Multiscale enhanced path sampling based on the Onsager-Machlup action: Application to a model polymer

Abstract

We propose a novel path sampling method based on the Onsager-Machlup (OM) action by generalizing the multiscale enhanced sampling (MSES) technique suggested by Moritsugu and coworkers (J. Chem. Phys. 133, 224105 (2010)). The basic idea of this method is that the system we want to study (for example, some molecular system described by molecular mechanics) is coupled to a coarse-grained (CG) system, which can move more quickly and computed more efficiently than the original system. We simulate this combined system (original + CG system) using (underdamped) Langevin dynamics where different heat baths are coupled to the two systems. When the coupling is strong enough, the original system is guided by the CG system, and able to sample the configuration and path space more efficiency. We need to correct the bias caused by the coupling, however, by employing the Hamiltonian replica exchange where we prepare many path replica with different coupling strengths. As a result, an unbiased path ensemble for the original system can be found in the weakest coupling path ensemble. This strategy is easily implemented because a weight for a path calculated by the OM action is formally the same as the Boltzmann weight if we properly define the path "Hamiltonian". We apply this method to a model polymer with Asakura-Oosawa interaction, and compare the results with the conventional transition path sampling method.

Theoretical frameworks for multiscale modeling and simulation

“…Different spatial scales may evolve over different timescales according to different equations of motion. From a technical standpoint, artificial coupling to a low-resolution model can facilitate conformational sampling of a high-resolution model [55,57,58]. In other cases, separation of the simulations in different regions [59] or of different components [61] can be designed for efficient calculation of biophysical properties.…”

“…The Hamiltonian replica exchange method [56] was then adopted, in which replicas were assigned various coupling strengths, with zero coupling resulting in the pure atomistic model. This scheme was applied to study the folding of a β-hairpin [55] and the disorder-to-order transition of a loop in a protein [57], and has been generalized to path sampling [58]. …”

Multiscale enhanced sampling driven by multiple coarse-grained models

“…The CG simulation time step was 10 fs. The problem of using different time steps in the MM and CG simulations can be bypassed by taking into account the scaling of the CG variables [27]. Eight replicas in which k MMCG k MMCG1 = k MMCG2 = 0, 0.004, 0.01, 0.02, 0.04, 0.08, 0.12, and 0.2 kcal/mol/Å 2 were used for the Hamiltonian exchange mcMSES.…”

Molecular dynamics coupled with a virtual system for effective conformational sampling

“…Similarly, the virtual system was combined with AUS and was designated as a virtual‐system coupled AUS (V‐AUS) . A somewhat similar method was proposed to sample protein conformations, where a coarse‐grained protein model interacts with an all‐atom protein model (the real system) . In a certain sense, our virtual system corresponds to their coarse‐grained model.…”