High resolution approach to the native state ensemble kinetics and thermodynamics

Abstract

Many biologically interesting functions such as allosteric switching or protein-ligand binding are determined by the kinetics and mechanisms of transitions between various conformational substates of the native basin of globular proteins. To advance our understanding of these processes, we constructed a two-dimensional free energy surface (FES) of the native basin of a small globular protein, Trp-cage. The corresponding order parameters were defined using two native substructures of Trp-cage. These calculations were based on extensive explicit water all-atom molecular dynamics simulations. Using the obtained two-dimensional FES, we studied the transition kinetics between two Trp-cage conformations, finding that switching process shows a borderline behavior between diffusive and weakly-activated dynamics. The transition is well-characterized kinetically as a biexponential process. We also introduced a new one-dimensional reaction coordinate for the conformational transition, finding reasonable qualitative agreement with the two-dimensional kinetics results. We investigated the distribution of all the 38 native nuclear magnetic resonance structures on the obtained FES, analyzing interactions that stabilize specific low-energy conformations. Finally, we constructed a FES for the same system but with simple dielectric model of water instead of explicit water, finding that the results were surprisingly similar in a small region centered on the native conformations. The dissimilarities between the explicit and implicit model on the larger-scale point to the important role of water in mediating interactions between amino acid residues.

FIGURE 1

A sketch of a hierarchical organization of native substates at the bottom of the energy funnel is shown. Native state on this schematic picture consists of two substates I and J interchanging on some timescale. On shorter timescales and higher resolution in energy, each one of them also splits into substates. The substate I splits into G and H, which split further into yet another level of substates and corresponding microbasins.

FIGURE 2

Two-dimensional free energy surface (2D-FES) of Trp-cage native basin as a function of collective coordinates Q₁ and Q₃₇, indicating corresponding similarities to NMR models 1 and 37, was obtained using WHAM in 914 simulation windows (see Methods and Data S1). An all-atom MD simulation of 1.2 ns in duration was carried out in each window. Open circles, marking FES, represent the 38 NMR structures in the Q₁ and Q₃₇ coordinates. Spacing between contour lines is 0.22 kcal/mol (0.37 kT). White rectangles mark the deepest and the second deepest basins corresponding to model 1 (lower right corner) and model 16 (upper left corner), respectively. The difference of ∼0.6 kT in free energy is created by rotation of Tyr-3, cation-π interaction between Arg-16 and Trp-6 and disappearance of 3-10 α-helix.

FIGURE 3

Brownian dynamics of the transition between states corresponding to NMR structures numbered 1 and 37. (top) Two sample trajectories: one (white) is from the peak of FPT distribution in panel bottom right, and the other one (magenta) is from the shoulder. (bottom left) Part of the surface with trajectory shown in higher resolution revealing finer features of the surface and their influence on the trajectory. (bottom right) First passage time (FPT) distributions for conformational transition between 1 and 37. FPTs were computed at two additional temperatures to obtain the corresponding coefficients of variation, to provide reference for categorizing the nature of the dynamical regime at room temperature.

FIGURE 4

Arrhenius plot shows the dependence of the mean FPT with temperature for the conformational transition from 37 to 1 on fixed FES (computed at 282 K), where the FES is temperature-independent. The inset zooms into higher temperature region using a semireciprocal plot. Two regimes are clearly seen: exponential at low temperatures, and linear at high temperatures. The near room temperature (282 K) result is near the crossover.

FIGURE 5

FES was computed for the dielectric solvent model (see text). Two of the partially unfolded structures from the open square are shown in the corners. The lower basin is absent in the explicit solvent FES. On the other hand, a number of barriers have disappeared in the DSM FES. The vicinities of the reference points 1 and 37 are very similar between explicit and DSM FESs.

FIGURE 6

The difference between explicit solvent FES and DSM FES. In the Qs ≲ 0.95 region, it mainly represents the hydrophobic effect. The structures in the corners are taken from the hydrophobically favorable and unfavorable regions. The hydrophobic core is shown in van der Waals spheres, so that its opening is visually noticeable.