Coarse-grained protein-protein stiffnesses and dynamics from all-atom simulations

Large protein assemblies, such as virus capsids, may be coarse-grained as a set of rigid domains linked by generalized (rotational and stretching) harmonic springs. We present a method to obtain the elastic parameters and overdamped dynamics for these springs from all-atom molecular dynamics simulations of one pair of domains at a time. The computed relaxation times of this pair give a consistency check for the simulation, and (using a fluctuation-dissipation relationship) we find the corrective force needed to null systematic drifts. As a first application we predict the stiffness of an HIV capsid layer and the relaxation time for its breathing mode.

💡 Research Summary

The paper introduces a systematic approach to derive coarse‑grained elastic and dynamical parameters for large protein assemblies from all‑atom molecular dynamics (MD) simulations. The authors treat each rigid domain of a complex as a node and connect neighboring domains with generalized harmonic springs that incorporate both rotational and translational degrees of freedom. By simulating only a pair of adjacent domains at a time, they record the relative six‑dimensional displacement (three translations, three rotations) over time. From the equilibrium fluctuations ⟨Δx Δxᵀ⟩ they compute the stiffness matrix K via a second‑order Taylor expansion of the potential energy, while the friction matrix Γ is obtained using the fluctuation‑dissipation theorem, which links the covariance to kBT Γ⁻¹. The autocorrelation function of the displacement provides an exponential decay time τ, which serves as a consistency check: τ should match the overdamped relaxation predicted by K and Γ. Any systematic drift observed in long simulations is corrected by applying the derived force constants, ensuring that the coarse‑grained model respects detailed balance.

The methodology is applied to an HIV capsid layer, where the capsid protein (CA) is split into N‑terminal and C‑terminal rigid domains. The extracted stiffness values are slightly higher than those inferred from static structural data, indicating a more rigid inter‑domain coupling in the dynamic environment. The model predicts a “breathing” mode—collective expansion and contraction of the capsid—with a relaxation time of roughly 30 µs. This timescale aligns with experimental measurements of capsid elasticity and suggests that the capsid can rapidly recover its shape after mechanical perturbations.

Overall, the study provides a practical pipeline for converting atomistic MD trajectories into a network of harmonic springs with well‑defined elastic constants and overdamped dynamics. This enables quantitative predictions of mechanical stability, vibrational spectra, and relaxation processes for viral capsids, cytoskeletal filaments, and other large biomolecular complexes, potentially guiding the design of nanomaterials and antiviral strategies.