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.

Exact penalties for variational inequalities with applications to nonlinear complementarity problems

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best theoretical results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We close the paper with some preliminary computational tests on the use of a semismooth Newton method to solve the equation derived from the new reformulation. We also compare its performance with the Newton method applied to classical reformulations based on the Fischer-Burmeister function and on the minimum. The new reformulation combines the best features of the classical ones, being as easy to solve as the reformulation that uses the Fischer-Burmeister function while requiring as few Newton steps as the one that is based on the minimum.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.