Reverse Coarse-Graining for Equation-Free Modeling: Application to Multiscale Molecular Dynamics

Abstract

Constructing atom-resolved states from low-resolution data is of practical importance in many areas of science and engineering. This problem is addressed in this paper in the context of multiscale factorization methods for molecular dynamics. These methods capture the crosstalk between atomic and coarse-grained scales arising in macromolecular systems. This crosstalk is accounted for by Trotter factorization, which is used to separate the all-atom from the coarse-grained phases of the computation. In this approach, short molecular dynamics runs are used to advance in time the coarse-grained variables, which in turn guide the all-atom state. To achieve this coevolution, an all-atom microstate consistent with the updated coarse-grained variables must be recovered. This recovery is cast here as a non-linear optimization problem that is solved with a quasi-Newton method. The approach yields a Boltzmann-relevant microstate whose coarse-grained representation and some of its fine-scale features are preserved.Embedding this algorithm in multiscale factorization is shown to be accurate and scalable for simulating proteins and their assemblies.

Temporally Coarse-Grained All-Atom Molecular Dynamics Achieved via Stochastic Padé Approximants

“…An increase in the minimized U is observed with increased Δ/δ (Figures S18 and S19). Note that the microstate sparse reconstruction scheme (MSR) 39 cannot be applied to a nonbonded system since it optimizes only bonded parameters, such as interatomic bond and angle distances.…”

“…The efficiency of APIMD is sensitive to the amount of energy minimization, since the latter determines the number of steps in thermal equilibration to prepare a configuration from which the short conventional MD can be launched, thus enabling the next APIMD time step. Therefore, more sophisticated energy minimization schemes 104 and constraint techniques 39 should be tested to decrease the time spent in energy minimization stage. A preliminary evaluation of the MSR 39 is presented in the Supporting Information (Figures S21−S24).…”

“…Therefore, more sophisticated energy minimization schemes 104 and constraint techniques 39 should be tested to decrease the time spent in energy minimization stage. A preliminary evaluation of the MSR 39 is presented in the Supporting Information (Figures S21−S24).…”

“…Like our previous multiscale coevolution MD methods, , APIMD avoids the need to introduce and calibrate phenomenological rate laws, making it equation-free (as appeared in the literature in application to all-atom MD), multiscale coevolution MD method. The objective is to develop a method that not only avoids the need to introduce CG forces and dynamical equations but also avoids the dynamic reconstruction of the atom-resolved state consistent with the updated CG state − (as needed in other coevolution methods where phenomenological CG forces are introduced with attending uncertainty). The main problem to be resolved in the temporal coarse-graining of all-atom states is the abundance of arising atomic steric clashes.…”

Molecular Structuring and Percolation Transition in Hydrated Sulfonated Poly(ether ether ketone) Membranes

“…33,39,40,42−45 The superposition has recently been formulated as an optimization problem, which minimizes the least-squares difference between the atomistic and CG coordinates. 46,47 Back-mapping has also been successfully applied to nonequilibrium situation such as CG polymer under shear flow. 48 Generic back-mapping schemes have been proposed for CG models based on random walk polymer model, 49 DPD, 50 Martini, 51,52 soft sphere model 53 and, very recently, for adaptive resolution scheme (AdResS).…”