Organisers

• Emanuele Paci (University of Leeds)
• Peter Olmsted (University of Leeds )
• Robert Best (National Institutes of Health)

Supports

 CECAM

 COST - MolSimu

Description

The recent development of experimental techniques for the mechanical manipulation of single molecules permits the measurement of forces and fluctuations on a molecular scale. However, measurements on such microscopic systems need to be analyzed differently from macroscopic phenomena (see e.g., Ref [1]). This has stimulated several theorists to develop approaches for extracting (possibly novel) information from the experiments, but only recently have these approaches been applied to real experimental data. In addition, many of the theoretical approaches may also be useful for interpreting atomistic molecular simulations. In fact, simulations of detailed models, particularly when large systems such as biomacromolecules are considered, do not easily allow the estimation of free energies changes related to large conformational changes.

The newly developed approaches can in principle allow the estimation of the relevant free energy differences from short, non-equilibrium simulations, although only few applications have been so far reported. Thus there exists a need for a discourse between the theoretical, simulation and experimental communities to strengthen the theoretical interpretation of single molecule force experiments and simulations and stimulate the development of new theory and experiments.

We propose to put together scientists who have been involved in the past few years in either developing theories relevant to single molecule pulling experiments, such as Jarzynski [2], Crooks [3], Szabo and Hummer [4, 5], with those who have performed simulations on more or less complex protein models, starting from Schulten [6], and experimentalists such as Bustamante whose work has made a close connection with single molecule theory to estimate free energies directly from the experiment [7]. For example, the remarkable result contained in the "Jarzynski identity", relates equilibrium quantities to non-equilibrium experiments or simulations, and is both fundamental and of great potential usefulness. In parallel, several "Fluctuation Theorems", which quantify the fluctuations that "violate" the Second Law of Thermodynamics in small systems, i.e. the deviations from average extensive thermodynamic behaviour [8], have been developed.

An open question about the Jarzynski identity is its practical utility in predicting macroscopic properties of systems such as proteins, that have many internal degrees of freedom, and its convergence in cases of practical interest.

Scientific Objectives

The main objective of the workshop is to assess achievements and limitations of theory, and possible tests of its usefulness by either molecular simulations or directly by experiment. An important consideration here is the application of theory to "noisy" experimental data, when the true fluctuations of the molecule are important, since this aspect is often ignored by theorists. Discussion of recent single molecule experiments, with which most of the participants are familiar, will hopefully address some of the controversies over their interpretation, or suggest new experiments which may do so. The practical applications to real biophysical problems will be a second objective, for example the extraction of binding free energies from either pulling experiments or simulations [9], or determining energy landscape "roughness" as suggested by Thirumalai [10]. Of particular interest is what information can be uniquely determined from single molecule pulling experiments (or simulations) and how it could improve our understanding of more general fields such as protein folding or protein-protein interaction. We also wish to evaluate the fundamental advancement that the novel single molecule techniques and the theoretical advancements provide to our understanding of the protein folding. For example, most recent applications of atomic force microscopy to mechanically unfold proteins have provided detailed and reliable information of the mechanical resistance of proteins when pulled in different "directions" [11], and also been able to record single refolding events [12, 13]; how could these advancements effectively contribute to our understanding of the folding mechanism? Computational issues The use of non-equilibrium approaches to computing free energy changes raises a number of specific computational questions. Can such simulations be used to obtain free energy differences more efficiently than conventional methods? Are there other advantages to using such approaches, for example, simpler utilization of computer clusters? The meeting will examine these and other practical issues involved in applying non-equilibrium theory to molecular simulation. To date, there are few applications of such methods in the literature, and so they are relatively poorly understood compared to conventional methods; by addressing the various technical issues, this meeting should open the way to more widespread applications.

References

[1] Bustamante, C, Liphardt, J, and Ritort, F. 2005. The nonequilibrium thermodynamics of small systems Physics Today 58:43­48.
[2] Jarzynski, C. 1997. Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach Phys. Rev. E 56:5018­5035.
[3] Crooks, G. E. 2000. Path-ensemble averages in systems driven far from equilibrium Phys. Rev. E 61:2361­2366.
[4] Hummer, G and Szabo, A. 2001. Free energy reconstruction from nonequilibrium singlemolecule pulling experiments Proc. Natl. Acad. Sci. USA 98:3658­3661.
[5] Hummer, G and Szabo, A. 2003. Kinetics from nonequilibrium single-molecule pulling experiments Biophys. J. 85:5­15.
[6] Gullingsrud, J. R, Braun, R, and Schulten, K. 1999. Reconstructing potentials of mean force through time series analysis of steered molecular dynamics simulations J. Comput. Phys. 151:190­211.
[7] Liphardt, J, Dumont, S, Smith, S. B, Tinoco, I, and Bustamante, C. 2002. Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality Science 296:1832­1835.
[8] Evans, D. J and Searles, D. J. 2002. The fluctuation theorem Adv. in Physics 51:1529­1585.
[9] Evans, E. 1999. Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces explored with dynamic force spectroscopy Faraday Discuss. 111:1­16.
[10] Hyeon, C and Thirumalai, D. 2003. Can energy landscape roughness of proteins and RNA be measured by using mechanical unfolding experiments? Proc. Natl. Acad. Sci. USA 100:10249­10253.
[11] Brockwell, D. J, Paci, E, Zinober, R. C, Beddard, G. S, Olmsted, P. D, Smith, D. A, Perham, R. N, and Radford, S. E. 2003. Pulling geometry defines the mechanical resistance of a sheet protein Nature Struct. Biol. 10:731­737.
[12] Fernandez, J. M and Li, H. 2004. Force-clamp spectroscopy monitors the folding trajectory of a single protein Science 303:1674­1678.
[13] Best, R. B and Hummer, G. 2005. Comment on "Force-clamp spectroscopy monitors the folding trajectory of a single protein" Science 308:498.