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Free energy profiles from single-molecule pulling experiments.

ABSTRACT: Nonequilibrium pulling experiments provide detailed information about the thermodynamic and kinetic properties of molecules. We show that unperturbed free energy profiles as a function of molecular extension can be obtained rigorously from such experiments without using work-weighted position histograms. An inverse Weierstrass transform is used to relate the system free energy obtained from the Jarzynski equality directly to the underlying molecular free energy surface. An accurate approximation for the free energy surface is obtained by using the method of steepest descent to evaluate the inverse transform. The formalism is applied to simulated data obtained from a kinetic model of RNA folding, in which the dynamics consists of jumping between linker-dominated folded and unfolded free energy surfaces.

SUBMITTER: Hummer G

PROVIDER: S-EPMC3003121 | biostudies-literature | 2010 Dec

REPOSITORIES: biostudies-literature

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Free energy profiles from single-molecule pulling experiments.

Hummer Gerhard G Szabo Attila A

Proceedings of the National Academy of Sciences of the United States of America 20101122 50

Nonequilibrium pulling experiments provide detailed information about the thermodynamic and kinetic properties of molecules. We show that unperturbed free energy profiles as a function of molecular extension can be obtained rigorously from such experiments without using work-weighted position histograms. An inverse Weierstrass transform is used to relate the system free energy obtained from the Jarzynski equality directly to the underlying molecular free energy surface. An accurate approximation ...[more]

PMID: 21098304

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Project description:Protein conformations change among distinct thermodynamic states as solution conditions (temperature, denaturants, pH) are altered or when they are subjected to mechanical forces. A quantitative description of the changes in the relative stabilities of the various thermodynamic states is needed to interpret and predict experimental outcomes. We provide a framework based on the Molecular Transfer Model (MTM) to account for pH effects on the properties of globular proteins. The MTM utilizes the partition function of a protein calculated from molecular simulations at one set of solution conditions to predict protein properties at another set of solution conditions. To take pH effects into account, we utilized experimentally measured pK(a) values in the native and unfolded states to calculate the free energy of transferring a protein from a reference pH to the pH of interest. We validate our approach by demonstrating that the native-state stability as a function of pH is accurately predicted for chymotrypsin inhibitor 2 (CI2) and protein G. We use the MTM to predict the response of CI2 and protein G subjected to a constant force (f) and varying pH. The phase diagrams of CI2 and protein G as a function of f and pH are dramatically different and reflect the underlying pH-dependent stability changes in the absence of force. The calculated equilibrium free energy profiles as functions of the end-to-end distance of the two proteins show that, at various pH values, CI2 unfolds via an intermediate when subjected to f. The locations of the two transition states move toward the more unstable state as f is changed, which is in accord with the Hammond-Leffler postulate. In sharp contrast, force-induced unfolding of protein G occurs in a single step. Remarkably, the location of the transition state with respect to the folded state is independent of f, which suggests that protein G is mechanically brittle. The MTM provides a natural framework for predicting the outcomes of ensemble and single-molecule experiments for a wide range of solution conditions.

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Free energy profiles from single-molecule pulling experiments.

Publications

Free energy profiles from single-molecule pulling experiments.

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