Georgia Institute of Technology College of Sciences

The behavior and function of proteins necessarily occurs during nonequilibrium conditions such as when a protein unfolds or binds. The need to treat both the dynamics and the high-dimensionality of proteins and their environments presents significant challenges to theoretical or computational methods. The present work attempts to reign in this complexity by way of capturing the dominant energetic pathway in a particular protein motion. In particular, the energetics of an unfolding event can be formally obtained using steered molecular dynamics (SMD) and Jarzynski’s inequality but the cost of the calculation increases dramatically with the length of the pathway. An adaptive algorithm has been introduced that allows for this pathway to be nonlinear and staged while reducing the computational cost. The potential of mean force (PMF) obtained for neuropeptide Y (NPY) in water along an unfolding path confirmed that the monomeric form of NPY adopts the pancreatic-polypeptide (PP) fold. [J. Chem. Theory Comput. 6, 3026-3038 (2010); 10.1021/ct100320g.] Adaptive SMD can also be used to reconstruct the PMF obtained earlier for stretching decaalanine in vacuum at lower computational cost. [J. Chem. Phys. 136, 215104 (2012); 10.1063/1.4725183.] The PMF for stretching decaalanine in water solvent (using the TIP3P water potential) at 300K has now been obtained using adaptive SMD. [J. Chem. Theory Comput. 8, 4837 (2012); 10.1021/ct300709u] Not surprisingly, the stabilization from the water solvent reduces the overall work required to unfold it. However, the PMF remains structured suggesting that some regions of the energy landscape act partially as doorways. This is also further verified through a study of the hydrogen-bond breaking and formation along the stretching paths of decaalanine in vacuum and solvent. (Rescheduled from Feb 12th.)

Given a surface in space with a set of curves on it, one can ask whichpossible combinatorial arrangement of curves are possible. We give anenriched formulation of this question in terms of which two-dimensionalfans occur as the tropicalization of an algebraic surface in space. Ourmain result is that the arrangement is either degenerate or verycomplicated. Along the way, we introduce tropical Laplacians, ageneralization of graph Laplacians, explain their relation to the Colin deVerdiere invariant and to tensegrity frameworks in dynamics.This is joint work with June Huh.

Resonances are important in the study of transient phenomenaassociated with the wave equation, especially in understanding the largetime behavior of the solution to the wave equation when radiation lossesare small. In this talk, I will present recent studies on the scatteringresonances for photonic structures and Schrodinger operators. I will beginwith a study on the finite symmetric photoinc structure to illustrate theconvergence behavior of resonances. Then a general perturbation approachwill be introduced for the analysis of near bound-state resonances for bothcases. In particular, it is shown that, for a finite one dimensionalphotonic crystal with a defect, the near bound-state resonances converge tothe point spectrum of the infinite structure with an exponential rate whenthe number of periods increases. An analogous exponential decay rate alsoholds for the Schrodinger operator with a potential function that is alow-energy well surrounded by a thick barrier. The analysis also leads to asimple and accurate numerical approach to approximate the near bound-stateresonances. This is a joint work with Prof. Fadil Santosa in University ofMinnesota.

Kelly will be leading the discussion and presenting topics from Chapter 2 Section 4 of Bounded Analytic Functions.