Experimental parameterization of an energy function for the simulation of unfolded proteins

The determination of conformational preferences in unfolded and disordered proteins is an important challenge in structural biology. We here describe an algorithm to optimize energy functions for the simulation of unfolded proteins. The procedure is based on the maximum likelihood principle and employs a fast and efficient gradient descent method to find the set of parameters of the energy function that best explain the experimental data. We first validate the method by using synthetic reference data, and subsequently apply the algorithms to data from nuclear magnetic resonance spin-labeling experiments on the Delta131Delta fragment of Staphylococcal nuclease. A significant strength of the procedure that we present is that it directly uses experimental data to optimize the energy parameters, without relying on the availability of high resolution structures. The procedure is fully general and can be applied to a range of experimental data and energy functions including the force fields used in molecular dynamics simulations.