Three-dimensional distribution function theory for the prediction of protein-ligand binding sites and affinities: application to the binding of noble gases to hen egg-white lysozyme in aqueous solution

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl^-, [ClO]^- (a two-site anion), and [NO₂]^- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl^-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

RNA-ligand molecular docking: advances and challenges

With rapid advances in computer algorithms and hardware, fast and accurate virtual screening has led to a drastic acceleration in selecting potent small molecules as drug candidates. Computational modeling of RNA-small molecule interactions has become an indispensable tool for RNA-targeted drug discovery. The current models for RNA-ligand binding have mainly focused on the docking-and-scoring method. Accurate docking and scoring should tackle four crucial problems: (1) conformational flexibility of ligand, (2) conformational flexibility of RNA, (3) efficient sampling of binding sites and binding poses, and (4) accurate scoring of different binding modes. Moreover, compared with the problem of protein-ligand docking, predicting ligand binding to RNA, a negatively charged polymer, is further complicated by additional effects such as metal ion effects. Thermodynamic models based on physics-based and knowledge-based scoring functions have shown highly encouraging success in predicting ligand binding poses and binding affinities. Recently, kinetic models for ligand binding have further suggested that including dissociation kinetics (residence time) in ligand docking would result in improved performance in estimating in vivo drug efficacy. More recently, the rise of deep-learning approaches has led to new tools for predicting RNA-small molecule binding. In this review, we present an overview of the recently developed computational methods for RNA-ligand docking and their advantages and disadvantages.

Molecular Recognition and Self-Organization in Life Phenomena Studied by a Statistical Mechanics of Molecular Liquids, the RISM/3D-RISM Theory

There are two molecular processes that are essential for living bodies to maintain their life: the molecular recognition, and the self-organization or self-assembly. Binding of a substrate by an enzyme is an example of the molecular recognition, while the protein folding is a good example of the self-organization process. The two processes are further governed by the other two physicochemical processes: solvation and the structural fluctuation. In the present article, the studies concerning the two molecular processes carried out by Hirata and his coworkers, based on the statistical mechanics of molecular liquids or the RISM/3D-RISM theory, are reviewed.

New Protocol for Predicting the Ligand-Binding Site and Mode Based on the 3D-RISM/KH Theory

An efficient algorithm to find the binding position and mode of small ligands bound at an active site of protein is proposed based on the spatial distribution function (SDF) obtained from the three-dimensional reference interaction site model (3D-RISM) theory with the Kovalenko-Hirata (KH) closure relation. The ligand examined includes hydrophobic, acidic, and basic molecules and zwitterions. Eighteen different types of proteins, which serve as targets for those ligands, are selected to examine the robustness of the algorithm. An imaginary atom, referred to as an "anchor site", is defined at the center of geometry of a ligand molecule that serves as a center for searching the binding position and mode of the ligand molecule in the translational and rotational spaces. The probable binding sites (PBSs) are identified based on the SDFs of the ligand molecules around the protein, and the PBS is ranked according to the peak height of SDF. The deviations from the mean height of the peak values of SDFs for 50 PBSs are analyzed based on the z-score, which is a measure of prominence of the site. The PBS found at the closest distance from the anchor site of the crystal structure is referred to as the "nearest site". The orientation of the ligand molecule at each PBS is explored by changing the Euler angles, and the most probable binding mode is determined based on the superposition approximation. The binding position of ligand molecules is successfully predicted as one of the distinct peaks in SDF of the anchor site, with a few exceptions. The binding mode of the ligand molecule predicted based on the superposition approximation is consistent with the X-ray crystal structure in nine systems, a half of the systems investigated. The significance of the results is discussed in detail. An application of the new protocol to fragment-based drug discovery is suggested.

Massive in Silico Study of Noble Gas Binding to the Structural Proteome

Noble gases are chemically inert, and it was therefore thought they would have little effect on biology. Paradoxically, it was found that they do exhibit a wide range of biological effects, many of which are target-specific and potentially useful and some of which have been demonstrated in vivo. The underlying mechanisms by which useful pharmacology, such as tissue and neuroprotection, anti-addiction effects, and analgesia, is elicited are relatively unexplored. Experiments to probe the interactions of noble gases with specific proteins are more difficult with gases than those with other chemicals. It is clearly impractical to conduct the large number of gas-protein experiments required to gain a complete picture of noble gas biology. Given the simplicity of atoms as ligands, in silico methods provide an opportunity to gain insight into which noble gas-protein interactions are worthy of further experimental or advanced computational investigation. Our previous validation studies showed that in silico methods can accurately predict experimentally determined noble gas binding sites in X-ray structures of proteins. Here, we summarize the largest reported in silico reverse docking study involving 127 854 protein structures and the five nonradioactive noble gases. We describe how these computational screening methods are implemented, summarize the main types of interactions that occur between noble gases and target proteins, describe how the massive data set that this study generated can be analyzed (freely available at group18.csiro.au), and provide the NDMA receptor as an example of how these data can be used to understand the molecular pharmacology underlying the biology of the noble gases. We encourage chemical biologists to access the data and use them to expand the knowledge base of noble gas pharmacology, and to use this information, together with more efficient delivery systems, to develop "atomic drugs" that can fully exploit their considerable and relatively unexplored potential in medicine.

Solvent Composition Effects on the Structural Properties of the Aβ42 Monomer from the 3D-RISM-KH Molecular Theory of Solvation

Structural characterization of amyloid (A)β peptides implicated in Alzheimer's disease is a challenging problem due to their intrinsically disordered nature and their high propensity for aggregation. Only limited information is currently available from experiments on conformational properties and aggregation pathways of the peptides in cellular environments. In silico modeling complements experimental information, providing atomistic insight into structure and dynamics of different Aβ species. All-atom explicit solvent molecular dynamics (MD) simulations with a properly selected force field can deliver reliable structural and dynamic information. In the case of intrinsically disordered Aβ peptides, enhanced sampling simulations beyond the nanosecond time scale are required to obtain statistically meaningful results even for simple solvent conditions. To overcome the challenges of conformational sampling in crowded cellular environments, alternative approaches have to be used, including postprocessing of MD data. In this study, we employ the statistical-mechanical, three-dimensional reference interaction site model with the Kovalenko-Hirata closure integral equation molecular theory of solvation to describe solvent composition effects on the conformational equilibrium in a structural ensemble of the Aβ42 (covering residues 1-42) monomer based on a statistical reweighting technique. The methodology enables a computationally efficient prediction on how different factors in the cellular environment, such as solvent composition, nonpolar solvation, and macromolecular crowding, affect the structural properties of the monomer. Similarities have been identified between changes in the structural ensemble caused by nonpolar solvation and crowded environments modeled by ionic solution with large negative ions. In particular, both solvent conditions reduce the random coil content and enhance the helical structure content of the monomer. In contrast to the previous studies, which reported increased α-helical content of peptides in crowded environments, this work attributes these structural features to the difference in solvent exposure of hydrophilic residues of the monomer for different secondary structure elements, rather than to (entropic) excluded volume effects.

A Systematic Analysis of the Binding Affinity between the Pim-1 Kinase and Its Inhibitors Based on the MM/3D-RISM/KH Method

A systematic study of the binding affinities of 16 lead compounds targeting the Pim-1 kinase based on the 3D-RISM/KH theory and MD simulations is reported. The results show a correlation coefficient R = 0.69 between the theoretical and experimental values of the binding free energy. This demonstrates that the method is applicable to the problem of compound screening and lead optimization, for which relative values of the free energy among the compounds have significance. We elucidate the contribution of the ligand fragments to the binding free energy. Our results indicate that the interactions between the residues and the triazolo[4,3-b]pyridazine scaffold as well as the phenyl ring of the ligand molecule make significant contributions to stabilization of the complex. Using the 3D-RISM/KH theory, we further analyze the probability distribution of a ligand fragment around the protein-ligand complex in which the substituent around the phenyl ring is removed from the ligand. The results demonstrate that the 3D-RISM/KH theory is capable of predicting the position of substitution on a ligand that has a higher affinity to a target protein.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Structural Basis for Xenon Inhibition in a Cationic Pentameric Ligand-Gated Ion Channel

GLIC receptor is a bacterial pentameric ligand-gated ion channel whose action is inhibited by xenon. Xenon has been used in clinical practice as a potent gaseous anaesthetic for decades, but the molecular mechanism of interactions with its integral membrane receptor targets remains poorly understood. Here we characterize by X-ray crystallography the xenon-binding sites within both the open and "locally-closed" (inactive) conformations of GLIC. Major binding sites of xenon, which differ between the two conformations, were identified in three distinct regions that all belong to the trans-membrane domain of GLIC: 1) in an intra-subunit cavity, 2) at the interface between adjacent subunits, and 3) in the pore. The pore site is unique to the locally-closed form where the binding of xenon effectively seals the channel. A putative mechanism of the inhibition of GLIC by xenon is proposed, which might be extended to other pentameric cationic ligand-gated ion channels.

Pred-binding: large-scale protein-ligand binding affinity prediction

Drug target interactions (DTIs) are crucial in pharmacology and drug discovery. Presently, experimental determination of compound-protein interactions remains challenging because of funding investment and difficulties of purifying proteins. In this study, we proposed two in silico models based on support vector machine (SVM) and random forest (RF), using 1589 molecular descriptors and 1080 protein descriptors in 9948 ligand-protein pairs to predict DTIs that were quantified by Ki values. The cross-validation coefficient of determination of 0.6079 for SVM and 0.6267 for RF were obtained, respectively. In addition, the two-dimensional (2D) autocorrelation, topological charge indices and three-dimensional (3D)-MoRSE descriptors of compounds, the autocorrelation descriptors and the amphiphilic pseudo-amino acid composition of protein are found most important for Ki predictions. These models provide a new opportunity for the prediction of ligand-receptor interactions that will facilitate the target discovery and toxicity evaluation in drug development.

A comparative study of family-specific protein-ligand complex affinity prediction based on random forest approach

The assessment of binding affinity between ligands and the target proteins plays an essential role in drug discovery and design process. As an alternative to widely used scoring approaches, machine learning methods have also been proposed for fast prediction of the binding affinity with promising results, but most of them were developed as all-purpose models despite of the specific functions of different protein families, since proteins from different function families always have different structures and physicochemical features. In this study, we proposed a random forest method to predict the protein-ligand binding affinity based on a comprehensive feature set covering protein sequence, binding pocket, ligand structure and intermolecular interaction. Feature processing and compression was respectively implemented for different protein family datasets, which indicates that different features contribute to different models, so individual representation for each protein family is necessary. Three family-specific models were constructed for three important protein target families of HIV-1 protease, trypsin and carbonic anhydrase respectively. As a comparison, two generic models including diverse protein families were also built. The evaluation results show that models on family-specific datasets have the superior performance to those on the generic datasets and the Pearson and Spearman correlation coefficients (R p and Rs) on the test sets are 0.740, 0.874, 0.735 and 0.697, 0.853, 0.723 for HIV-1 protease, trypsin and carbonic anhydrase respectively. Comparisons with the other methods further demonstrate that individual representation and model construction for each protein family is a more reasonable way in predicting the affinity of one particular protein family.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Placevent: an algorithm for prediction of explicit solvent atom distribution-application to HIV-1 protease and F-ATP synthase

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the three-dimensional (3D) continuous distribution resulting from a 3D reference interaction site model (3D-RISM) calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure and the solvent composition. We show examples of predicting water molecules near the KNI-272 bound form of HIV-1 protease and predicting both sodium ions and water molecules near the rotor ring of F-adenosine triphosphate (ATP) synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.39-0.65 Å. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D-RISM output within minutes. It is extremely useful for examining multiple specific solvent-solute interactions, as a convenient method for generating initial solvent structures for molecular dynamics calculations, and may assist in refinement of experimental structures. © 2012 Wiley Periodicals, Inc.

A New Approach for Investigating the Molecular Recognition of Protein: Toward Structure-Based Drug Design Based on the 3D-RISM Theory

A new approach to investigate a molecular recognition process of protein is presented based on the three-dimensional reference interaction site model (3D-RISM) theory, a statistical mechanics theory of molecular liquids. Numerical procedure for solving the conventional 3D-RISM equation consists of two steps. In step 1, we solve ordinary RISM (or 1D-RISM) equations for a solvent mixture including target ligands in order to obtain the density pair correlation functions (PCF) among molecules in the solution. Then, we solve the 3D-RISM equation for a solute-solvent system to find three-dimensional density distribution functions (3D-DDF) of solvent species around a protein, using PCF obtained in the first step. A key to the success of the method was to regard a target ligand as one of "solvent" species. However, the success is limited due to a difficulty of solving the 1D-RISM equation for a solvent mixture, including large ligand molecules. In the present paper, we propose a method which eases the limitation concerning solute size in the conventional method. In this approach, we solve a solute-solute 3D-RISM equations for a protein-ligand system in which both proteins and ligands are regarded as "solutes" at infinite dilution. The 3D- and 1D-RISM equations are solved for protein-solvent and ligand-solvent systems, respectively, in order to obtain the 3D- and 1D-DDF of solvent around the solutes, which are required for solving the solute-solute 3D-RISM equation. The method is applied to two practical and noteworthy examples concerning pharmaceutical design. One is an odorant binding protein in the Drosophila melanogaster , which binds an ethanol molecule. The other is phospholipase A2, which is known as a receptor of acetylsalicylic acid or aspirin. The result indicates that the method successfully reproduces the binding mode of the ligand molecules in the binding sites measured by the experiments.

Integral equations in the study of polar and ionic interaction site fluids

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids.

Ion and solvent density distributions around canonical B-DNA from integral equations

We calculate the water and ion spatial distributions around charged oligonucleotides using a renormalized three-dimensional reference interaction site theory coupled with the HNC closure. Our goal is to understand the balance between inter-DNA strand forces and solvation forces as a function of oligonucleotide length in the short strand limit. The DNA is considered in aqueous electrolyte solutions of 1 M KCl, 0.1 M KCl, or 0.1 M NaCl. The current theoretical results are compared to molecular dynamics (MD) simulations and experiments. It is found that the integral equation (IE) theory replicates the MD and the experimental results for the base-specific hydration patterns in both the major and the minor grooves. We are also able to discern characteristic structural pattern differences between Na(+) and K(+) ions. When compared to Poisson-Boltzmann methods, the IE theory, like simulation, predicts a richly structured ion environment, which is better described as multilayer rather than double layer.

Association thermodynamics and conformational stability of beta-sheet amyloid beta(17-42) oligomers: effects of E22Q (Dutch) mutation and charge neutralization

Amyloid fibrils are associated with many neurodegenerative diseases. It was found that amyloidogenic oligomers, not mature fibrils, are neurotoxic agents related to these diseases. Molecular mechanisms of infectivity, pathways of aggregation, and molecular structure of these oligomers remain elusive. Here, we use all-atom molecular dynamics, molecular mechanics combined with solvation analysis by statistical-mechanical, three-dimensional molecular theory of solvation (also known as 3D-RISM-KH) in a new MM-3D-RISM-KH method to study conformational stability, and association thermodynamics of small wild-type Abeta(17-42) oligomers with different protonation states of Glu(22), as well the E22Q (Dutch) mutants. The association free energy of small beta-sheet oligomers shows near-linear trend with the dimers being thermodynamically more stable relative to the larger constructs. The linear (within statistical uncertainty) dependence of the association free energy on complex size is a consequence of the unilateral stacking of monomers in the beta-sheet oligomers. The charge reduction of the wild-type Abeta(17-42) oligomers upon protonation of the solvent-exposed Glu(22) at acidic conditions results in lowering the association free energy compared to the wild-type oligomers at neutral pH and the E22Q mutants. The neutralization of the peptides because of the E22Q mutation only marginally affects the association free energy, with the reduction of the direct electrostatic interactions mostly compensated by the unfavorable electrostatic solvation effects. For the wild-type oligomers at acidic conditions such compensation is not complete, and the electrostatic interactions, along with the gas-phase nonpolar energetic and the overall entropic effects, contribute to the lowering of the association free energy. The differences in the association thermodynamics between the wild-type Abeta(17-42) oligomers at neutral pH and the Dutch mutants, on the one hand, and the Abeta(17-42) oligomers with protonated Glu(22), on the other, may be explained by destabilization of the inter- and intrapeptide salt bridges between Asp(23) and Lys(28). Peculiarities in the conformational stability and the association thermodynamics for the different models of the Abeta(17-42) oligomers are rationalized based on the analysis of the local physical interactions and the microscopic solvation structure.

Ligand mapping on protein surfaces by the 3D-RISM theory: toward computational fragment-based drug design

In line with the recent development of fragment-based drug design, a new computational method for mapping of small ligand molecules on protein surfaces is proposed. The method uses three-dimensional (3D) spatial distribution functions of the atomic sites of the ligand calculated using the molecular theory of solvation, known as the 3D reference interaction site model (3D-RISM) theory, to identify the most probable binding modes of ligand molecules. The 3D-RISM-based method is applied to the binding of several small organic molecules to thermolysin, in order to show its efficiency and accuracy in detecting binding sites. The results demonstrate that our method can reproduce the major binding modes found by X-ray crystallographic studies with sufficient precision. Moreover, the method can successfully identify some binding modes associated with a known inhibitor, which could not be detected by X-ray analysis. The dependence of ligand-binding modes on the ligand concentration, which essentially cannot be treated with other existing computational methods, is also investigated. The results indicate that some binding modes are readily affected by the ligand concentration, whereas others are not significantly altered. In the former case, it is the subtle balance in the binding affinity between the ligand and water that determines the dominant ligand-binding mode.

Molecular recognition in biomolecules studied by statistical-mechanical integral-equation theory of liquids

Recent progress in the theory of molecular recognition in biomolecules is reviewed, which has been made based on the statistical mechanics of liquids or the RISM/3D-RISM theory during the last five years in the authors' group. The method requires just the structure of protein and the potential energy parameters for the biomolecules and solutions as inputs. The calculation is carried out in two steps. The first step is to obtain the pair correlation functions for solutions consisting of water and ligands based on the RISM theory. Then, given the pair correlation functions prepared in the first step, we calculate the 3D-distribution functions of water and ligands around and inside protein based on the 3D-RISM theory. The molecular recognition of a ligand by the protein is realized by the 3D-distribution functions: if one finds some conspicuous peaks in the distribution of a ligand inside protein, then the ligand is regarded as "recognized" by the protein. Some biochemical processes are investigated, which are intimately related to the molecular recognition of small ligands including water, noble gases, and ions by a protein.