Analysis of ligand-bound water molecules in high-resolution crystal structures of protein-ligand complexes

We have performed a comprehensive analysis of water molecules at the protein-ligand interfaces observed in 392 high-resolution crystal structures. There are a total of 1829 ligand-bound water molecules in these 392 complexes; 18% are surface water molecules, and 72% are interfacial water molecules. The number of ligand-bound water molecules in each complex structure ranges from 0 to 21 and has an average of 4.6. Of these interfacial water molecules, 76% are considered to be bridging water molecules, characterized by having polar interactions with both ligand and protein atoms. Among a number of factors that may influence the number of ligand-bound water molecules, the polar van der Waals (vdw) surface area of ligands has the highest Pearson linear correlation coefficient of 0.63. Our regression analysis predicted that one more ligand-bound water molecule is expected for every additional 24 A2 in the polar vdw surface area of the ligand. In contrast to the observation that the resolution is the primary factor influencing the number of water molecules in crystallographic models of proteins, we found that there is only a weak relationship between the number of ligand-bound water molecules and the resolution of the crystal structures. An analysis of the isotropic B factors of buried ligand-bound water molecules suggested that, when water molecules have fewer than two polar interactions with the protein-ligand complex, they are more mobile than protein atoms in the crystal structures; when they have more than three polar interactions, they are significantly less mobile than protein atoms.     

Evaluation of protein-ligand binding free energy focused on its entropic components

The binding free energy for FK506-binding protein-ligand systems is evaluated as a sum of two entropic components, the water-entropy gain, and the configurational-entropy loss for the protein and ligand molecules upon the binding. The two entropic components are calculated using morphometric thermodynamics combined with a statistical-mechanical theory for molecular liquids and the normal mode analysis, respectively. We find that there is an excellent correlation between the calculated and experimental values of the binding free energy. This result is compared with those of several other binding-free energy calculation methods, including MM-PB/SA. The binding can well be elucidated by competition of the two entropic components. Upon the protein-ligand binding, the total volume available to the translational displacement of the coexisting water molecules increases, leading to an increase in the number of accessible configurations of the water. The water-entropy gain, by which the binding is driven, originates primarily from this effect. This study sheds new light on the theoretical prediction of the protein-ligand binding free energy.     

A water-swap reaction coordinate for the calculation of absolute protein-ligand binding free energies

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies.     

Thermodynamics of buried water clusters at a protein-ligand binding interface

The structure of the complex of cyclophilin A (CypA) with cyclosporin A (CsA, 1) shows a cluster of four water molecules buried at the binding interface, which is rearranged when CsA is replaced by (5-hydroxynorvaline)-2-cyclosporin (2). The thermodynamic contributions of each bound water molecule in the two complexes are explored with the inhomogeneous fluid solvation theory and molecular dynamics simulations. Water (WTR) 133 in complex 1 contributes little to the binding affinity, while WTR6 and 7 in complex 2 play an essential role in mediating protein-ligand binding with a hydrogen bond network. The calculations reveal that the rearrangement of the water molecules contributes favorably to the binding affinity, even though one of them is displaced going from ligand 1 to 2. Another favorable contribution comes from the larger protein-ligand interactions of ligand 2. However, these favorable contributions are not sufficient to overcome the unfavorable desolvation free energy change and the conformational entropy of the hydroxylpropyl group of ligand 2 in the complex, leading to a lower binding affinity of ligand 2. These physical insights may be useful in the development of improved scoring functions for binding affinity prediction.     

Insights into Modeling Approaches in Chemistry: Assessing Ligand-Protein Binding Thermodynamics Based on Rigid-Flexible Model Molecules

In the field of chemistry, model compounds find extensive use for investigating complex objects. One prime example of such object is the protein-ligand supramolecular interaction. Prediction the enthalpic and entropic contribution to the free energy associated with this process, as well as the structural and dynamic characteristics of protein-ligand complexes poses considerable challenges. This review exemplifies modeling approaches used to study protein-ligand binding (PLB) thermodynamics by employing pairs of conformationally constrained/flexible model molecules. Strategically designing the model molecules can reduce the number of variables that influence thermodynamic parameters. This enables scientists to gain deeper insights into the enthalpy and entropy of PLB, which is relevant for medicinal chemistry and drug design. The model studies reviewed here demonstrate that rigidifying ligands may induce compensating changes in the enthalpy and entropy of binding. Some “rules of thumb” have started to emerge on how to minimize entropy-enthalpy compensation and design efficient rigidified or flexible ligands.     

Standard free energy of releasing a localized water molecule from the binding pockets of proteins: double-decoupling method

Localized water molecules in the binding pockets of proteins play an important role in noncovalent association of proteins and small drug compounds. At times, the dominant contribution to the binding free energy comes from the release of localized water molecules in the binding pockets of biomolecules. Therefore, to quantify the energetic importance of these water molecules for drug design purposes, we have used the double-decoupling approach to calculate the standard free energy of tying up a water molecule in the binding pockets of two protein complexes. The double-decoupling approach is based on the underlying principle of statistical thermodynamics. We have calculated the standard free energies of tying up the water molecule in the binding pockets of these complexes to be favorable. These water molecules stabilize the protein-drug complexes by interacting with the ligands and binding pockets. Our results offer ideas that could be used in optimizing protein-drug interactions, by designing ligands that are capable of targeting localized water molecules in protein binding sites. The resulting free energy of ligand binding could benefit from the potential free energy gain accompanying the release of these water molecules. Furthermore, we have examined the theoretical background of the double-decoupling method and its connection to the molecular dynamics thermodynamic integration techniques.     

应用MM/PBSA方法研究CDK2活性口袋内溶剂水分子对CDK2-配体结合自由能的影响

应用MM/PBSA方法研究了CDK2活性口袋内溶剂水分子对CDK2-配体结合自由能的影响. 结果表明, 活性口袋内溶剂水分子对CDK2-配体相互作用自由能有一定的贡献, 其贡献的大小随配体不同而有所差异, 导致这种差异的主要原因是活性位点内溶剂水分子与蛋白残基和配体之间形成了不同的氢键相互作用网络.     

The effect of water displacement on binding thermodynamics: concanavalin A

Interactions at the binding interface of biomolecular complexes are often mediated by ordered water molecules. In this work, we considered two concanavalin A-carbohydrate complexes. In the first, a water molecule is buried at the binding interface. In the second, this water molecule is displaced by a modification of the ligand (Clarke, C.; Woods, R. J.; Gluska, J.; Cooper, A.; Nutley, M. A.; Boons, G. J. J. Am. Chem. Soc. 2001, 123, 12238-12247). We computed the contribution of this water molecule to the thermodynamic properties using statistical mechanical formulas for the energy and entropy and molecular dynamics simulations. Other contributions to the binding affinity, including desolvation, entropy of conformational restriction, and interaction between the ligand and protein, were also computed. The thermodynamic consequences of displacement of the ordered water molecule by ligand modification were in qualitative agreement with experimental data. The free energy contribution of the water molecule (-17.2 kcal/mol; -19.2 enthalpic and +2 entropic) was nearly equivalent to the additional protein-ligand interactions in trimannoside 2 (-18.9 kcal/mol). The two structural ions interact more strongly with the water than with the hydroxyl of trimannoside 2, thus favoring trimannoside 1. The contributions from desolvation and conformational entropy are much smaller but significant, compared to the binding free energy difference. The picture that emerges is that the final outcome of water displacement is sensitive to the details of the binding site and cannot be predicted by simple empirical rules.     

Hydration in drug design. 3. Conserved water molecules at the ligand-binding sites of homologous proteins

Summary Water molecules are known to play an important rôle in mediating protein-ligand interactions. If water molecules are conserved at the ligand-binding sites of homologous proteins, such a finding may suggest the structural importance of water molecules in ligand binding. Structurally conserved water molecules change the conventional definition of binding sites by changing the shape and complementarity of these sites. Such conserved water molecules can be important for site-directed ligand/drug design. Therefore, five different sets of homologous protein/protein-ligand complexes have been examined to identify the conserved water molecules at the ligand-binding sites. Our analysis reveals that there are as many as 16 conserved water molecules at the FAD binding site of glutathione reductase between the crystal structures obtained from human and E. coli. In the remaining four sets of high-resolution crystal structures, 2–4 water molecules have been found to be conserved at the ligand-binding sites. The majority of these conserved water molecules are either bound in deep grooves at the protein-ligand interface or completely buried in cavities between the protein and the ligand. All these water molecules, conserved between the protein/protein-ligand complexes from different species, have identical or similar apolar and polar interactions in a given set. The site residues interacting with the conserved water molecules at the ligand-binding sites have been found to be highly conserved among proteins from different species; they are more conserved compared to the other site residues interacting with the ligand. These water molecules, in general, make multiple polar contacts with protein-site residues.     

Hydration in drug design. 2. Influence of local site surface shape on water binding

Summary If water molecules are strongly bound at a protein-ligand interface, they are unlikely to be displaced during ligand binding. Such water molecules can change the shape of the ligand binding site and thus affect strategies for drug design. To understand the nature of water binding, and factors influencing it, water molecules at the ligand binding sites of 26 high-resolution protein-ligand complexes have been examined here. Water molecules bound in deep grooves and cavities between the protein and the ligand are located in the indentations on the protein-site surface, but not in the indentations on the ligand surface. The majority of the water molecules bound in deep indentations on the protein-site surface make multiple polar contacts with the protein surface. This may indicate a strong binding of water molecules in deep indentations on protein-site surfaces. The local shape of the site surface may influence the binding of water molecules that mediate protein-ligand interactions.     

Steric and allosteric effects of fatty acids on the binding of warfarin to human serum albumin revealed by molecular dynamics and free energy calculations

Human serum albumin (HSA) binds with drugs and fatty acids (FAs). This study was initiated to elucidate the relationship between the warfarin binding affinity of HSA and the positions of bound FA molecules. Molecular dynamics simulations of 11 HSA-warfarin-myristate complexes were performed. HSA-warfarin binding free energy was then calculated for each of the complexes by the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method. The results indicated that the magnitude of the binding free energy was smaller in HSA-warfarin complexes that had 4 or more myristate molecules than in complexes with no myristate molecules. The unfavorable effect on the HSA-warfarin binding affinity was caused sterically by the binding of a myristate molecule to the FA binding site closest to the warfarin binding site. On the other hand, the magnitude of HSA-warfarin binding free energy was largest when 3 myristate molecules were bound to the high-affinity sites. The strongest HSA-warfarin binding was attributable to favorable entropic contribution related to larger atomic fluctuations of the amino acid residues at the warfarin binding site. In the binding of 2 myristate molecules to the sites with the highest and second-highest affinities, allosteric modulation that enhanced electrostatic interactions between warfarin and some of the amino acid residues around the warfarin binding site was observed. This study clarified the structural and energetic properties of steric/allosteric effects of FAs on the HSA-warfarin binding affinity and illustrated the approach to analyze protein-ligand interactions in situations such that multiple ligands bind to the other sites of the protein.     

Computation of the contribution from the cavity effect to protein-ligand binding free energy

We present results of the investigation of the cavity creation/annihilation effect in view of formation of the protein-ligand (PL) complexes. The protein and ligand were considered as rigid structures. The change of the cavity creation/annihilation free energy DeltaG(cav) was calculated for three PL complexes using the thermodynamic integration procedure with the original algorithm for growing the interaction potential between the cavity and the water molecules. The thermodynamic cycle consists of two stages, annihilation of the cavity of the ligand for the unbound state and its creation at the active site of the protein (bound state). It was revealed that for all complexes under investigation, the values of DeltaG(cav) are negative and favorable for binding. The main contribution to DeltaG(cav) appears due to the annihilation of the cavity of the ligand. All computations were made using the parallel version of CAVE code, elaborated in our preceding work.     

Interpretation of protein/ligand crystal structure using QM/MM calculations: case of HIV-1 protease/metallacarborane complex

Deltahedral metallacarborane compounds have recently been discovered as potent, specific, stable, and nontoxic inhibitors of HIV-1 protease (PR), the major target for AIDS therapy. The 2.15 A-resolution X-ray structure has exhibited a nonsymmetrical binding of the parental compound [Co(3+)-(C2B9H11)2](-) (GB-18) into PR dimer and a symmetrical arrangement in the crystal of two PR dimer complexes into a tetramer. In order to explore structural and energetic details of the inhibitor binding, quantum mechanics coupled with molecular mechanics approach was utilized. Realizing the close positioning of anionic inhibitors in the active site cavity, the possibility of an exchange of structural water molecules Wat50 and Wat128 by Na+ counterions was studied. The energy profiles for the rotation of the GB-18 molecules along their longitudinal axes in complex with PR were calculated. The results show that two Na+ counterions are present in the active site cavity and provide energetically favorable and unfavorable positions for carbon atoms within the carborane cages. Eighty-one rotamer combinations of four molecules of GB-18 bound to PR out of 4 x 10(5) are predicted to be highly populated. These results lay ground for further calculations of interaction energies between GB-18 and amino acids of PR active site and will make it possible to interpret computationally the binding of similar metallacarborane molecules to PR as well as to resistant PR variants. Moreover, this computational tool will allow the design of new, more potent metallacarborane-based HIV-1 protease inhibitors.     

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.     

Effect of molecular weight on the radial growth rates of polymer spherulites

Data existing in the literature for the spherulitic growth rate of molecular weight fractions of linear polyethylene, poly-(tetramethyl-p-silphenylene)siloxane, and trans-1,4-polyisoprene have been analyzed according to nucleation theory on taking into account the influence of chain length on the free energy of fusion. All three polymers display very similar behavior in that the interfacial free energy reaches an asymptotic value at high molecular weights, decreases as the molecular weight is lowered, and appears to also reach an asymptotic value at low molecular weights. Although the changes in the interfacial energy with molecular weight are quite distinct, the relative change is much less than has been previously reported when a molecular crystal analysis is used. The same general behavior observed points out the dominating influence of the chain-like character of the molecules in governing the growth rate.     

Challenges in predicting and controlling particle morphology in latices of commercial complexity

Independent, quantitative models for free energy associated with crosslinked seed latices, and monomer and surfactant at the polymer/water interface have been integrated into a predictive model for latex particle morphology. It has been found that very low levels of crosslinking are predicted to influence the particle morphology in a dramatic fashion. Free energy calculation also highlight the often critical role played by surfactant. Highly active surfactants tend to equalize the two polymer/water interfacial tensions and allow the polymer/water interfacial energy to significantly influence the particle morphology.     

The molecular mechanism studies of chirality effect of PHA-739358 on Aurora kinase A by molecular dynamics simulation and free energy calculations

Aurora kinase family is one of the emerging targets in oncology drug discovery and several small molecules targeting aurora kinases have been discovered and evaluated under early phase I/II trials. Among them, PHA-739358 (compound 1r) is a 3-aminopyrazole derivative with strong activity against Aurora A under early phase II trial. Inhibitory potency of compound 1r (the benzylic substituent at the pro-R position) is 30 times over that of compound 1s (the benzylic substituent at the pro-S position). In present study, the mechanism of how different configurations influence the binding affinity was investigated using molecular dynamics (MD) simulations, free energy calculations and free energy decomposition analysis. The predicted binding free energies of these two complexes are consistent with the experimental data. The analysis of the individual energy terms indicates that although the van der Waals contribution is important for distinguishing the binding affinities of these two inhibitors, the electrostatic contribution plays a more crucial role in that. Moreover, it is observed that different configurations of the benzylic substituent could form different binding patterns with protein, thus leading to variant inhibitory potency of compounds 1r and 1s. The combination of different molecular modeling techniques is an efficient way to interpret the chirality effects of inhibitors and our work gives valuable information for the chiral drug design in the near future.     

Hydration in drug design. 1. Multiple hydrogen-bonding features of water molecules in mediating protein-ligand interactions

Summary Water is known to play an important rôle in the recognition and stabilization of the interaction between a ligand and its site. This has important implications for drug design. Analyses of 19 high-resolution crystal structures of protein-ligand complexes reveal the multiple hydrogen-bonding feature of water molecules mediating protein-ligand interactions. Most of the water molecules (nearly 80%) involved in bridging the protein and the ligand can make three or more hydrogen bonds when distance and bond angles are used as criteria to define hydrogen-bonding interactions. Isotropic B-factors have been used to take into account the mobility of water molecules. The water molecules at binding sites bridge the protein and ligand, and interact with other water molecules to form a complex network of interconnecting hydrogen bonds. Some water molecules at the site do not directly bridge between the protein and the ligand, but may contribute indirectly to the stability of the complex by holding bridging water molecules in the right position through a network of hydrogen bonds. These water networks are probably crucial for the stability of the protein-ligand complex and are important for any site-directed drug design strategies.     

Influence of metal cofactors and water on the catalytic mechanism of creatininase-creatinine in aqueous solution from molecular dynamics simulation and quantum study

The reaction mechanism of creatinine-creatininase binding to form creatine as a final product has been investigated by using a combined ab initio quantum mechanical/molecular mechanical approach and classical molecular dynamics (MD) simulations. In MD simulations, an X-ray crystal structure of the creatininase/creatinine was modified for creatininase/creatinine complexes and the MD simulations were run for free creatininase and creatinine in water. MD results reveal that two X-ray water molecules can be retained in the active site as catalytic water. The binding free energy from Molecular Mechanics Poisson-Boltzmann Surface Area calculation predicted the strong binding of creatinine with Zn²⁺, Asp45 and Glu183. Two step mechanisms via Mn²⁺/Zn²⁺ (as in X-ray structure) and Zn²⁺/Zn²⁺ were proposed for water adding step and ring opening step with two catalytic waters. The pathway using synchronous transit methods with local density approximations with PWC functional for the fragment in the active region were obtained. Preferable pathway Zn²⁺/Zn²⁺ was observed due to lower activation energy in water adding step. The calculated energy in the second step for both systems were comparable with the barrier of 26.03 and 24.44 kcal/mol for Mn²⁺/Zn²⁺ and Zn²⁺/Zn²⁺, respectively.