Extended Peptide Basis Set for Variational Markov Models: Secondary Structure, Orthonormality, and Undersampled Transitions

The variational approach to conformational dynamics offers a systematic way to con- struct kinetic models from molecular dynamics simulations, using an arbitrary set of basis functions. We have recently proposed a basis set for peptide systems that only depends on the sequence of amino acids in the system. This basis set is not data- driven and can therefore be used to compare models for different MD simulations. Here we introduce an orthonormality condition for this basis set as a requirement for the variational models to remain directly interpretable. The orthonormality condi- tion naturally leads to a way of detecting correlations between the sampled marginal stationary probability distributions at each residue in the peptide sequence. We show how these correlations emerge from either undersampled transitions or from inher- ent dynamical dependencies between the residues. Our basis set relies on a tensor structure obtained from residue-centered ansatz functions. We demonstrate that this structure is sufficient to model both β-sheet and α-helix formation in peptides.