Overcoming barriers in macromolecular simulations: non-Boltzmann thermodynamic integration
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A new combination of non-Boltzmann sampling (umbrella sampling) and thermodynamic integration for the computation of free energies of flexible systems is described and compared with other methods in terms of its accuracy, efficiency, and viability for simulations of macromolecules. The non-Boltzmann sampling is achieved through the definition of a surrogate potential function that uniformly reduces barriers between energy minima of a given molecule while retaining the overall features of its torsional profile. The influence of the surrogate potential on the free energy calculation is taken into account by a correction similar to umbrella sampling. This work is tested by computation of the free energy of hydration difference between butane and propanol. The free energy difference converges to the experimentally measured value in one tenth of the computer time required for a simulation employing conventional thermodynamic integration without the umbrella potential. Moreover, the deviations of the computed free energies for similar sampling periods are greatly reduced with the new method. Finally, an accurate free energy difference is obtained in one third of the number of simulations that are necessary for the multi-state isomeric method.
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