Assessment and Optimization of Collective Variables for Protein Conformational Landscape: GB1 β-hairpin as a Case Study

Abstract

Collective variables (CV), when chosen judiciously, can play an important role in recognizing rate-limiting processes and rare events in any biomolecular systems. However, high dimensionality and inherent complexities associated with such biochemical systems render the identification of an optimal CV a challenging task, which in turn precludes the elucidation of underlying conformational landscape in su cient details. In this context, a relevant model system is presented by 16-residue -hairpin of GB1 protein. Despite being the target of numerous theoretical and computational studies for understanding the protein folding, the set of CVs optimally characterizing the conformational landscape of -hairpin of GB1 protein has remained elusive, resulting in a lack of consensus on its folding mechanism. Here we address this by proposing a pair of optimal CVs which can resolve the underlying free energy landscape of GB1 hairpin quite e ciently. Expressed as a linear combination of a number of traditional CVs, the optimal CV for this system is derived by employing recently introduced Time-structured Independent Component Analysis (TICA) approach on a large number of independent unbiased simulations. By projecting the replica-exchange simulated trajectories along these pair of optimized CVs, the resulting free energy landscape of this system are able to resolve four distinct well-separated metastable states encompassing the extensive ensembles of folded,unfolded and molten globule states. Importantly, the optimized CVs were found to be capable of automatically recovering a novel partial helical state of this protein, without needing to explicitly invoke helicity as a constituent CV. Furthermore, a quantitative sensitivity analysis of each constituent in the optimized CV provided key insights on the relative contributions of the constituent CVs in the overall free energy landscapes. Finally, the kinetic pathways connecting these metastable states, constructed using a Markov State Model, provide an optimum description of underlying folding mechanism of the peptide. Taken together, this work o↵ers a quantitatively robust approach towards comprehensive mapping of the underlying folding landscape of a quintessential model system along its optimized collective variables.