Integrated Calendar

Throughout evolution, biology has harnessed this modularity to carry out specialized roles and regulate higher-order functions such as allostery. Cooperative communication between such protein regions is important for catalysis, regulation, and efficient folding; indeed, lack of domain coupling has been implicated in the formation of fibrils and other misfolding pathologies. How domains communicate and contribute to a protein’s energetics and folding, however, is still poorly understood. Bulk methods rely on a simultaneous and global perturbation of the system (temperature or chemical denaturants) and can miss potential intermediates, thereby overestimating protein cooperativity and domain coupling. I will show that by using optical tweezers it is possible to mechanically induce the selective unfolding of particular regions of single T4 lysozyme molecules and establish the response of regions not directly affected by the force. In particular, I will discuss how the coupling between distinct domains in the protein depends on the topological organization of the polypeptide chain. To reveal the status of protein regions not directly subjected to force, we determined the free energy changes during mechanical unfolding using Crooks’ Fluctuation Theorem. We evaluate the cooperativity between domains by determining the unfolding energy of topological variants pulled along different directions. We show that topology of the polypeptide chain critically determines the folding cooperativity between domains and, thus, what parts of the folding/unfolding landscape are explored. We speculate that proteins may have evolved to select certain topologies that increase coupling between regions to avoid areas of the landscape that lead to kinetic trapping and misfolding.

In Hele-Shaw flows a boundary of a viscous fluid develops unstable fingering patterns. At vanishing surface tension, fingers evolve to cusp-like singularities which prevent a smooth flow. In the talk I argue that the Hele-Shaw problem admits a unique " weak solution", where a singularity triggers shocks. Shocks form a growing, branching tree of a line distribution of vorticity where pressure has a finite discontinuity. A condition that the flow remains curl-free at a macroscale uniquely determines peculiar shock graph structure.