Calculating the Sensitivity and Robustness of Binding Free Energy Calculations to Force Field Parameters

Binding free energy calculations offer a thermodynamically rigorous method to compute protein-ligand binding, and they depend on empirical force fields with hundreds of parameters. We examined the sensitivity of computed binding free energies to the ligand's electrostatic and van der Waals parameters. Dielectric screening and cancellation of effects between ligand-protein and ligand-solvent interactions reduce the parameter sensitivity of binding affinity by 65%, compared with interaction strengths computed in the gas-phase. However, multiple changes to parameters combine additively on average, which can lead to large changes in overall affinity from many small changes to parameters. Using these results, we estimate that random, uncorrelated errors in force field nonbonded parameters must be smaller than 0.02 e per charge, 0.06 Å per radius, and 0.01 kcal/mol per well depth in order to obtain 68% (one standard deviation) confidence that a computed affinity for a moderately-sized lead compound will fall within 1 kcal/mol of the true affinity, if these are the only sources of error considered

Separated topologies—A method for relative binding free energy calculations using orientational restraints

Orientational restraints can improve the efficiency of alchemical free energy calculations, but they are not typically applied in relative binding calculations, which compute the affinity difference been two ligands. Here, we describe a new “separated topologies” method, which computes relative binding free energies using orientational restraints and which has several advantages over existing methods. While standard approaches maintain the initial and final ligand in a shared orientation, the separated topologies approach allows the initial and final ligands to have distinct orientations. This avoids a slowly converging reorientation step in the calculation. The separated topologies approach can also be applied to determine the relative free energies of multiple orientations of the same ligand. We illustrate the approach by calculating the relative binding free energies of two compounds to an engineered site in Cytochrome C Peroxidase

Dataset for article: "Massively parallel de novo protein design for targeted therapeutics", DOI: 10.1038/nature23912

"Massively parallel de novo protein design for targeted therapeutics" DOI: 10.1038/nature23912 Supplementary Information. Archive of designs, Rosetta metrics and experimental results. Authors: Aaron Chevalier*, Daniel-Adriano Silva*, Gabriel J. Rocklin*, Derrick R. Hicks, Renan Vergara, Patience Murapa, Steffen M. Bernard, Lu Zhang, Kwok-ho Lam, Guorui Yao, Christopher D. Bahl, Shin-ichiro Miyashita, Inna Goreshnik, James T. Fuller, Merika T. Koday, Cody Jenkins, Tom Colvin, Lauren Carter, Alan Bohn, Cassie M. Bryan, D. Alejandro Fernández-Velasco, Lance Stewart, Min Dong, Xuhui huang, Rongsheng Jin, Ian A. Wilson, Deborah H. Fuller & David Baker *These authors contributed equally to this work. Correspondence to: [email protected] Dataset Compiled by D-A.S. Date: 13/Sep/201

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning

Prediction and validation of a protein's free energy surface using hydrogen exchange and (importantly) its denaturant dependence

[Image: see text] The denaturant dependence of hydrogen–deuterium exchange (HDX) is a powerful measurement to identify the breaking of individual H-bonds and map the free energy surface (FES) of a protein including the very rare states. Molecular dynamics (MD) can identify each partial unfolding event with atomic-level resolution. Hence, their combination provides a great opportunity to test the accuracy of simulations and to verify the interpretation of HDX data. For this comparison, we use Upside, our new and extremely fast MD package that is capable of folding proteins with an accuracy comparable to that of all-atom methods. The FESs of two naturally occurring and two designed proteins are so generated and compared to our NMR/HDX data. We find that Upside’s accuracy is considerably improved upon modifying the energy function using a new machine-learning procedure that trains for proper protein behavior including realistic denatured states in addition to stable native states. The resulting increase in cooperativity is critical for replicating the HDX data and protein stability, indicating that we have properly encoded the underlying physiochemical interactions into an MD package. We did observe some mismatch, however, underscoring the ongoing challenges faced by simulations in calculating accurate FESs. Nevertheless, our ensembles can identify the properties of the fluctuations that lead to HDX, whether they be small-, medium-, or large-scale openings, and can speak to the breadth of the native ensemble that has been a matter of debate