Mapping the Intramolecular Vibrational Energy Flow in Proteins Reveals Functionally Important Residues

Unveiling the mechanisms of energy relaxation in biomolecules is key to our understanding of protein stability, allostery, intramolecular signaling, and long-lasting quantum coherence phenomena at ambient temperatures. Yet, the relationship between the pathways of energy transfer and the functional role of the residues involved remains largely unknown. Here, we develop a simulation method of mapping out residues that are highly efficient in relaxing an initially localized excess vibrational energy and perform site-directed mutagenesis functional assays to assess the relevance of these residues to protein function. We use the ligand binding domains of thyroid hormone receptor (TR) subtypes as a test case and find that conserved arginines, which are critical to TR transactivation function, are the most effective heat diffusers across the protein structure. These results suggest a hitherto unsuspected connection between a residue`s ability to mediate intramolecular vibrational energy redistribution and its functional relevance.

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.