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The free energy landscape of a protein is a function of many interdependent degrees of freedom. For this reason, conceptual constructs (e.g., funnels) have been useful to visualize these landscapes. One relatively new construct is the idea of a hub-like native state that is the final destination of many non-interconverting folding pathways. This is in contrast to the idea of a single predominant folding pathway connecting the native state to a rapidly interconverting ensemble of unfolded states. The key quantity to distinguish between these two ideas is the connectivity of the unfolded ensemble. We present a metric to determine this connectivity for a given network, which can be calculated either from continuous folding trajectories, or a Markov model. The metric determines how often a region of space is used as an intermediate on transition paths that connect two other regions of space, and we use it here to determine how often two parts of the unfolded ensemble are connected directly, versus how often these transitions are mediated by the native state.

Quantifying Hub-like Behavior in Protein Folding Networks