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Protein unfolding from free-energy calculations: Integration of the Gaussian network model with bond binding energies

Amit Srivastava1,* and Rony Granek1,2,†

  • 1The Stella and Avram Goren-Goldstein Department of Biotechnology Engineering, Ben-Gurion University of The Negev, Beer Sheva 84105, Israel
  • 2The Ilse Katz Institute for Meso and Nanoscale Science and Technology, Ben-Gurion University of The Negev, Beer Sheva 84105, Israel

  • *Present address: Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 28223, USA.
  • †Corresponding author: rgranek@bgu.ac.il
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Phys. Rev. E 91, 022708 – Published 17 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.022708

Abstract

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

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Outline

Information

Phys. Rev. E 91, 022708– Published 17 February, 2015
  • Received 1 May 2014
  • Revised 10 October 2014

©2015 American Physical Society

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