Longer simulations sample larger subspaces of conformations while maintaining robust mechanisms of motion

Abstract

Recent studies suggest that protein motions observed in molecular simulations are related to biochemical activities, although the computed time scales do not necessarily match those of the experimentally observed processes. The molecular origin of this conflicting observation is explored here for a test protein, cyanovirin-N (CV-N), through a series of molecular dynamics simulations that span a time range of three orders of magnitude up to 0.4 μs. Strikingly, increasing the simulation time leads to an approximately uniform amplification of the motional sizes, while maintaining the same conformational mechanics. Residue fluctuations exhibit amplitudes of 1-2 Å in the nanosecond simulations, whereas their average sizes increase by a factor of 4-5 in the microsecond regime. The mean-square displacements averaged over all residues (y) exhibit a power law dependence of the form y ∝ x(0.26) on the simulation time (x). Essential dynamics analysis of the trajectories, on the other hand, demonstrates that CV-N has robust preferences to undergo specific types of motions that already can be detected at short simulation times, provided that multiple runs are performed and carefully analyzed.

Keywords: equilibrium fluctuations of cyanovirin-N; global motions; molecular dynamics simulations; power law; structure-encoded dynamics.

Figure 1

Experimental and computational literature data exhibit similar motional behavior for short and long times. (A) Order parameters S² of G protein B 3 extracted from NMR data: spin-relaxation, dashed black; and RDC, solid black. (B) Order parameters S² of GB1 extracted from MD trajectories of 10 ns (dashed black) and 175 ns (solid black). Secondary structure elements are depicted at the top of each panel.

Figure 2

Mean-square-fluctuation profiles of CV-N from simulations with different durations. The MSFs <(ΔR_i)²> of residues averaged over twenty independent 1 ns, sixteen 5 ns, twelve 25 ns, eight 100 ns and two 400 ns runs are shown in blue, red, green, magenta, and black, respectively. Secondary structure elements of the protein are depicted at the top with disulfide bonds represented by dashed yellow lines and residues in the sugar binding sites labeled by asterisks. The inset shows the CV-N structure in ribbon representation. Domains A and B are colored green and blue, respectively, and the two sugar binding sites are colored red. Amino acid sequence positions are labeled for every 10^th residue.

Figure 3

The magnitude of the fluctuations increases with increasing simulation time. (A) and (B) Comparison of MSFs for different simulations. (A) <(ΔR_i)²> of residue i in the 5 ns simulation (y axis) is plotted against <(ΔR_i)²> of the same residue in the 1 ns simulation (x axis). (B) <(ΔR_i)²> of residue i in the 400 ns simulation (y axis) versus <(ΔR_i)²> of the same residue in the 25 ns simulation (x axis). (C) The relationship between MSF and simulation time is a power function, with exponent 0.26. The MSF scaling factors for different simulations are plotted against the corresponding ratios of simulation lengths.

Figure 4

Power law exponents for CV-N residues. The results are shown on domain A (green), and domain B (blue). The upper abscissa displays residue positions in domain A, and the lower abscissa, the residue positions in domain B. The secondary structures with disulfide bonds (dashed yellow lines) are represented on the top, and residues comprising the binding sites are labeled by asterisks.

Figure 5

Shared global mode between theory and simulations. The CV-N backbone structure is shown in tube representation (red) with the directions of the global motion for the 1 ns simulation (A) and the 400 ns simulation (B), or the second mode predicted by the ANM (C) depicted by blue, green, and yellow arrows, respectively. The correlation coefficients between pairs of modes displayed are 0.77 (blue/green), 0.69 (blue/yellow), and 0.64 (green/yellow). Primary sequence positions are labeled for every 10^th residue.