Unraveling the Motions behind Enterovirus 71 Uncoating

Abstract

Enterovirus 71 can be a severe pathogen in small children and immunocompromised adults. Virus uncoating is a critical step in the infection of the host cell; however, the mechanisms that control this process remain poorly understood. We applied normal mode analysis and perturbation response scanning to several complexes of the virus capsid and present a coarse-graining approach to analyze the full capsid. We show that our method offers an alternative to expressing the system as a set of rigid blocks and accounts for the interconnection between nodes within each subunit and protein interfaces across the capsid. In our coarse-grained approach, the modes associated with capsid expansion are captured in the first three nondegenerate modes and correspond to the changes observed in structural studies of the virus. We show that the resolution of the analysis may be modified without losing information on the global motions leading to uncoating. Perturbation response scanning revealed that a protomer cannot serve as a functional unit to explain deformations of the capsid. Instead, we define a pentamer as the minimum functional unit to investigate changes within the capsid. From the modal analysis and perturbation response scanning, we locate a hotspot region surrounding the fivefold axis. The range of the effect of these single, hotspot residues extend to 140 Å. The perturbation of internal capsid residues in this region displayed greatest propensity to capsid expansion, thus indicating the significant role that the RNA genome may play in triggering uncoating.

Introduction

Hand, foot, and mouth disease (HFMD) is a highly infectious viral illness that is characterized by the appearance of small lesions in the mouth and on the distal extremities. Infections most commonly appear in infants, young children, and immunocompromised adults (1). HFMD is a major health threat across the Asia Pacific region, with an average incidence rate of up to 1,000,000 cases per year (2), and 1,700,000 cases reported in China in 2010 (3). Enterovirus 71 (EV71) is the primary agent of the disease (1). EV71 belongs to the Enterovirus genus of the Picornaviridae family and is closely related to Coxsackievirus A16, the other causative agent of HFMD (1). Infections caused by A16 are usually mild, whereas EV71 can cause acute systemic infections with severe neurological and respiratory complications (1, 4); for instance, Acute EV71 infections led to 905 reported deaths in China in 2010 (3). At present, there are no antivirals to treat enteroviruses and a successful vaccine against EV71 is yet to be developed (5).

The EV71 virion is nonenveloped and contains a single-stranded, positive RNA genome of 7.5 kb. The genome is enclosed in an icosahedral capsid, which has a diameter of ∼300 Å. The capsid comprises 60 protomeric units, each of which contain four heterogenic subunits VP1–VP4 (6). The capsid is assembled through stepwise oligomerization: a single copy of the proteins VP0, VP1, and VP3 interact to form a protomer, five protomers then assemble into a pentamer and 12 pentamers oligomerize into a full capsid. Although infectious virions contain the RNA genome, it is well known that enteroviruses also produce empty viral particles (3, 6, 7, 8, 9). Viral particles that contain RNA undergo a stabilizing maturation process in which the precursor protein VP0 is cleaved into VP2 and VP4. The VP1–VP3 subunits follow a pseudosymmetry T = 3 arrangement and constitute the external capsid proteins. The VP4 subunit resides on the internal side of the capsid (3, 10, 11). The capsid has five-, three-, and twofold axes of symmetry. The fivefold axis, located in the center of the 12-pentamer structures of the capsid, is surrounded by the VP1 and VP3 proteins of adjacent protomer units. The two- and threefold axes are formed by the VP2 and VP3 proteins of adjacent protomers located at the pentameric interface (Fig. 1 A).

Figure 1.

Structures of the Enterovirus 71 capsid. Capsid subunits VP1–VP4 are colored as green, VP1; blue, VP2; orange, VP3; and yellow, VP4. (A) Structure of the mature capsid (PDB ID: 3VBS). Axes of symmetry are indicated as fivefold, threefold, and twofold. Cross section of the capsid shows the VP4 protein located on the internal side of the capsid. A closeup of three interacting pentamers indicates the VP1 N-terminus is located under the twofold axis at the pentameric interface. (B) Homology model of the EV71 A-particle. The VP4 protein and the VP1 N-terminus have been externalized and become disordered; therefore, they are missing from the structure. Perforations formed at the twofold axis. (C) Coarse-grained complexes of the EV71 capsid. Complexes consist of a subset of the β-carbon atoms. CG4, coarse-grained in every four atoms; CG12, coarse-grained in every twelve atoms (see text for details on how the coarse-graining has been carried out). To see this figure in color, go online.

Infection with EV71 is initiated by attachment factors on the host cell. These factors, including heparin sulfate and sialylated glycan, attract the virus to the host cell and facilitate the interaction between the virus and an entry receptor on the cell surface (5, 12). For successful infection to occur, the virus must release its RNA genome into the cytoplasm of the host cell. It has been reported that EV71 enters the cell through endocytosis. However, the mechanism by which the virus uncoats to release its RNA remains poorly understood (5, 13, 14). Structural studies of EV71 and other enteroviruses have outlined the infection process. The RNA release intermediate has been captured for EV71, Coxsackievirus A16, Coxsackievirus A9, Poliovirus (PV), and Human Rhinoviruses (HRVs) (3, 15, 16, 17, 18). It has been proposed that the process is triggered upon binding to the host cell. Enterovirus capsids have a distinctive hydrophobic pocket that is often the binding site of the host cell receptor. The pocket is located in a canyonlike depression surrounding the fivefold axis (19, 20, 21). A lipid naturally occupies this pocket and acts to stabilize the capsid. The release of this lipid has appeared as a necessity for RNA release in enteroviruses (22, 23). Upon binding, the lipid is dislodged, resulting in the rearrangement of the protomeric units within the capsid (24). This rearrangement prepares the virus for RNA release. The virion expands and the VP1 N-terminus and the full VP4 protein are externalized from the capsid. This expanded RNA-release intermediate is termed the “A-particle” (3, 15, 16, 25, 26). A subsequent uncoating process then occurs, in which the RNA is expelled from the capsid and an empty B-particle is left behind. Early studies of enteroviruses suggested that the RNA is released through the fivefold axis (25), whereas recent studies point to pore formation at the two- and threefold axes (3, 15, 16, 27). The exit site is still being debated.

Two host cell receptors for EV71 have been identified: scavenger receptor class B2 (SCARB2) and P-selectin glycoprotein ligand-1 (28, 29). SCARB2, considered to be the primary receptor, induces the formation of the EV71 A-particle. The efficiency of SCARB2 is significantly increased in a low pH environment, suggesting that the initial uncoating takes places in early endosomes (14, 30). Structural investigation by Wang et al. (3) proposes a mechanism for particle expansion of EV71 that is accompanied by conformational shifts within the protomeric units as well as the rearrangement of the individual protomeric units. Within the protomeric unit, the fivefold proximal end of the VP1 β-barrel rotates in a jackknife extension, about a pivot that appears to be centered on the hydrophobic pocket. It is proposed that the binding of the host cell to this pocket triggers the conformational changes that lead to expansion. Notably, the hydrophobic pockets are collapsed in the expanded particle. Capsid expansion is also associated with a counterclockwise rotation of the individual protomeric units about the threefold axis. This screwlike motion may assist in pulling VP2 away from the twofold axis for pore formation (3).

The functional mechanisms of a macromolecule are inferred by the structural dynamics of its constituent proteins. However, the investigation into the dynamics of such large complexes has been hindered by limitations in computational power (31, 32). Earlier research has focused on the mechanical properties of viral capsids and invoked continuum modeling or coarse-graining to investigate the collapse of viral capsids under an applied force (33). Broadening on this, atomic force-probe molecular dynamics (34, 35) simulations of the complete shell of the Southern Bean Mosaic Virus was applied to examine the heterogeneity of mechanical properties across an icosahedral capsid (33). As an alternative approach, normal mode analysis (NMA), incorporating the construction of coarse-grained elastic network models, has previously been used to investigate the motions of viral capsids (36, 37, 38, 39, 40, 41). The anisotropic network model (ANM) is a tool of NMA that reveals the internal motions of a protein subject to a harmonic potential (42). The application of ANM involves the diagonalization of a Hessian matrix of size 3N × 3N, where N is the number of residues in the system. Due to the enormous size of viral particles, this calculation is not computationally feasible and only a select number of studies have explored the normal modes that describe the change between the conformations of a viral capsid (36, 38, 40, 43). To reduce this expense, previous studies have exploited the symmetry of the virus capsid and defined the system as a set of rigid blocks under the rotation-translation of blocks method (44, 45). Although this method accounts for all atoms in the system, it represents an artificial rigidification of motions. Under the rotation-translation of blocks method, groups of atoms or, in the application to virus capsids, entire proteins are clustered to constitute a single rigid unit that can undergo rotation and translation about the three principle axes (36, 45). The method allows for a reduced basis set to approximate the normal modes of the complex; however, the relative motions of the blocks are significantly restricted. In a similar study, group theory was employed to determine the effect that the triangular protein arrangement may have on the global motions of an icosahedral capsid. To account for the capsid tiling, individual proteins were modeled as a single bead connected by springs with strength scaling with the association energy between respective capsid proteins (41).

Although these variants of NMA disclose the natural motions of the system at equilibrium, it is also of interest to predict the motions under external perturbations, e.g., upon binding of the capsid to the cell. To this purpose, one may exploit the perturbation response scanning (PRS) method, developed to investigate the interconversion propensity between two conformational states of a protein by employing fictitious external forces on the system (46). More specifically, PRS determines single residues that play a role in activating the conformational change in proteins. The method has previously been used to locate allosteric regions (47, 48) and explore protein-ligand interactions (49). PRS has also been applied to an enzyme in complex with its inhibitor to map sites responsible for inhibited conformations (50).

In this study, we present an approach to analyze the modes associated with viral uncoating in EV71 by investigating those respective subcomplexes of the capsid that were systematically coarse-grained to varying degrees. We also apply PRS to complexes of a viral capsid for the first time, to our knowledge, to map hotspots that may be actively involved in the conformational change across the macromolecular assembly. We describe three distinctive modes that correspond to the rearrangement of the protomeric units as outlined in the literature (3, 10). Our results suggest that local changes within the pentameric unit can be captured through the analysis of a subset of capsid protomers, regardless of additional coarse-graining of the complexes. Moreover, through PRS analysis, we suggest that the pentamer complex is an appropriate functional unit to explain the deformations when the capsid is perturbed.

Materials and Methods

Capsid structures

The structure of a mature RNA containing capsid of Enterovirus 71 strain C4, Protein Data Bank entry (PDB): 3VBS (3), was investigated by modal analysis and PRS. The VP1–VP4 subunits of the virus capsid consist of 297, 254, 242, and 69 residues, respectively. However, within the structure of PDB: 3VBS, residues 1–9 of VP2 and 1–11 of VP4 are missing in the PDB entry. Thus, the complexes used in this study contain the following number of residues: 842 residues in a protomer, 4210 residues in a pentamer, and 50,520 residues in a full capsid. For the conformation of the expanded intermediate capsid, we have used PDB: 4N43 (10) as a template to model the corresponding A-particle of PDB: 3VBS. The mature capsid PDB: 3VBS was crystalized in 30% PEG400, 0.2 N Tri-sodium citrate, 0.1 M Tris-HCl (pH 8.5) at 20°C (3). The expanded intermediate (PDB: 4N43) was crystalized in 0.1 M cacodylate containing 1.6 M sodium acetate (pH 7) at 16°C (10). The reasons why such conditions resulted in expansion are unknown (10). In the A-particle, residues 1–71 of VP1, 1–15 and 48–53 of VP2, 251–254 of VP3, and the full VP4 subunit are disordered. Therefore, when comparing the two capsid conformations, we consider 677 common residues per protomer complex. The two structures are displayed in Fig. 1, A and B. The root mean square deviation (RMSD) between the common residues is 4.9 Å. Complexes consisting of three pentamers that we term “pentamer interface complex” throughout the text have also been shown enlarged from the internal side of the capsid.

Homology modeling of the 3VBS A-particle

The early RNA-release intermediate structure of Enterovirus 71 strain C4 (PDB: 4N43) was used as a template to model the corresponding A-particle of PDB: 3VBS. Over 100% coverage, the amino acid sequence of the PDB: 4N43 protomer complex has 99% identity to that of PDB: 3VBS. Although the structures represent the same strain of Enterovirus 71, the subunits of PDB: 3VBS contain five point mutations that arose due to natural adaption during virus expression. The point mutations are: VP1 K98E and C225M, VP2 T144S, VP3 N93S, and K227E. Homology models of the PDB: 3VBS A-particle protomer complex were calculated using the software MODELER 9v15 (51), set to generate 100 unique models through very slow refinement. The models were initially evaluated according to the normalized DOPE Z score. Before the construction of the expanded virus capsid, the lowest energy model, with a score of −0.94, was visualized in the software PyMOL (https://pymol.org/2/) for the identification of any geometric discrepancies. To construct the capsid structure of the PDB: 3VBS A-particle in PyMOL, 60 of the modeled protomers were superimposed on the respective protomers of the biological assembly of the template capsid PDB: 4N43. The resulting structure is displayed in Fig. 1 B.

Construction of coarse-grained complexes

In this study, we have examined the normal modes of various coarse-grained complexes of the RNA-containing capsid PDB: 3VBS. The investigation included the analysis of an individual protomer complex, an individual pentamer complex, and the whole viral capsid. In addition, to investigate the normal modes associated with pore formation at the twofold axis, we constructed a subcomplex of the capsid that comprised three interacting pentamers. We refer to this subcomplex as the “pentamer interface complex”. Coarse-grained complexes comprising of the β-carbon atoms of all residues in the structure were constructed for the protomer, pentamer, and pentamer-interface complex. Due to computational cost, we did not consider all β-carbon atoms for the NMA of the full capsid structure. Following previous studies of elastic network models of proteins whereby a whole residue is represented by a single atom (42), we have selected the β-carbons of a residue as these atoms provide a better representation of the side-chain orientation (52). Although this approach does not account for all atoms in the system, previous studies have shown that coarse-grained models may accurately describe the collective motions of a protein and that the results are comparable with all-atom simulations and crystallographic data (52, 53, 54, 55). We have constructed a second set of further coarse-grained complexes by using an in-house PYTHON script to select a subset of the β-carbons that were equally distributed in 3D space. Specifically, we used the script to coarse-grain a single protomer (the asymmetric unit) and subsequently built the corresponding coarse-grained pentamer, pentamer-interface, and capsid structures, thus the symmetries of the complexes were maintained. This coarse-graining approach was applied at two levels. First, we obtained a coarse-grained protomer comprising approximately a quarter of the number of atoms (209 out of 842 atoms). Second, a coarse-grained protomer of approximately one-twelfth of the number of atoms (72 out of 842 atoms) was obtained. We refer to these complexes as CG4 and CG12, respectively. Examples of coarse-grained capsids and the pentamer interface structure are displayed in Fig. 1 C.

ANM

The normal modes of the respective complexes of the viral capsid were calculated using the ANM (42). In ANM, for a given protein complex, we construct a coarse-grained elastic network of N nodes on the atomic coordinates of the C_β atoms given in the Protein Data Bank files. In this network, the protein complex is modeled as a collection of nodes and springs, where all pairs of β-carbons separated by a defined cutoff distance, r_c, are connected. Therefore, the network comprises M springs representing the total number of interactions defined in the network, where any given pair of nodes within r_c of each other will interact in accord with a conventional harmonic potential. In the absence of an external force on the system, the equilibrium condition for each residue requires that the respective sums of the x-, y-. and z-components of the internal forces (f) that act on the residue must be equal to zero, i.e.,

$$\begin{array}{c}{\sum }_j{f}^{ij}\cos {\propto }_{ij}^X={\sum }_j{f}^{ij}\left(X_i-X_j\right)/s_{ij}=0,\\ {\sum }_j{f}^{ij}\cos {\propto }_{ij}^Y={\sum }_j{f}^{ij}\left(Y_i-Y_j\right)/s_{ij}=0,\\ {\sum }_j{f}^{ij}\cos {\propto }_{ij}^Z={\sum }_j{f}^{ij}\left(Z_i-Z_j\right)/s_{ij}=0,\end{array}$$ (1)

where s_ij equals the separation vectors between the nodes i and j, and ${\propto }_{ij}^X$ is the angle between the X axis and the force f_ij. This force balance can be generalized to the complete set of N sites and M interactions as to obtain the 3N × M direction cosine matrix B:

$${\left[\mathbf{B}\right]}_{3\text{N}\mathrm{\times }\text{M}}{\left[\mathbf{f}\right]}_{\text{M}\times 1}={\left[0\right]}_{3\text{N}\times 1}.$$ (2)

For a defined cutoff distance r_c, we note that the 3N equalities in Eq. 2 are fewer than the number of unknown forces (M). To solve the system for all unknown we can invoke two additional properties. Firstly, we can relate the forces to the deformations Δs by the linear approximation:

$${\left[\mathbf{f}\right]}_{\text{M}\times 1}={\left[\mathbf{K}\right]}_{\text{M}\times \text{M}}{\left[\Delta \mathbf{s}\right]}_{\text{M}\times 1},$$ (3)

where [K]_MxM is a diagonal matrix whose ith element is the force constant of the ith residue pair. Secondly, the kinematics relationship between the deformations and the residue positions is given by

$${\left[\mathbf{B}\right]}_{\text{M}\times 3\text{N}}^{\text{T}}{\left[\Delta \mathbf{R}\right]}_{3\text{N}\times 1}={\left[\Delta \mathbf{s}\right]}_{\text{M}\times 1}.$$ (4)

We can substitute Eqs. 3 and 4 into Eq. 2 to obtain the following relationship:

$${\left[\mathbf{B}\right]}_{3\text{N}\times \text{M}}{\left[\mathbf{K}\right]}_{\text{M}\times \text{M}}{\left[\mathbf{B}\right]}_{\text{M}\times 3\text{N}}^{\text{T}}{\left[\Delta \mathbf{R}\right]}_{3\text{N}\times 1}={\left[\text{0}\right]}_{3\text{N}\times 1}\text{.}$$ (5)

If we assume harmonic interactions with uniform force constants for all M bonds in the network, then [B][B]^T is equivalent to the Hessian matrix H. In the general case of N residues connected by M springs, H is a 3N × 3N super-matrix. Alternatively, the Hessian may also be derived from the second derivatives of the overall potential V, with respect to the components of R_i, where R_i are the fluctuation vectors of the individual residues. The Hessian therefore describes the force constant of the system. H is composed of N × N super-elements, i.e.,

$$\mathbf{H}=\left[\begin{array}{cccc}{\mathbf{H}}_{11}& {\mathbf{H}}_{12}& \cdots & {\mathbf{H}}_{1\mathbf{N}}\\ {\mathbf{H}}_{21}& & & {\mathbf{H}}_{2\mathbf{N}}\\ ⋮& & & ⋮\\ {\mathbf{H}}_{\mathbf{N}1}& & & {\mathbf{H}}_{\mathbf{N}\mathbf{N}}\end{array}\right]\text{,}$$ (6)

where each super-element H_ij is a 3 × 3 matrix that holds the anisotropic information regarding the orientation of nodes i,j. The ijth super-element (i ≠ j) of H is defined as

$${\mathbf{H}}_{\mathbf{ij}}=\left[\begin{array}{ccc}{\partial }^{2}V/\partial X_i\partial X_j& {\partial }^{2}V/\partial X_i\partial Y_j& {\partial }^{2}V/\partial X_i\partial Z_j\\ {\partial }^{2}V/\partial Y_i\partial X_j& {\partial }^{2}V/\partial Y_i\partial Y_j& {\partial }^{2}V/\partial Y_i\partial Z_j\\ {\partial }^{2}V/\partial Z_i\partial X_j& {\partial }^{2}V/\partial Z_i\partial Y_j& {\partial }^{2}V/\partial Z_i\partial Z_j\end{array}\right].$$ (7)

At equilibrium, the second derivatives may be calculated for the ANM using the β-carbon position vectors of databank structures such that the elements of the off-diagonal H_ij are given by

$${\partial }^{2}V/\partial X_i\partial Y_j=-\gamma \left(X_j-X_i\right)\left(Y_j-Y_i\right)/S_{ij}^2,$$ (8)

and the elements of the diagonal super-elements H_ii are given by

$${\partial }^2\text{V}/\partial {\text{ X}}_{\text{i}}^2=\gamma \sum _j{\left(X_j-X_i\right)}^2/S_{ij}^2,$$ (9)

for the diagonal elements of H_ii, and

$${\partial }^2\text{V}/\partial {\text{ X}}_{\text{i}}\partial {\text{ Y}}_{\text{j}}=\gamma \sum _j\left(X_j-X_i\right){\left(Y_j-Y\right)}_i/S_{ij}^2$$ (10)

for the off-diagonal elements of H_ii. Note that H and [B][B]^T are equivalent to each other, thus all elements of [B][B]^T and H are equal. As an example, consider the first diagonal element of H₁₁ of H,

$${\left[\gamma \mathbf{B}{\mathbf{B}}^{\text{T}}\right]}_{11}=\gamma \sum _{j}co{s}^2{\alpha }_{1j}^X=\gamma {\sum _j\left(X_j-X_1\right)}^2/S_{1j}^2.$$ (11)

The decomposition of H yields 3N-6 eigenvalues and 3N-6 eigenvectors that correspond to the respective frequencies and directions of the individual modes. The inverse of H is equivalent to the covariance matrix C that is composed of N× N super-elements. Each ijth super-element of H⁻¹ contains the 3 × 3 matrix of correlations among the x-, y-, and z-components of fluctuation vectors of residues i and j, whereas the ith super-element of H⁻¹ describes the self-correlations between the components of fluctuation vectors of residue i. The mean square fluctuations of individual residues may be obtained by summing the fluctuations in the respective modes.

The overlap between a predicted displacement, ΔR_j, and an experimentally known conformational change calculated over each residue i, ΔS_i = S_1i – S_2i, is defined as

$$O_j={\left(\Delta {\mathbf{R}}_j\right)}^i\cdot {\left(\Delta \mathbf{S}\right)}^i/\left|{\left(\Delta {\mathbf{R}}_j\right)}^i\right|\left|{\left(\Delta \mathbf{S}\right)}^{\mathit{i}}\right|.$$ (12)

To measure the similarity between an individual normal mode with eigenvector A_j and the experimentally known conformational change, we used the above equation with ΔR_j = A_j to calculate the overlap between the two vectors A_j and ΔS. An overlap of 1 indicates that the normal mode acts in the same direction of the conformational change ΔS, whereas a value of zero indicates the mode and the experimental change vectors are orthogonal.

Modal analysis

All steps of the modal analysis were performed using the MODE-TASK package, developed from in-house scripts (53). Individual coarse-grained elastic network models were constructed on the β-carbons of the protomer, pentamer, and the pentamer-interface complexes of the Enterovirus 71 RNA containing capsid (PDB: 3VBS). Additional elastic network models were assembled on the β-carbons of CG4 protomer, pentamer, pentamer-interface, and viral capsid structures. A single elastic network was also assembled on the β-carbons of the CG12 capsid structure. The interacting cutoff distance, r_c, was defined as 24 Å for all eight networks. The virus capsid has an approximate diameter of 300 Å, with a fivefold channel spanning 15 Å located at the center of each pentamer. In addition, the width of the pentamer interface ranges from 15 to 30 Å. Subsequent to a series of analyses performed at increasing cutoff distances, it was found that 24 Å was the minimum r_c, which yielded six trivial modes, thus allowing for sufficient connection between nodes of adjacent protomers in all coarse-grained models. The Hessian matrix for each network was constructed from the atomic coordinates in the PDB: 3VBS entry based on Eqs. 8, 9, and 10. The pseudoinverse of H⁻¹ was calculated by matrix decomposition using the C++ library ALGLIB (http://www.alglib.net). For each of the eight complexes, individual normal modes that have similarity to the conformational change between the full capsid (PDB: 3VBS) and its early RNA intermediate (PDB: 3VBS A-particle) were identified using Eq. 12. Note that the overlap calculation was based only on the eigenvectors that corresponded to the 677 common residues, per protomer, between the two capsid structures. To further compare these high overlap modes that were identified from the separate analysis of the eight complexes; a comparative analysis of the mean square fluctuations of the individual residues of a common central protomer in each complex was performed.

PRS

PRS is a method used to investigate the interconversion propensity between two conformational states of a protein by employing external forces on the system (46). Here we apply PRS to analyze the conformational changes associated with the expansion of the Enterovirus 71 viral capsid.

Given the network of β-carbon atoms described above, if an external force, ΔF, is applied to the system, then the equilibrium condition for each residue imposes that the summation of the internal interacting forces must be equal to the external force applied on that residue. Thus, Eq. 2 can be expressed as

$${\left[\mathbf{B}\right]}_{3\text{N}\mathrm{\times }\text{M}}{\left[\mathbf{f}\right]}_{\text{M}\mathrm{\times }1}={\left[\mathbf{\Delta F}\right]}_{3\text{N}\mathrm{\times }1}.$$ (13)

The external forces result in the displacement of each residue, ΔR, where ΔR is defined as the positional displacement vector. This displacement causes the bond distance between any two residues to change by Δr in accord with the positional displacements of the interacting residues. Therefore, there exists a relationship between the 3N positional displacement vectors and the resultant changes in the internal residue-residue distances. As there are M interactions defined in the network, there will be a total of M distortions:

$${\left[{\mathbf{B}}^{\mathbf{T}}\right]}_{\text{M}\mathrm{\times }3\text{N}}{\left[\mathbf{\Delta R}\right]}_{3\text{N}\mathrm{\times }1}={\left[\mathbf{\Delta r}\right]}_{\text{M}\mathrm{\times }1}.$$ (14)

By invoking Hooke’s law, we can relate the residual interaction forces, Δf, to the change in the distance between the residues Δr as

$${\left[\mathbf{K}\right]}_{\text{M}\mathrm{\times }\text{M}}{\left[\mathbf{\Delta r}\right]}_{\text{M}\mathrm{\times }1}={\left[\mathbf{\Delta f}\right]}_{\text{M}\mathrm{\times }1}.$$ (15)

We can rearrange Eqs. 10, 11, and 12 to solve for the forces required to induce a point-by-point displacement of the residues:

$$\left[\mathbf{B}\right]\left[\mathbf{K}\right]{\left[\mathbf{B}\right]}^{\text{T}}\left[\mathbf{\Delta R}\right]=\left[\mathbf{\Delta F}\right],$$ (16)

where, for the simple case, we can take [K] to be equivalent such that [B][K][B]^T is equal to the Hessian matrix. From this, we can follow the response of the network due to the perturbation of a single residue or group of residues as

$${\left[\mathbf{H}\right]}^{-1}\left[\mathbf{\Delta F}\right]=\left[\mathbf{\Delta R}\right],$$ (17)

where the vectors of [ΔF] comprise the directional components of the external force applied to the system.

Using PRS, we have investigated the conformational changes associated with the expansion of a mature capsid of Enterovirus 71 to its early RNA-release intermediate. The respective PDB: 3VBS and 3VBS A-particle protomers, pentamers, and pentamer-interface complexes were superimposed, followed by the calculation of the displacement vectors ΔS for each complex. The displacement vectors were calculated from the C_β atoms that were common between the two conformational complexes. PRS was applied to the protomer, pentamer, and pentamer-interface complexes of the mature capsid, by applying a random force to the C_β atom of each residue. Each complex was scanned by consecutively perturbing each residue i. For each perturbation, an external force ΔF was applied to the system, where the only nonzero elements of ΔF were ΔF_3i-2, ΔF_3i-1, and ΔF_3i. The response of each complex, upon the perturbation of each residue, was recorded by calculating ΔR from Eq. 17. For the perturbation of each residue i, the overlap between the known conformational change ΔS, and the predicted displacement ΔR was again calculated using Eq. 12. Those ΔF vectors leading to high overlaps were recorded for further analysis.

Results and Discussion

Residue displacement profiles observed during capsid expansion

To examine the changes associated with the expansion of EV71 to its A-particle (Fig. 1), respective complexes of the two viral capsids were superimposed. The RMSD values among the common residues within a protomer, pentamer, pentamer-interface, and an assembled capsid are listed in Table 1 with further details in Figs. S1 and S2. First, the individual protomer of the A-particle was superimposed on the corresponding protomer of native EV71 (PDB: 3VBS). A cartoon depiction of the superimposition is shown in Fig. 2 A. The fivefold proximal end of the VP1 in the A-particle was rotated about a point centered on the hydrophobic pocket (shown by the solid dot). This rotation (shown with the arrow) corresponded to the jackknife motion described by Wang et al. (3). In comparison to the individual protomer complex, there was a noticeable increase in the RMSD of the pentamer complex, with additional increases in the RMSD between the pentamer interface complexes and an assembled capsid. This was consistent with the rearrangement of individual protomers within a pentamer complex, and an additional shift at the pentamer-pentamer interface. The superimpositions of the individual pentamer, pentamer-interface complex, and the assembled viral capsids of two conformations are shown in Fig. 3 in a hierarchical manner. To observe the overall change, the surfaces of the superimposed complexes were visualized. As evident in Fig. 3, the central regions of the pentamers were expanded, whereas the edges of the pentamers appeared to collapse inwards at the pentamer-pentamer interface. To determine if the residues of all 60 protomers were uniformly displaced during expansion, the pointwise displacement between each common residue in the pentamer complex was compared to the displacement calculated across the pentamer interface complex. Plots of the magnitude of displacement for each residue in the pentamer and pentamer interface complex have been included in Figs. S1 and S2. In the pentamer complex, the respective residues of each of the five protomers were displaced uniformly in magnitude. In contrast, the superimposition of the pentamer interface complexes revealed that the residues of respective protomers within each pentamer complex were not equally displaced. Rather, equal displacement of residues was observed in protomers that were arranged symmetrically about the threefold axis across the pentamer-pentamer interface (Fig. 2 B1). This indicated an additional the shift of the pentamers about the threefold axis. This was consistent with suggestions by Wang et al. (3) that the mechanism of capsid expansion is accompanied by the counterclockwise rotation of the respective protomers about the threefold axis. Further insight into the dominating motions of the structure may be obtained by a modal analysis.

Table 1.

RMSD Values between the Common Residues of a Full EV 71 Capsid and Its Early RNA Release Intermediate Particle

Complex	RMSD (Å)	Number of Common Residues
Protomer	1.3	677
Pentamer	3.1	3385
Pentamer interface complex	4.0	10,155
Assembled capsid	4.9	40,620

The pointwise displacement between each common residue in the pentamer complex in comparison to the displacement calculated across the pentamer interface complex was also calculated. Plots of the magnitude of displacement for each residue can be found in the Supporting Material.

Figure 2.

The normal modes of capsid expansion in Enterovirus 71. (A) Conformational change within the protomeric unit. On the left a cartoon depiction of the superimposed protomers, the structures of the mature capsid, and A-particle are shown. The protomer of the mature capsid is colored by subunit (VP1, green; VP2, blue; VP3, orange; VP4, yellow) and the protomer of the A-particle is gray. The VP1 protein undergoes a jackknife rotation, indicated by the black arrow, about a pivot (black dot) centered on the hydrophobic pocket. On the right, the corresponding motion is depicted by arrows of the modal displacement vectors for each residue. (B) The first three nondegenerate modes obtained from the CG4 capsid. (B1) Snapshots of the counterclockwise rotation about the threefold axis (the third nondegenerate mode of the capsid: GC4 Mode 113) are given. The interface complex on the right shows a schematic illustration of the distribution of residue displacement across the pentamer-pentamer interface during capsid expansion. The magnitude of the displacement of each residue, in each protomer, between the full and empty capsid was calculated. Protomer complexes that contained residues of identical displacement have been depicted in the same color. (B2) Shown here are eigenvector arrows corresponding to the radial expansion projected onto a single protomer (CG4 Mode 27). (B3) Shown here are eigenvector arrows corresponding to CG4 Mode 75. Curved dashed line represents the capsid surface. The 2-, 3-, and 5-fold axes have been indicated on the figures. To see this figure in color, go online.

Figure 3.

Expansion of the central region of the pentamer. A common mode was captured from models of the full capsid (A, CG4 and CG12 mode 75), pentamer interface complex (B, mode 17), and pentamer (C, mode 3). The motion is accompanied by the outward rotation of the individual protomer complexes. The motion has been visualized as static images of a stepwise set of modal vectors from each model, and has been compared to the conformational change observed from the superimposition of the two conformations. The superimposition of the structures in the first column are colored as red for the native, mature capsid, and blue for the RNA-release intermediate. The corresponding stepwise projection of the eigenvalues (columns 2 and 3) are colored from first frame (red) to last frame (blue). To see this figure in color, go online.

Modal analysis

Coarse-graining approach is validated by degeneracy of the normal modes

Virus capsids present a large amount of symmetry. It follows that NMA analysis performed on icosahedral capsids give modes that are degenerate or nondegenerate. Degenerate modes appear with identical eigenvalues and correspond to normal modes for which any spatial rotation will result in a valid representation of the mode with identical frequency (54). The set of all solutions of identical frequencies form an irreducible representation (irrep) that can be expressed as a linear combination of the basis of the mode space. The dimension of the irrep is defined by the number of elements in the basis, which also corresponds to the degeneracy of the mode. The degeneracy of a mode is constrained by the symmetry groups of the complex, thus for an icosahedron only a precise set of degeneracies are allowed: 1 (nondegenerate), 3, 4, or 5. The degenerate modes arise from rotations about the two-, three-, and fivefold axes of rotational symmetries (54). Likewise, normal modes obtained from the pentamer should present in accordance with the allowed degeneracies of a regular pentagon. The defined dimensions of the irreps for a pentagon are 1, 1, 2, 2 (55). Table 2 shows the degeneracy of eigenvalues obtained from modal analysis. As shown, the modes obtained from the pentamer complexes adhered to the allowed degeneracies of a pentagon, whereas the modes obtained from the CG4 and CG12 capsid presented in accordance with the allowed degeneracies of an icosahedron. This result validated the coarse-graining approach presented in this study. Moreover, the comparison of the eigenvalues obtained from the pentamer and its CG4 model, and the eigenvalues of the interface complex and its CG4 model, showed that the degeneracies of the individual modes were maintained during coarse-graining. This is testament to the construction of each complex from a single coarse-grained protomer that allowed symmetry to be retained in the coarse-grained complexes.

Table 2.

ANM Eigenvalues and Degeneracy of Complexes of the EV-71 Capsid

Mode	Eigenvalue		Degeneracy
	Pentamer	Pentamer CG4
1–2	0.0491	0.1252	2
3∗	0.1238∗	0.3112∗	1∗
	Pentamer Interface	Pentamer Interface CG4
1–2	0.0052	0.0143	2
3∗	0.0087∗	0.0242∗	1∗
4∗	0.0216∗	0.0561∗	1∗
5–6	0.0371	0.0978	2
7–8	0.0681	0.1700	2
9∗	0.0864∗	0.2124∗	1∗
10–11	0.1146	0.2760	2
12–13	0.1200	0.2937	2
14–15	0.1352	0.3338	2
16∗	0.1410∗	0.3463∗	1∗
17∗	0.1659∗	0.4166∗	1∗
	Capsid CG4	Capsid CG12
1–5	0.0730	0.0211	5
6–8 (6–9)	0.1418	0.0415	3 (4)
9–12 (10–12)	0.1423	0.0421	4 (3)
13–17	0.1704	0.0502	5
18–22	0.2465	0.0757	5
23–26	0.2569	0.0767	4
27∗	0.3129∗	0.0904∗	1∗
28–31	0.4070	0.1178	4
32–34	0.4184	0.1198	3
35–37 (35–39)	0.4339	0.1270	3 (5)
38–42 (40–42)	0.4348	0.1277	5 (3)
43–45	0.4443	0.1345	3
46–48	0.4458	0.1380	3
49–53	0.6688	0.1861	5
54–56 (54–58)	0.6811	0.2019	3 (5)
57–61 (59–62)	0.7093	0.2116	5 (4)
62–65 (63–65)	0.7306	0.2140	4 (3)
66–70	0.7373	0.2189	5
71–74	0.7418	0.2312	4
75∗	0.7615∗	0.2326∗	1∗
76–78	1.0064	0.2619	3
79–82	1.0152	0.2930	4
83–87	1.0396	0.3102	5
88–90	1.0709	0.3233	3
91–95	1.0849	0.3272	5
96-98	1.1199	0.3325	3
99–101	1.1970	0.3571	3
102–105	1.2934	0.3792	4
106–108 (106–109)	1.4023	0.4123	3 (4)
109–112 (110–112)	1.4200	0.4173	4 (3)
113∗ (113–117)	1.4226∗	0.4224	1∗ (5)
114–116 (118–120)	1.4837	0.4316	3 (3)
(117–121) (121)∗	1.4872	0.4414∗	5 (1)∗

ANM eigenvalues for respective complexes of the EV71 capsid. Nondegenerate modes are indicated with an asterisk. In the comparison between the CG4 and CG12 capsid, values in brackets pertain to the CG12 capsid as certain clusters of degenerate modes are presented in a different order for each capsid.

Normal modes of protomer capture the intraprotomer rotation of VP1

From the NMA of an individual protomer and its coarse-grained model, two modes in each system were identified to overlap with the experimental change observed in the protomer unit (Table 3). Although the overlap was relatively low (in the range 0.18–0.34), the modes corresponded to the slowest mode in each complex, as well as the sixth and fourth slowest modes in the protomer and its CG4 model, respectively. It must be noted that all low frequency modes obtained from the protomer and CG4 protomer were nondegenerate and appeared with unique eigenvalues. This was expected because the protomer comprises four heterogenic subunits and serves as the asymmetric unit of the capsid. The low overlaps with conformational change may be due to the fact that an elastic network model of an individual protomer does not account for the motions induced by neighboring protomers in an assembled capsid and cannot account for the rearrangement of protomeric units during capsid expansion. Rather, the modes obtained may correspond to local changes that take place within the protomeric unit. A jackknife rotation of the VP1 protein was captured in the sixth slowest mode of the protomer (fourth slowest mode in the CG4 protomer). The visualization of the sixth slowest mode is illustrated in Fig. 2 A. The vector arrows indicated the rotation of the VP1 protein about a point located at the VP1–VP3 intraprotomer interface, centered near the bottom of the hydrophobic pocket. This motion resembled the previously described rotation of VP1; in which the protein flexes to straighten the protomer unit during expansion (3). The mode was also visualized in the Movie S1.

Table 3.

Normal Mode Analysis Results for Respective Complexes of the Enterovirus 71 Viral Capsid

Complex	Number of Residues	Total Number of Nontrivial Modes (3N-6)a	Mode Identified to Overlap Capsid Expansion	Maximum Overlap
Protomer	842	2520	1	0.24
			6a	0.18
Protomer CG4	209	621	1	0.34
			4	0.28
Pentamer	4210	12,624	3b∗	0.71∗
Pentamer CG4	1045	3129	3∗	0.71∗
Pentamer interface	12,630	37,884	17c∗	0.71∗
Pentamer interface CG4	3135	9399	17∗	0.70∗
Capsid CG4	12,540	37,614	27d	0.67
			75e∗	0.53∗
			113f	0.20
			combination	0.80
Capsid CG12	4320	12,954	27	0.64
			75∗	0.60∗
			121	0.20
			combination	0.77

NMA results for respective complexes of the EV71 viral capsid. Maximum overlapping modes with capsid expansion, as determined from the experimental structures, were identified. A common mode was identified across the pentamer, pentamer interface complex, and coarse-grained capsid structures. This common mode is indicated with an asterisk. Movies of the respective capsid complexes are in the Supporting Material.

^aMovie S1.

^bMovie S2.

^cMovie S3.

^dMovie S4.

^eMovie S5.

^fMovie S6.

Capsid expansion is accomplished by a combination of nondegenerate modes

In the case of nondegenerate modes, the motions of each protomer are identical as the mode adheres to icosahedral symmetry across the entire system. Structural studies show that expanded enterovirus capsids also follow icosahedral symmetry (3, 15, 16, 17, 18). Therefore only nondegenerate modes that adhere to icosahedral symmetry were expected to overlap with the conformational change of the capsid. In fact, in previous studies the overall translation that dominates the motion between two conformational states of a virus has been captured in a combination of one or two nondegenerate normal modes (36, 38, 40).

Our findings extended on previous results reported for the NMA of viral capsids. Analysis of the full capsid revealed three nondegenerate modes that overlapped with expansion (Table 3). For the CG4 and CG12 capsids, the largest overlap of ∼0.65 was obtained with the first nondegenerate mode. This mode corresponded to uniform radial expansion (Movie S4). As an example, Fig. 2 B2 depicts the radial expansion of only a single capsid protomer. Radial expansion has been reported in studies of Chlorotic Mottle Virus (36) and PV (38). Interestingly, the uniform expansion of each PV protomer was reported to have a distinctive hinge-bending motion about the fivefold canyon (hydrophobic pocket). As shown in Fig. 2 B2, the fivefold proximal end of EV71 VP1 also moved upwards to the right, depicting a very similar motion as previously described for PV (38). Some enteroviruses, including PV and HRV-14 (56, 57, 58), are thought to exist in a metastable state, undergoing a reversible process called “breathing”. Under physiological conditions, the VP1 N-terminus and VP4 are transiently exposed on the surface of the capsid and then retract into the particle. However, under certain triggers such as receptor binding, acidic pH, or elevated temperature, the changes associated with breathing become irreversible (59). The radial expansion observed in the modal analysis may represent the breathing motion under physiological conditions, whereas the additional overlapping modes may accompany the conformational switch as the breathing motion becomes irreversible. This may be triggered by the extension of the hinge at the hydrophobic pocket, upon host cell binding.

Notably, the third nondegenerate mode captured a screwlike motion about the threefold axis (Fig. 2 B1; Movie S6). As suggested by Wang et al. (3), this screwlike motion may assist in pulling VP2 away from the twofold axis for pore formation. The mode also explained the residue displacements across the pentamer interface that indicated an additional shift at the pentameric interface (Figs. 2 B1, S1, and S2). Structural studies of PV suggested that the VP1 N-terminus may be externalized through a junction channel at the threefold axis (27, 60). In the EV-71 A-particle, the ordered region begins at residue S72, which is located at the center of the threefold axis (10). Thus, this shift may be critical for RNA release.

With the exception of the two protomer complexes, overlap values >0.5 were obtained for each analysis. This suggested that the dominant motions associated with capsid expansion may only be obtained from the analysis of an assembled complex of protomers, an explanation consistent with previous suggestions that the conformational change involves the major rearrangement of protomer complexes within the capsid (3, 10). The modes associated with radial expansion and the screwlike motions about the threefold axis were not identified from analyzing the pentamer interface or pentamer complex.

Local rearrangement of protomers may be captured from a subcomplex of the capsid

The second nondegenerate mode of the full capsid (overlap of ∼0.55) resembled the counterpart to a common mode obtained from the pentamer and pentamer interface models. This mode had the highest overlap of ∼0.70 in both sets of the pentamer and pentamer interface complexes (Table 3). It corresponded to the first nondegenerate mode in the pentamer and only the fifth nondegenerate mode in the interface complex. This suggested that the mode represents the dominant and local rearrangement of the protomers within the pentameric complex. To characterize this mode, we constructed static images depicting the displacement vectors as a set of increasing frames in the direction of each mode (movies have been included in the Movies S2, S3, and S5). To compare these modes with the experimental change in Fig. 3, we projected mode 75 of the CG4 and CG12 capsid onto the full capsid structure (Fig. 3 A), mode 17 of the pentamer interface onto the structure of the interface complex (Fig. 3 B), and mode 3 of the pentamer onto a single pentamer structure (Fig. 3 C). The superimpositions of the complexes from the two capsid structures suggested that the central region of the pentamer was expanded, whereas the edges of the pentamer collapsed at the pentamer-pentamer interface. Visualized frames of the modal vectors were consistent with this, and we observed the outward motion of the central region of the pentamer in all models. Eigenvectors for this mode were plotted as arrows across a single protomer. As shown in Fig. 2 B3, the complete protomer rotated counterclockwise about the twofold axis; thus, as the twofold proximal side of the protomer collapsed inward, the fivefold region expanded outward from the center of the capsid. In the mature full capsid, the VP4 protein and the N-terminus of VP1 are located on the internal side of the capsid (Fig. 1 A), and may provide a scaffoldlike support mechanism for the capsid. Moreover, the N-terminus of VP1 lies directly beneath the twofold axis, forming an internal bridge between the pentameric interfaces. This interpentameric support provided by the N-terminus of VP1 may be lost during its expulsion from the capsid, resulting in an expected collapse at the pentamer-pentamer interface. The visualization of these modes also suggested that the VP4 protein exits the capsid at the fivefold axis (Movies S2, S3, and S5).

To further validate that the modes depicted in Fig. 3 represented the same motion in each complex, a comparative analysis of the mean square fluctuations of the respective residues was performed. The results have been shown in Fig. S3. We obtained similar fluctuations for all six complexes, and thus confirmed that the same motion was revealed from analyzing a coarse-grained capsid, a pentamer interface complex, or a pentamer complex of the capsid. We also noted that the results obtained from analyzing one-twelfth of the viral capsid (CG12) were comparable with those obtained from the analysis of one-fourth (CG4).

Flexible residues are located in regions associated with capsid stability

To investigate the most flexible regions during capsid expansion, we examined the mean square fluctuations obtained from the best overlapping mode of the full pentamer interface complex (Fig. 5). This model is the most detailed and contains nodes from all residues in the experimental structure. The complex sufficiently connected protomers at the pentamer interface and residue fluctuations of the overlapping mode had remarkable resemblance to those obtained from a model of the full capsid (Fig. S3). Four major regions of flexibility were identified: VP1, 131–155; 163–193; 233–257; VP3, 1–31 and VP4, 12–42 (Fig. 4 A). Structural investigation showed that these regions are located in the central region of the pentamer and expand toward the hydrophobic pocket (Fig. 4 B). Within the three flexible regions of VP1, the residues with largest fluctuation were P148, L150, K182, S184, and V238, respectively. It has been suggested that the conformation at the fivefold axis of EV71 is maintained by an elaborate network of hydrogen bonds established by the VP1 K182 residue, a residue conserved in Enterovirus A and D species (10). The enlarged portion in Fig. 4 B defines the hydrophobic pocket. The fluctuating regions overlap with certain residues located within the pocket including VP1 F131, F155, V190, V192, and G233 as well as the VP3 I24 that forms the bottom of the pocket. Other fluctuating regions pertained to the N-terminus of VP3 and VP4. Both these regions are located on the internal side of the capsid and interact directly with the viral RNA. In particular, the C-terminus of VP3 has been reported to interact with RNA in the A-particle of HRV-2, subsequent to the release of VP4 (15).

Figure 5.

PRS of the Enterovirus 71 capsid complexes. Depictions of the β-carbon atoms that were perturbed in a network were constructed on the respective (A) protomer, (B) pentamer, and (C) pentamer-interface complexes. In each complex the nodes that were perturbed have been colored according to subunit: green, VP1; blue, VP2; orange, VP3; and yellow, VP4. They are shown as spheres. In the pentamer-interface complex, specific regions haves been marked out by dashed lines. Protomers of interest have been colored and labeled. To see this figure in color, go online.

Figure 4.

Residue fluctuations during capsid expansion. A common overlapping mode was captured from models of the full capsid, pentamer interface complex, and pentamer. (A) Mean square fluctuations of the residues of the respective VP1-VP4 subunits, were obtained from a protomer in the pentamer-interface complex. (B) Structural mapping of flexible regions were identified from the overlapping mode. The regions have been mapped to a cartoon depiction of pentamer interface complex. Subunits are colored as green, VP1; blue, VP2; orange, VP3; and yellow, VP4. Flexible regions are located in the center of each pentamer and are mapped as clusters of spheres: VP1, 131–155, 163–193, and 233–257; VP3, 1–31; and VP4, 12–42. A closeup of the capsid canyon shows the residues that constitute the hydrophobic pocket; residue colors are as in (A). The natural lipid, sphingosine, is shown in red. To see this figure in color, go online.

PRS

We next explored the application of PRS to virus capsids for the first time, to our knowledge, and have used the method to investigate the transition of the mature EV-71 capsid to its expanded A-particle. PRS is a site-specific technique and relies on the systematic application of forces at single residues selected across the protein complex. For each perturbed residue, the linear response of the entire complex is recorded (46). In considering the sensitivity of PRS, we applied the method to complexes constituting all residues, and excluded the additional coarse-grained CG4 and CG12 complexes from the analysis. The complexes that were analyzed by PRS are shown in Fig. 5. Specifically, PRS was applied to an individual protomer (Fig. 5 A), individual pentamer (Fig. 5 B), and the pentamer-interface complex (Fig. 5 C) of the mature capsid. Given that the pentamer and pentamer-interface complex comprise five and fifteen identical protomeric units that are assembled with symmetric arrangement, only a single protomer from each complex was perturbed (Fig. 5, B and C). With respect to the interface complex, residues within a single central protomer located at the pentameric interface were systematically perturbed (Fig. 5 C). We then assessed the response of the following: 1) the complete interface complex, 2) the local pentamer in which the perturbed protomer is assembled, 3) an adjacent pentamer within the interface complex, 4) the perturbed protomer within the complex, 5) a neighboring protomer assembled in an adjacent pentamer (red protomer in Fig. 5 C), and 6) a nonneighboring protomer located in an adjacent pentamer (purple protomer in Fig. 5 C). This approach gave a detailed understanding of the distribution of the applied force across the pentamer interface complex. The selected protomer of each complex was scanned by consecutively applying 100 random forces to the C_β atom of each residue. For every force applied to each residue of a single protomer within the macrocomplex, the predicted displacement ΔR of the respective complex was recorded and the overlap between the known conformational change ΔS was calculated. The displacement vectors of ΔS between the mature capsid and the A-particle were calculated across the superimposed protomers, pentamers, and pentamer-interface complexes, respectively.

Internal capsid forces reveal propensity to expansion

In the mature EV-71 virion, VP4 and the N-terminal extensions of VP1, VP2, and VP3 are packed in layers in the interior of the capsid and interact with the RNA genome (10). The interaction of the RNA with this arrangement of proteins imposes internal pressure within the capsid that may be contained under physiological conditions when the capsid is stable. However, under certain conditions, such as receptor binding or an acidic environment, this pressure may contribute to capsid expansion. The perturbation of individual residues using PRS within the pentamer complex revealed regions that may contribute significantly to the expansion (Table 4). Highest overlap with the conformational change across the pentamer complex was obtained upon the perturbation of single residues in VP4 12–14, and 27–36, and VP3 N-terminus regions. Significant hotspots were also identified in the VP1 subunit; however, these regions were not located in the N-terminal extension that bridges the twofold pentameric interface. To determine if the structural location of these hotspots may have implication in the mechanisms that modulate expansion, these regions were mapped to the pentamer complex. Fig. 6 shows a channel of residues, formed from the inside out, located at the center of the pentamer complex. Interestingly, the highest overlap values correlated to the most internal capsid residues that interact directly with the RNA genome. A hotspot channel that spanned the thickness of the capsid was then formed by residues packed above these VP4 residues at the fivefold axis. The hotspot regions observed in the VP1 subunit surround the fivefold axis and extend radially toward the hydrophobic pocket. These VP1 residues are located directly above the critical VP4 residues and at the interface between VP1 and VP3. The hotspot residues identified here corresponded to regions that have been associated with capsid assembly. In a recent study on another picornavirus, Parechovirus 1, it was suggested that RNA folding provides a scaffold for capsid assembly that is enabled by the RNA making 60 identical contacts with conserved residues in the protein shell. These residues were located in the VP3 N-terminus and VP1 residues at the VP1–VP3 interface. The VP3 N-terminus extends into the fivefold axis to interlock with the RNA. The disruption of the contacts between the RNA and amino acids of the capsid were reported to be deleterious to viral assembly (61). Therefore, if these contacts are critical to the assembly process, they may also play a fundamental role in capsid expansion. The PRS results indicated that residues in this region may be trigger points for expansion. This study has shown that PRS may be successfully applied to study the mechanisms that modulate changes within a viral capsid. In the future, this approach may be applied to other viral capsid or macromolecules to elucidate potential drug targets or for bioengineering purposes. Notably, the regions identified from the PRS analysis directly correlated to the most flexible regions identified from the modal analysis (Fig. 4). In particular, the perturbation of VP1 S184 revealed an overlap of 0.65 across the pentamer. This residue was observed to have the highest mean square fluctuation in the VP1 subunit. Moreover, the perturbation of the most flexible VP4 residues, S12 and Y32, resulted in the highest overlap of 0.67. A similar correlation was observed for other residues in the VP3 and VP4 N-terminal extensions.

Table 4.

PRS Results for Complexes of the Enterovirus 71 Capsid

Subunit	Residues	Protomer	Pentamer			Pentamer Interface Complex
		Average Overlap	Average Overlap	Highest Overlap		Average Overlap
						Complex	Pentamers		Protomers
							1	2	1	7	10
VP1	136–140	0.21	0.61	A139	0.62	0.17	0.58	0.24	0.58	0.33	0.60
	146	0.14	0.62	V146	0.62	0.13	0.61	0.18	0.60	0.40	0.54
	149–152	0.17	0.62	L150	0.63	0.14	0.55	0.16	0.58	0.34	0.38
	179–191	0.11	0.63	S184	0.65	0.19	0.58	0.33	0.64	0.40	0.55
	238	0.16	0.61	V238	0.61	0.12	0.50	0.08	0.57	0.35	0.33
VP3	1–14	0.14	0.63	K7	0.64	0.19	0.51	0.33	0.60	0.35	0.69
	17–23	0.11	0.63	V20	0.64	0.16	0.60	0.32	0.67	0.36	0.68
VP4	12–18	0.18	0.65	S12	0.67	0.14	0.58	0.29	0.72	0.30	0.66
	20–23	0.26	0.62	E21	0.63	0.16	0.62	0.29	0.72	0.34	0.62
	25–47	0.20	0.64	Y32	0.67	0.16	0.59	0.30	0.72	0.32	0.66

Figure 6.

PRS results obtained for a single pentamer complex. Forces that inferred significant overlap have been plotted as arrows and act outwards from the center of the viral particle. Hot-spot residues form a channel from the inside-out at the center of the pentamer complex. The capsid subunits are colored as green, VP1; blue, VP2; orange, VP3; and yellow, VP4. To see this figure in color, go online.

To fully understand the inference of the applied force to capsid expansion, the relationship between the overlap and direction in which the force is applied was investigated. For each residue in the identified hotspots, only a small percentage of the 100 random forces inferred significant (>0.6) overlap with expansion. These forces were mapped to the corresponding β-carbon atoms and only forces that acted outwards from the center of the capsid particle implied overlap with expansion (Fig. 6). These results strongly substantiate the suggestion that the interaction between the genome and the internal capsid proteins plays a considerable role in RNA release.

The pentamer complex serves as the functional unit of the capsid

PRS was applied to an individual protomer, an individual pentamer, and the pentamer interface complex. Table 4 comparatively depicts the response of each respective complex upon single residue perturbations. The results indicated that significant overlap with expansion was only observed for an individual pentamer, whereas significantly lower overlap values were obtained when regions were perturbed in an individual protomer and interface complex. Table 4 also includes a systematic analysis of the response of specific regions within the interface complex. Single residue perturbations of a protomer assembled in the pentamer-interface complex resulted in a significant local response within the individual protomer. This was evident by the 0.72 overlap observed upon perturbing residues in the VP4 protein. In contrast, when the same residues were perturbed in a standalone protomer, the highest overlap observed was 0.26. These results suggested that when the protomer was not constrained by interactions with its neighboring protomers, the force was distributed across the system, thus the propensity to change the conformation was not observed. Therefore, the protomer cannot be considered as a functional unit to investigate capsid expansion; this is consistent with the low overlap values obtained from modal analysis. Furthermore, the low overlap values observed across the full interface complex indicated that protomers cannot manipulate the capsid in a bottom-up fashion with a single residue perturbation. The pentamer-interface complex is a particularly large and nonrigid system (12,630 nodes), thus the perturbation of a single node could not sufficiently induce changes across the entire system. To substantiate this, we investigated the response of selected regions across the complex. Fig. 5 C depicts the regions of the pentamer interface that were considered for analysis. As shown in Table 4, single residue perturbations were capable of inferring a response across a neighboring protomer, spanning a distance of 140 Å (Table 4; Protomer 10). However, the applied force had a notably lower effect on a nonneighboring protomer (Table 4; Protomer 7). This was also evident in the low overlap values observed across the adjacent pentamer within the interface complex (Table 4; Pentamer 2). However, we observed that the single residue perturbations of a protomer could cause a significant response within the local pentamer (Table 4; Pentamer 1). Given this observation and the high overlap values obtained for a system based on an individual pentamer, we suggest that for the investigation of a full capsid comprising 60 protomers, the pentamer complex is the appropriate functional unit to explain the deformations when the capsid is perturbed.

Conclusions

The motions associated with EV71 uncoating were investigated through NMA of respective coarse-grained complexes of the capsid. In addition to analyzing capsid expansion through NMA, the construction of elastic networks across all β-carbon atoms of subcomplexes of the virus capsids allowed us to further investigate the key residues that may play a significant role in capsid expansion. In regard to symmetry, the motions that lead to the formation of the A-particle were captured in a combination of three nondegenerate modes. These modes were captured regardless of the degree of coarse-graining and represent the changes described from structural studies of the EV71 capsid. We pinpointed hot-spot regions surrounding the fivefold axis and the hydrophobic pocket, supporting previous suggestions that the pocket plays a critical role in capsid stability (22, 23). Furthermore, the PRS results suggested that the interaction of the RNA with internal capsid proteins also contributes significantly to capsid expansion. Thus, the uncoating process may not be solely dependent on host-cell receptor binding. In fact, this is in support of the emerging view that RNA helps viruses assemble their protein shells (61). Lastly, we observed that the deformations in the capsid upon perturbation can be explained from a single pentamer complex, but a single protomer does not act as the functional unit to explain the changes associated with uncoating.

Author Contributions

C.J.R. designed research, developed scripting tools, performed the research, analyzed and interpreted data, wrote the paper, and constructed figures and movies. A.R.A., O.T.B., and C.A. designed research, guided tool development and data analysis with theoretical knowledge, interpreted data, guided in the structure and contents of the paper, and edited the paper.

Editor: Madan Babu Mohan.

Supporting Material

Movie S1. Protomer Mode 6 Motions

A jackknife rotation of the VP1 protein was captured in the sixth slowest mode of the protomer (for details, see Table 3 and the legend for Figure 2A).

Movie S2. Pentamer Mode 3 Motions

This mode is the first non-degenarate mode in the pentamer and shows an overlap of 0.71 with capsid expansion. The motion suggests the VP4 protein exits the capsid at the five-fold axis (for details, see Table 3).

Movie S3. Pentamer Interface Mode 3 Motions

This mode is the fifth non-degenarate mode in the interface complex and shows an overlap of 0.71 with capsid expansion. The motion suggests the VP4 protein exits the capsid at the five-fold axis (for details, see Table 3).

Movie S4. Full Capsid Mode 27 Motions

This mode is the first non-degenerate mode of the full capsid and corresponds to uniform radial expansion with an overlap of 0.67 with capsid expansion (for details, see Table 3).

Movie S5. Full Capsid Mode 75 Motions

This mode the second non-degenerate mode of the full capsid and shows an overlap of 0.53 with capsid expansion. The motion suggests the VP4 protein exits the capsid at the five-fold axis (for details, see Table 3).

Movie S6. Full Capsid Mode 113 Motions

This mode is the third non-degenerate mode capturing a screw-like motion around the three-fold axis and shows an overlap of 0.20 with capsid expansion (for details, see Table 3).