Complex network analysis of free-energy landscapes

doi:10.1073/pnas.0608099104

Complex network analysis of free-energy landscapes

^†Laboratoire de Biophysique Statistique, SB/ITP, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland;
^§Department of Biochemistry, University of Zurich, CH-8057 Zurich, Switzerland;
^‖Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, I-00184 Rome, Italy; and
^††Dipartimento di Fisica, Universita di Roma “La Sapienza,” I-00185 Rome, Italy

Edited by Hans Frauenfelder, Los Alamos National Laboratory, Los Alamos, NM, and approved November 28, 2006 (received for review September 14, 2006)

Abstract

The kinetics of biomolecular isomerization processes, such as protein folding, is governed by a free-energy surface of high dimensionality and complexity. As an alternative to projections into one or two dimensions, the free-energy surface can be mapped into a weighted network where nodes and links are configurations and direct transitions among them, respectively. In this work, the free-energy basins and barriers of the alanine dipeptide are determined quantitatively using an algorithm to partition the network into clusters (i.e., states) according to the equilibrium transitions sampled by molecular dynamics. The network-based approach allows for the analysis of the thermodynamics and kinetics of biomolecule isomerization without reliance on arbitrarily chosen order parameters. Moreover, it is shown on low-dimensional models, which can be treated analytically, as well as for the alanine dipeptide, that the broad-tailed weight distribution observed in their networks originates from free-energy basins with mainly enthalpic character.

Footnotes

^¶To whom correspondence may be addressed. E-mail: francesco.rao{at}roma1.infn.it or caflisch{at}bioc.unizh.ch
Author contributions: D.G. and F.R. designed research; D.G., P.D.L.R., and F.R. performed research; D.G., P.D.L.R., A.C., and F.R. analyzed data; and A.C. and F.R. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS direct submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0608099104/DC1.
Abbreviations:

CSN,

configuration space network;

MD,

molecular dynamics;

MCL,

Markov clustering;

Q,

modularity;

DG,

disconnectivity graph.