Unexpected relative aqueous solubilities of a phosphotyrosine analogue and two phosphonate derivatives

Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

We attempt to optimize the efficiency of thermodynamic integration, as defined by the minimal number of unphysical intermediate states required for the computation of accurate and precise free energy differences. The suitability of various numerical quadrature methods is tested. In particular, we compare the trapezoidal rule, Simpson's rule, Gauss-Legendre, Gauss-Kronrod-Patterson, and Clenshaw-Curtis integration, as well as integration based on a cubic spline approximation of the integrand. We find that Simpson's rule and spline integration are already significantly more efficient that the trapezoidal rule, i.e., correct free energy differences can be obtained using fewer λ-states. We demonstrate that Simpson's rule can be used advantageously with nonequidistant values of the abscissa, which increases the flexibility of the method. Efficiency is enhanced even further if higher order methods, such as Gauss-Legendre, Gauss-Kronrod-Patterson, or Clenshaw-Curtis integration, are used; no more than seven λ-states, which in the case of Clenshaw-Curtis integration include the physical end states, were required for accurate results in all test problems studied. Thus, the performance of thermodynamic integration can equal that of Bennett's acceptance ratio method. We also show, however, that the high efficiency found here relies on the particular functional form of the soft-core potential used; overall, thermodynamic integration is more susceptible to the details of the hybrid Hamiltonian used than Bennett's acceptance ratio method. Therefore, we recommend Bennett's acceptance ratio method as the most robust method to compute alchemical free energy differences; nevertheless, scenarios when thermodynamic integration may be preferable are discussed.

Unorthodox uses of Bennett's acceptance ratio method

We illustrate the application of Bennett's acceptance ratio method (BAR) to problems in which standard methods to compute free energy differences (thermodynamic integration, exponential formula) are not practical. Our starting point is the observation that BAR can often compute the free energy difference between two states without the need for intermediate states usually employed (and necessary) in alchemical free energy simulations. This is demonstrated first for the free energy difference between ethane and methanol in aqueous solution. We then show how BAR can be used to compute directly rather unusual free energy differences, such as the free energy difference resulting from changing the treatment of electrostatic interactions, from switching the force field, or from using an implicit solvent model. Calculations of this kind should prove useful for force field development and the validation of implicit solvent methods.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Guanidinium derivatives bind preferentially and trigger long-distance conformational changes in an engineered T4 lysozyme

The binding of guanidinium ion has been shown to promote a large-scale translation of a tandemly duplicated helix in an engineered mutant of T4 lysozyme. The guanidinium ion acts as a surrogate for the guanidino group of an arginine side chain. Here we determine whether methyl- and ethylguanidinium provide better mimics. The results show that addition of the hydrophobic moieties to the ligand enhances the binding affinity concomitant with reduction in ligand solubility. Crystallographic analysis confirms that binding of the alternative ligands to the engineered site still drives the large-scale conformational change. Thermal analysis and NMR data show, in comparison to guanidinium, an increase in protein stability and in ligand affinity. This is presumably due to the successive increase in hydrophobicity in going from guanidinium to ethylguanidinium. A fluorescence-based optical method was developed to sense the ligand-triggered helix translation in solution. The results are a first step in the de novo design of a molecular switch that is not related to the normal function of the protein.