CGI – Accurate Free Energy Differences from Non-Equilibrium Simulations

Goette, M.; Grubmuller, H.: Accuracy and convergence of free energy differences calculated from nonequilibrium switching processes. Journal of Computational Chemistry 30 (3), pp. 447 - 456 (2009)
Schematic Gaussian work distributions for the switching from state A to B for a forward [Pf (W ), solid line] and a reverse [Pr (−W ), dashed line] process. Wf, σf, −Wr, and σr are the means and standard deviations of Pf (W ) and Pr (−W ), respectively. These values are used to calculate the free energy difference FCGI .

The molecular-dynamics-based calculation of accurate free energy differences for biomolecular systems is a challenging task. Accordingly, convergence and accuracy of established equilibrium methods has been subject of many studies, often focusing on small test systems. In contrast, the potential of more recently proposed nonequilibrium methods (based on Fast Growth Thermodynamic Integration, FGTI), derived from the Jarzynski and Crooks equalities, has not yet fully been explored.

Comparison of free energy calculations (A) System E2M, (B) System W2G. The total simulation time is shown on a logarithmic time scale. The upper scale shows the corresponding number of FGTI trajectories used (unidirectional). For each Slow Growth Thermodynamic Integration (SGTI) free energy calculation, one trajectory was used.

We compare the performance of these methods by calculating free energy differences for test systems at different levels of complexity and varying the extent of the involved perturbations. We consider the interconversion of ethane into methanol, the switching of a tryptophane side chain into a tripeptide, and the binding of two different ligands to the globular protein snurportin 1. On the basis of our results, we suggest and assess a new nonequilibrium free energy method, Crooks Gaussian Intersection (CGI), which combines the advantages of existing methods. CGI is highly parallelizable and, for the test systems considered here, is shown to outperform the other studied equilibrium and nonequilibrium methods.

Convergence of Non-Equilibrium-Work free energies for differing FGTI trajectory lengths on a logarithmic scale (A) system E2M, (B) system W2G, (C) system SPN. Trajectory lengths vary from 1 to 200 ps. The errors of the BAR method for the very short trajectories (1–25 ps) are often very large and are therefore not shown in the plot.

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