Absolute versus Relative Entropy Parameter Estimation in a Coarse-Grain Model of DNA

Abstract

Abstract. Maximum entropy procedures for estimating coarse-grain parameters from molecular dynamics (MD) simulation data are considered within the specific context of the sequence-dependent cgDNA rigid-base model of DNA. We describe a quite general approach that exploits a maximum absolute entropy principle to fit an observed matrix of covariances subject to the constraint of only allowing a prescribed sparsity pattern of nearest-neighbor interactions in the free energy. We also allow indefinite local stiffness-matrix parameter blocks that nevertheless always generate a positive-definite model stiffness matrix. Beginning from a database of atomic-resolution MD simulations of a library of short DNA oligomers in explicit solvent, these procedures deliver a complete parameter set for the cgDNA model. Due to the intrinsic linear structure of DNA and the convergence characteristics of the MD time series data, the maximum absolute entropy parameter set yields significantly improved predictions of persistence lengths, when compared to a previous parameter set that was fit to the same MD data, but using a maximum relative entropy fitting principle and local stiffness-matrix parameter blocks that were constrained to be semidefinite.Key words. entropy principles, parameter estimation, molecular modeling, statistical mechanics AMS subject classifications. 62H12, 82B05, 82D60, 15A83, 15A09 DOI. 10.1137/16M10860911. Introduction. An important problem in molecular biology is to understand how the mechanical properties of DNA depend on the sequence of bases along its two backbones. Properties that influence bending, twisting, shearing, and stretching in different directions along and across the two strands are believed to be essential in various biological processes such as DNA looping [34], nucleosome positioning [35], and other DNA-protein interactions, and gene regulation [26], all of which depend on the probability of DNA to adopt various three-dimensional configurations [4]. Consequently models at differing length scales are needed to quantify how the mechanical properties of DNA depend upon its sequence. The intermediate scales of a few tens to a few hundreds of base pairs are of particular biological interest. The study of sequence-dependent effects at such scales requires the development of specialized coarse-grain models, because, with contemporary computational resources, all-atom molecular dynamics (MD) simulations at these lengths remain intensive, particularly given the large number of possible sequences, while sequence-dependent behavior is

Deciphering the mechanical properties of B‐DNA duplex

“…Originally, the authors interpreted as a frustration energy 76 necessary to deform the monomers and dimers from their intrinsically optimal conformations to their ground‐state conformation in the oligomer given by . However, since in the current parameterization, 155 the monomer and dimer energies are allowed to be indefinite, that is, take both positive and negative values for a nonzero deformation (although the resulting oligomer energy is always positive definite), this meaning of seems to have been lost.…”

“…Gonzalez et al inferred the model parameters from a pool of atomic‐resolution MD simulations of DNA sequences covering all the tetramers, augmented by additional simulations. The current parameters were obtained using an improved parameter estimation procedure 155 . The model is available as a standalone software package, cgDNA, 77 as well as via a web interface called cgDNAweb 156 …”

Statistical inference for Bures-Wasserstein barycenters

“…Scale-location families attract lots of attention in modern data analysis and appear in many practical applications, as this concept is user-friendly in terms of theoretical analysis and, at the same time, possess very high modelling power. For example, it is widely used in medical imaging Wassermann et al ( 2010), modelling of molecular dynamic Gonzalez et al (2017), clustering procedures del Barrio et al (2017), climate modelling Mallasto and Feragen (2017), embedding of complex objects in low dimensional spaces Muzellec and Cuturi (2018) and so on.…”

“…A subspace Sym(d) ⊂ H(d) of real-valued symmetric matrices is also of great interest: points in Sym(d) are widely used for description of systems in engineering applications, medical studies, neural sciences, evolutionary biology e.t.c. Usually such data sets are considered to be randomly sampled from an unknown distribution P (Goodnight and Schwartz (1997); Calsbeek and Goodnight (2009); Álvarez-Esteban et al (2015); del Barrio et al (2017); Gonzalez et al (2017)), and statistical characteristics of P such as, in particular, mean and variance, appear to be of interest for further planning of an experiment and analysis of obtained results fur further development of natural science models. The current study focuses on a space of positive semi-definite Hermitian matrices H + (d) ⊂ H(d) and presents a possible approach to analysis and aggregation of relevant statistical information from data-sets, for which the linearity assumption might be violated.…”

cgDNAweb: a web interface to the cgDNA sequence-dependent coarse-grain model of double-stranded DNA

“…The inputs to the cgDNA model of a dsDNA oligomer with N base pairs is a sequence S of N letters drawn from the {A,T,C,G} alphabet (corresponding to the bases along the reading or Watson strand in the 5′ → 3′ direction), along with a model parameter set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mathcal {P}$\end{document} . Various parameter sets are available corresponding either to different mathematical choices in the parameter estimation techniques ( 31 ) or to different MD training set data, which in turn can depend on both different MD simulation protocols, or on physically different solvent conditions, e.g. different ion species and concentration.…”