Non-Equilibrium Fluctuation Theorems, Redundant Paths in Proteins, and Elucidating Conformational Changes by Single-Residue Perturbations

Abstract

Recently we have put forward the efficacy of single residue perturbations for a protein to populate its alternative conformational states[1-3]. In this work, we explain why mutation or protonation of a single-residue can create substantial conformational changes. First, we introduce a methodology which couples the network-based perturbation-response scanning (PRS) technique[4] with repeated constant force-steered molecular dynamics (CF-SMD)[5] simulations. Second, we utilize Crooks’ fluctuation theorem[6] to measure the free-energy differences between conformational states to classify the circumstances under which a mutation or protonation achieves population shifts. Finally, we trace the relationship between the non-equilibrium trajectories(NET) from CF-SMD and redundant pathways in residue networks[1], and employ this relationship in interpreting the outcomes of the fluctuation theorems so as to ferret out the degree of collectivity in residue fluctuations.Here are the procedure and sample results for calmodulin: (i)PRS takes the most-populated calmodulin conformation(3cln) and identifies E31whose directional-sensitive perturbations results in positional changes that yields the best overlap with considerably less populated states[7,2];(ii) through extensive MD simulations, E31A mutation reproduces structures consistent with those from NMR experiments[8];(iii) repeated CF-SMD runs for E31A produce NET between the two states, while those for E31 protonation do not;(iv) via Crooks’ fluctuation theorem, we find the free-energy barrier between the two states to be +0.60kcal/mole for E31A. E31A MD runs reproduce conformational changes between states three orders of magnitude faster than in wild type[7]. Analysis of the NET for redundant paths reveals collectivity induced by strategically inserted point mutations.1. Atilgan et al., Annu. Rev. Biophys. 41, 205(2012).2. Atilgan et al., J. Chem. Phys. 135, 155102(2011).3. Atilgan et al., Biophys. J. 99, 933(2010).4. Atilgan and Atilgan, PLoS Comput. Biol. 5, e1000544(2009).5. Izrailev et al., Biophys. J.72, 1568(1997).6. Crooks, Phys.Rev.E 60, 2721(1999).7. Slaughter et al., J.Phys.Chem.B 109, 12658(2005).8. Gsponer et al., Structure 16, 736(2008).