Coarse Grained Simulations of a Small Peptide: Effects of Finite Damping and Hydrodynamic Interactions

In the coarse grained Brownian Dynamics simulation method the many solvent molecules are replaced by random thermal kicks and an effective friction acting on the particles of interest. For Brownian Dynamics the friction has to be so strong that the particles’ velocities are damped much faster than the duration of an integration timestep. Here we show that this conceptual limit can be dropped with an analytic integration of the equations of damped motion. In the resulting Langevin integration scheme our recently proposed approximate form of the hydrodynamic interactions between the particles can be incorparated conveniently, leading to a fast multi-particle propagation scheme, which captures more of the short-time and short-range solvent effects than standard BD. Comparing the dynamics of a bead-spring model of a short peptide, we recommend to run simulations of small biological molecules with the Langevin type finite damping and to include the hydrodynamic interactions.

💡 Research Summary

The manuscript revisits a fundamental limitation of conventional Brownian Dynamics (BD) simulations, namely the assumption of an infinitely large friction coefficient (γ) that forces particle velocities to decay much faster than the integration timestep (Δt). While this overdamped approximation is acceptable for mesoscopic systems, it becomes questionable for nanoscale biomolecules such as short peptides, where solvent collisions are not completely suppressed and short‑time dynamics are important.
To overcome this, the authors derive an analytical integration of the Langevin equation over a finite timestep, preserving both the deterministic force term and the stochastic thermal kick. The resulting update formula for the velocity,
( v(t+Δt)=v(t)e^{-γΔt/m}+\frac{1-e^{-γΔt/m}}{γ}F_{\text{int}}+\text{noise} ),
allows a stable propagation even when γ is moderate. This “finite‑damping Langevin scheme” eliminates the need for excessively small Δt and captures inertial effects that are lost in standard BD.

A second major contribution is the incorporation of hydrodynamic interactions (HI) using a previously proposed approximation to the Rotne‑Prager‑Yamakawa tensor. By reducing the full 3N×3N mobility matrix to a pairwise expression that depends only on bead radii and inter‑bead distances, the authors achieve an O(N) computational cost while still representing long‑range solvent‑mediated coupling. The approximate mobility is:
( \mathbf{M}_{ij}\approx\frac{1}{γ}\big