MSCALE: A General Utility for Multiscale Modeling

Abstract

The combination of theoretical models of macromolecules that exist at different spatial and temporal scales has become increasingly important for addressing complex biochemical problems. This work describes the extension of concurrent multiscale approaches, introduces a general framework for carrying out calculations, and describes its implementation into the CHARMM macromolecular modeling package. This functionality, termed MSCALE, generalizes both the additive and subtractive multiscale scheme (e.g. QM/MM ONIOM-type), and extends its support to classical force fields, coarse grained modeling (e.g. ENM, GNM, etc.), and a mixture of them all. The MSCALE scheme is completely parallelized with each subsystem running as an independent, but connected calculation. One of the most attractive features of MSCALE is the relative ease of implementation using the standard MPI communication protocol. This allows external access to the framework and facilitates the combination of functionality previously isolated in separate programs. This new facility is fully integrated with free energy perturbation methods, Hessian based methods, and the use of periodicity and symmetry, which allows the calculation of accurate pressures. We demonstrate the utility of this new technique with four examples; (1) subtractive QM/MM and QM/QM calculations; (2) multi-force field alchemical free energy perturbation; (3) integration with the SANDER module of AMBER and the TINKER package to gain access to potentials not available in CHARMM; and (4) mixed resolution (i.e. coarse grain / all-atom) normal mode analysis. The potential of this new tool is clearly established and in conclusion an interesting mathematical problem is highlighted and future improvements are proposed.

Figure 1

Illustration of the subroutine calling sequence of the MSCALE facility; showing the information flow of a typical energy (ENER), minimization (MINI), or normal mode analysis (DIAG) calculation. The broadcast and receive routines handle both coordinate and energy/gradient communication. Routines in blue are executed on the main processor (client) while those in yellow take place on the subsystems (servers). Thin black lines represent information being passed between subroutines where the thick black lines represent MPI calls and the sharing of information between the controlling client process and the server process, which acts only as an energy, force, or Hessian engine. The EMSCALE subroutine is called twice from CHARMM’s main energy routine, once at the beginning to send the data to the servers and again at the end to receive the energy, force, etc. terms from them. Therefore, the servers and clients are performing calculations in parallel. Further details of how MSCALE is implemented is given in the supporting information.

Figure 2

Conformations of pentane.

Figure 3

ΔG as a function of window for (A) the OH move of methanol and (B) the alanine dipeptide moving from the CHARMM22 to AMBER99SB force fields. In both cases the free energy curve is smooth, representing a gradual shift from one force field or structure to another.

Figure 4

Ramachandran free energy landscapes of alanine dipeptide with standard AMBER and CHARMM-MSCALE-AMBER simulations. Both free energy proffiles are very similar. Slight differences are expected even though same force field and solvent method are used since the molecular dynamics runs were performed with different packages with their own implementations of Langevin Dynamics.

Figure 5

The sum of squares of the off diagonal upper triangular elements of the 5×5 matrix obtained by dotting the normalized shape difference vectors against one another for the ENM and all-atom cases (see section 3.4.1 for details) as a function of the weighting between the third and second order moments. Since off-diagonal elements are expected to be minimal, the optimal weighting was determined to be 0.12 in each case, but slightly higher for the ENM than the all-atom model.