Tools for Local Elasticity Calculations and their Applications to Simulations of Lipid Biomembranes

Modeling the physical and chemical properties of a biological system present a unique challenge due to the varying length and time scales of many biological processes.  Our Research Group has developed tools using the Irving-Kirkwood-Noll Statistical mechanics framework for the purpose of modeling biological processes.  Here I will present our development and implementation of the tools for the elasticity calculations in an open-source library MDstress and the GROMACS-LS post-processing analysis code. We Implement the stress-stress fluctuation formula in three parts in order to compute the local elasticity tensor for a variety of materials. To compute the so-called ‘Born term’ of the stress-stress fluctuation formula, we derive relations for the second derivatives of 2, 3, and 4-body potentials commonly used in biomolecular simulations. We validate our numerical implementation on a simple suite of tests on liquids and solids including, solid and liquid Argon, liquid water, and a fluid lipid bilayer using the coarse-grained MARTINI force field. Preliminary results show the efficacy of our tools and results in good agreement with prior simulations and experiments. Furthermore, we explore important questions regarding the elastic properties and fluidity of models of lipid membranes.