I am an applied mathematician interested in the dynamics of potential systems - i.e., systems with multiple unique energy minima. One of the best examples of such systems are protein folding potentials. From sources like This one I know that the potential, $$ V(x) $$ exists and is a function of the positions of each residue in space and their interactions with each other. Since such a function exists, there should (mathematically) be a set of ordinary differential equations that capture the dynamics described by the potential.
However, although I have seen definitions of $V(x)$ in the literature, for the life of me I can't figure out exactly what the set of differential equations associated with this system is - i.e., the system is usually written out in a generalized form that applies to all proteins, but the exact information required to build such a potential for one such protein is unclear.
Does anyone have an example of of a particular $V(x)$ (for a particular, short, set of amino acids, say) where all the parameters are known and the system can be solved numerically as a set of ordinary differential equations?