Analysis of cyclosporin A and a set of analogs as inhibitors of a T. cruzi cyclophilin by docking and molecular dynamics

Cyclophilins (CyPs) are enzymes involved in protein folding. In Trypanosoma cruzi (T. cruzi), the most abundantly expressed CyP is the isoform TcCyP19. It has been shown that TcCyP19 is inhibited by the immunosuppressive drug cyclosporin A (CsA) and analogs, which also proved to have potent trypanosomicidal activity in vitro. In this work, we continue and expand a previous study on the molecular interactions of CsA, and a set of analogs modeled in complexes with TcCyP19. The modeled complexes were used to evaluate binding free energies by molecular dynamics (MD), applying the Linear Interaction Energy (LIE) method. In addition, putative binding sites were identified by molecular docking. In our analysis, the binding free energy calculations did not correlate with experimental data. The heterogeneity of the non-bonded energies and the variation in the pattern of hydrogen bonds suggest that the systems may not be suitable for the application of the LIE method. Further, the docking calculations identified two other putative binding sites with comparable scoring energies to the active site, a fact that may also explain the lack of correlation found. Kinetic experiments are needed to confirm or reject the multiple binding sites hypothesis. In the meantime, MD simulations at the alternative sites, employing other methods to compute binding free energies, might be successful at finding good correlations with the experimental data.     

Computational Prediction of Alanine Scanning and Ligand Binding Energetics in G-Protein Coupled Receptors

Site-directed mutagenesis combined with binding affinity measurements is widely used to probe the nature of ligand interactions with GPCRs. Such experiments, as well as structure-activity relationships for series of ligands, are usually interpreted with computationally derived models of ligand binding modes. However, systematic approaches for accurate calculations of the corresponding binding free energies are still lacking. Here, we report a computational strategy to quantitatively predict the effects of alanine scanning and ligand modifications based on molecular dynamics free energy simulations. A smooth stepwise scheme for free energy perturbation calculations is derived and applied to a series of thirteen alanine mutations of the human neuropeptide Y1 receptor and series of eight analogous antagonists. The robustness and accuracy of the method enables univocal interpretation of existing mutagenesis and binding data. We show how these calculations can be used to validate structural models and demonstrate their ability to discriminate against suboptimal ones.     

Density functional theory calculations on entire proteins for free energies of binding: Application to a model polar binding site

In drug optimization calculations, the molecular mechanics Poisson‐Boltzmann surface area (MM‐PBSA) method can be used to compute free energies of binding of ligands to proteins. The method involves the evaluation of the energy of configurations in an implicit solvent model. One source of errors is the force field used, which can potentially lead to large errors due to the restrictions in accuracy imposed by its empirical nature. To assess the effect of the force field on the calculation of binding energies, in this article we use large‐scale density functional theory (DFT) calculations as an alternative method to evaluate the energies of the configurations in a “QM‐PBSA” approach. Our DFT calculations are performed with a near‐complete basis set and a minimal parameter implicit solvent model, within the self‐consistent calculation, using the ONETEP program on protein–ligand complexes containing more than 2600 atoms. We apply this approach to the T4‐lysozyme double mutant L99A/M102Q protein, which is a well‐studied model of a polar binding site, using a set of eight small aromatic ligands. We observe that there is very good correlation between the MM and QM binding energies in vacuum but less so in the solvent. The relative binding free energies from DFT are more accurate than the ones from the MM calculations, and give markedly better agreement with experiment for six of the eight ligands. Furthermore, in contrast to MM‐PBSA, QM‐PBSA is able to correctly predict a nonbinder. Proteins 2014; 82:3335–3346. © 2014 Wiley Periodicals, Inc.     

Prediction of protein complexes using empirical free energy functions.

A long sought goal in the physical chemistry of macromolecular structure, and one directly relevant to understanding the molecular basis of biological recognition, is predicting the geometry of bimolecular complexes from the geometries of their free monomers. Even when the monomers remain relatively unchanged by complex formation, prediction has been difficult because the free energies of alternative conformations of the complex have been difficult to evaluate quickly and accurately. This has forced the use of incomplete target functions, which typically do no better than to provide tens of possible complexes with no way of choosing between them. Here we present a general framework for empirical free energy evaluation and report calculations, based on a relatively complete and easily executable free energy function, that indicate that the structures of complexes can be predicted accurately from the structures of monomers, including close sequence homologues. The calculations also suggest that the binding free energies themselves may be predicted with reasonable accuracy. The method is compared to an alternative formulation that has also been applied recently to the same data set. Both approaches promise to open new opportunities in macromolecular design and specificity modification.     

Binding free energy calculations of adenosine deaminase inhibitors

The interactions between four inhibitors and adenosine deaminase (ADA) were examined by calculating their binding free energies after molecular dynamics simulations. A bonded model was used to represent the electrostatic potentials of the zinc coordination site. The charge distribution of the model was derived by using a two-stage electrostatic potential fitting calculations. The calculated binding free energies are in good agreement with the experimental data and the ranking of binding affinities is well reproduced. Notably, our findings suggest that non-polar contributions play an important role for ADA-inhibitor interactions.     

McVol - A program for calculating protein volumes and identifying cavities by a Monte Carlo algorithm

In this paper, we describe a Monte Carlo method for determining the volume of a molecule. A molecule is considered to consist of hard, overlapping spheres. The surface of the molecule is defined by rolling a probe sphere over the surface of the spheres. To determine the volume of the molecule, random points are placed in a three-dimensional box, which encloses the whole molecule. The volume of the molecule in relation to the volume of the box is estimated by calculating the ratio of the random points placed inside the molecule and the total number of random points that were placed. For computational efficiency, we use a grid-cell based neighbor list to determine whether a random point is placed inside the molecule or not. This method in combination with a graph-theoretical algorithm is used to detect internal cavities and surface clefts of molecules. Since cavities and clefts are potential water binding sites, we place water molecules in the cavities. The potential water positions can be used in molecular dynamics calculations as well as in other molecular calculations. We apply this method to several proteins and demonstrate the usefulness of the program. The described methods are all implemented in the program McVol, which is available free of charge from our website at .     

Interactions of the M2delta segment of the acetylcholine receptor with lipid bilayers: a continuum-solvent model study

M2delta, one of the transmembrane segments of the nicotinic acetylcholine receptor, is a 23-amino-acid peptide, frequently used as a model for peptide-membrane interactions. In this and the companion article we describe studies of M2delta-membrane interactions, using two different computational approaches. In the present work, we used continuum-solvent model calculations to investigate key thermodynamic aspects of its interactions with lipid bilayers. M2delta was represented in atomic detail and the bilayer was represented as a hydrophobic slab embedded in a structureless aqueous phase. Our calculations show that the transmembrane orientation is the most favorable orientation of the peptide in the bilayer, in good agreement with both experimental and computational data. Moreover, our calculations produced the free energy of association of M2delta with the lipid bilayer, which, to our knowledge, has not been reported to date. The calculations included 10 structures of M2delta, determined by nuclear magnetic resonance in dodecylphosphocholine micelles. All the structures were found to be stable inside the lipid bilayer, although their water-to-membrane transfer free energies differed by as much as 12 kT. Although most of the structures were roughly linear, a single structure had a kink in its central region. Interestingly, this structure was found to be the most stable inside the lipid bilayer, in agreement with molecular dynamics simulations of the peptide and with the recently determined structure of the intact receptor. Our analysis showed that the kink reduced the polarity of the peptide in its central region by allowing the electrostatic masking of the Gln13 side chain in that area. Our calculations also showed a tendency for the membrane to deform in response to peptide insertion, as has been previously found for the membrane-active peptides alamethicin and gramicidin. The results are compared to Monte Carlo simulations of the peptide-membrane system, as presented in the accompanying article.     

Electrostatic interactions play an essential role in DNA repair and cold-adaptation of Uracil DNA glycosylase

Life has adapted to most environments on earth, including low and high temperature niches. The increased catalytic efficiency and thermoliability observed for enzymes from organisms living in constantly cold regions when compared to their mesophilic and thermophilic cousins are poorly understood at the molecular level. Uracil DNA glycosylase (UNG) from cod (cUNG) catalyzes removal of uracil from DNA with an increased k_cat and reduced K_m relative to its warm-active human (hUNG) counterpart. Specific issues related to DNA repair and substrate binding/recognition (K_m) are here investigated by continuum electrostatics calculations, MD simulations and free energy calculations. Continuum electrostatic calculations reveal that cUNG has surface potentials that are more complementary to the DNA potential at and around the catalytic site when compared to hUNG, indicating improved substrate binding. Comparative MD simulations combined with free energy calculations using the molecular mechanics-Poisson Boltzmann surface area (MM-PBSA) method show that large opposing energies are involved when forming the enzyme-substrate complexes. Furthermore, the binding free energies obtained reveal that the Michaelis-Menten complex is more stable for cUNG, primarily due to enhanced electrostatic properties, suggesting that energetic fine-tuning of electrostatics can be utilized for enzymatic temperature adaptation. Energy decomposition pinpoints the residual determinants responsible for this adaptation. Figure Electrostatic isosurfaces of cod uracil DNA glycosylase in complex with double stranded DNA     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

Understanding the substituent effect on the acidity of alcohols and para-substituted phenols

We carried out Hartree–Fock (HF) and density functional theory calculations on the conjugated bases of phenols and alcohols for 23 compounds and analysed their acid–base behaviour using molecular orbital (MO) energies and their dependence on solvent effects. Despite the well-known correlation between highest-occupied MO (HOMO) energies and proton affinity (PA), we observed that HOMO energies are inadequate to describe the acid–base behaviour of these compounds. Therefore, we established a criterion to identify the best frontier MO for describing PA values and also to understand why the HOMO approach fails. The MO that fits our criterion provided very good correlations with PA values, much better than those obtained by the HOMO energies. Since the frontier MOs are those which drive the acid–base reactions in each compound, they were called frontier effective-for-reaction MOs, or FERMOs. By using the FERMO concept, the reactions that are HOMO driven, and those that are not, can be better explained, independent of the calculation method used, since both HF and Kohn–Sham methodologies lead to the same FERMO.     

Outer membrane phospholipase A in phospholipid bilayers: a model system for concerted computational and experimental investigations of amino acid side chain partitioning into lipid bilayers

Understanding the forces that stabilize membrane proteins in their native states is one of the contemporary challenges of biophysics. To date, estimates of side chain partitioning free energies from water to the lipid environment show disparate values between experimental and computational measures. Resolving the disparities is particularly important for understanding the energetic contributions of polar and charged side chains to membrane protein function because of the roles these residue types play in many cellular functions. In general, computational free energy estimates of charged side chain partitioning into bilayers are much larger than experimental measurements. However, the lack of a protein-based experimental system that uses bilayers against which to vet these computational predictions has traditionally been a significant drawback. Moon & Fleming recently published a novel hydrophobicity scale that was derived experimentally by using a host-guest strategy to measure the side chain energetic perturbation due to mutation in the context of a native membrane protein inserted into a phospholipid bilayer. These values are still approximately an order of magnitude smaller than computational estimates derived from molecular dynamics calculations from several independent groups. Here we address this discrepancy by showing that the free energy differences between experiment and computation become much smaller if the appropriate comparisons are drawn, which suggests that the two fields may in fact be converging. In addition, we present an initial computational characterization of the Moon & Fleming experimental system used for the hydrophobicity scale: OmpLA in DLPC bilayers. The hydrophobicity scale used OmpLA position 210 as the guest site, and our preliminary results demonstrate that this position is buried in the center of the DLPC membrane, validating its usage in the experimental studies. We further showed that the introduction of charged Arg at position 210 is well tolerated in OmpLA and that the DLPC bilayers accommodate this perturbation by creating a water dimple that allows the Arg side chain to remain hydrated. Lipid head groups visit the dimple and can hydrogen bond with Arg, but these interactions are transient. Overall, our study demonstrates the unique advantages of this molecular system because it can be interrogated by both computational and experimental practitioners, and it sets the stage for free energy calculations in a system for which there is unambiguous experimental data. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Evaluation of the Accuracy of Calculation of the Standard Binding Entropy of Molecules from their Average Mobility in Molecular Crystals

One of the main problems in attempts to predict the binding constants of molecules (or free energies of their binding) is the correct evaluation of configurational binding entropy. This evaluation is possible by methods of molecular dynamics simulation, but these simulations require a lot of computational time. Earlier, we have developed an alternative approach which allows the fast calculation of the binding entropy from summarizing the available data on sublimation of crystals. Our method is based on evaluating the mean amplitude of the movements that are restricted in the bound molecule, e.g., in a crystal, but are not restricted in the free state, e.g., in vapor. In this work, it is shown that the standard entropy of binding of molecules by crystals under standard conditions (1 atm, 25°C) can be assessed rather accurately from geometric and physical parameters of the molecule and the average amplitude of the molecule motions in crystals estimated in our previous work.     

Neutron crystallography, molecular dynamics, and quantum mechanics studies of the nature of hydrogen bonding in cellulose Ibeta

In the crystal structure of cellulose I beta, disordered hydrogen bonding can be represented by the average of two mutually exclusive hydrogen bonding schemes that have been designated A and B. An unanswered question is whether A and B interconvert dynamically, or whether they are static but present in different regions of the microfibril (giving temporally or a spatially averaged structures, respectively). We have used neutron crystallographic techniques to determine the occupancies of A and B at 295 and 15 K, quantum mechanical calculations to compare the energies of A and B, and molecular dynamics calculations to look at the stability of A. Microfibrils are found to have most chains arranged in a crystalline I beta structure with hydrogen bonding scheme A. Smaller regions of static disorder exist, perhaps at defects within or between crystalline domains in which the hydrogen bonding is complex but with certain features that are found in B.     

Ligand binding to the voltage-gated Kv1.5 potassium channel in the open state--docking and computer simulations of a homology model

The binding of blockers to the human voltage-gated Kv1.5 potassium ion channel is investigated using a three-step procedure consisting of homology modeling, automated docking, and binding free energy calculations from molecular dynamics simulations, in combination with the linear interaction energy method. A reliable homology model of Kv1.5 is constructed using the recently published crystal structure of the Kv1.2 channel as a template. This model is expected to be significantly more accurate than earlier ones based on less similar templates. Using the three-dimensional homology model, a series of blockers with known affinities are docked into the cavity of the ion channel and their free energies of binding are calculated. The predicted binding free energies are in very good agreement with experimental data and the binding is predicted to be mainly achieved through nonpolar interactions, whereas the relatively small differences in the polar contribution determine the specificity. Apart from confirming the importance of residues V505, I508, V512, and V516 for ligand binding in the cavity, the results also show that A509 and P513 contribute significantly to the nonpolar binding interactions. Furthermore, we find that pharmacophore models based only on optimized free ligand conformations may not necessarily capture the geometric features of ligands bound to the channel cavity. The calculations herein give a detailed structural and energetic picture of blocker binding to Kv1.5 and this model should thus be useful for further ligand design efforts.     

A comprehensive examination of the contributions to the binding entropy of protein–ligand complexes

One of the most important requirements in computer‐aided drug design is the ability to reliably evaluate the binding free energies. However, the process of ligand binding is very complex because of the intricacy of the interrelated processes that are difficult to predict and quantify. In fact, the deeper understanding of the origin of the observed binding free energies requires the ability to decompose these free energies to their contributions from different interactions. Furthermore, it is important to evaluate the relative entropic and enthalpic contributions to the overall free energy. Such an evaluation is useful for assessing temperature effects and exploring specialized options in enzyme design. Unfortunately, calculations of binding entropies have been much more challenging than calculations of binding free energies. This work is probably the first to present microscopic evaluation of all of the relevant components to the binding entropy, namely configurational, polar solvation, and hydrophobic entropies. All of these contributions are evaluated by the restraint release approach. The calculated results shed an interesting light on major compensation effects in both the solvation and hydrophobic effect and, despite some overestimate, can provide very useful insight. This study also helps in analyzing some problems with the widely used molecular mechanics/Poisson‐Boltzmann surface area approach. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Insights from free-energy calculations: protein conformational equilibrium, driving forces, and ligand-binding modes

Accurate free-energy calculations provide mechanistic insights into molecular recognition and conformational equilibrium. In this work, we performed free-energy calculations to study the thermodynamic properties of different states of molecular systems in their equilibrium basin, and obtained accurate absolute binding free-energy calculations for protein-ligand binding using a newly developed M2 algorithm. We used a range of Asp-Phe-Gly (DFG)-in/out p38α mitogen-activated protein kinase inhibitors as our test cases. We also focused on the flexible DFG motif, which is closely connected to kinase activation and inhibitor binding. Our calculations explain the coexistence of DFG-in and DFG-out states of the loop and reveal different components (e.g., configurational entropy and enthalpy) that stabilize the apo p38α conformations. To study novel ligand-binding modes and the key driving forces behind them, we computed the absolute binding free energies of 30 p38α inhibitors, including analogs with unavailable experimental structures. The calculations revealed multiple stable, complex conformations and changes in p38α and inhibitor conformations, as well as balance in several energetic terms and configurational entropy loss. The results provide relevant physics that can aid in designing inhibitors and understanding protein conformational equilibrium. Our approach is fast for use with proteins that contain flexible regions for structure-based drug design.     

Computer simulations of structure-activity relationships for HERG channel blockers

The hERG potassium channel is of major pharmaceutical importance, and its blockade by various compounds, potentially causing serious cardiac side effects, is a major problem in drug development. Despite the large amounts of existing biochemical data on blockade of hERG by drugs and druglike compounds, relatively little is known regarding the structural basis of binding of blockers to the channel. Here, we have used a recently developed homology model of hERG to conduct molecular docking experiments with a series of channel blockers, followed by molecular dynamics simulations of the complexes and evaluation of binding free energies with the linear interaction energy method. The calculations yield a remarkably good agreement with experimental binding affinities and allow for a rationalization of three-dimensional structure-activity relationships in terms of a number of key interactions. Two main interaction regions of the channel are thus identified with implications for further mutagenesis experiments and design of new compounds.     

Validation of an automated procedure for the prediction of relative free energies of binding on a set of aldose reductase inhibitors

Among the available methods for predicting free energies of binding of ligands to a protein, the molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) and molecular mechanics generalized Born surface area (MM-GBSA) approaches have been validated for a relatively limited number of targets and compounds in the training set. Here, we report the results of an extensive study on a series of 28 inhibitors of aldose reductase with experimentally determined crystal structures and inhibitory activities, in which we evaluate the ability of MM-PBSA and MM-GBSA methods in predicting binding free energies using a number of different simulation conditions. While none of the methods proved able to predict absolute free energies of binding in quantitative agreement with the experimental values, calculated and experimental free energies of binding were significantly correlated. Comparing the predicted and experimental ΔG of binding, MM-PBSA proved to perform better than MM-GBSA, and within the MM-PBSA methods, the PBSA of Amber performed similarly to Delphi. In particular, significant relationships between experimental and computed free energies of binding were obtained using Amber PBSA and structures minimized with a distance-dependent dielectric function. Importantly, while free energy predictions are usually made on large collections of equilibrated structures sampled during molecular dynamics in water, we have found that a single minimized structure is a reasonable approximation if relative free energies of binding are to be calculated. This finding is particularly relevant, considering that the generation of equilibrated MD ensembles and the subsequent free energy analysis on multiple snapshots is computationally intensive, while the generation and analysis of a single minimized structure of a protein–ligand complex is relatively fast, and therefore suited for high-throughput virtual screening studies. At this aim, we have developed an automated workflow that integrates all the necessary steps required to generate structures and calculate free energies of binding. The procedure is relatively fast and able to screen automatically and iteratively molecules contained in databases and libraries of compounds. Taken altogether, our results suggest that the workflow can be a valuable tool for ligand identification and optimization, being able to automatically and efficiently refine docking poses, which sometimes may not be accurate, and rank the compounds based on more accurate scoring functions.