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Register a new userAlchemical Transfer Approach to Absolute Binding Free Energy Estimation
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The Alchemical Transfer Method (ATM) for the calculation of standard binding free energies of non-covalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk, and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of ATM is as straightforward as for physical pathway methods of binding. The method is applicable in principle with any force field, it does not require splitting the alchemical transformations into electrostatic and non-electrostatic steps, and it does not require soft-core pair potentials. We have implemented ATM as a freely available and open-source plugin of the OpenMM molecular dynamics library. The method and its implementation are validated on the SAMPL6 SAMPLing host-guest benchmark set. The work paves the way to streamlined alchemical relative and absolute binding free energy implementations on many molecular simulation packages and with arbitrary energy functions including polarizable, quantum-mechanical, and artificial neural network potentials.
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We present an extension of Alchemical Transfer Method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional as well as scaffold-hopping alchemical transformations. The method, named ATM-RBFE, implemented in the free and open-source OpenMM molecular simulation package, aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than is currently available. The method is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly using a single solvent box prepared using conventional setup tools, without splitting of electrostatic and non-electrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against a benchmark set of estrogen receptor $alpha$ complexes. In each case, the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies, reference literature values as well as experimental measurements.
Although the importance of protein dynamics in protein function is generally recognized, the role of protein fluctuations in allosteric effects scarcely has been considered. To address this gap, the Kullback-Leibler divergence (Dx) between protein conformational distributions before and after ligand binding was proposed as a means of quantifying allosteric effects in proteins. Here, previous applications of Dx to methods for analysis and simulation of proteins are first reviewed, and their implications for understanding aspects of protein function and protein evolution are discussed. Next, equations for Dx suggest that k_{B}TDx should be interpreted as an allosteric free energy -- the free energy associated with changing the ligand-free protein conformational distribution to the ligand-bound conformational distribution. This interpretation leads to a thermodynamic model of allosteric transitions that unifies existing perspectives on the relation between ligand binding and changes in protein conformational distributions. The definition of Dx is used to explore some interesting mathematical relations among commonly recognized thermodynamic and biophysical quantities, such as the total free energy change upon ligand binding, and ligand-binding affinities for individual protein conformations. These results represent the beginnings of a theoretical framework for considering the full protein conformational distribution in modeling allosteric transitions. Early applications of the framework have produced results with implications both for methods for coarsed-grained modeling of proteins, and for understanding the relation between ligand binding and protein dynamics.
Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of bridging potential energy functions representing emph{alchemical} intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations, including relative and absolute small molecule binding free energy calculations to biomolecular targets.
We report the results of our participation in the SAMPL8 GDCC Blind Challenge for host-guest binding affinity predictions. Absolute binding affinity prediction is of central importance to the biophysics of molecular association and pharmaceutical discovery. The blinded SAMPL series have provided an important forum for assessing the reliability of binding free energy methods in an objective way. In this blinded challenge, we employed two binding free energy methods, the newly developed alchemical transfer method (ATM) and the well-established potential of mean force (PMF) physical pathway method, using the same setup and force field model. The calculated binding free energies from the two methods are in excellent quantitative agreement. Importantly, the results from the two methods were also found to agree well with the experimental binding affinities released subsequently, with an $R^2$ of 0.89 (ATM) and 0.83 (PMF). Given that the two free energy methods are based on entirely different thermodynamic pathways, the close agreement between the results from the two methods and their general agreement with the experimental binding free energies are a testament to the high quality achieved by theory and methods. The study provides further validation of the novel ATM binding free energy estimation protocol and it paves the way to further extensions of the method to more complex systems.
Signal transduction in biological cells is effected by signaling pathways that typically include multiple feedback loops. Here we analyze information transfer through a prototypical signaling module with biochemical feedback. The module switches stochastically between an inactive and active state; the input to the module governs the activation rate while the output (i.e., the product concentration) perturbs the inactivation rate. Using a novel perturbative approach, we compute the rate with which information about the input is gained from observation of the output. We obtain an explicit analytical result valid to first order in feedback strength and to second order in the strength of input. The total information gained during an extended time interval is found to depend on the feedback strength only through the total number of activation/inactivation events.
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