Unraveling internal friction in a coarse-grained protein model

Understanding the dynamic behavior of complex biomolecules requires simplified models that not only make computations feasible but also reveal fundamental mechanisms. Coarse-graining (CG) achieves this by grouping atoms into beads, whose stochastic dynamics can be derived using the Mori-Zwanzig formalism, capturing both reversible and irreversible interactions. In liquid, the dissipative bead-bead interactions have so far been restricted to hydrodynamic couplings. However, friction does not only arise from the solvent but, notably, from the internal degrees of freedom missing in the CG beads. This leads to an additional "internal friction" whose relevance is studied in this contribution. By comparing with all-atom molecular dynamics (MD), we neatly show that in order to accurately reproduce the dynamics of a globular protein in water using a CG model, not only a precise determination of elastic couplings and the Stokesian self-friction of each bead is required. Critically, the inclusion of internal friction between beads is also necessary for a faithful representation of protein dynamics. We propose to optimize the parameters of the CG model through a self-averaging method that integrates the CG dynamics with an evolution equation for the CG parameters. This approach ensures that selected quantities, such as the radial distribution function and the time correlation of bead velocities, match the corresponding MD values.