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

Imperfect symmetry facilitated the evolution of specificity and high-order stoichiometry in vertebrate hemoglobin

Many proteins form paralogous multimers - molecular complexes in which evolutionarily related proteins are arranged into specific quaternary structures. Little is known about the mechanisms by which they acquired their stoichiometry (the number of total subunits in the complex) and heterospecificity (the preference of subunits for their paralogs rather than other copies of the same protein). Here we use ancestral protein reconstruction and biochemical experiments to study historical increases in stoichiometry and specificity during the evolution of vertebrate hemoglobin (Hb), a α2β2 heterotetramer that evolved from a homodimeric ancestor after a gene duplication. We show that the mechanisms for this evolutionary transition was simple. One hydrophobic substitution in subunit β after the gene duplication was sufficient to cause the ancestral dimer to homotetramerize with high affinity across a new interface. During this same interval, a single-residue deletion in subunit α at the older interface conferred specificity for the heterotetrameric form and the trans-orientation of subunits within it. These sudden transitions in stoichiometry and specificity were possible because the interfaces in Hb are isologous - involving the same surface patch on interacting subunits, rotated 180° relative to each other - but the symmetry is slightly imperfect. This architecture amplifies the impacts of individual mutations on stoichiometry and specificity, especially in higher-order complexes, and allows single substitutions to differentially affect heteromeric vs homomeric interactions. Many multimers are isologous, and symmetry in proteins is always imperfect; our findings therefore suggest that elaborate and specific molecular complexes may often evolve via simple genetic and physical mechanisms.

Protein Cages: From Fundamentals to Advanced Applications

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

Of capsid structure and stability: The partnership between charged residues of E-loop and P-domain of the bacteriophage P22 coat protein

Tailed dsDNA bacteriophages and herpesviruses form capsids using coat proteins that have the HK97 fold. In these viruses, the coat proteins first assemble into procapsids, which subsequently mature during DNA packaging. Generally interactions between the coat protein E-loop of one subunit and the P-domain of an adjacent subunit help stabilize both capsomers and capsids. Based on a recent 3.3 Å cryo-EM structure of the bacteriophage P22 virion, E-loop amino acids E52, E59 and E72 were suggested to stabilize the capsid through intra-capsomer salt bridges with the P-domain residues R102, R109 and K118. The glutamic acid residues were each mutated to alanine to test this hypothesis. The substitutions resulted in a WT phenotype and did not destabilize capsids; rather, the alanine substituted coat proteins increased the stability of procapsids and virions. These results indicate that different types of interactions must be used between the E-loop and P-domain to stabilize phage P22 procapsids and virions.

Dissecting macromolecular recognition sites in ribosome: implication to its self-assembly

Interactions between macromolecules play a crucial role in ribosome assembly that follows a highly coordinated process involving RNA folding and binding of ribosomal proteins (r-proteins). Although extensive studies have been carried out to understand macromolecular interactions in ribosomes, most of them are confined to either large or small ribosomal-subunit of few species. A comparative analysis of macromolecular interactions across different domains is still missing. We have analyzed the structural and physicochemical properties of protein-protein (PP), protein-RNA (PR) and RNA-RNA (RR) interfaces in small and large subunits of ribosomes, as well as in between the two subunits. Additionally, we have also developed Random Forest (RF) classifier to catalog the r-proteins. We find significant differences as well as similarities in macromolecular recognition sites between ribosomal assemblies of prokaryotes and eukaryotes. PR interfaces are substantially larger and have more ionic interactions than PP and RR interfaces in both prokaryotes and eukaryotes. PP, PR and RR interfaces in eukaryotes are well packed compared to those in prokaryotes. However, the packing density between the large and the small subunit interfaces in the entire assembly is strikingly low in both prokaryotes and eukaryotes, indicating the periodic association and dissociation of the two subunits during the translation. The structural and physicochemical properties of PR interfaces are used to predict the r-proteins in the assembly pathway into early, intermediate and late binders using RF classifier with an accuracy of 80%. The results provide new insights into the classification of r-proteins in the assembly pathway.

Loading the dice: The orientation of virus-like particles adsorbed on titanate assisted organosilanized surfaces

The organization of virus-like particles (VLPs) on surfaces is a relevant matter for both fundamental and biomedical sciences. In this work, the authors have tailored surfaces with different surface tension components aiming at finding a relationship with the affinity of the different geometric/surface features of icosahedral P22 VLPs. The surfaces have been prepared by titanate assisted organosilanization with glycidyloxy, amino, and perfluoro silanes. Vibrational and photoelectron spectroscopies have allowed identifying the different functional groups of the organosilanes on the surfaces. Atomic force microscopy (AFM) showed that, irrespective of the organosilane used, the final root mean square roughness remains below 1 nm. Contact angle analyses confirm the effective formation of a set of surface chemistries exhibiting different balance among surface tension components. The study of the adsorption of P22 VLPs has involved the analysis of the dynamics of virus immobilization by fluorescence microscopy and the interpretation of the final VLP orientation by AFM. These analyses give rise to statistical distributions pointing to a higher affinity of VLPs toward perfluorinated surfaces, with a dominant fivefold conformation on this hydrophobic surface, but threefold and twofold symmetries dominating on hydrophilic surfaces. These results can be explained in terms of a reinforced hydrophobic interaction between the perfluorinated surface and the dominating hydrophobic residues present at the P22 pentons.

Changes in the stability and biomechanics of P22 bacteriophage capsid during maturation

The capsid of P22 bacteriophage undergoes a series of structural transitions during maturation that guide it from spherical to icosahedral morphology. The transitions include the release of scaffold proteins and capsid expansion. Although P22 maturation has been investigated for decades, a unified model that incorporates thermodynamic and biophysical analyses is not available. A general and specific model of icosahedral capsid maturation is of significant interest to theoreticians searching for fundamental principles as well as virologists and material scientists seeking to alter maturation to their advantage. To address this challenge, we have combined the results from orthogonal biophysical techniques including differential scanning fluorimetry, atomic force microscopy, circular dichroism, and hydrogen-deuterium exchange mass spectrometry. By integrating these results from single particle and population measurements, an energy landscape of P22 maturation from procapsid through expanded shell to wiffle ball emerged, highlighting the role of metastable structures and the thermodynamics guiding maturation. The propagation of weak quaternary interactions across symmetric elements of the capsid is a key component for stability in P22. A surprising finding is that the progression to wiffle ball, which lacks pentamers, shows that chemical and thermal stability can be uncoupled from mechanical rigidity, elegantly demonstrating the complexity inherent in capsid protein interactions and the emergent properties that can arise from icosahedral symmetry. On a broader scale, this work demonstrates the power of applying orthogonal biophysical techniques to elucidate assembly mechanisms for supramolecular complexes and provides a framework within which other viral systems can be compared.

Energetic cost of building a virus

Viruses are incapable of autonomous energy production. Although many experimental studies make it clear that viruses are parasitic entities that hijack the molecular resources of the host, a detailed estimate for the energetic cost of viral synthesis is largely lacking. To quantify the energetic cost of viruses to their hosts, we enumerated the costs associated with two very distinct but representative DNA and RNA viruses, namely, T4 and influenza. We found that, for these viruses, translation of viral proteins is the most energetically expensive process. Interestingly, the costs of building a T4 phage and a single influenza virus are nearly the same. Due to influenza's higher burst size, however, the overall cost of a T4 phage infection is only 2-3% of the cost of an influenza infection. The costs of these infections relative to their host's estimated energy budget during the infection reveal that a T4 infection consumes about a third of its host's energy budget, whereas an influenza infection consumes only ≈ 1%. Building on our estimates for T4, we show how the energetic costs of double-stranded DNA phages scale with the capsid size, revealing that the dominant cost of building a virus can switch from translation to genome replication above a critical size. Last, using our predictions for the energetic cost of viruses, we provide estimates for the strengths of selection and genetic drift acting on newly incorporated genetic elements in viral genomes, under conditions of energy limitation.

Structure based sequence analysis of viral and cellular protein assemblies

It is well accepted that, in general, protein structural similarity is strongly related to the amino acid sequence identity. To analyze in great detail the correlation, distribution and variation levels of conserved residues in the protein structure, we analyzed all available high-resolution structural data of 5245 cellular complex-forming proteins and 293 spherical virus capsid proteins (VCPs). We categorized and compare them in terms of protein structural regions. In all cases, the buried core residues are the most conserved, followed by the residues at the protein-protein interfaces. The solvent-exposed surface shows greater sequence variations. Our results provide evidence that cellular monomers and VCPs could be two extremes in the quaternary structural space, with cellular dimers and oligomers in between. Moreover, based on statistical analysis, we detected a distinct group of icosahedral virus families whose capsid proteins seem to evolve much slower than the rest of the protein complexes analyzed in this work.

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.

Highly Symmetric and Congruently Tiled Meshes for Shells and Domes

We describe the generation of all possible shell and dome shapes that can be uniquely meshed (tiled) using a single type of mesh face (tile), and following a single meshing (tiling) rule that governs the mesh (tile) arrangement with maximal vertex, edge and face symmetries. Such tiling arrangements or congruently tiled meshed shapes, are frequently found in chemical forms (fullerenes or Bucky balls, crystals, quasi-crystals, virus nano shells or capsids), and synthetic shapes (cages, sports domes, modern architectural facades). Congruently tiled meshes are both aesthetic and complete, as they support maximal mesh symmetries with minimal complexity and possess simple generation rules. Here, we generate congruent tilings and meshed shape layouts that satisfy these optimality conditions. Further, the congruent meshes are uniquely mappable to an almost regular 3D polyhedron (or its dual polyhedron) and which exhibits face-transitive (and edge-transitive) congruency with at most two types of vertices (each type transitive to the other). The family of all such congruently meshed polyhedra create a new class of meshed shapes, beyond the well-studied regular, semi-regular and quasi-regular classes, and their duals (platonic, Catalan and Johnson). While our new mesh class is infinite, we prove that there exists a unique mesh parametrization, where each member of the class can be represented by two integer lattice variables, and moreover efficiently constructable.

Encapsulation of nanoparticles in virus protein shells

The self-assembly of virus-like particles may lead to materials which combine the unique characteristics of viruses, such as precise size control and responsivity to environmental cues, with the properties of abiotic cargo. For a few different viruses, shell proteins are amenable to the in vitro encapsulation of non-genomic cargo in a regular protein cage. In this chapter we describe protocols of high-efficiency in vitro self-assembly around functionalized gold nanoparticles for three examples of icosahedral and non-icosahedral viral protein cages derived from a plant virus, an animal virus, and a human retrovirus. These protocols can be readily adapted with small modifications to work for a broad variety of inorganic and organic nanoparticles.

Viral capsid proteins are segregated in structural fold space

Viral capsid proteins assemble into large, symmetrical architectures that are not found in complexes formed by their cellular counterparts. Given the prevalence of the signature jelly-roll topology in viral capsid proteins, we are interested in whether these functionally unique capsid proteins are also structurally unique in terms of folds. To explore this question, we applied a structure-alignment based clustering of all protein chains in VIPERdb filtered at 40% sequence identity to identify distinct capsid folds, and compared the cluster medoids with a non-redundant subset of protein domains in the SCOP database, not including the viral capsid entries. This comparison, using Template Modeling (TM)-score, identified 2078 structural "relatives" of capsid proteins from the non-capsid set, covering altogether 210 folds following the definition in SCOP. The statistical significance of the 210 folds shared by two sets of the same sizes, estimated from 10,000 permutation tests, is less than 0.0001, which is an upper bound on the p-value. We thus conclude that viral capsid proteins are segregated in structural fold space. Our result provides novel insight on how structural folds of capsid proteins, as opposed to their surface chemistry, might be constrained during evolution by requirement of the assembled cage-like architecture. Also importantly, our work highlights a guiding principle for virus-based nanoplatform design in a wide range of biomedical applications and materials science.

Structural, evolutionary, and assembly principles of protein oligomerization

In the protein universe, 30-50% of proteins self-assemble to form symmetrical complexes consisting of multiple copies of themselves, called homomers. The prevalence of homomers motivates us to review many of their properties. In Section 1, we describe the methods and challenges associated with quaternary structure inference-these methods are indeed at the basis of any analysis on homomers. In Section 2, we describe the morphological properties of homomers, as well as the database 3DComplex, which provides a taxonomy for both homomeric and heteromeric protein complexes. In Section 3, we review interface properties of homomeric complexes. In Section 4, we then present recent findings on the evolution of homomer interfaces, which we link in Section 5 to the evolution of homomers as entire entities. In Section 6, we discuss mechanisms involved in their assembly and how these mechanisms can be linked to evolution.

Assembly, stability and dynamics of virus capsids

Most viruses use a hollow protein shell, the capsid, to enclose the viral genome. Virus capsids are large, symmetric oligomers made of many copies of one or a few types of protein subunits. Self-assembly of a viral capsid is a complex oligomerization process that proceeds along a pathway regulated by ordered interactions between the participating protein subunits, and that involves a series of (usually transient) assembly intermediates. Assembly of many virus capsids requires the assistance of scaffolding proteins or the viral nucleic acid, which interact with the capsid subunits to promote and direct the process. Once assembled, many capsids undergo a maturation reaction that involves covalent modification and/or conformational rearrangements, which may increase the stability of the particle. The final, mature capsid is a relatively robust protein complex able to protect the viral genome from physicochemical aggressions; however, it is also a metastable, dynamic structure poised to undergo controlled conformational transitions required to perform biologically critical functions during virus entry into cells, intracellular trafficking, and viral genome uncoating. This article provides an updated general overview on structural, biophysical and biochemical aspects of the assembly, stability and dynamics of virus capsids.

Conversion of a dodecahedral protein capsid into pentamers via minimal point mutations

Protein self-assembly relies upon the formation of stabilizing noncovalent interactions across subunit interfaces. Identifying the determinants of self-assembly is crucial for understanding structure-function relationships in symmetric protein complexes and for engineering responsive nanoscale architectures for applications in medicine and biotechnology. Lumazine synthases (LS's) comprise a protein family that forms diverse quaternary structures, including pentamers and 60-subunit dodecahedral capsids. To improve our understanding of the basis for this difference in assembly, we attempted to convert the capsid-forming LS from Aquifex aeolicus (AaLS) into pentamers through a small number of rationally designed amino acid substitutions. Our mutations targeted side chains at ionic (R40), hydrogen bonding (H41), and hydrophobic (L121 and I125) interaction sites along the interfaces between pentamers. We found that substitutions at two or three of these positions could reliably generate pentameric variants of AaLS. Biophysical characterization indicates that this quaternary structure change is not accompanied by substantial changes in secondary or tertiary structure. Interestingly, previous homology-based studies of the assembly determinants in LS's had identified only one of these four positions. The ability to control assembly state in protein capsids such as AaLS could aid efforts in the development of new systems for drug delivery, biocatalysis, or materials synthesis.

Membrane remodeling by the double-barrel scaffolding protein of poxvirus

In contrast to most enveloped viruses, poxviruses produce infectious particles that do not acquire their internal lipid membrane by budding through cellular compartments. Instead, poxvirus immature particles are generated from atypical crescent-shaped precursors whose architecture and composition remain contentious. Here we describe the 2.6 Å crystal structure of vaccinia virus D13, a key structural component of the outer scaffold of viral crescents. D13 folds into two jellyrolls decorated by a head domain of novel fold. It assembles into trimers that are homologous to the double-barrel capsid proteins of adenovirus and lipid-containing icosahedral viruses. We show that, when tethered onto artificial membranes, D13 forms a honeycomb lattice and assembly products structurally similar to the viral crescents and immature particles. The architecture of the D13 honeycomb lattice and the lipid-remodeling abilities of D13 support a model of assembly that exhibits similarities with the giant mimivirus. Overall, these findings establish that the first committed step of poxvirus morphogenesis utilizes an ancestral lipid-remodeling strategy common to icosahedral DNA viruses infecting all kingdoms of life. Furthermore, D13 is the target of rifampicin and its structure will aid the development of poxvirus assembly inhibitors.

Poxviruses are arguably the largest viruses infecting humans. The unique brick-shape architecture of their infectious virus particles sets them apart from any other viral family in the virosphere. The infectious particles are produced through a series of assembly steps where intermediates of distinct composition and architecture can be identified. In particular, atypical crescent-shaped precursors of immature particles have generated much controversy regarding their structure and the origin of their lipidic membrane. Here, we used a combination of X-ray crystallography and electron microscopy to investigate the role of a crucial structural component of viral crescents called D13. Our atomic structure of D13 firmly establishes an evolutionary link between poxviruses and a group of large DNA viruses. In addition, we show that, when tethered to artificial membranes, this protein assembles into a scaffold analogous to that in immature particles. The resulting pseudo-atomic model of the honeycomb lattice reveals similarities to the mimivirus, which suggests that giant viral shells use common assembly principles. Overall, our findings reveal that poxviruses utilize an ancestral lipid-remodeling strategy common to DNA viruses infecting all kingdoms of life. They also provide a basis for structure-based design of assembly inhibitors against poxvirus pathogens.

Critical salt bridges guide capsid assembly, stability, and maturation behavior in bacteriophage HK97

HK97 is a double-stranded DNA bacteriophage that undergoes dramatic conformational changes during viral capsid maturation and for which x-ray structures, at near atomic resolution, of multiple intermediate and mature capsid states are available. Both amide H/(2)H exchange and crystallographic comparisons between the pre-expanded Prohead II particles and the expanded Head II of bacteriophage HK97 revealed quaternary interactions that remain fixed throughout maturation and appear to maintain intercapsomer integrity at all quasi- and icosahedral 3-fold axes. These 3-fold staples are formed from Arg and Glu residues and a metal binding site. Mutations of either Arg-347 or Arg-194 or a double mutation of E344Q and E363A resulted in purification of the phage in capsomer form (hexamers and pentamers). Mutants that did assemble had both decreased thermal stability and decreased in vitro expansion rates. Amide H/(2)H exchange mass spectrometry showed that in the wild type capsid some subunits had a bent "spine" helix (highly exchanging), whereas others were straight (less exchanging). Similar analysis of the never assembled mutant capsomers showed uniform amide exchange in all of these that was higher than that of the straight spine helices (characterized in more mature intermediates), suggesting that the spine helix is somewhat bent prior to capsid assembly. The result further supports a previously proposed mechanism for capsid expansion in which the delta domains of each subunit induce a high energy intermediate conformation, which now appears to include a bent helix during capsomer assembly.

Self-assembly and evolution of homomeric protein complexes

We introduce a simple "patchy particle" model to study the thermodynamics and dynamics of self-assembly of homomeric protein complexes. Our calculations allow us to rationalize recent results for dihedral complexes. Namely, why evolution of such complexes naturally takes the system into a region of interaction space where (i) the evolutionarily newer interactions are weaker, (ii) subcomplexes involving the stronger interactions are observed to be thermodynamically stable on destabilization of the protein-protein interactions, and (iii) the self-assembly dynamics are hierarchical with these same subcomplexes acting as kinetic intermediates.

The thermodynamics of virus capsid assembly

Virus capsid assembly is a critical step in the viral life cycle. The underlying basis of capsid stability is key to understanding this process. Capsid subunits interact with weak individual contact energies to form a globally stable icosahedral lattice; this structure is ideal for encapsidating the viral genome and host partners and protecting its contents upon secretion, yet the unique properties of its assembly and inter-subunit contacts allow the capsid to dissociate upon entering a new host cell. The stability of the capsid can be analyzed by treating capsid assembly as an equilibrium polymerization reaction, modified from the traditional polymer model to account for the fact that a separate nucleus is formed for each individual capsid. From the concentrations of reactants and products in an equilibrated assembly reaction, it is possible to extract the thermodynamic parameters of assembly for a wide array of icosahedral viruses using well-characterized biochemical and biophysical methods. In this chapter we describe this basic analysis and provide examples of thermodynamic assembly data for several different icosahedral viruses. These data provide new insights into the assembly mechanisms of spherical virus capsids, as well as into the biology of the viral life cycle.

A novel method to map and compare protein-protein interactions in spherical viral capsids

Viral capsids are composed of multiple copies of one or a few chemically distinct capsid proteins and are mostly stabilized by inter subunit protein-protein interactions. There have been efforts to identify and analyze these protein-protein interactions, in terms of their extent and similarity, between the subunit interfaces related by quasi- and icosahedral symmetry. Here, we describe a new method to map quaternary interactions in spherical virus capsids onto polar angle space with respect to the icosahedral symmetry axes using azimuthal orthographic diagrams. This approach enables one to map the nonredundant interactions in a spherical virus capsid, irrespective of its size or triangulation number (T), onto the reference icosahedral asymmetric unit space. The resultant diagrams represent characteristic fingerprints of quaternary interactions of the respective capsids. Hence, they can be used as road maps of the protein-protein interactions to visualize the distribution and the density of the interactions. In addition, unlike the previous studies, the fingerprints of different capsids, when represented in a matrix form, can be compared with one another to quantitatively evaluate the similarity (S-score) in the subunit environments and the associated protein-protein interactions. The S-score selectively distinguishes the similarity, or lack of it, in the locations of the quaternary interactions as opposed to other well-known structural similarity metrics (e.g., RMSD, TM-score). Application of this method on a subset of T = 1 and T = 3 capsids suggests that S-score values range between 1 and 0.6 for capsids that belong to the same virus family/genus; 0.6-0.3 for capsids from different families with the same T-number and similar subunit fold; and <0.3 for comparisons of the dissimilar capsids that display different quaternary architectures (T-numbers). Finally, the sequence conserved interface residues within a virus family, whose spatial locations were also conserved have been hypothesized as the essential residues for self-assembly of the member virus capsids.

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.

Assembly reflects evolution of protein complexes

A homomer is formed by self-interacting copies of a protein unit. This is functionally important, as in allostery, and structurally crucial because mis-assembly of homomers is implicated in disease. Homomers are widespread, with 50-70% of proteins with a known quaternary state assembling into such structures. Despite their prevalence, their role in the evolution of cellular machinery and the potential for their use in the design of new molecular machines, little is known about the mechanisms that drive formation of homomers at the level of evolution and assembly in the cell. Here we present an analysis of over 5,000 unique atomic structures and show that the quaternary structure of homomers is conserved in over 70% of protein pairs sharing as little as 30% sequence identity. Where quaternary structure is not conserved among the members of a protein family, a detailed investigation revealed well-defined evolutionary pathways by which proteins transit between different quaternary structure types. Furthermore, we show by perturbing subunit interfaces within complexes and by mass spectrometry analysis, that the (dis)assembly pathway mimics the evolutionary pathway. These data represent a molecular analogy to Haeckel's evolutionary paradigm of embryonic development, where an intermediate in the assembly of a complex represents a form that appeared in its own evolutionary history. Our model of self-assembly allows reliable prediction of evolution and assembly of a complex solely from its crystal structure.

Residue conservation in viral capsid assembly

To evaluate the evolutionary constraints placed on viral proteins by the structure and assembly of the capsid, we calculate Shannon entropies in the aligned sequences of 45 polypeptide chains in 32 icosahedral viruses, and relate these entropies to the residue location in the three-dimensional structure of the capsids. Three categories of residues have entropies lower than the chain average implying that they are better conserved than average: residues that are buried within a subunit (the protein core), residues that contain atoms buried at an interface between subunits (the interface core), and residues that contribute to several such interfaces. The interface core is also conserved in homomeric proteins and in transient protein-protein complexes, which have only one interface whereas capsids have many. In capsids, the subunit interfaces implicate most of the polypeptide chain: on average, 66% of the capsid residues are at an interface, 34% at more than one, and 47% at the interface core. Nevertheless, we observe that the degree of residue conservation can vary widely between interfaces within a capsid and between regions within an interface. The interfaces and regions of interfaces that show a low sequence variability are likely to play major roles in the self-assembly of the capsid, with implications on its mechanism that we discuss taking adeno-associated virus as an example.