Multiscale Computer Simulation of the Immature HIV-1 Virion

Abstract

Multiscale computer simulations, employing a combination of experimental data and coarse-graining methods, are used to explore the structure of the immature HIV-1 virion. A coarse-grained (CG) representation is developed for the virion membrane shell and Gag polypeptides using molecular level information. Building on the results from electron cryotomography experiments, the simulations under certain conditions reveal the existence of an incomplete p6 hexameric lattice formed from hexameric bundles of the Gag CA domains. In particular, the formation and stability of the immature Gag lattice at the CG level requires enhanced interfacial interactions of the CA protein C-terminal domains (CTDs). An exact mapping of the CG representation back to the molecular level then allows for detailed atomistic molecular dynamics studies to confirm the existence of these enhanced CA_CTD interactions and to probe their possible origin. The multiscale simulations further provide insight into potential CA_CTD mutations that may disrupt or modify the Gag immature lattice assembly process in the immature HIV-1 virion.

Introduction

The human immunodeficiency virus type 1 (HIV-1) begins assembly with multimerization of the Gag polyprotein at the plasma membrane of infected cells (1–3). Once assembled, an immature virion buds, which also requires recruitment of various components of the cellular endosomal sorting complex required for transport machinery (4). The HIV-1 Gag polypeptide contains all the structural proteins required to form the mature, infectious virion, including the N-terminal matrix (MA) domain, capsid (CA) domain, spacer peptides SP1 and SP2, and a C-terminal nucleocapsid (NC) domain between the two spacer peptides.

The immature HIV-1 virion consists of a membrane shell with diameters in the range of 115–140 nm, having an average at ∼127 nm (2). The Gag polypeptides bind with the membrane via a cotranslationally myristoylated MA domain (5–7); however, both the MA domain as well as the CA N-terminal domain (CA_NTD) are not absolutely required for immature particle assembly (8,9), although mutations in the CA_NTD can reduce the efficiency of immature particle assembly (10). In contrast, the CA_CTD, SP1 spacer, and NC regions play critical roles in immature virion formation (11–13).

There has been debate over exactly how many Gags are in the immature virion, given the 8-nm p6 hexagonal unit cell spacing of the CA domain (14). Recently, it has been observed with electron cryotomography that the arrangement of Gags does satisfy 8-nm p6 hexagonal unit cell spacing (compared to the 9.6-nm unit cell in the mature viral core (15)), but the Gag lattice is incomplete, with large regions of the virion apparently not occupied by Gag. Within the Gag polypeptide itself, only the regions corresponding to the two CA domains and the adjacent SP1 spacer exhibit hexagonal order, whereas the regions occupied by the NC and MA domains lack any regular quaternary structure. These surprising results have also recently been confirmed (3) and a more refined structure of the immature Gag lattice has been proposed. It was also shown that the regions without ordered Gag lattices lack Gag molecules entirely. Furthermore, it was found that the CA domains were arranged as hexagonal bundles in which several residues in the CA_CTD domain come into very close contact (3). For example, residues 153–159 in one CA_CTD domain were found to be very close to residues 212–219 in the other; this arrangement is markedly different from the intrahexamer contacts in the mature capsid.

Complementary mutagenesis studies (10) explored how various mutations affected virion morphology, viral maturation, and immature particle assembly. It was found that alanine mutations of residues K158 and D197 resulted in reduced immature virion particle release, altered morphologies, and also affected immature particle assembly. The hypothesis was that these mutations might disrupt key Gag-Gag interactions that facilitate a closed immature particle lattice. It was proposed that the effect of the mutations, in terms of altering immature particle production, arose from the disruption of important interactions during the Gag assembly process.

Atomistic modeling of the immature virion via computer simulation requires, at a minimum, a predefined Gag model (1), which is complicated by the fact that detailed atomic-level structures of some regions of Gag, along with the linkers connecting the domains, have not yet been fully resolved (e.g., the SP1 domain). Recent MD simulations of the CA domain (16,17) have examined regions of Gag at an all-atom level of detail. A recent study (18) of the HIV-1 viral capsid employed the atomic-level structure of the CA protein and entire domains were then modeled with only a few coarse-grained (CG) sites. Moreover, the length-scale of the immature virion, of ∼125 nm in diameter (at ∼10⁹ atoms, including the surrounding water), rules out both atomic-level molecular dynamics (MD) as well as commonly used CG approaches (19,20), which would require ∼10⁸ CG sites (including a CG water solvent). Thus, alternative CG approaches are needed. A solvent free methodology is an obvious first choice, where the interactions between the CG sites implicitly contain averaged solvent effects (21–24). Furthermore, an adaptive and evolutionary CG model (25,26) that is tightly coupled with experimental electron cryotomographic data (2,3), and that employs methodologies developed from the hybrid analytic-systematic (HAS) CG approach (24,27), can allow for an iteratively refined Gag model, as well as a greatly simplified solvent free CG membrane, where some regions contain a higher degree of detail while others have less.

It is desirable to have as much atomic-level interaction information as possible incorporated into key features of the CG model, because the behavior at the CG level can be mapped back, systematically, to atomic-level interactions (25–27). However, in those regions where the Gag model has a low degree of atomic-level information, the parameterizations of the CG model must also be tested over a range of values to ensure that the overall behavior of the virion is not affected by small variations in the CG model characteristics. If it is found that a particular region is very sensitive to parameterization details, then some means of justifying and/or validating that particular set of CG parameterizations is needed.

This article will aim to examine the entire HIV-1 virion within a hybrid multiscale simulation approach. In particular, CG simulation will be used at the largest length-scales to identify key structural details of the Gag lattice in the immature virion, while MD simulations of the resulting specific domains of the Gag will then be carried out to give a more refined description of the interactions in these selected regions. The large length-scale CG model can then be refined based on this more detailed information and the refinement process iterated, in principle. A comparison of the simulation results with electron cryotomography studies (2,3) is an essential feature of this hybrid multiscale simulation methodology.

Methods

Coarse-grained Gag/membrane model

Atomic-level structures for the MA, CA_NTD, CA_CTD, NC, and SP1 Gag domains were taken from recently published structures. The MA domain structure was obtained from solution NMR of the HIV-1 matrix protein bound to di-C4-phophatidylinositol-(4,5)-biphosphate (7) (PDB ID:2H3Z). The CA domain was constructed from previously resolved structures (18,28,29), while the structure for the NC domain (30) was found from solution NMR (PDB ID: 1F6U). The proposed SP1 structure was that given in the literature (1,2). For each structure, the α-carbons determined the residues composing each CG site using coarse-graining methods recently developed (25,26), resulting in an anisotropic elastic network model for each Gag domain (31). Electrostatic interactions were then included between the CG sites and were based on the underlying atomic-level charge distribution of each CG site up to the dipole level. The adaptive nature of the methodology allows for the Gag model to be updated and refined as new experimental structural information becomes available.

The CG model of the wild-type (WT) Gag/membrane system is shown in Fig. 1, where the entire system is divided into N_D domains and each domain contains N_α CG sites. Each CG site is specified by its Cartesian location, r, along with a unit vector, e. In the case of a lipid modeled by an ellipsoid of revolution, e lies along the major axis. In the case of a Gag CG site, e lies along the dipole moment. Thus, for example, the i_α CG site in domain α is specified by ${\mathbf{r}}_{i_{\mathit{\alpha }}}$ and ${\mathbf{e}}_{i_{\mathit{\alpha }}}$. Each site interacts with the other sites via a total of γ different types of pairwise interactions. The Gag is decomposed into a total of 14 domains, and each lipid (24) contains two domains (the ellipsoidal body along with the headgroup CG site), thus this particular system consists of 16 domains. The total energy of the Gag/membrane system is given by the summation of the i_α CG site in domain α with the j_β site in domain β,

$$U=\frac{1}{2}\sum _{\mathit{\alpha }=1}^{N_D}\sum _{i_{\mathit{\alpha }}=1}^{N_{\mathit{\alpha }}}\sum _{\mathit{\beta }=1}^{N_D}\sum _{j_{\mathit{\beta }}^{\ast }=1}^{N_{\mathit{\beta }}}\sum _{\mathit{\gamma }=1}^{N_{\mathit{\gamma }}}{\mathit{\zeta }}_{\mathit{\gamma }}^{\mathit{\alpha \beta }}{u}_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\mathit{\gamma }},$$ (1)

where $u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\mathit{\gamma }}$is a general pairwise interaction of type γ and ${\mathit{\zeta }}_{\mathit{\gamma }}^{\mathit{\alpha \beta }}$ is a switching function that is either 0 or 1, depending on whether that particular interaction is required for that i_α, j_β pair. The prime on the fourth summation indicates that the summation excludes terms with i_α = j_β γ when α = β and when $\left|{\mathbf{r}}_{i_{\mathit{\alpha }}}-{\mathbf{r}}_{j_{\mathit{\beta }}}\right|>r_c$, where r_c is a preset cutoff radius. The following set of interactions was employed: γ = 1 is a Gag domain elastic network interaction, γ = 2 is a Gag CG site shorter range interaction, γ = 3 is a lipid-Gag or lipid-lipid interaction, and γ = 4 is a screened (Yukawa) electrostatic interaction that includes both charge and dipolar contributions (32) between the CG sites. The details for the different interactions are given in Table 1, while the exact residues corresponding to each domain, as well as the switching function, ${\zeta }_{\gamma }^{\alpha \beta }$, are given in the Supporting Material.

Figure 1.

A schematic of the Gag/membrane CG model. (Left panel) Domain decomposition of the Gag and PS/PC membrane. (Small spheres) Linker sites. Detailed atomic-level information was used to parameterize the MA, CA, and NC/RNA domains. Close-contact CG sites 34, 35, 40, 42, 43, and 44 in the CA_CTD domain are highlighted. (Right panel) Initial virion structure; 2034 Gags, each in bundles of six, were replicated in a 125-nm diameter virion. The initial p6 hexagonal lattice spacing was 10 nm, with the Gags relatively uniformly spaced.

Table 1.

Decomposition of the various terms in the energy expression for the Gag/ membrane system, as appearing in Eq. 1

γ	Description/functional form	Parameters
1	Elastic network	kE: 10–100 kcal mol−1 nm−2 (domain structure not overly dependent on parameter choice).
		kΩ: 10–100 kcal mol−1.
		r0, Ω0: varies depending on preset CG site locations and orientations.
2	Shorter range (12-6 inverse power)	ɛL: Nonenhanced interactions have ɛL =1–1.5 kcal mol−1. Enhanced interactions have ɛL = 3–4 kcal mol−1.
		σL: 1 nm (approximate excluded volume of 10 residues in a coarse-grained site).
3	Lipid-protein, or lipid-lipid interaction	ɛ0: 3 kcal mol−1 (estimated from a similar calculation of charged residues with charged lipids (27)).
		$\Delta U_{i_{\alpha }{j}_{\beta }}\left(r\right)$: HAS interaction between lipids.
		σ0: 0.76 nm (diameter of the lipids).
4	Yukawa charge-charge, charge-dipole, dipole-dipole	$q_{{\alpha }_i}$: net charge of CG site αi.
		${\mu }_{{\alpha }_i}$: magnitude of the dipole moment for CG site αi.
		${\mathbf{e}}_{{\alpha }_i}$: dipole moment unit vector for CG site αi.
		αY: Yukawa screening constant (Eq. 5) was set at 7.6 nm−1.

In all instances, $r=\left|{\mathbf{r}}_{i_{\alpha }}-{\mathbf{r}}_{j_{\beta }}\right|$, where ${\mathbf{r}}_{i_{\alpha }}$is the Cartesian location of CG site i_α; likewise for j_β.

Referring to Fig. 1, Gag domains 1–14 are elastic networks connected by flexible linkers (small open sites). Within a single domain, only the elastic network interactions are evaluated. The attractive strength of the γ = 2 (shorter range) interactions between Gag CG sites can be varied, but must be justified via atomic-level considerations or other means. Cross interactions between CG lipids and Gag CG sites include both shorter range and electrostatics. The lipids interact via the HAS CG membrane interaction (24,27), which has been parameterized previously (27).

Virion simulation setup

Initially a hexameric bundle of six Gags was generated following the recently proposed electron microscopy (EM) reconstruction (3); however, in principle any reasonable starting configuration could be employed. Note that the simulation is not dependent on this initial structure and it is able to explore new configurations and conformations. In the spirit of an adaptive modeling approach, new Gag arrangements could also be employed as viable initial starting states. In fact, the only constraint was that the 8-nm p6 lattice spacing should be conserved. Consider a Cartesian axis system with the z axis in the vertical direction. The Gags were arranged parallel to z axis with the last CG site in domain 14 at z = 0. The Gags were then placed in a hexagonal arrangement in the x-y plane such that the center of the CA domain was 4 nm from the bundle center at x = 0, y = 0 (to ensure an 8-nm p6 hexagonal spacing). An initial simulation at 273 K of the bundle was then performed to anneal this structure. To keep the bundle intact, and to model the effect of the surrounding Gags, an additional conical wall interaction was included in this equilibration procedure. The final structure of the equilibrated bundle was found to be similar to the original EM configuration, suggesting that this proposed CG structure (3) is a viable representation of local Gag arrangements in the virion (see the Supporting Material for more detail). A small set of CG sites in one Gag was found to be in close contact (<1 nm) with CG sites in the adjacent Gag in the bundle. All of these sites resided in the CA_CTD domain, as labeled in Fig. 1. CG site 35 in one Gag was found to be in close contact with CG sites 42, 43, and 44 in the next. In addition, CG site 40 was found to be in close contact with CG site 43, and CG site 34 was in close contact with CG site 44. In subsequent discussions, these will be denoted as the close-contact CG sites. The atomic-level residues corresponding to the close-contact CG sites can be readily identified because there is a mathematical mapping between the atomistic and CG representations (25,26) (see the Supporting Material for the CG site- residue breakdown). It was found that the close-contact CG sites have a clear correspondence with the close-contact residues proposed recently at the atomistic level (3), where residues 153–159 (e.g., CG sites 34 and 35) were found to be in close contact with residues 212–219 (e.g., CG sites 43 and 44).

The initial configuration of the Gag/membrane virion is shown in the right panel of Fig. 1. The virion size was selected to match recent experimental electron cryotomography studies (2,3). A 125-nm-diameter liposome was created employing 135,802 HAS CG lipids (24); the number of lipids in the inner and outer leaflets was adjusted in order to balance the lipid densities in each leaflet. The single equilibrated bundle was then replicated and radially arranged such that the Gag MA domain in each was ∼0.5 nm off the membrane surface. Given that the 2034 Gags occupied ∼62% of the available surface area, there was still significant vacant space. The initial p6 hexagonal lattice spacing was 10 nm on average, slighter larger than the 8 nm spacing. There were a total of 268,012 CG sites in the simulations, effectively representing 6 × 10⁸ atoms, including water solvent.

Virion simulations were initiated with a brief annealing at 200 K, followed by equilibration runs of 10 ns and production runs of 100 ns at 273 and 308 K. The two temperatures were motivated based on experimental observations of ice crystals in the electron cryotomography experiments (2), in addition to the physiological temperature. It should be noted that the simulations are able to model physiological temperatures. The electron cryotomography experiments are usually performed at liquid nitrogen temperatures, while the virions are assembled at 310 K and then flash-frozen. The choice of 273 K in the simulations is designed to reflect, approximately, the electron cryotomography conditions. The initial annealing at 200 K indicated that the structures were also stable at even lower temperatures (which is not overly surprising). It should be further noted that CG time is not related to real-time, and in fact is generally a significant underestimate (by one or two orders of magnitude) (33). The final structures that were observed from the simulations were stable over the entire production run. Much longer simulations would be required to examine, for example, the transition from immature to mature virions via the HIV viral protease (1). The RNA site (CG site 60 in domain 11) was also fixed, and the remaining CG sites in domain 11 were bonded to it with a weak harmonic tether (e.g., as in the first term in Eq. 2), in order to model the RNA binding site (30). Variations where the RNA site was frozen and then unfrozen over various time intervals (e.g., every 20–50 ps) were also examined; the final Gag structures were essentially independent of the details of the mechanism whereby the RNA site was constrained. Future studies will resolve this component at a more refined level of detail, including an explicit CG model for RNA.

Determining the γ = 2 (shorter range) interaction strength between Gag CG sites required an array of parallel simulations where the interaction strengths were varied between different Gag CG sites (see the Appendix for the exact functional forms employed, Table 1 for parameterizations, and additional information in the Supporting Material). For each parameterization set, the effects on the structure of the virion were analyzed in terms of p6 order parameters, simulation snapshots, and radial distribution functions (see the Supporting Material for more information). In general, the effects of the γ = 2 (shorter range) interactions fell into two categories:

Category 1: They had little or no effect on Gag structure and were relatively insensitive to the exact interaction strength; or

Category 2: They had a significant effect on Gag structure and the resulting parameterizations had to be selected within a narrow range.

Those γ = 2 (shorter range) interactions that fell into Category 1 were not examined further. Those γ = 2 (shorter range) interactions that fell into Category 2 were targeted to be examined at an all-atom level of detail in order to justify the required parameterization at the CG scale.

The previously noted close-contact CG sites in the CA_CTD domain (see Fig. 1) were the only γ = 2 (shorter range) Category 2 interactions; all others were Category 1. These interactions were found to be responsible for maintaining p6 hexagonal order in the Gag assembly, and furthermore they required an interaction strength of ∼3–4 kcal mol⁻¹ to do so. (These sites also correspond well to the residues recently predicted to be in close contact (3)). Weaker interaction strengths for these CG sites, ∼1–1.5 kcal mol⁻¹, resulted in the significant reduction of p6 hexagonal symmetry in the Gag lattice (compare to Fig. 2). The term “enhanced interactions” will thus refer to the more strongly attractive interactions (e.g., in the range of 3–4 kcal mol⁻¹) between the close-contact CG sites in the CA_CTD domain. The term “nonenhanced” will apply when the interaction strength between these sites is weaker (e.g., 1–1.5 kcal mol⁻¹). Importantly, no other γ = 2 (shorter range) interactions between Gag domains could generate or maintain this p6 hexagonal lattice structure. As such, the regions of Gag that were targeted for further all-atom MD analysis were the CA_CTD and CA_NTD domains. Details of the atomic-level simulations will be described in the next section.

Figure 2.

Final CG simulation snapshots of shells of the enhanced (left column) and nonenhanced (right column) virion simulations at 273 K. In descending order from the top of the image the different domains are shown, lipids, MA, CA, and then the SP1/NC and RNA site. Only the CA domain with enhanced interactions exhibits p6 hexagonal order.

Atomic MD simulation of a hexamer of CA domains

To explore the key interactions in the CG model more closely, all-atom MD simulations of a fully solvated, isolated hexamer of CA domains were performed by replicating the all-atom CA domain structure that was used in the construction of the CG Gag model in a arrangement mirroring the recently proposed EM reconstruction (3). All-atom MD simulations were performed using the GROMACS MD package (34) with the GROMOS force field (35) and the simple-point charge water model. The time step was 0.002 ps and electrostatic interactions were calculated with a particle-mesh Ewald summation (36). A linear constraint solver algorithm was employed for all constraints (37). An initial energy minimization of the fully solvated and charge neutral system was performed followed by two 15-ns equilibrations under isothermal, isobaric conditions (1 atm). The first equilibration was done at 300 K, with the α-carbons frozen, while the second was at 273 K. A final simulation of 30 ns was used for the collection of potential-of-mean-force (PMF) data. Two temperatures were examined: the first at 273 K (38), to better reproduce the experimental EM conditions (2), and the second at 308 K to explore physiological conditions. Mutant simulations, described later, employed the same simulation protocol. The choice to only examine the CA domain with MD is largely motivated by the previously described CG result where only a few CG sites in the CA_CTD were responsible for maintaining the p6 hexagonal structure in the virion, and that this particular region exhibited a well-defined p6 hexagonal structure.

The CA domain in Gag is connected to the MA and SP1 domains (see Fig. 1); however, in the MD simulations, only the CA domain was modeled. Thus, three different constraints were examined to implicitly model the rest of Gag: Constraint 1 was a free boundary; The N-and C-terminus of the CA domain were unconstrained. Constraint 2 froze the first and last α-carbons in the structure, while Constraint 3 froze only the α-carbon at the N terminus. Deducing which constraint was “the best” is difficult. Ideally, a more fully resolved CA domain complete with linkers and surrounded by other CA domains would be best. At this point, Constraint 1 or 3 was the best in that it did not overly trap the system into a predetermined hexagonal arrangement and the results (at least in terms of the final PMFs) were quite similar. Constraint 2 most likely overly emphasized hexagonal structure.

Results

Coarse-grained virion simulation

Fig. 2 shows simulation snapshots of various shells of the entire HIV-1 immature virion using both enhanced (left column) and nonenhanced (right column) interaction conditions. Recall that simulations with enhanced γ = 2 interactions have attractive interaction strengths between the close-contact CG sites in the CA_CTD domain increased over the nonenhanced case shown in the left column (e.g., ∼3–4 kcal mol⁻¹ compared with ∼1 kcal mol⁻¹). The different domains are shown in descending order, beginning with the membrane. Overall, the radial spacing was in good agreement with that observed experimentally (2); however, and most importantly, only the CA domains in the system with enhanced CA_CTD interactions exhibited any significant p6 hexagonal order—which agrees with the experimental observation (2). In the case of the CA domain, clear rings of intact bundles of CA domains exist and, like the lattice structure recently proposed (3), the lattice does not fully occupy all of the available space, but instead coalesces into islands of p6 hexagonally ordered regions adjacent to unoccupied (or nearly unoccupied space). In the system with nonenhanced CA_CTD interactions, the CA domains very quickly reached greatly diminished p6 hexagonal order. From these simulations, it was also difficult to observe any well-defined order in the SP1 domain (lower panel in Fig. 2). However, the SP1 domain structure in the CG Gag model presented here originated from a recently proposed model structure (1,2), which will no doubt undergo further experimental refinement in the future.

Close-up images of the p6 hexagonal order in the WT CA domains are given in Fig. 3, where panel A is from a T = 273 K simulation while panel B is at 308 K. Importantly, the p6 immature Gag lattice order persists at physiological temperature. The p6 hexagonal order is found by locating the hole in each ring composed of six CA domains and then connecting the holes together. A hexagonal arrangement of holes then emerges, and the lattice spacing is found from the distance between them. The highlighted CA_CTD domains in yellow demonstrate how the p6 hexagonal order is generated. Each bundle of six Gag hexamers has relaxed into similar ringlike structures, and then each bundle coalesces with the others to form a p6 lattice. In both snapshots, it is evident how the coalesced bundles form isolated hexagonal islands of ordered Gags, separated by open space. At the edges of the islands, the p6 hexagonal structure is less well defined, and in some instances, it is possible to find collapsed bundles. It should be noted that only the enhanced γ = 2 interactions originating from the close-contact CG sites in the CA_CTD domain could stabilize this structure. Increasing the attraction strength of the other γ = 2 (shorter range) interactions in the CA_NTD, MA, or NC domains could not stabilize this p6 hexagonal lattice. In those cases, highly distorted structures much like that observed with the nonenhanced system in Fig. 2 were observed.

Figure 3.

CG simulation snapshots of the CA domain p6 hexagonal order: (A) from 273 K WT simulation, (B) WT result at 308 K, and (C) K158A/D197A double mutant at 308 K. Transparent blue (darker) regions depict the CA_NTD domain while yellow (lighter) regions correspond to the CA_CTD domain. The predominance of yellow (lighter) regions in panel C is due to the CA_NTD domains occupying the interstitial space between the hexameric bundles in the double mutant.

The degree of hexagonal order can be quantified by examining various hexagonal order parameters (39,40) (see the Supporting Material for background detail on the order parameters and Fig. S1). In particular, the value of $\sqrt{\langle {\mathit{\psi }}_{6,g}^2\rangle }$ measures the global hexagonal order associated with the inner ring of the CA_CTD hexameric bundle, while $\sqrt{\langle {\mathit{\psi }}_{6,l}^2\rangle }$ measures the average local hexagonal order of the CA_CTD hexameric bundles themselves. The value of $\sqrt{g_6\left(r^{\ast }\right)}$ measures the bond order correlation between pairs of hexameric bundles (the asterisk on the r, the distance between bundle pairs, indicates that the value is taken at the height of the first peak in the correlation function) where

$$g_6\left(r\right)=\langle {\mathit{\psi }}_{6,l}^{\ast }\left(0\right){\mathit{\psi }}_{6,l}\left(r\right)\rangle .$$

Generally speaking, $\sqrt{\langle {\mathit{\psi }}_{6,g}^2\rangle }>0.6$ indicates that the lattice spacing between the centers of the rings arises from strongly hexagonal correlations. Likewise, $\sqrt{\langle {\mathit{\psi }}_{6,l}^2\rangle }>0.6$ indicates that each bundle is highly ordered with a hexagonal arrangement of CA_CTD domains. The value of $\sqrt{g_6\left(r^{\ast }\right)}$ is quite sensitive and indicates that the orientation of one bundle is correlated to the next. When all three correlation functions have nonzero values, then the system exhibits strong p6 hexagonal correlations. If one of the order parameters is near zero, then, strictly speaking p6 order is not evident, even if the other order parameters are nonzero. Table 2 gives results for the WT, the K158A/D197A double mutant, and the WT nonenhanced CA_CTD CG interaction system. The mutant results will be discussed in more detail shortly. Across the board, all three systems have $\sqrt{\langle {\mathit{\psi }}_{6,g}^2\rangle }$ at ∼0.7, suggesting strong hexagonal order is associated with the centers of the rings of the CA_CTD hexameric bundles. However, the WT system with enhanced CA_CTD interactions has $\sqrt{\langle {\mathit{\psi }}_{6,l}^2\rangle }$ at ∼0.8, much higher than the other systems, indicating that the hexameric bundles themselves are strongly ordered and intact. This is also visually clear from Fig. 3, A and B. Furthermore, only this system has a nonnegligible $\sqrt{g_6\left(r^{\ast }\right)}$, indicating that there is a short-ranged correlation between CA_CTD hexameric bundles. It is also possible that with much longer simulations, $\sqrt{g_6\left(r^{\ast }\right)}$ would further increase as the p6 hexagonal structure further anneals; however, the present CG simulations were already of a large computation scale.

Table 2.

Bond orientational p6 symmetry order parameters

System	$\sqrt{\langle {\psi }_{6,g}^2\rangle }$	$\sqrt{\langle {\psi }_{6,l}^2\rangle }$	$\sqrt{g_6\left(r^{\ast }\right)}$
WT	0.77 ± 0.1	0.89 ± 0.09	0.42
K158A/D197A	0.75 ± 0.1	0.65 ± 0.07	0.01
WT (nonenhanced)	0.76 ± 0.1	0.54 ± 0.08	0.05

The asterisk indicates the value of g₆ at the first peak of the correlation function (∼ r =7 nm).

These CG simulation results, combined with the fact that only the enhanced interactions in the CA_CTD domain can stabilize the hexameric bundles, suggest that it is the interactions in the residues corresponding to the close-contact CG sites in the CA_CTD domain that are largely responsible for forming and maintaining the p6 hexameric lattice structure in the immature HIV-1 virion. Further work, including an even more refined CG model and perhaps also utilizing new experimental data, will be required to deduce a high-resolution structure where the actual Gag domains could be located with a high degree of accuracy. At this stage, given the results of the previous order parameter analysis, the hexameric structure is reminiscent of the Briggs reconstruction, although thermal fluctuations and the inherent loss of degrees-of-freedom associated with the highly CG model allows for other possible reconstructions to describe the Gag hexameric structures in the simulation.

All-atom MD simulation

The large-scale CG results indicated that the enhanced interactions in the close-contact CG sites in the CA_CTD domain may be responsible for maintaining the p6 hexagonal structure in the immature virion. Modulation of other interactions in other domains did not result in p6 hexagonal lattice stabilization. It therefore needed to be demonstrated that these enhanced interactions at the CG scale are faithful representations of the average interactions that would be observed at the underlying all-atom level. Here is where the hybrid multiscale aspect of this work arises, as all-atom simulations were then employed in an inverse fashion to identify and better understand the existence of the enhanced interactions that were used at the CG scale. This can be accomplished by calculating a PMF (see the Supporting Material for details of this calculation).

All-atom MD simulations as previously described in Methods were therefore performed. The PMF was calculated for all three boundary conditions, and averaged over all the close-contact CG sites. Fig. 4 shows the WT PMF at 273 K in solid representation where the light-shaded error bars arise from the three different boundary conditions (the PMF for the system at 308 K was well within the light-shaded error bars). The minimum of the energy is ∼3.5 kcal mol⁻¹, suggesting that indeed there is a real enhanced attractive interaction between the close-contact CG sites in the WT hexamer and that the CG model with enhanced γ = 2 interactions is effectively modeling this behavior. Also, a repulsive wall at ∼1 nm justifies the excluded volume parameter, σ_L (see Appendix), used in the γ = 2 (shorter range) interactions.

Figure 4.

Potential of mean force (PMF) U(r) for the residues from all-atom MD simulations that correspond to the enhanced interaction CG sites. The black curve is for the WT at 273 K (with a molecular snapshot in the lower-right of the image) with the shaded error bars giving the fluctuations due to the three different constraints (free, N-terminal α-carbon frozen, N- and C-terminal α-carbon frozen). The PMF at 308 K was well within the error bars. The shaded (red online) curve is for the K158A/D197A double mutant at 308 K (a similar PMF was found at 273 K) with a snapshot in the upper left. In each of the molecular structure snapshots, the residues corresponding to CG sites 35 and 42 are highlighted. The inner ring connects CG site 42 on adjacent CA domains, giving a qualitative estimate of the size of the hexamer bundle pore in the CA_NTD domain. The line between CG sites 35 and 42 shows the interaction between CC sites on adjacent domains. In the K158A/D197A double mutant, the mutated residues are shown by the dots (D197A dark shaded, purple online and K158A light shaded, cyan online).

A simulation snapshot of the WT CA hexamer is given in the lower-right of Fig. 4 for the 273 K system. In order to visualize the size of the hole at the center of the hexamer (and hence the size of the hexamer bundle), CG site 42 on each CA_CTD domain was connected to its adjacent CG site 42, giving the red hexagonal ring superimposed on the snapshot. The interaction with CG site 35 on the neighboring CA_CTD is shown by the additional red line. Overall, a spread-out star-map structure results, and the distortions from a perfect hexagonal order are evident.

K158A/D197A double mutant

Two different mutations were also examined based on recent mutagenesis studies. The first was inspired by the work in von Schwedler et al. (10) and involved a two point mutation, K158A and D197A. Experimentally, these mutations resulted in reduced particle formation and altered virion morphologies, presumably via disruptions during Gag assembly. The second set of mutations were inspired by the observations in Briggs et al. (3), where it was noted that residues 153–159 were in close proximity to residues 212–219 in the Gag bundle. Combining this with the close-contact CG sites, a two-point mutation was thus selected: D152A (corresponding to CG site 35) and K201A (corresponding to CG site 42). The results presented here will focus on the K158A and D197A mutation, because this mutation has been directly examined with experimental mutagenesis studies (10); however, the behavior of the D152A/K201A mutant was remarkably similar.

All-atom MD simulations as previously described for the WT were performed. The hexameric structure of the CA domain, in all mutations, was preserved, but slightly altered. The PMF from all-atom MD simulations for the K158A and D197A mutation at 308 K is shown in red in Fig. 4. (The PMF at 273 K, and for the D152A/K201A mutant was quite similar.) The PMF in the mutant exhibits a minimum at ∼0.5 nm, a location almost one-half of that observed in the WT case. The well itself is also slightly deeper at ∼−4 kcal mol⁻¹. The multiple potential wells arise because the PMFs between close-contact CG sites were averaged together. The mutant PMF suggests that some sort of collapse of the hexameric structure has occurred. Indeed, when a simulation snapshot from the all-atom MD is examined (upper left of Fig. 4), this seems to be the case. If the same ring of adjacent CG sites 42 is constructed, the resulting ring is significantly smaller than in the WT case (in fact, it has decreased ∼34%). It should be noted that the mutated sites (shown as dots) are quite close to the CG sites, and thus are part of the structural collapse. These simulation results suggest that the double mutation results in a partial collapse of the hexameric structure that is most likely hydrophobic in origin, because the substitutions were polar groups by alanines. At larger length-scales, the effect can also be examined.

The enhanced CA_CTD interactions for the close-contact CG sites can be refined to model the K158A/D197A mutation at 308 K by decreasing the excluded volume parameter, σ_L, to 0.5 nm, and by increasing the well depth to −4.2 kcal mol⁻¹. The resulting structure of the HIV-1 mutant virion at the CG simulation level is shown in Fig. 3 C, where is it evident that the well-resolved rings of CA domains in the WT case have partially collapsed upon themselves. One will also note that the CA_CTD domains appear more yellow than in the WT case. This is because the semitransparent blue-colored CA_NTD domains have actually splayed out somewhat into the interstitial space, rather than residing directly above the CA_CTD domains. (This rearrangement can also be detected in Fig. S1, where the short-ranged hexameric correlations—i.e., those <4 nm—have been smeared out.)

Table 2 gives further insight into the role of the mutation on the structure of the CA_CTD domains. The local hexagonal order of the hexameric bundles has been decreased significantly compared to the WT (e.g., $\sqrt{\langle {\mathit{\psi }}_{6,l}^2\rangle }$ is ∼0.6) and only contains weak hexagonal correlations. Furthermore, there is essentially no correlation between the orientation of one CA_CTD hexameric bundle and its nearest neighbor. Thus, the mutation seems to have the effect of strongly disrupting p6 hexagonal order at the local level.

These results can be connected with the experimentally observed reduced particle formation and altered virion morphologies of key mutants. The mutation, at least at this stage in virion formation, appears to contract the Gag lattice at the expense of p6 order. This alteration could have an effect on the Gag assembly and virion budding process, as well as in the later stages of the HIV-1 maturation cycle, i.e., Gag processing by the viral protease (1).

Concluding Remarks

This article has employed coarse-grained and all-atom simulation in a hybrid multiscale fashion to examine the immature HIV-1 virion. The approach taken here was not to propose a single set of CG parameters, but instead to explore a range of them in critical regions, with the aim to identify the key interactions at the CG level that are critical to maintaining the experimentally observed structure of the virion. Then, the information at the CG level was used in an inverse fashion to guide select all-atom MD simulations of select regions in order to refine the CG model.

For the WT immature HIV-1 virion, a few CG sites in the CA_CTD domain were found to be responsible for maintaining the p6 hexagonal symmetry of the entire CA domain in the immature Gag lattice of the virion. No other interactions could achieve this behavior at the CG level. Moreover, to stabilize this region, the interaction strength between CA_CTD CG sites had to be in the range of ∼3–4 kcal mol⁻¹. All-atom MD simulations of an isolated hexamer of CA domains, as guided by the large-scale CG modeling, confirmed that there exists a real enhanced interaction in this region, thereby refining the CG parameterization.

Computational mutagenesis studies produced similarly interesting results, and they suggested that some mutations such as K158A/D197A may have the effect of overstabilizing and even strongly distorting the hexameric CA domain bundle structure in the immature virion Gag lattice. It is possible that the effect of mutations, in terms of virion structure and infectivity, may have something to do with these alterations in the local arrangements of hexameric Gag bundles, especially at the CA domain location. It will be interesting in the future 1), to confirm whether this is the origin of the altered virion structure and reduced infectivity as found from experimental mutagenesis studies (10), and 2), to study other possible mutants that may affect the Gag lattice in the immature virion.

Appendix: Functional forms for the Interactions in the Coarse-Grained Model

In this Appendix, the functional forms for the interactions given in Eq. 1 will be described. In all instances,

$$r=\left|\mathbf{r}\right|=\left|{\mathbf{r}}_{i_{\alpha }}-{\mathbf{r}}_{j_{\beta }}\right|,$$

where ${\mathbf{r}}_{i_{\mathit{\alpha }}}$is the Cartesian location of CG site i_α; likewise for j_β. For the Gag CG sites, e is a unit normal along the dipole moment of the CG site; and for the lipid sites, it gives the orientation of the CG lipids, in this case modeled with the HAS lipid model (24,27), which combines a modified Gay-Berne ellipsoidal liquid crystal model (41) with a systematically obtained force field using the multiscale coarse-graining (42,43) approach. The terms in Eq. 1 of the main text are as follows:

Term 1: γ = 1, elastic network ($u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(1\right)}$)

This interaction gives the elastic network for the various domains as well as connects different domains together. It also constrains the orientation of the dipole moments, e, of the Gag CG sites to the orientations specified in the original Gag domain CG elastic network. The functional form for Ω in Eq. 2 below couples the dipole moments to the geometry of the domain, although other forms could also be employed. The functional form is given by

$$\begin{array}{c}{u}_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(1\right)}=\frac{k_E}{2}{\left(r-r_0\right)}^2+\frac{k_{\Omega }}{2}\left[{\left(\Omega -{\Omega }_0\right)}^2\right]\\ \Omega ={\mathbf{e}}_{i_{\mathit{\alpha }}}•{\widehat{\mathbf{r}}}_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}-{\mathbf{e}}_{j_{\mathit{\beta }}}•{\widehat{\mathbf{r}}}_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}\end{array},$$ (2)

where Ω₀ is the initial value in the starting structure.

Term 2: γ = 2, shorter-range interaction ($u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(2\right)}$)

This interaction models the shorter range of the Gag CG sites, the corresponding effective attractive van der Waals interactions at the CG level, and the lipid headgroup-Gag interaction. The functional form is given by

$$u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(2\right)}=4{\mathit{\varepsilon }}_L\left[{\left(\frac{{\sigma }_L}{r}\right)}^{12}-{\left(\frac{{\sigma }_L}{r}\right)}^6\right].$$ (3)

Further details can be found in the Supporting Material. The excluded volume, σ_L, was set to 1 nm (see Table 1 and the Supporting Material for a more detailed justification).

Term 3: γ = 3, lipid-protein, and lipid-lipid CG interaction ($u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(3\right)}$)

This interaction modeled the interaction between the CG lipids as well as between the Gag CG sites and the center of the lipid ellipsoid. In the case of the lipids, the HAS approach was employed (24), and the functional form is given by

$$\begin{array}{c}{u}_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(3\right)}=4{\mathit{\varepsilon }}_0{\mathit{\varepsilon }}_G\left(\widehat{\mathbf{r}},{\mathbf{e}}_{i_{\mathit{\alpha }}},{\mathbf{e}}_{j_{\mathit{\beta }}}\right)\left[{\mathit{\varsigma }}^{-12}-{\mathit{\varsigma }}^{-6}\right]+\Delta U_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}\left(r\right)\\ \mathit{\varsigma }=\frac{r-\mathit{\sigma }\left(\widehat{\mathbf{r}},{\mathbf{e}}_{i_{\mathit{\alpha }}},{\mathbf{e}}_{j_{\mathit{\beta }}}\right)+{\mathit{\sigma }}_0}{{\mathit{\sigma }}_0}\end{array},$$ (4)

where $\Delta U_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}\left(r\right)$ is the systematic component of the HAS interaction and is obtained from a multiscale coarse-graining (42,43) analysis of MD-generated data for a specific bilayer. See the Supporting Material for additional details regarding the HAS lipid model.

Term 4: γ = 4, charge, and dipolar electrostatics ($u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(4\right)}$)

Each CG site in the Gag contains both screened charge and dipolar electrostatics as found from the original structures used to generate the different domains (e.g., the MA, CA, and NC domains). In those domains where no structures were available, the charge, q, as well as dipole moment, μ, were set to zero. The functional form for the screened interaction relies on a Yukawa screened charge-charge, charge-dipole, dipole-dipole interaction (32) and has the functional form

$$u_{i_{\mathit{\alpha }}{j}_{\mathit{\beta }}}^{\left(4\right)}=(q_{i_{\mathit{\alpha }}}{q}_{j_{\mathit{\beta }}}-q_{i_{\mathit{\alpha }}}{\mathit{\mu }}_{j_{\mathit{\beta }}}{\mathbf{e}}_{j_{\mathit{\beta }}}•{\nabla }_{\mathbf{r}}+{\mathit{\mu }}_{i_{\mathit{\alpha }}}{q}_{j_{\mathit{\beta }}}{\mathbf{e}}_{i_{\mathit{\alpha }}}•{\nabla }_{\mathbf{r}}-{\mathit{\mu }}_{j_{\mathit{\beta }}}{\mathit{\mu }}_{i_{\mathit{\alpha }}}{\mathbf{e}}_{i_{\mathit{\alpha }}}•{\nabla }_{\mathbf{r}}{\mathbf{e}}_{j_{\mathit{\beta }}}•{\nabla }_{\mathbf{r}})\Psi \left({\mathit{\alpha }}_Y,r\right),$$ (5)

where

$$\Psi \left({\mathit{\alpha }}_Y,r\right)=\exp \left[-{\mathit{\alpha }}_{Y}r\right]/r$$

is the screened Yukawa interaction and α_Y is the screening coefficient (see Table 1 for parameterizations).