Structure-kinetic-thermodynamic relationships for peptide secondary structure formation identified from transition network properties

Molecular simulation models have provided immense, often general, insight into the complex behavior of protein systems. Even for very detailed, e.g., atomistic, models, the generation of quantitatively accurate dynamical properties remains a formidable challenge. This lack of consistent dynamics largely hinders simulation models, especially coarse-grained models, from providing structural interpretations for kinetic experiments. In this work, we investigate to what extent a simple, native-biased coarse-grained model is capable of reproducing the dynamics, or more specifically kinetic properties, of an underlying helix-coil transition. In order to accurately represent the underlying structural ensemble, this model employs near-atomistic steric interactions. We investigate structure-kinetic relationships in order to identify the structural constraints necessary to guarantee consistent kinetics, given the implicit restrictions enforced by the physics of the model. From each set of simulations, we construct a Markov state model to efficiently and systematically assess the system kinetics. We demonstrate that the accurate representation of the structural ensemble results in a rather large restriction in the topology of the resulting kinetic networks. As a consequence, relatively weak structural constraints are needed in order to nearly quantitatively reproduce many kinetic properties of the underlying system. Not surprisingly, while structural constraints determine the kinetics at a single temperature, fixing the structure over multiple temperatures determines the thermodynamics, i.e., cooperativity, of the transition. Remarkably, topological features of the kinetic networks characterizing the degree of randomness of pathways traveling between the helix and coil states at a single reference temperature dictate the relative cooperativity of the resulting transition.