Automated Force Field Parameterization for Nonpolarizable and Polarizable Atomic Models Based on Ab Initio Target Data

Classical molecular dynamics (MD) simulations based on atomistic models are increasingly used to study a wide range of biological systems. A prerequisite for meaningful results from such simulations is an accurate molecular mechanical force field. Most biomolecular simulations are currently based on the widely used AMBER and CHARMM force fields, which were parametrized and optimized to cover a small set of basic compounds corresponding to the natural amino acids and nucleic acid bases. Atomic models of additional compounds are commonly generated by analogy to the parameter set of a given force field. While this procedure yields models that are internally consistent, the accuracy of the resulting models can be limited. In this work, we propose a method, general automated atomic model parameterization (GAAMP), for generating automatically the parameters of atomic models of small molecules using the results from ab initio quantum mechanical (QM) calculations as target data. Force fields that were previously developed for a wide range of model compounds serve as initial guesses, although any of the final parameter can be optimized. The electrostatic parameters (partial charges, polarizabilities, and shielding) are optimized on the basis of QM electrostatic potential (ESP) and, if applicable, the interaction energies between the compound and water molecules. The soft dihedrals are automatically identified and parametrized by targeting QM dihedral scans as well as the energies of stable conformers. To validate the approach, the solvation free energy is calculated for more than 200 small molecules and MD simulations of three different proteins are carried out

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost

Simulating the Distance Distribution between Spin-Labels Attached to Proteins

EPR/DEER spectroscopy is playing an increasingly important role in the characterization of the conformational states of proteins. In this study, force field parameters for the bifunctional spin-label (RX) used in EPR/DEER are parametrized and tested with molecular dynamics (MD) simulations. The dihedral angles connecting the C_α atom of the backbone to the nitroxide ring moiety of the RX spin-label attached to <i>i</i> and <i>i</i> + 4 positions in a polyalanine α-helix agree very well with those observed in the X-ray crystallography. Both RX_{<i>i</i>,<i>i</i>+4} and RX_{<i>i</i>,<i>i</i>+3} are more rigid than the monofunctional spin-label (R1) commonly used in EPR/DEER, while RX_{<i>i</i>,<i>i</i>+4} is more rigid and causes less distortion in a protein backbone than RX_{<i>i</i>,<i>i</i>+3}. Simplified dummy spin-label models with a single effective particle representing the RX_{<i>i</i>,<i>i</i>+3} and RX_{<i>i</i>,<i>i</i>+4} are also developed and parametrized from the all-atom simulations. MD simulations with dummy spin-labels (MDDS) provide distance distributions that can be directly compared to distance distributions obtained from EPR/DEER to rapidly assess if a hypothetical three-dimensional (3D) structural model is consistent with experiment. The dummy spin-labels can also be used in the restrained-ensemble MD (re-MD) simulations to carry out structural refinement of 3D models. Applications of this methodology to T4 lysozyme, KCNE1, and LeuT are shown to provide important insights about their conformational dynamics

Computational Analysis of the Binding Specificity of Gleevec to Abl, c‑Kit, Lck, and c‑Src Tyrosine Kinases

Gleevec, a well-known cancer therapeutic agent, is an effective inhibitor of several tyrosine kinases, including Abl and c-Kit, but displays less potency to inhibit closely homologous tyrosine kinases, such as Lck and c-Src. Because many structural features of the binding site are highly conserved in these homologous kinases, the molecular determinants responsible for the binding specificity of Gleevec remain poorly understood. To address this issue, free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent was used to compute the binding affinity of Gleevec to Abl, c-Kit, Lck, and c-Src. The results of the FEP/MD calculations are in good agreement with experiments, enabling a detailed and quantitative dissection of the absolute binding free energy in terms of various thermodynamic contributions affecting the binding specificity of Gleevec to the kinases. Dominant binding free energy contributions arises from the van der Waals dispersive interaction, compensating about two-thirds of the unfavorable free energy penalty associated with the loss of translational, rotational, and conformational freedom of the ligand upon binding. In contrast, the contributions from electrostatic and repulsive interactions nearly cancel out due to solvent effects. Furthermore, the calculations show the importance of the conformation of the kinase activation loop. Among the kinases examined, Abl provides the most favorable binding environment for Gleevec via optimal protein–ligand interactions and a small free energy cost for loss of the translational, rotational, and conformational freedom upon ligand binding. The FEP/MD calculations additionally reveal that Lck and c-Src provide similar nonbinding interactions with the bound-Gleevec, but the former pays less entropic penalty for the ligand losing its translational, rotational, and conformational motions to bind, examining the empirically observed differential binding affinities of Gleevec between the two Src-family kinases

Committor-Consistent Variational String Method

The treatment of slow and rare transitions in the simulation of complex systems poses a great computational challenge. A powerful approach to tackle this challenge is the string method, which represents the transition path as a one-dimensional curve in a multidimensional space of collective variables. Commonly used strategies for pathway optimization include aligning the tangent of the string to the local mean force or to the mean drift determined from swarms of short trajectories. Here, a novel strategy is proposed, allowing the string to be optimized based on a variational principle involving the unidirectional reactive flux expressed in terms of the time-correlation function of the committor. The method is illustrated with model systems and then probed with the alanine dipeptide and a coarse-grained model of the barstar-barnase protein complex. Successive iterations variationally refine the string toward an optimal transition pathway following the gradient of the committor between two metastable states

Computational Study of the “DFG-Flip” Conformational Transition in c‑Abl and c‑Src Tyrosine Kinases

Protein tyrosine kinases are crucial to cellular signaling pathways regulating cell growth, proliferation, metabolism, differentiation, and migration. To maintain normal regulation of cellular signal transductions, the activities of tyrosine kinases are also highly regulated. The conformation of a three-residue motif Asp-Phe-Gly (DFG) near the N-terminus of the long “activation” loop covering the catalytic site is known to have a critical impact on the activity of c-Abl and c-Src tyrosine kinases. A conformational transition of the DFG motif can switch the enzyme from an active (DFG-in) to an inactive (DFG-out) state. In the present study, the string method with swarms-of-trajectories was used to computationally determine the reaction pathway connecting the two end-states, and umbrella sampling calculations were carried out to characterize the thermodynamic factors affecting the conformations of the DFG motif in c-Abl and c-Src kinases. According to the calculated free energy landscapes, the DFG-out conformation is clearly more favorable in the case of c-Abl than that of c-Src. The calculations also show that the protonation state of the aspartate residue in the DFG motif strongly affects the in/out conformational transition in c-Abl, although it has a much smaller impact in the case of c-Src due to local structural differences

The Activation of c‑Src Tyrosine Kinase: Conformational Transition Pathway and Free Energy Landscape

Tyrosine kinases are important cellular signaling allosteric enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Their activity must be tightly controlled, and malfunction can lead to a variety of diseases, particularly cancer. The nonreceptor tyrosine kinase c-Src, a prototypical model system and a representative member of the Src-family, functions as complex multidomain allosteric molecular switches comprising SH2 and SH3 domains modulating the activity of the catalytic domain. The broad picture of self-inhibition of c-Src via the SH2 and SH3 regulatory domains is well characterized from a structural point of view, but a detailed molecular mechanism understanding is nonetheless still lacking. Here, we use advanced computational methods based on all-atom molecular dynamics simulations with explicit solvent to advance our understanding of kinase activation. To elucidate the mechanism of regulation and self-inhibition, we have computed the pathway and the free energy landscapes for the “inactive-to-active” conformational transition of c-Src for different configurations of the SH2 and SH3 domains. Using the isolated c-Src catalytic domain as a baseline for comparison, it is observed that the SH2 and SH3 domains, depending upon their bound orientation, promote either the inactive or active state of the catalytic domain. The regulatory structural information from the SH2–SH3 tandem is allosterically transmitted via the N-terminal linker of the catalytic domain. Analysis of the conformational transition pathways also illustrates the importance of the conserved tryptophan 260 in activating c-Src, and reveals a series of concerted events during the activation process

Comparison between Mean Forces and Swarms-of-Trajectories String Methods

The original formulation of the string method in collective variable space is compared with a recent variant called string method with swarms-of-trajectories. The assumptions made in the original method are revisited and the significance of the minimum free energy path (MFEP) is discussed in the context of reactive events. These assumptions are compared to those made in the string method with swarms-of-trajectories, and shown to be equivalent in a certain regime: in particular an expression for the path identified by the swarms-of-trajectories method is given and shown to be closely related to the MFEP. Finally, the algorithmic aspects of both methods are compared

Standard Binding Free Energies from Computer Simulations: What Is the Best Strategy?

Accurate prediction of standard binding free energies describing protein–ligand association remains a daunting computational endeavor. This challenge is rooted to a large extent in the considerable changes in conformational, translational, and rotational entropies underlying the binding process that atomistic simulations cannot easily sample. In spite of significant methodological advances, reflected in a continuously improving agreement with experiment, a characterization of alternate strategies aimed at measuring binding affinities, notably their respective advantages and drawbacks, is somewhat lacking. Here, two distinct avenues to determine the standard binding free energy are compared in the case of a short, proline-rich peptide associating to the Src homology domain 3 of tyrosine kinase Abl. These avenues, one relying upon alchemical transformations and the other on potentials of mean force (PMFs), invoke a series of geometrical restraints acting on collective variables designed to alleviate sampling limitations inherent to classical molecular dynamics simulations. The experimental binding free energy of Δ<i>G</i>_bind = −7.99 kcal/mol is well reproduced by the two strategies developed herein, with Δ<i>G</i>_bind = −7.7 for the alchemical route and Δ<i>G</i>_bind = −7.8 kcal/mol for the alternate PMF-based route. In detailing the underpinnings of these numerical strategies devised for the accurate determination of standard binding free energies, many practical elements of the proposed rigorous, conceptual framework are clarified, thereby paving way to tackle virtually any recognition and association phenomenon

The Activation of c‑Src Tyrosine Kinase: Conformational Transition Pathway and Free Energy Landscape

Tyrosine kinases are important cellular signaling allosteric enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Their activity must be tightly controlled, and malfunction can lead to a variety of diseases, particularly cancer. The nonreceptor tyrosine kinase c-Src, a prototypical model system and a representative member of the Src-family, functions as complex multidomain allosteric molecular switches comprising SH2 and SH3 domains modulating the activity of the catalytic domain. The broad picture of self-inhibition of c-Src via the SH2 and SH3 regulatory domains is well characterized from a structural point of view, but a detailed molecular mechanism understanding is nonetheless still lacking. Here, we use advanced computational methods based on all-atom molecular dynamics simulations with explicit solvent to advance our understanding of kinase activation. To elucidate the mechanism of regulation and self-inhibition, we have computed the pathway and the free energy landscapes for the “inactive-to-active” conformational transition of c-Src for different configurations of the SH2 and SH3 domains. Using the isolated c-Src catalytic domain as a baseline for comparison, it is observed that the SH2 and SH3 domains, depending upon their bound orientation, promote either the inactive or active state of the catalytic domain. The regulatory structural information from the SH2–SH3 tandem is allosterically transmitted via the N-terminal linker of the catalytic domain. Analysis of the conformational transition pathways also illustrates the importance of the conserved tryptophan 260 in activating c-Src, and reveals a series of concerted events during the activation process