Program

I.3 -- Invited, IWTCP-3

Date: Monday, 27 July 2015

Time: 14h00 - 14h35

A rigorous approach to the derivation of analytical potentials in physics-based coarse-grained force fields

Adam K. Sieradzan, Agnieszka G. Lipska and Adam Liwo*

Faculty of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland

Coarse-grained approaches, which implement simplified representations of molecules, are widely used in biomolecular simulations. These approaches offer a tremendous reduction of the cost of computations compared with the all-atom models. However, designing the functional forms of the coarse-grained energy terms poses a serious problem and these terms are very often imported from all-atom force fields or assigned on a heuristic basis. In such approaches at coarse-graining the multibody terms (which are necessary to generate regular structures [1]) are not considered and inadequate variables are often chosen to express the effective energy terms.

Based on statistical physics, the coarse-grained energy functions originate from the potentials of mean force (PMF), also termed restricted free-energy functions (RFE) of the systems under consideration, where the degrees of freedom that are not considered explicitly in the coarse-grained model (the so-called fine-grain degrees of freedom) are integrated out [1,2]. Expansion of the PMF into Kubo cluster-cumulant functions [3], termed factor expansion (FE) [1] or use of the force-matching (FM) method [2] enable us to split the PMF into specific terms. Additionally, approximate analytical formulas for the effective energy terms are possible to derive trough generalized Kubo cumulant expansion [3] of the PMF factors.

In this work, the FE approach is pursued further to design a general method for the determination of the energy expressions in the coarse-grained force fields. The all-atom potential energy is expressed in terms of the squares of interatomic distances, which (and, thereby, also the energy) are then expanded into the Taylor series in the fine-grain degrees of freedom. By using the Kubo cumulant expansion of the factors [3] and averaging over the fine-grain degrees of freedom, the combinations of variables which the effective energy terms depend on, and approximated energy expressions can be determined. This new systematic approach to the coarse-grained force-field derivation is illustrated with the example of the local and correlation energy terms in the UNRES force field developed in our laboratory [1,4]. In particular, it is demonstrated that pure ‘torsional’ potentials are meaningless with coarse-grained force fields, because the trigonometric functions of the virtual-bond-dihedral angles are always multiplied by the sines of the adjacent virtual-bond-valence angles. The new formalism also enables us to rationalize the dependence between the backbone-virtual-bond-dihedral angles and the adjacent backbone-virtual-bond-valence angles in proteins derived from the Protein Data Bank.

Supported by grant DEC-2012/06/A/ST4/00376 from the National Science Center of Poland and grant Mistrz 7./2013 from the Foundation for Polish Science. Calculations were carried out using the computer resources at the Academic Computer Centre in Gdansk (CI TASK) and Interdisciplinary Center of Mathematical and Computer Modeling, University of Warsaw.

[1] Liwo, A., Czaplewski, C., Pillardy, J., Scheraga, H. A., J. Chem. Phys., 115, 2323–2347 (2001).
[2] Ayton, G. S., Noid, W. G., Voth, G. A., Curr. Opinion Struct. Biol., 17, 192–198 (2007).
[3] Kubo, R., J. Phys. Soc. Japan, 17, 1100–1120 (1962).
[4] Liwo, A., Czaplewski, C., Ołdziej, S., Rojas, A. V., Kaźmierkiewicz, R., Makowski, M., Murarka, R. K. and Scheraga, H. A. “Simulation of protein structure and dynamics with the coarse-grained UNRES force field”. In Voth, G., editor, Coarse-Graining of Condensed Phase and Biomolecular Systems, chapter 8, 1391–1411, CRC Press, (2008).

Presenter: Adam Liwo