Soliton driven relaxation dynamics and universality in protein collapse

Protein collapse can be viewed as a dynamical phase transition, during which new scales and collective variables become excited while the old ones recede and fade away. This causes formidable computational bottle-necks in approaches that are based on atomic scale scrutiny. Here we consider an effective dynamical Landau theory to model the folding process at biologically relevant time and distance scales. We reach both a substantial decrease in the execution time and improvement in the accuracy of the final configuration, in comparison to more conventional approaches. As an example we inspect the collapse of HP35 chicken villin headpiece subdomain, where there are detailed molecular dynamics simulations to compare with. We start from a structureless, unbend and untwisted initial configuration. In less than one second of wall-clock time on a single processor personal computer we consistently reach the native state with 0.5 Angstrom root mean square distance (RMSD) precision. We confirm that our folding pathways are indeed akin those obtained in recent atomic level molecular dynamics simulations. We conclude that our approach appears to have the potential for a computationally economical method to accurately understand theoretical aspects of protein collapse.

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