altering the assembly path of "spherical" particles is a means of controlling the distribution of products, which has broad applicability to self-assembly reactions.

Lattice Transformations and Subunit Conformational Changes in Phage Capsid Maturation

A general feature of the pathways for the assembly of double-stranded DNA phages and viruses is the assembly of coat and scaffolding subunits into a precursor shell or procapsid, followed by packaging of the genomic DNA into the shell. Coupled to this DNA packaging process is the loss of the scaffolding subunits and expansion and re-organization of the procapsid lattice to the lattice of the mature virus. Such lattice transitions have also been observed with adenoviruses and herpesviruses. In re-organizing into the mature capsid lattice, each subunit of the precursor lattice must change its conformation, or its relationship with its neighbours, or both. We briefly review here recent structural data for phages P22 and HK97, and describe the motions and conformational changes associated with this lattice transition. Possible functions of such constrained transformations within the virus life-cycle are discussed.

A Stochastic Model of Icosahedral Capsid Growth

A model of growth of icosahedral capsids is proposed. It is similar to the stochastic model of fullerene growth, but takes into account variations in the composition of pentamers and hexamers that are responsible for the final capsid size. We show that the observed high yield of capsid production implies a high level of self-organization of the elementary building blocks.

Self-assembly of polyhedral shells: a molecular dynamics study

The use of reduced models for investigating the self-assembly dynamics underlying protein shell formation in spherical viruses is described. The spontaneous self-assembly of these polyhedral, supramolecular structures, in which icosahedral symmetry is a conspicuous feature, is a phenomenon whose dynamics remain unexplored; studying the growth process by means of computer simulation provides access to the mechanisms underlying assembly. In order to capture the more universal aspects of self-assembly, namely the manner in which component shapes influence structure and assembly pathway, in this exploratory study low-resolution approximations are used to represent the basic protein building blocks. Alternative approaches involving both irreversible and reversible assembly are discussed, models based on both schemes are introduced, and examples of the resulting behavior described.

In vitro papillomavirus capsid assembly analyzed by light scattering

Pentamers of the L1 major capsid protein of human papillomavirus (HPV type 11) were purified after expression in E. coli and analyzed for the kinetics of in vitro capsid self-assembly using multi-angle light scattering (MALS). Pentamers self-assembled into capsid-like structures at a rate that was a function of protein concentration. The kinetics of capsid formation were sigmoidal with a concentration-dependent lag phase, followed by a rapid increase in polymerization. Nucleation size and the rate order of subsequent subunit addition were calculated from the concentration dependence of the extent of capsid formation and the rate of the fast phase, respectively. Assembly was second order with a nucleation size of two pentamers. Thus, we suggest that dimers of pentamers are the nucleus for L1 assembly into capsid-like structures, with rapid sequential addition of single pentamers to the growing shell. Although studied in vitro without accessory factors that may be present in vivo, these data are in contrast with the "five-around-one" assembly nucleus previously proposed for polyomaviruses.

Self-assembly of double-stranded RNA bacteriophages

Double-stranded RNA viruses infecting bacterial hosts belong to the Cystoviridae family. Bacteriophage phi6 is one of the best characterized dsRNA viruses and shares structural as well as functional similarities with other well-studied eukaryotic dsRNA viruses (e.g. L-A, rotavirus, bluetongue virus, and reovirus). The assembly pathway of the enveloped, triple-layered phi6 virion has been well documented and can be divided into four distinct steps which are (1) procapsid formation, (2) genome encapsidation and replication, (3) nucleocapsid surface shell assembly, and (4) envelope formation. In this review, we focus primarily on the procapsid and nucleocapsid assembly for which in vitro systems have been established. The in vitro assembly systems have been instrumental in revealing assembly intermediates and conformational changes that are common to phi6 and phi8, two cystoviruses with negligible sequence homology. Two viral enzymes, the packaging NTPase (P4) and the RNA-dependent RNA polymerase (P2), were found essential for the nucleation step. The nucleation complex contains one or more tetramers of the major procapsid protein (P1) and is further stabilized by protein P4. Interaction of P1 and P4 during assembly is accompanied by an additional folding of their respective polypeptide chains. The in vitro assembled procapsids were shown to selectively package and replicate the genomic ssRNA. Furthermore, in vitro assembly of infectious nucleocapsids has been achieved in the case of phi6. The in vitro studies indicate that the nucleocapsid coat protein (P8) assembles around the polymerase complex in a template-assisted manner. Implications for the assembly of other dsRNA viruses are also presented.

Association of villin with phosphatidylinositol 4,5-bisphosphate regulates the actin cytoskeleton

Villin, an epithelial cell actin-binding protein, severs actin in vitro and in vivo. Previous studies report that phosphatidylinositol 4,5-bisphosphate (PIP(2)) regulates actin severing by villin, presumably by interaction with villin. However, direct association of villin with PIP(2) has never been characterized. In this report, we presented mutational analysis to identify the PIP(2)-binding sites in villin. Villin (human) binds PIP(2) with a K(d) of 39.5 microm, a stoichiometry of 3.3, and a Hill coefficient of 1. We generated deletion mutants of villin lacking putative PIP(2)-binding sites and examined the impact of these mutations on PIP(2) binding and actin dynamics. Our analysis revealed the presence of three PIP(2)-binding sites, two in the amino-terminal core and one in the carboxyl-terminal headpiece of human villin. Synthetic peptides analogous with these sites confirmed the binding domains. Circular dichroism and quenching of intrinsic tryptophan fluorescence revealed a significant conformational change in these peptides ensuing in their association with PIP(2). By using site-directed mutagenesis (arginine 138 to alanine), we demonstrated the presence of an identical F-actin and PIP(2)-binding site in the capping and severing domain of villin. In contrast, the mutants lysine 822 and 824 to alanine demonstrated the presence of an overlapping F-actin and PIP(2)-binding site in the actin cross-linking domain of villin. Consistent with this observation, association of villin with PIP(2) inhibited the actin capping and severing functions of villin and enhanced the actin bundling function of villin. Our studies revealed that structural changes induced by association with PIP(2) could regulate the actin-modifying functions of villin. This study provided biochemical proof of the functional significance of villin association with PIP(2) and identified the molecular mechanisms involved in the regulation of actin dynamics by villin and PIP(2).

Assembly of the herpes simplex virus capsid: identification of soluble scaffold-portal complexes and their role in formation of portal-containing capsids

The herpes simplex virus type 1 (HSV-1) portal complex is a ring-shaped structure located at a single vertex in the viral capsid. Composed of 12 U(L)6 protein molecules, the portal functions as a channel through which DNA passes as it enters the capsid. The studies described here were undertaken to clarify how the portal becomes incorporated as the capsid is assembled. We tested the idea that an intact portal may be donated to the growing capsid by way of a complex with the major scaffolding protein, U(L)26.5. Soluble U(L)26.5-portal complexes were found to assemble when purified portals were mixed in vitro with U(L)26.5. The complexes, called scaffold-portal particles, were stable during purification by agarose gel electrophoresis or sucrose density gradient ultracentrifugation. Examination of the scaffold-portal particles by electron microscopy showed that they resemble the 50- to 60-nm-diameter "scaffold particles" formed from purified U(L)26.5. They differed, however, in that intact portals were observed on the surface. Analysis of the protein composition by sodium dodecyl sulfate-polyacrylamide gel electrophoresis demonstrated that portals and U(L)26.5 combine in various proportions, with the highest observed U(L)6 content corresponding to two or three portals per scaffold particle. Association between the portal and U(L)26.5 was antagonized by WAY-150138, a small-molecule inhibitor of HSV-1 replication. Soluble scaffold-portal particles were found to function in an in vitro capsid assembly system that also contained the major capsid (VP5) and triplex (VP19C and VP23) proteins. Capsids that formed in this system had the structure and protein composition expected of mature HSV-1 capsids, including U(L)6, at a level corresponding to approximately 1 portal complex per capsid. The results support the view that U(L)6 becomes incorporated into nascent HSV-1 capsids by way of a complex with U(L)26.5 and suggest further that U(L)6 may be introduced into the growing capsid as an intact portal.