Correction to “Remarkable Insensitivity of Protein Diffusion to Protein Charge”

Abstract

Calculations of diffusion constants from molecular dynamics (MD) simulations require finite-size corrections. (1) The diffusion constant D_MD calculated with periodic boundary conditions (PBC) employed in MD needs correction for hydrodynamic effects of viscous solvent flow within the lattice of periodically replicated images of the tagged diffusive particle. For a cubic simulation box of length L, one obtains the diffusion constant of the infinite system D from the PBC value D_MD according to the following equation. (1) We have recently reported MD simulations of the diffusion constants of two proteins, green fluorescent protein (GFP) and plastocyanin (PC), in TIP3P water. (3) The finite-size term in eq 1 was incorrectly calculated, and the corrected D values in Table 2 of ref (3) were close to the MD values D_MD. When we re-examined the reported values, we noticed that D ≃ 257 μm²/s from eq 1 significantly exceeds D_MD ≃ 20.8 μm²/s for the system size of L ≃ 86 Å (≃18,000 TIP3P water molecules). The finite-size correction, ≃236 μm²/s, is thus significantly higher than the MD result itself (η = 0.306 cP for TIP3P water (4) was applied in eq 1). Given approximations involved in deriving the correction term, (1) this observation puts under doubt the validity of D calculated according to eq 1. Here, we present additional data from MD simulations of GFP and PC diffusion in simulation boxes of different size to show that eq 1 highly overestimates D(L) (Figure 1 and Table 1). The MD simulation protocol follows ref (3), with modifications to the box size and the number of water molecules. From charge mutants studied in ref (3), only the wild-type GFP with a charge of −6 is considered here. PC is in its reduced state with the charge of −9. We find strongly divergent values of D(L) and D_MD(L) (Figure 1), while extrapolation to L^–1 → 0 gives consistent results for D(∞) and D_MD(∞) (black dots in Figure 1). Figure 1. D_MD(L) (blue) and size-corrected D(L) (red, eq 1) vs L^–1 for GFP and PC proteins. The solid lines are linear fits of the MD results (points). The black dots indicate crossing of two interpolations to the infinite-size limit L^–1 → 0. Equilibrium trajectories for 50 ns, with dynamics calculated from 10 ns trajectories with the integration time of 1 fs and saving time of 5 fs. Same simulation parameters for PC, except for 100 ns equilibration trajectories. Variations between D_F(L) data points are caused by corresponding variations in the force variance since τ_m is independent of L. D_F refers to eq 2. We have also calculated diffusion constants from the dynamics of the force F acting on the protein from water. (5−7) D is calculated from the corrected (3,7) Kirkwood equation in which the memory function relaxation time τ_m replaces the force relaxation time in the original formulation (5) This research was supported by the National Science Foundation (CHE-2154465). This work used CPU resources through allocation MCB080071 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program and through ASU’s Research Computing. This article references 10 other publications. This article has not yet been cited by other publications.