Coupling Atomistic Simulation to a Continuum Based Model to Compute the Mechanical Properties of Focal Adhesions

Abstract

Mechanical Ventilation is causing inflammation in the lung either by rupture of tissue or by overstretching cells and starting signalling cascades. To prevent starting these, it is of great interest to connect ventilation parameters to stresses and strains in the lung on a cellular level.In order to quantify forces transferred from the tissue to the cell, the mechanical properties of integrins play an important role. Large time and length scale differences between the cell and the integrin molecules make such computations difficult. Given the utility of continuum models based on Finite Element Method, it would be useful to couple the continuum methods to molecular dynamics techniques in order to compute forces between cells and tissue.For coupling molecular information to the continuum level, we present a technique based on energy transition. Hereby the mechanical properties of on integrin bonds are computed with help of molecular dynamics. In order to model the complete focal adhesion, a spring recruitment model is included on the continuum side, representing more than one molecular bond. The approach includes dynamic effects from both scales. The focal adhesion is represented by a layer of finite elements with the intergin molecule bound to collagen. The deformation gradient of the element is scaled to the size of the protein. The actual gradient and the one from one time step earlier are transferred to the molecular scale. In the molecular dynamics simulations, the energy difference between both deformations is simulated first by slowly deforming and secondly equilibrating the protein. This information is transferred back to the continuum level and, under the assumption that focal adhesions remain connected, the number of bonds are calculated and modelled as multiple non-linear neo-Hookean material, representing parallel springs.