A meshfree method for mechanics and conformational change of proteins and their assemblies

Mechanical properties of proteins play an important role in their biological function. For example, microtubules carry large loads to transport organelles inside the cell, and virus shells undergo changes in shape and mechanical properties during maturation which affect their infectivity. Various theoretical models including continuum elasticity have been applied to study these structural properties, and a significant success has been achieved. But, the previous frameworks lack a connection between the atomic and continuum descriptions. Here this is accomplished through the development of a meshfree framework based on reproducing kernel shape functions for the large deformation mechanics of protein structures. The framework is validated by comparing thermal fluctuations of small proteins against well established elastic network model. To demonstrate the usability of this framework, solutions to several other problems are presented. The response of virus shells to indentation under atomic force microscope tip is simulated and compared to the finite element results. Finally, the large scale conformational changes of viruses are analyzed by computing the deformations/strains associated with the conformational motions. Excellent agreement with the previously published results is observed while increasing the efficiency of numerical analysis. Furthermore, the results provide insights into the continuum behavior of proteins and the optimum amount of geometric details necessary for calculating their mechanical properties.