Analysis of the Free-Energy Surface of Proteins from Reversible Folding Simulations

Allen, Lucy R.; Krivov, Sergei V.; Paci, Emanuele
July 2009
PLoS Computational Biology;Jul2009, Vol. 5 Issue 7, p1
Academic Journal
Computer generated trajectories can, in principle, reveal the folding pathways of a protein at atomic resolution and possibly suggest general and simple rules for predicting the folded structure of a given sequence. While such reversible folding trajectories can only be determined ab initio using all-atom transferable force-fields for a few small proteins, they can be determined for a large number of proteins using coarse-grained and structure-based force-fields, in which a known folded structure is by construction the absolute energy and free-energy minimum. Here we use a model of the fast folding helical λ-repressor protein to generate trajectories in which native and non-native states are in equilibrium and transitions are accurately sampled. Yet, representation of the free-energy surface, which underlies the thermodynamic and dynamic properties of the protein model, from such a trajectory remains a challenge. Projections over one or a small number of arbitrarily chosen progress variables often hide the most important features of such surfaces. The results unequivocally show that an unprojected representation of the free-energy surface provides important and unbiased information and allows a simple and meaningful description of many-dimensional, heterogeneous trajectories, providing new insight into the possible mechanisms of fast-folding proteins.


Related Articles

  • Free energy for protein folding from nonequilibrium simulations using the Jarzynski equality. West, Daniel K.; Olmsted, Peter D.; Paci, Emanuele // Journal of Chemical Physics;11/28/2006, Vol. 125 Issue 20, p204910 

    The equilibrium free energy difference between two long-lived molecular species or “conformational states” of a protein (or any other molecule) can in principle be estimated by measuring the work needed to shuttle the system between them, independent of the irreversibility of the...

  • Introducing sampling entropy in repository based adaptive umbrella sampling. Han Zheng; Yingkai Zhang // Journal of Chemical Physics;12/7/2009, Vol. 131 Issue 21, p214105 

    Determining free energy surfaces along chosen reaction coordinates is a common and important task in simulating complex systems. Due to the complexity of energy landscapes and the existence of high barriers, one widely pursued objective to develop efficient simulation methods is to achieve...

  • Universal simulation method to compute surface and interfacial free energies of disordered solids. Grochola, Gregory; Russo, Salvy P.; Snook, Ian K.; Yarovsky, Irene // Journal of Chemical Physics;10/22/2002, Vol. 117 Issue 16, p7685 

    Previously we studied λ-integration paths for the calculation of "exact" surface and interfacial free energies that were limited to simulation methods where atomic interactions can be scaled using a multiplicative parameter λ, as is the case for analytical empirical potentials. Here we...

  • Computing absolute free energies of disordered structures by molecular simulation. Schilling, T.; Schmid, F. // Journal of Chemical Physics;12/21/2009, Vol. 131 Issue 23, p231102 

    We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from a configuration which is representative for the state...

  • Analytical solutions describing the phase separation driven by a free energy functional... Ohnishi, Isamu; Nishiura, Yasumasa; Imai, Masaki; Matsushita, Yushu // Chaos;Jun99, Vol. 9 Issue 2, p329 

    Provides analytical solutions describing the phase separation driven by a free energy functional containing a long-range interaction term. Thermodynamic equilibrium state of the phase separation phenomenon; Characterization of the periodic structure of the global minimizer of the functional.

  • Solution of the Percus–Yevick equation for hard spherocylinders. I. The entire pair correlation function. Lago, S.; Sevilla, P. // Journal of Chemical Physics;10/1/1988, Vol. 89 Issue 7, p4349 

    The Percus–Yevick equation for hard spherocylinders has been numerically solved using a recent algorithm to calculate the shortest distances between rods proposed by ourselves. The equation is solved for four different reduced densities to η=0.3879 and length-to-breadth ratio L*=1.0....

  • Thermodynamic integration of the free energy along a reaction coordinate in Cartesian coordinates. den Otter, W. K.; den Otter, W.K. // Journal of Chemical Physics;5/1/2000, Vol. 112 Issue 17 

    A generalized formulation of the thermodynamic integration (TI) method for calculating the free energy along a reaction coordinate is derived. Molecular dynamics simulations with a constrained reaction coordinate are used to sample conformations. These are then projected onto conformations with...

  • A closure for the Ornstein-Zernike relation that gives rise to the thermodynamic consistency. Byung Chan Eu; Rah, Kyunil // Journal of Chemical Physics;8/22/1999, Vol. 111 Issue 8, p3327 

    Proposes a closure for the direct correlation function in the grand canonical ensemble theory that gives rise to the thermodynamic consistency. Calculation of the excess chemical potentials by means of the thermodynamic derivative and statiscal mechanical formula; Integral equation for the pair...

  • Biased Metropolis Sampling for Rugged Free Energy Landscapes. Berg, Bernd A. // AIP Conference Proceedings;2003, Vol. 690 Issue 1, p63 

    Metropolis simulations of all-atom models of peptides (i.e. small proteins) are considered. Inspired by the funnel picture of Bryngelson and Wolyness, a transformation of the updating probabilities of the dihedral angles is defined, which uses probability densities from a higher temperature to...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics