Homologous ligands accommodated by discrete conformations of a buried cavity

PopShift: A Thermodynamically Sound Approach to Estimate Binding Free Energies by Accounting for Ligand-Induced Population Shifts from a Ligand-Free Markov State Model

Obtaining accurate binding free energies from in silico screens has been a long-standing goal for the computational chemistry community. However, accuracy and computational cost are at odds with one another, limiting the utility of methods that perform this type of calculation. Many methods achieve massive scale by explicitly or implicitly assuming that the target protein adopts a single structure, or undergoes limited fluctuations around that structure, to minimize computational cost. Others simulate each protein-ligand complex of interest, accepting lower throughput in exchange for better predictions of binding affinities. Here, we present the PopShift framework for accounting for the ensemble of structures a protein adopts and their relative probabilities. Protein degrees of freedom are enumerated once, and then arbitrarily many molecules can be screened against this ensemble. Specifically, we use Markov state models (MSMs) as a compressed representation of a protein's thermodynamic ensemble. We start with a ligand-free MSM and then calculate how addition of a ligand shifts the populations of each protein conformational state based on the strength of the interaction between that protein conformation and the ligand. In this work we use docking to estimate the affinity between a given protein structure and ligand, but any estimator of binding affinities could be used in the PopShift framework. We test PopShift on the classic benchmark pocket T4 Lysozyme L99A. We find that PopShift is more accurate than common strategies, such as docking to a single structure and traditional ensemble docking─producing results that compare favorably with alchemical binding free energy calculations in terms of RMSE but not correlation─and may have a more favorable computational cost profile in some applications. In addition to predicting binding free energies and ligand poses, PopShift also provides insight into how the probability of different protein structures is shifted upon addition of various concentrations of ligand, providing a platform for predicting affinities and allosteric effects of ligand binding. Therefore, we expect PopShift will be valuable for hit finding and for providing insight into phenomena like allostery.

PopShift: A thermodynamically sound approach to estimate binding free energies by accounting for ligand-induced population shifts from a ligand-free MSM

Obtaining accurate binding free energies from in silico screens has been a longstanding goal for the computational chemistry community. However, accuracy and computational cost are at odds with one another, limiting the utility of methods that perform this type of calculation. Many methods achieve massive scale by explicitly or implicitly assuming that the target protein adopts a single structure, or undergoes limited fluctuations around that structure, to minimize computational cost. Others simulate each protein-ligand complex of interest, accepting lower throughput in exchange for better predictions of binding affinities. Here, we present the PopShift framework for accounting for the ensemble of structures a protein adopts and their relative probabilities. Protein degrees of freedom are enumerated once, and then arbitrarily many molecules can be screened against this ensemble. Specifically, we use Markov state models (MSMs) as a compressed representation of a protein's thermodynamic ensemble. We start with a ligand-free MSM and then calculate how addition of a ligand shifts the populations of each protein conformational state based on the strength of the interaction between that protein conformation and the ligand. In this work we use docking to estimate the affinity between a given protein structure and ligand, but any estimator of binding affinities could be used in the PopShift framework. We test PopShift on the classic benchmark pocket T4 Lysozyme L99A. We find that PopShift is more accurate than common strategies, such as docking to a single structure and traditional ensemble docking-producing results that compare favorably with alchemical binding free energy calculations in terms of RMSE but not correlation - and may have a more favorable computational cost profile in some applications. In addition to predicting binding free energies and ligand poses, PopShift also provides insight into how the probability of different protein structures is shifted upon addition of various concentrations of ligand, providing a platform for predicting affinities and allosteric effects of ligand binding. Therefore, we expect PopShift will be valuable for hit finding and for providing insight into phenomena like allostery.

Ligand binding free energy evaluation by Monte Carlo Recursion

The correct evaluation of ligand binding free energies by computational methods is still a very challenging active area of research. The most employed methods for these calculations can be roughly classified into four groups: (i) the fastest and less accurate methods, such as molecular docking, designed to sample a large number of molecules and rapidly rank them according to the potential binding energy; (ii) the second class of methods use a thermodynamic ensemble, typically generated by molecular dynamics, to analyze the endpoints of the thermodynamic cycle for binding and extract differences, in the so-called 'end-point' methods; (iii) the third class of methods is based on the Zwanzig relationship and computes the free energy difference after a chemical change of the system (alchemical methods); and (iv) methods based on biased simulations, such as metadynamics, for example. These methods require increased computational power and as expected, result in increased accuracy for the determination of the strength of binding. Here, we describe an intermediate approach, based on the Monte Carlo Recursion (MCR) method first developed by Harold Scheraga. In this method, the system is sampled at increasing effective temperatures, and the free energy of the system is assessed from a series of terms W(b,T), computed from Monte Carlo (MC) averages at each iteration. We show the application of the MCR for ligand binding with datasets of guest-hosts systems (N = 75) and we observed that a good correlation is obtained between experimental data and the binding energies computed with MCR. We also compared the experimental data with an end-point calculation from equilibrium Monte Carlo calculations that allowed us to conclude that the lower-energy (lower-temperature) terms in the calculation are the most relevant to the estimation of the binding energies, resulting in similar correlations between MCR and MC data and the experimental values. On the other hand, the MCR method provides a reasonable view of the binding energy funnel, with possible connections with the ligand binding kinetics, as well. The codes developed for this analysis are publicly available on GitHub as a part of the LiBELa/MCLiBELa project (https://github.com/alessandronascimento/LiBELa).

Accelerated Enveloping Distribution Sampling (AEDS) Allows for Efficient Sampling of Orthogonal Degrees of Freedom

One of the most challenging aspects in the molecular simulation of proteins is the study of slowly relaxing processes, such as loop rearrangements or ligands that adopt different conformations in the binding site. State-of-the-art methods used to calculate binding free energies rely on performing several short simulations (lambda steps), in which the ligand is slowly transformed into the endstates of interest. This makes capturing the slowly relaxing processes even more difficult, as they would need to be observed in all of the lambda steps. One attractive alternative is the use of a reference state capable of sampling all of the endstates of interest in a single simulation. However, the energy barriers between the states can be too high to overcome, thus hindering the sampling of all of the relevant conformations. Accelerated enveloping distribution sampling (AEDS) is a recently developed reference state technique that circumvents the high-energy-barrier challenge by adding a boosting potential that flattens the energy landscape without distorting the energy minima. In the present work, we apply AEDS to the well-studied benchmark system T4 lysozyme L99A. The T4 lysozyme L99A mutant contains a hydrophobic pocket in which there is a valine (valine 111), whose conformation influences the binding efficiencies of the different ligands. Incorrectly sampling the dihedral angle can lead to errors in predicted binding free energies of up to 16 kJ mol^-1. This protein constitutes an ideal scenario to showcase the advantages and challenges when using AEDS in the presence of slow relaxing processes. We show that AEDS is able to successfully sample the relevant degrees of freedom, providing accurate binding free energies, without the need of previous information of the system in the form of collective variables. Additionally, we showcase the capabilities of AEDS to efficiently screen a set of ligands. These results represent a promising first step toward the development of free-energy methods that can respond to more intricate molecular events.

Large-Scale Ligand Perturbations of the Protein Conformational Landscape Reveal State-Specific Interaction Hotspots

Protein flexibility is important for ligand binding but often ignored in drug design. Considering proteins as ensembles rather than static snapshots creates opportunities to target dynamic proteins that lack FDA-approved drugs, such as the human chaperone, heat shock protein 90 (Hsp90). Hsp90α accommodates ligands with a dynamic lid domain, yet no comprehensive analysis relating lid conformations to ligand properties is available. To date, ∼300 ligand-bound Hsp90α crystal structures are deposited in the Protein Data Bank, which enables us to consider ligand binding as a perturbation of the protein conformational landscape. By estimating binding site volumes, we classified structures into distinct major and minor lid conformations. Supported by retrospective docking, each conformation creates unique hotspots that bind chemically distinguishable ligands. Clustering revealed insightful exceptions and the impact of crystal packing. Overall, Hsp90α’s plasticity provides a cautionary tale of overinterpreting individual crystal structures and motivates an ensemble-based view of drug design.

Improving the Potential of Mean Force and Nonequilibrium Pulling Simulations by Simultaneous Alchemical Modifications

We present an approach combining alchemical modifications and physical-pathway methods to calculate absolute binding free energies. The employed physical-pathway method is either a stratified umbrella sampling to calculate a potential of mean force or nonequilibrium pulling. We devised two basic approaches: the simultaneous approach (S-approach), where, along the physical unbinding pathway, an alchemical transformation of ligand-protein interactions is installed and deinstalled, and the prior-plus-simultaneous approach (PPS-approach), where, prior to the physical-pathway simulation, an alchemical transformation of ligand-protein interactions is installed in the binding site and deinstalled during the physical-pathway simulation. Using a mutant of T4 lysozyme with a benzene ligand as an example, we show that installation and deinstallation of soft-core interactions concurrent with physical ligand unbinding (S-approach) allow successful potential of mean force calculations and nonequilibrium pulling simulations despite the problems posed by the occluded nature of the lysozyme binding pocket. Good agreement between the potential of the mean-force-based S-approach and double decoupling simulations as well as a remarkable efficiency and accuracy of the nonequilibrium-pulling-based S-approach is found. The latter turned out to be more compute-efficient than the potential of mean force calculation by approximately 70%. Furthermore, we illustrate the merits of reducing ligand-protein interactions prior to potential of mean force calculations using the murine double minute homologue protein MDM2 with a p53-derived peptide ligand (PPS-approach). Here, the problem of breaking strong interactions in the binding pocket is transferred to a prior alchemical transformation that reduces the free-energy barrier between the bound and unbound state in the potential of mean force. Besides, disentangling physical ligand displacement from the deinstallation of ligand-protein interactions was seen to allow a more uniform sampling of distance histograms in the umbrella sampling. In the future, physical ligand unbinding combined with simultaneous alchemical modifications may prove useful in the calculation of protein-protein binding free energies, where sampling problems posed by multiple, possibly sticky interactions and potential steric clashes can thus be reduced.

Accelerated Ligand-Mapping Molecular Dynamics Simulations for the Detection of Recalcitrant Cryptic Pockets and Occluded Binding Sites

The identification and characterization of binding sites is a critical component of structure-based drug design (SBDD). Probe-based/cosolvent molecular dynamics (MD) methods that allow for protein flexibility have been developed to predict ligand binding sites. However, cryptic pockets that appear only upon ligand binding and occluded binding sites with no access to the solvent pose significant challenges to these methods. Here, we report the development of accelerated ligand-mapping MD (aLMMD), which combines accelerated MD with LMMD, for the detection of these challenging binding sites. The method was validated on five proteins with what we term "recalcitrant" cryptic pockets, which are deeply buried pockets that require extensive movement of the protein backbone to expose, and three proteins with occluded binding sites. In all the cases, aLMMD was able to detect and sample the binding sites. Our results suggest that aLMMD could be used as a general approach for the detection of such elusive binding sites in protein targets, thus providing valuable information for SBDD.

Analysis of changes of cavity volumes in predefined directions of protein motions and cavity flexibility

Dynamics of protein cavities associated with protein fluctuations and conformational plasticity is essential for their biological function. NMR ensembles, molecular dynamics (MD) simulations, and normal mode analysis (NMA) provide appropriate frameworks to explore functionally relevant protein dynamics and cavity changes relationships. Within this context, we have recently developed analysis of null areas (ANA), an efficient method to calculate cavity volumes. ANA is based on a combination of algorithms that guarantees its robustness against numerical differentiations. This is a unique feature with respect to other methods. Herein, we present an updated and improved version that expands it use to quantify changes in cavity features, like volume and flexibility, due to protein structural distortions performed on predefined biologically relevant directions, for example, directions of largest contribution to protein fluctuations (principal component analysis [PCA modes]) obtained by MD simulations or ensembles of NMR structures, collective NMA modes or any other direction of motion associated with specific conformational changes. A web page has been developed where its facilities are explained in detail. First, we show that ANA can be useful to explore gradual changes of cavity volume and flexibility associated with protein ligand binding. Secondly, we perform a comparison study of the extent of variability between protein backbone structural distortions, and changes in cavity volumes and flexibilities evaluated for an ensemble of NMR active and inactive conformers of the epidermal growth factor receptor structures. Finally, we compare changes in size and flexibility between sets of NMR structures for different homologous chains of dynein.

Flexible CDOCKER: Hybrid Searching Algorithm and Scoring Function with Side Chain Conformational Entropy

The binding of small-molecule ligands to protein or nucleic acid targets is important to numerous biological processes. Accurate prediction of the binding modes between a ligand and a macromolecule is of fundamental importance in structure-based structure-function exploration. When multiple ligands with different sizes are docked to a target receptor, it is reasonable to assume that the residues in the binding pocket may adopt alternative conformations upon interacting with the different ligands. In addition, it has been suggested that the entropic contribution to binding can be important. However, only a few attempts to include the side chain conformational entropy upon binding within the application of flexible receptor docking methodology exist. Here, we propose a new physics-based scoring function that includes both enthalpic and entropic contributions upon binding by considering the conformational variability of the flexible side chains within the ensemble of docked poses. We also describe a novel hybrid searching algorithm that combines both molecular dynamics (MD)-based simulated annealing and genetic algorithm crossovers to address the enhanced sampling of the increased search space. We demonstrate improved accuracy in flexible cross-docking experiments compared with rigid cross-docking. We test our developments by considering five protein targets, thrombin, dihydrofolate reductase(DHFR), T4 L99A, T4 L99A/M102Q, and PDE10A, which belong to different enzyme classes with different binding pocket environments, as a representative set of diverse ligands and receptors. Each target contains dozens of different ligands bound to the same binding pocket. We also demonstrate that this flexible docking algorithm may be applicable to RNA docking with a representative riboswitch example. Our findings show significant improvements in top ranking accuracy across this set, with the largest improvement relative to rigid, 23.64%, occurring for ligands binding to DHFR. We then evaluate the ability to identify lead compounds among a large chemical space for the proposed flexible receptor docking algorithm using a subset of the DUD-E containing receptor targets MCR, GCR, and ANDR. We demonstrate that our new algorithms show improved performance in modeling flexible binding site residues compared to DOCK. Finally, we select the T4 L99A and T4 L99A/M102Q decoy sets, containing dozens of binders and experimentally validated nonbinders, to test our approach in distinguishing binders from nonbinders. We illustrate that our new algorithms for searching and scoring have superior performance to rigid receptor CDOCKER as well as AutoDock Vina. Finally, we suggest that flexible CDOCKER is sufficiently fast to be utilized in high-throughput docking screens in the context of hierarchical approaches.

Energy penalties enhance flexible receptor docking in a model cavity

Protein flexibility remains a major challenge in library docking because of difficulties in sampling conformational ensembles with accurate probabilities. Here, we use the model cavity site of T4 lysozyme L99A to test flexible receptor docking with energy penalties from molecular dynamics (MD) simulations. Crystallography with larger and smaller ligands indicates that this cavity can adopt three major conformations: open, intermediate, and closed. Since smaller ligands typically bind better to the cavity site, we anticipate an energy penalty for the cavity opening. To estimate its magnitude, we calculate conformational preferences from MD simulations. We find that including a penalty term is essential for retrospective ligand enrichment; otherwise, high-energy states dominate the docking. We then prospectively docked a library of over 900,000 compounds for new molecules binding to each conformational state. Absent a penalty term, the open conformation dominated the docking results; inclusion of this term led to a balanced sampling of ligands against each state. High ranked molecules were experimentally tested by Tm upshift and X-ray crystallography. From 33 selected molecules, we identified 18 ligands and determined 13 crystal structures. Most interesting were those bound to the open cavity, where the buried site opens to bulk solvent. Here, highly unusual ligands for this cavity had been predicted, including large ligands with polar tails; these were confirmed both by binding and by crystallography. In docking, incorporating protein flexibility with thermodynamic weightings may thus access new ligand chemotypes. The MD approach to accessing and, crucially, weighting such alternative states may find general applicability.

Temperature artifacts in protein structures bias ligand-binding predictions

X-ray crystallography is the gold standard to resolve conformational ensembles that are significant for protein function, ligand discovery, and computational methods development. However, relevant conformational states may be missed at common cryogenic (cryo) data-collection temperatures but can be populated at room temperature. To assess the impact of temperature on making structural and computational discoveries, we systematically investigated protein conformational changes in response to temperature and ligand binding in a structural and computational workhorse, the T4 lysozyme L99A cavity. Despite decades of work on this protein, shifting to RT reveals new global and local structural changes. These include uncovering an apo helix conformation that is hidden at cryo but relevant for ligand binding, and altered side chain and ligand conformations. To evaluate the impact of temperature-induced protein and ligand changes on the utility of structural information in computation, we evaluated how temperature can mislead computational methods that employ cryo structures for validation. We find that when comparing simulated structures just to experimental cryo structures, hidden successes and failures often go unnoticed. When using structural information in ligand binding predictions, both coarse docking and rigorous binding free energy calculations are influenced by temperature effects. The trend that cryo artifacts limit the utility of structures for computation holds across five distinct protein classes. Our results suggest caution when consulting cryogenic structural data alone, as temperature artifacts can conceal errors and prevent successful computational predictions, which can mislead the development and application of computational methods in discovering bioactive molecules.

Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches

The accurate calculation of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein-ligand binding affinity.

Property-Unmatched Decoys in Docking Benchmarks

Enrichment of ligands versus property-matched decoys is widely used to test and optimize docking library screens. However, the unconstrained optimization of enrichment alone can mislead, leading to false confidence in prospective performance. This can arise by over-optimizing for enrichment against property-matched decoys, without considering the full spectrum of molecules to be found in a true large library screen. Adding decoys representing charge extrema helps mitigate over-optimizing for electrostatic interactions. Adding decoys that represent the overall characteristics of the library to be docked allows one to sample molecules not represented by ligands and property-matched decoys but that one will encounter in a prospective screen. An optimized version of the DUD-E set (DUDE-Z), as well as Extrema and sets representing broad features of the library (Goldilocks), is developed here. We also explore the variability that one can encounter in enrichment calculations and how that can temper one's confidence in small enrichment differences. The new tools and new decoy sets are freely available at http://tldr.docking.org and http://dudez.docking.org.

A Geometric Definition of Short to Medium Range Hydrogen-Mediated Interactions in Proteins

We present a method to rapidly identify hydrogen-mediated interactions in proteins (e.g., hydrogen bonds, hydrogen bonds, water-mediated hydrogen bonds, salt bridges, and aromatic π-hydrogen interactions) through heavy atom geometry alone, that is, without needing to explicitly determine hydrogen atom positions using either experimental or theoretical methods. By including specific real (or virtual) partner atoms as defined by the atom type of both the donor and acceptor heavy atoms, a set of unique angles can be rapidly calculated. By comparing the distance between the donor and the acceptor and these unique angles to the statistical preferences observed in the Protein Data Bank (PDB), we were able to identify a set of conserved geometries (15 for donor atoms and 7 for acceptor atoms) for hydrogen-mediated interactions in proteins. This set of identified interactions includes every polar atom type present in the Protein Data Bank except OE1 (glutamate/glutamine sidechain) and a clear geometric preference for the methionine sulfur atom (SD) to act as a hydrogen bond acceptor. This method could be readily applied to protein design efforts.

Protein-ligand binding with the coarse-grained Martini model

The detailed understanding of the binding of small molecules to proteins is the key for the development of novel drugs or to increase the acceptance of substrates by enzymes. Nowadays, computer-aided design of protein–ligand binding is an important tool to accomplish this task. Current approaches typically rely on high-throughput docking essays or computationally expensive atomistic molecular dynamics simulations. Here, we present an approach to use the recently re-parametrized coarse-grained Martini model to perform unbiased millisecond sampling of protein–ligand interactions of small drug-like molecules. Remarkably, we achieve high accuracy without the need of any a priori knowledge of binding pockets or pathways. Our approach is applied to a range of systems from the well-characterized T4 lysozyme over members of the GPCR family and nuclear receptors to a variety of enzymes. The presented results open the way to high-throughput screening of ligand libraries or protein mutations using the coarse-grained Martini model.

Computer-aided design of protein-ligand binding is important for the development of novel drugs. Here authors present an approach to use the recently re-parametrized coarse-grained Martini model to perform unbiased millisecond sampling of protein-ligand binding interactions of small drug-like molecules.

Exploring the strength of a hydrogen bond as a function of steric environment using 1,2-azaborine ligands and engineered T4 lysozyme receptors

A congeneric series of 1,2-azaborine ligands was used to study the relationship between the steric demand of the ligand and hydrogen bonding strength in the context of ligand-protein binding using engineered T4 lysozymes as the model biomacromolecules. The hydrogen bonding strength values were extracted from experimentally accessible binding free energies using the Double Mutant Cycle analysis. With the increasing steric demand, the NH…102Q hydrogen bonding interaction is weakened; however, this weakening of the hydrogen bonding interaction occurs in discrete steps rather than in an incremental fashion.

Escape of a Small Molecule from Inside T4 Lysozyme by Multiple Pathways

The T4 lysozyme L99A mutant is often used as a model system to study small-molecule binding to proteins, but pathways for ligand entry and exit from the buried binding site and the associated protein conformational changes have not been fully resolved. Here, molecular dynamics simulations were employed to model benzene exit from its binding cavity using the weighted ensemble (WE) approach to enhance sampling of low-probability unbinding trajectories. Independent WE simulations revealed four pathways for benzene exit, which correspond to transient tunnels spontaneously formed in previous simulations of apo T4 lysozyme. Thus, benzene unbinding occurs through multiple pathways partially created by intrinsic protein structural fluctuations. Motions of several α-helices and side chains were involved in ligand escape from metastable microstates. WE simulations also provided preliminary estimates of rate constants for each exit pathway. These results complement previous works and provide a semiquantitative characterization of pathway heterogeneity for binding of small molecules to proteins.

Enhancing Side Chain Rotamer Sampling Using Nonequilibrium Candidate Monte Carlo

Molecular simulations are a valuable tool for studying biomolecular motions and thermodynamics. However, such motions can be slow compared to simulation time scales, yet critical. Specifically, adequate sampling of side chain motions in protein binding pockets is crucial for obtaining accurate estimates of ligand binding free energies from molecular simulations. The time scale of side chain rotamer flips can range from a few ps to several hundred ns or longer, particularly in crowded environments like the interior of proteins. Here, we apply a mixed nonequilibrium candidate Monte Carlo (NCMC)/molecular dynamics (MD) method to enhance sampling of side chain rotamers. The NCMC portion of our method applies a switching protocol wherein the steric and electrostatic interactions between target side chain atoms and the surrounding environment are cycled off and then back on during the course of a move proposal. Between NCMC move proposals, simulation of the system continues via traditional molecular dynamics. Here, we first validate this approach on a simple, solvated valine-alanine dipeptide system and then apply it to a well-studied model ligand binding site in T4 lysozyme L99A. We compute the rate of rotamer transitions for a valine side chain using our approach and compare it to that of traditional molecular dynamics simulations. Here, we show that our NCMC/MD method substantially enhances side chain sampling, especially in systems where the torsional barrier to rotation is high (≥10 kcal/mol). These barriers can be intrinsic torsional barriers or steric barriers imposed by the environment. Overall, this may provide a promising strategy to selectively improve side chain sampling in molecular simulations.

Mechanisms for Benzene Dissociation through the Excited State of T4 Lysozyme L99A Mutant

The atomic-level mechanisms that coordinate ligand release from protein pockets are only known for a handful of proteins. Here, we report results from accelerated molecular dynamics simulations for benzene dissociation from the buried cavity of the T4 lysozyme Leu99Ala mutant (L99A). In these simulations, benzene is released through a previously characterized, sparsely populated room-temperature excited state of the mutant, explaining the coincidence for experimentally measured benzene off rate and apo protein slow-timescale NMR relaxation rates between ground and excited states. The path observed for benzene egress is a multistep ligand migration from the buried cavity to ultimate release through an opening between the F/G-, H-, and I-helices and requires a number of cooperative multiresidue and secondary-structure rearrangements within the C-terminal domain of L99A. These rearrangements are identical to those observed along the ground state to excited state transitions characterized by molecular dynamic simulations run on the Anton supercomputer. Analyses of the molecular properties of the residues lining the egress path suggest that protein surface electrostatic potential may play a role in the release mechanism. Simulations of wild-type T4 lysozyme also reveal that benzene-egress-associated dynamics in the L99A mutant are potentially exaggerations of the substrate-processivity-related dynamics of the wild type.

Biomolecular conformational changes and ligand binding: from kinetics to thermodynamics

The behaviour of biomolecular systems is governed by their thermodynamic and kinetic properties. It is thus important to be able to calculate, for example, both the affinity and rate of binding and dissociation of a protein-ligand complex, or the populations and exchange rates between distinct conformational states. Because these are typically rare events, calculating these properties from long molecular dynamics simulations remains extremely difficult. Instead, one often adopts a divide-and-conquer strategy in which equilibrium free-energy differences and the fastest state-to-state transition (e.g. ligand association or minor-to-major state conversion) are combined to estimate the slow rate (e.g. ligand dissociation) using a two-state assumption. Here we instead address these problems by using a previously developed method to calculate both the forward and backward rates directly from simulations. We then estimate the thermodynamics from the rates, and validate these values by independent means. We applied the approach to three systems of increasing complexity, including the association and dissociation of benzene to a fully buried cavity inside the L99A mutant variant of T4 lysozyme. In particular, we were able to determine both millisecond association and dissociation rates, and the affinity, of the protein-ligand system by directly observing dozens of rare events in atomic detail. Our approach both sheds light on the precision of methods for calculating kinetics and further provides a generally useful test for the internal consistency of kinetics and thermodynamics. We also expect our route to be useful for obtaining both the kinetics and thermodynamics at the same time in more challenging cases.

Gaussian Accelerated Molecular Dynamics: Theory, Implementation, and Applications

A novel Gaussian Accelerated Molecular Dynamics (GaMD) method has been developed for simultaneous unconstrained enhanced sampling and free energy calculation of biomolecules. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of the biomolecules. Furthermore, by constructing a boost potential that follows a Gaussian distribution, accurate reweighting of GaMD simulations is achieved via cumulant expansion to the second order. The free energy profiles obtained from GaMD simulations allow us to identify distinct low energy states of the biomolecules and characterize biomolecular structural dynamics quantitatively. In this chapter, we present the theory of GaMD, its implementation in the widely used molecular dynamics software packages (AMBER and NAMD), and applications to the alanine dipeptide biomolecular model system, protein folding, biomolecular large-scale conformational transitions and biomolecular recognition.

Capturing Invisible Motions in the Transition from Ground to Rare Excited States of T4 Lysozyme L99A

Proteins commonly sample a number of conformational states to carry out their biological function, often requiring transitions from the ground state to higher-energy states. Characterizing the mechanisms that guide these transitions at the atomic level promises to impact our understanding of functional protein dynamics and energy landscapes. The leucine-99-to-alanine (L99A) mutant of T4 lysozyme is a model system that has an experimentally well characterized excited sparsely populated state as well as a ground state. Despite the exhaustive study of L99A protein dynamics, the conformational changes that permit transitioning to the experimentally detected excited state (∼3%, ΔG ∼2 kcal/mol) remain unclear. Here, we describe the transitions from the ground state to this sparsely populated excited state of L99A as observed through a single molecular dynamics (MD) trajectory on the Anton supercomputer. Aside from detailing the ground-to-excited-state transition, the trajectory samples multiple metastates and an intermediate state en route to the excited state. Dynamic motions between these states enable cavity surface openings large enough to admit benzene on timescales congruent with known rates for benzene binding. Thus, these fluctuations between rare protein states provide an atomic description of the concerted motions that illuminate potential path(s) for ligand binding. These results reveal, to our knowledge, a new level of complexity in the dynamics of buried cavities and their role in creating mobile defects that affect protein dynamics and ligand binding.

Absolute Binding Free Energies between T4 Lysozyme and 141 Small Molecules: Calculations Based on Multiple Rigid Receptor Configurations

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. On the basis of T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root-mean-square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/surface area implicit solvent was comparable to that of previously reported free energy calculations.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

Full and Partial Agonism of a Designed Enzyme Switch

Chemical biology has long sought to build protein switches for use in molecular diagnostics, imaging, and synthetic biology. The overarching challenge for any type of engineered protein switch is the ability to respond in a selective and predictable manner that caters to the specific environments and time scales needed for the application at hand. We previously described a general method to design switchable proteins, called "chemical rescue of structure", that builds de novo allosteric control sites directly into a protein's functional domain. This approach entails first carving out a buried cavity in a protein via mutation, such that the protein's structure is disrupted and activity is lost. An exogenous ligand is subsequently added to substitute for the atoms that were removed by mutation, restoring the protein's structure and thus its activity. Here, we begin to ask what principles dictate such switches' response to different activating ligands. Using a redesigned β-glycosidase enzyme as our model system, we find that the designed effector site is quite malleable and can accommodate both larger and smaller ligands, but that optimal rescue comes only from a ligand that perfectly replaces the deleted atoms. Guided by these principles, we then altered the shape of this cavity by using different cavity-forming mutations, and predicted different ligands that would better complement these new cavities. These findings demonstrate how the protein switch's response can be tuned via small changes to the ligand with respect to the binding cavity, and ultimately enabled us to design an improved switch. We anticipate that these insights will help enable the design of future systems that tune other aspects of protein activity, whereby, like evolved protein receptors, remolding the effector site can also adjust additional outputs such as substrate selectivity and activation of downstream signaling pathways.

Hydrogen Bonding of 1,2-Azaborines in the Binding Cavity of T4 Lysozyme Mutants: Structures and Thermodynamics

Protein crystallography and calorimetry were used to characterize the binding of 1,2-azaborines to model cavities in T4 lysozyme in direct comparison to their carbonaceous counterparts. In the apolar L99A cavity, affinity for Ab dropped only slightly versus benzene. In the cavity designed to accommodate a single hydrogen bond (L99A/M102Q), Gln102═O···H-N hydrogen bonding for Ab and BEtAb was observed in the crystallographic complexes. The strength of the hydrogen bonding was estimated as 0.94 and 0.64 kcal/mol for Ab and BEtAb, respectively. This work unambiguously demonstrates that 1,2-azaborines can be readily accommodated in classic aryl recognition pockets and establishes one of 1,2-azaborine's distinguishing features from its carbonaceous isostere benzene: its ability to serve as an NH hydrogen bond donor in a biological setting.

Mapping transiently formed and sparsely populated conformations on a complex energy landscape

Determining the structures, kinetics, thermodynamics and mechanisms that underlie conformational exchange processes in proteins remains extremely difficult. Only in favourable cases is it possible to provide atomic-level descriptions of sparsely populated and transiently formed alternative conformations. Here we benchmark the ability of enhanced-sampling molecular dynamics simulations to determine the free energy landscape of the L99A cavity mutant of T4 lysozyme. We find that the simulations capture key properties previously measured by NMR relaxation dispersion methods including the structure of a minor conformation, the kinetics and thermodynamics of conformational exchange, and the effect of mutations. We discover a new tunnel that involves the transient exposure towards the solvent of an internal cavity, and show it to be relevant for ligand escape. Together, our results provide a comprehensive view of the structural landscape of a protein, and point forward to studies of conformational exchange in systems that are less characterized experimentally.

DOI:http://dx.doi.org/10.7554/eLife.17505.001

Proteins are the workhorses of cells, where they perform a wide range of roles. To do so, they adopt specific three-dimensional structures that enable them to interact with other molecules as necessary. Often a protein needs to be able to shift between different states with distinct structures as it goes about its job. To fully understand how a protein works, it is important to be able to characterize these different structures and how the protein changes between them.

Many of the experimental techniques used to study protein structure rely on isolating the individual structural forms of a protein. Since many structures only exist briefly, this can be very difficult. To complement experimental results, computer simulations allow researchers to model how atoms behave within a molecule. However, a number of factors limit how well these models represent what happens experimentally, such as the accuracy of the physical description used for the modeling.

Wang et al. set out to test and benchmark how well computer simulations could model changes in structure for a protein called T4 lysozyme, which has been studied extensively using experimental techniques. T4 lysozyme exists in two different states that have distinct structures. By comparing existing detailed experimental measurements with the results of their simulations, Wang et al. found that the simulations could capture key aspects of how T4 lysozyme changes its shape.

The simulations described the structure of the protein in both states and accurately determined the relative proportion of molecules that are found in each state. They could also determine how long it takes for a molecule to change its shape from one state to the other. The findings allowed Wang et al. to describe in fine detail – down to the level of individual atoms – how the protein changes its shape and how mutations in the protein affect its ability to do so. A key question for future studies is whether these insights can be extended to other proteins that are less well characterized experimentally than T4 lysozyme.

DOI:http://dx.doi.org/10.7554/eLife.17505.002

Sensitivity in Binding Free Energies Due to Protein Reorganization

Tremendous recent improvements in computer hardware, coupled with advances in sampling techniques and force fields, are now allowing protein-ligand binding free energy calculations to be routinely used to aid pharmaceutical drug discovery projects. However, despite these recent innovations, there are still needs for further improvement in sampling algorithms to more adequately sample protein motion relevant to protein-ligand binding. Here, we report our work identifying and studying such clear and remaining needs in the apolar cavity of T4 lysozyme L99A. In this study, we model recent experimental results that show the progressive opening of the binding pocket in response to a series of homologous ligands.1 Even while using enhanced sampling techniques, we demonstrate that the predicted relative binding free energies (RBFE) are sensitive to the initial protein conformational state. Particularly, we highlight the importance of sufficient sampling of protein conformational changes and demonstrate how inclusion of three key protein residues in the "hot" region of the FEP/REST simulation improves the sampling and resolves this sensitivity, given enough simulation time.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation

A Gaussian accelerated molecular dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calculation of biomolecules is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomolecular model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomolecules. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow us to identify distinct low-energy states of the biomolecules and characterize the protein-folding and ligand-binding pathways quantitatively.