A Multiscale Coarse-Graining Method for Biomolecular Systems

Abstract

A new approach is presented for obtaining coarse-grained (CG) force fields from fully atomistic molecular dynamics (MD) trajectories. The method is demonstrated by applying it to derive a CG model for the dimyristoylphosphatidylcholine (DMPC) lipid bilayer. The coarse-graining of the interparticle force field is accomplished by an application of a force-matching procedure to the force data obtained from an explicit atomistic MD simulation of the biomolecular system of interest. Hence, the method is termed a "multiscale" CG (MS-CG) approach in which explicit atomistic-level forces are propagated upward in scale to the coarse-grained level. The CG sites in the lipid bilayer application were associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic data. The resulting CG lipid bilayer model is shown to accurately reproduce the structural properties of the phospholipid bilayer.

Multiscale Coarse-Graining and Structural Correlations: Connections to Liquid-State Theory

“…It has been empirically demonstrated that even for highly complex systems the MS-CG method generates a useful and quantitatively accurate model. 16,17,[24][25][26][27][28]46 …”

“…17 The CG force field is obtained by minimizing a residual describing the difference between the instantaneous forces defined by the CG force field and the original atomistic force field. This difference is statistically averaged over all CG sites and all configurations sampled from the atomistic MD simulations.…”

“…Employing the definitions in eq (14)-eq (16), eq (10) may be re-expressed as: (17) As mentioned above, all information regarding atomistic forces is contained within b d . The left hand side of eq (17) depends only upon two-particle information, while the right hand expression reflects three-particle correlations through the term which couples the equations for different force table elements.…”

“…Furthermore, the equivalence of eq (23) and eq (35) indicates that the MS-CG method incorporates higher-order correlations in a mechanism that is consistent with the well-known statistical mechanics of the liquid state. 20 However, while the analysis of subsection 2.1 and subsection 2.2 and, in particular, the "normal" MS-CG equations presented in eq (17), are generally valid and may be applied to determine a CG force field for any system, the preceding analysis of subsection 2.3, which relates the MS-CG equations to the YBG theory, is strictly valid only for isotropic, homogeneous systems. Moreover, there exists no general proof that the two-and three-CG particle distribution functions measured from atomistic MD simulations may be related to a simple pair potential through a YBG-type equation.…”

“…This function reflects the influence of both direct and indirect excluded volume effects on the fluid structure and, ultimately, on the MS-CG interaction potential between CG sites. The three-particle correlations couple the equations for the force field elements, f d , according to eq (17). Figure 5 has been presented to highlight the fine structure of the three-particle correlations between CG sites within the atomistic system.…”