The (implicit) force is with you: an application of the implicit function theorem for automatic protein force fields reparametrization

Molecular dynamics simulations are powerful tools for studying protein behavior, yet their accuracy remains limited by the approximations of molecular force fields and the difficulty of determining their parameters. Moreover, existing force fields are largely optimized for globular proteins and can perform poorly on structurally distinct systems. Developing a universal force field that accurately describes all existing protein structures may be beyond reach with current physical models. Instead, we propose shifting generality from the force field itself to the method used to assign its parameters, enabling systematic reparameterization for restricted, structurally homogeneous classes of proteins. We formulate this task as a bilevel optimization problem and solve it using the implicit function theorem. We demonstrate this approach by reparameterizing AMBER for amyloid fibrils, optimizing its parameters to improve agreement with experimentally determined structures and enhance fibril stability during molecular dynamics simulations.