Accuracy and Reproducibility of Lipari-Szabo Order Parameters From Molecular Dynamics

Abstract

The Lipari-Szabo generalized order parameter probes the picosecond to nanosecond time scale motions of a protein and is useful for rationalizing a multitude of biological processes such as protein recognition and ligand binding. Although these fast motions are an important and intrinsic property of proteins, it remains unclear what simulation conditions are most suitable to reproduce methyl symmetry axis side chain order parameter data (S_axis²) from molecular dynamics simulations. In this study, we show that, while S_axis² tends to converge within tens of nanoseconds, it is essential to run 10 to 20 replicas starting from configurations close to the experimental structure to obtain the best agreement with experimental S_axis² values. Additionally, in a comparison of force fields, AMBER ff14SB outperforms CHARMM36m in accurately capturing these fast time scale motions, and we suggest that the origin of this performance gap is likely attributed to differences in side chain torsional parametrization and not due to differences in the global protein conformations sampled by the force fields. This study provides insight into obtaining accurate and reproducible S_axis² values from molecular simulations and underscores the necessity of using replica simulations to compute equilibrium properties.

Figure 1:

r² w.r.t exp bootstrapping results for the CHARMM36m force field.

Figure 2:

r² w.r.t exp bootstrapping results for the AMBER ff14SB force field.

Figure 3:

r² w.r.t self bootstrapping results for the CHARMM36m force field.

Figure 4:

r² w.r.t self bootstrapping results for the AMBER ff14SB force field.

Figure 5:

All simulation data was used (i.e., N = 100 and L = 30 ns.) A-C). Scatter plot between S² from experiment, CHARMM36m, and AMBER ff14SB. Residue identity is coded by color while protein identity is coded by shape. MUE is mean unsigned error, and τ is Kendall’s tau coefficient. D). Kernel density estimates of S² values.

Figure 6:

r², Kendall’s tau coefficient (τ), and mean unsigned error (MUE) of each residue type against experiment. All simulation data (i.e., N = 100 and L = 30 ns) are used.

Figure 7:

Alpha carbon RMSD (Å) heat map between the centroids of the top five clusters from CHARMM36m, AMBER ff14SB, as well as the experimental structure.