Calcium Binding Affinity in the Mutational Landscape of Troponin-C: Free Energy Calculation, Coevolution modeling and Machine Learning

Mutation in calcium-binding proteins (CBPs) can significantly influence Ca2+ binding affinity (BA), resulting in substantial impairment in the signaling process and leading to several lethal diseases. The knowledge behind the changes in the binding affinity can help in understanding the signaling process and designing inhibitors for therapeutic usage. However, accurate prediction of BA for a large number of mutations has been elusive. In this work, for an important calcium binding protein, cardiac Troponin-C, we have developed an integrative modeling approach that combines molecular dynamics (MD)-based binding free energy calculations, prediction of plausible mutants using evolutionary information, and an interpretable machine learning model to predict Ca2+ BA for a large number of mutations (seventy-six in all). For the binding free energy calculation, we have used a charge-scaling based MD simulation that considers the polarization in the system, which is critical for divalent ion binding with proteins. The well-known molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method was used for the binding free energy calculations. The calculated results for twenty-four disease mutants, which are associated with different cardiomyopathies and have experimental binding affinity, are in close agreement with the experimental results. To study other plausible mutations, we have probed the evolutionary landscape of cardiac Troponin-C and used the EVmutation method of Hopf et al.(Nature biotechnology 2017, 35, 128-135) to generate sixty-one additional mutants. Finally, a Support vector regression model was developed for both observed and plausible mutations. Our machine learning model used simple structure and sequence-based descriptors along with MD-based descriptors and gave a mean squared error (MSE) of only 0.16 kcal/mol. Assessment of the contribution of each descriptor shows that the number of water molecules within the Ca2+ binding site, type of amino acid substitution (e.g. polar to hydrophobic reduces the binding affinity), and the distance of mutation with Ca2+ are the most important factors in determining the binding affinity. This integrative modeling can be used for other CBPs and can lay the path for modeling the complex and astronomically large mutational landscape of Calcium-binding proteins.