Optimal Solution to the Torsional Coefficient Fitting Problem in Force Field Parametrization

Molecular modeling is an excellent tool for studying biological systems on the atomic scale. Depending on objects, which may be proteins, nucleic acids, or lipids, different force fields are recommended. The phospholipid bilayers constitute an example, in which behavior is extensively studied using molecular dynamics simulations due to limitations of experimental methods. The reliability of the results is strongly dependent on an appropriate description of these compounds. There are some deficiencies in the parametrization of intra- and intermolecular interactions that result in incorrect reproduction of phospholipid bilayer properties known from experimental studies, such as temperatures of phase transitions. Refinement of the force field parameters of nonbonded interactions present in the studied system is required to close these discrepancies. Such parameters as partial charges and torsional potential coefficients are crucial in this issue and not obtainable from experimental studies. This work presents a new fitting procedure for torsional coefficients that employs linear algebra theory and compares it with the Monte Carlo method. The proposed algebraic approach can be applied to any considered molecular system. In the manuscript, it is presented on the example of dimethyl phosphoric acid molecule. The advantages of our method encompass finding an optimal solution, the lack of additional parameters required by the algorithm, and significantly shorter computational time. Additionally, we indicate the importance of proper assignment of the partial charges.