Effective Riemannian Diffusion Model for Conformational Dynamics of Biomolecular Systems

by Fakharzadeh, A.; Moradi, M.

We present a Riemannian formalism for effective diffusion of biomolecules in collective variable spaces that provides a robust framework for conformational free Closed energy calculation methods. Unlike their Euclidean counterparts, the Riemannian potential State of mean force (PMF) and minimum free energy path (MFEP) are invariant under coordinate transformations. The presented formalism can be readily employed to modify the collective variable based enhanced sampling techniques, such as umbrella sampling (US) commonly used in biomolecular simulations, to take into account the role of intrinsic geometry of collective variable space. Although our model is mathematically equivalent to a Euclidean diffusion with a position-dependent diffusion tensor, the Riemannian formulation provides a more convenient framework for free energy calculation methods and path-finding algorithms aimed at characterizing the effective conformational dynamics of biomolecules. A simple three-dimensional toy model and a pentapeptide (metenkephalin) simulated in an explicit solvent environment are used to illustrate the workings of the formalism and its implementation.

Journal
Journal of Physical Chemistry Letters
Volume
7
Issue
24
Year
2016
Start Page
4980-4987
URL
https://dx.doi.org/10.1021/acs.jpclett.6b02208
ISBN/ISSN
1948-7185
DOI
10.1021/acs.jpclett.6b02208