Energy landscape of all-atom protein-protein interactions revealed by multiscale enhanced sampling

Abstract

Protein-protein interactions are regulated by a subtle balance of complicated atomic interactions and solvation at the interface. To understand such an elusive phenomenon, it is necessary to thoroughly survey the large configurational space from the stable complex structure to the dissociated states using the all-atom model in explicit solvent and to delineate the energy landscape of protein-protein interactions. In this study, we carried out a multiscale enhanced sampling (MSES) simulation of the formation of a barnase-barstar complex, which is a protein complex characterized by an extraordinary tight and fast binding, to determine the energy landscape of atomistic protein-protein interactions. The MSES adopts a multicopy and multiscale scheme to enable for the enhanced sampling of the all-atom model of large proteins including explicit solvent. During the 100-ns MSES simulation of the barnase-barstar system, we observed the association-dissociation processes of the atomistic protein complex in solution several times, which contained not only the native complex structure but also fully non-native configurations. The sampled distributions suggest that a large variety of non-native states went downhill to the stable complex structure, like a fast folding on a funnel-like potential. This funnel landscape is attributed to dominant configurations in the early stage of the association process characterized by near-native orientations, which will accelerate the native inter-molecular interactions. These configurations are guided mostly by the shape complementarity between barnase and barstar, and lead to the fast formation of the final complex structure along the downhill energy landscape.

Figure 1. MSES simulation.

(A) Probability distributions of V _MMCG, P(V _MMCG), defined in Eq. 1 for 12 replicas of MSES simulation. (B) Time course of V _MMCG for a representative model replica, i.e., the replica fixed not by k _MMCG, but by the configuration. (C–E) Quantities from the unbiased MSES ensemble (with k _MMCG = 0) as a function of simulation time: Root-mean-square displacement for C_α atoms (C_α RMSD) of barstar after fitting to barnase, RMSD_bs (C), center-of-mass (COM) distance between two COMs for barstar and barnase, respectively, d _COM (D), and number of polar contacts found in eight inter-molecular pairs, #3, 4, 6, 7, 8, 11, 12, and 13, listed in Table 1 (E). In (D), d _COM in conventional equilibrium MD simulation starting from complex structure (MM simulation) is also shown by red. In (F) and (G), arrangements of barstar observed in the unbiased MSES ensemble and in MM simulation are shown, respectively. Both coordinates were superimposed on barnase.

Figure 2. Funnel landscape of barnase-barstar interaction.

Distributions of centers of mass (COM) of barstar with various ranges of fraction of native inter-molecular contacts formed (Q) after superimposing barnase in unbiased ensemble of MSES simulation. (Top) Three-dimensional distributions at Q<0.2 (blue), 0.2<Q<0.4 (green), 0.4<Q<0.7 (yellow), and Q>0.7 (red). (Bottom) Distributions onto x-y plane and x-z plane at depicted Q ranges. The x-y plane was defined to be orthogonal to the vector connecting the two COM's of barnase and barstar (z-axis), and x-axis being the direction of the vector from C_α of Arg87 to C_α of Arg83 of barnase.

Figure 3. Narrowing of configurational space with increased Q.

Occupancy maps of barstar C_α atoms with various Q ranges in unbiased replica of MSES simulation generated by VMD . Three-dimensional grids are created using a bin width of 2 Å and the grid points occupied by C_α atoms in the unbiased MSES ensemble are shown in red. The coordinates are superimposed on the barnase molecule, which is shown in gray.

Figure 4. Free energy surfaces in terms of Q value.

(A) Average inter-molecular distance calculated between native contacts, d _N, which were given by average of inter-molecular distances for non-hydrogen atoms in simulation snapshots having specified Q value. (B) Number of inter-molecular contacts, N _C, which are non-hydrogen atoms within 4 Å. Number of native contacts found in the native complex structure is also shown. (C) Number of hydrated waters at interface, N _W, defined by oxygen atoms within 4 Å from interfacial non-hydrogen atoms. (D) Numbers of polar contacts for interfaces 1 and 2, respectively. The vertical lines are the standard deviations for each value.

Figure 5. 2-D Free energy surfaces in terms of Q value.

2-D free energy surfaces on x-y plane of probability distribution (FES), and numbers of contact atoms (N _C) and hydrated waters (N _W) are shown at depicted three Q ranges. The position is defined here as the center of mass of the interfacial atoms with inter-molecular contacts after superimposition to the crystal structure of barnase. The cartoon representation of barnase is also drawn for clarity in the N _C figure at 0.4<Q<0.7.

Figure 6. Formations of two localized interfaces.

(A) 2D representation of FES along RMSD1 (non-hydrogen-atom RMSD for interface 1) and RMSD2 (non-hydrogen-atom RMSD for interface 2). In (B), the situation is the same but when both interfaces are formed. (C) and (D) show probability distributions along RMSD1 and RMSD2, respectively, when designated number of polar contacts are formed. (E) Native polar contacts at interfaces 1 and 2 (identifier is same as in Table 1). (F) Side-chain positions of interfaces 1 (red) and 2 (blue) of barnase and barstar.

Figure 7. Free energy surfaces for two localized interfaces.

2-D free energy surfaces of barstar position on x-y plane of barnase: Two distributions are plotted on same figure for centers of mass of barstar residues comprising interface 1 (Tyr29, Asn33, and Asp39: upper right) and that for interface 2 (Asp35 and Glu76: lower left). In A–H, the distributions are drawn for the unbiased MSES ensemble under the respective conditions that the polar contacts given at the bottom (the identifier defined in Table 1) are formed. “Interface 1”, “interface 2”, and “interfaces 1&2” indicate the structures when all the polar contacts in interface 1 and/or 2 are formed, respectively. In I–K, the distributions obtained in the MM simulations starting from the complex structure are shown for the wild type (I) and the two mutants, bs:D35A (J) and bs:D39A (K).

Figure 8. Downhill FES via shape complementarity.

(A) Five snapshots of helix 3 (residues 34–42) of barstar for Q<0.1, together with helix 3 in native complex structure (black; in view from bottom). The white space filing model is barnase in which Arg59 (blue) and His102 (red) are colored in the figure. (B) and (C) 2D representation of FES along COM distance, d _COM, and rigid-body rotation angle of barstar from native complex structure, defined by change in direction of vector connecting Cα atoms of Asn33 and Asp83 between snapshot and native complex structure (see Fig. S3): (B) MSES simulation and (C) MM simulation.