Construction of Coarse-Grained Models by Reproducing Equilibrium Probability Density Function

Abstract

The present work proposes a novel methodology for constructing coarse-grained (CG) models, which aims at minimizing the difference between the CG model and its original system. The difference is defined as a functional of the ratio of equilibrium conformational probability densities to the original one, then is further expanded by equilibrium averages of a set of sufficient and independent physical quantities as basis functions. An orthonormalization strategy is adopted to get the independent basis functions from sufficiently preselected interesting physical quantities of the system. The probability density matching coarse-graining (PMCG) scheme effectively takes into account the overall characteristics of the original systems to form CG models, and it is a natural improvement of the usual CG scheme wherein equilibrium averages of many physical quantities are intuit chosen to reproduce without considering correlations among these quantities. We verify the general PMCG framework in constructing a one-site CG water model from TIP3P model. Both structure of liquids and pressure are found to be well reproduced at the same time in the one-site CG water model.

Systematically Constructing Kinetic Transition Network in Polypeptide from Top to Down: Trajectory Mapping

“…It is more efficient to select functions in coarse-grained conformational space as basis functions. More discussions about basis functions can be found in our previous works [ 19 , 20 , 48 ], or in some current approaches of MSM, such as tICA and the variational approach [ 44 – 47 ] where basis functions are similarly selected to expand the dynamics propagator.…”

Reweighted ensemble dynamics simulations: Theory, improvement, and application

“…The definition gives a measurement about the similarity of samples, can be generally applied to compare two samples. For example, we had used the formula to optimise coarse-grained models of the all-atomic water [37]. For assessing the completeness of basis functions in expansion of Peq(x) P init+ (x) , a reasonable method is to check the convergence of S 2 init+,eq while adding more and more basis functions.…”

“…For example, we had used the formula to optimize coarse-grained models of the all-atomic water. [37] For assessing the completeness of basis functions in the expansion of P eq (x)/[P init+ (x)], a reasonable method is to check the convergence of S 2 init+,eq while adding more and more basis functions. To calculate S 2 init+,eq , the sample for equilibrium distribution P eq (x), thus the trajectory weights {w i }, are necessary.…”

Determination of the vapor–liquid transition of square-well particles using a novel generalized-canonical-ensemble-based method

“…Recently, several novel algorithms beyond the traditional MC have been proposed, aiming to enhance the sampling efficiency or to predict the critical properties more precisely. A series of algorithms to enhance the sampling [30][31][32][33] of possible states has been systematically formulated based on a new ensemble, generalized canonical ensemble (GCE), [34][35][36] which overcomes the inability of sampling the metastable states or unstable phase-coexisting states during phase transitions by using the conventional numerical methods. They introduced the GCE into the canonical parallel tempering Monte Carlo (PTMC) [36] or the isobaric replica exchange molecular dynamics (REMD).…”