Combined conformational search and finite-difference Poisson-Boltzmann approach for flexible docking. Application to an operator mutation in the lambda repressor-operator complex

Improved local lattice approach for Coulombic simulations

An improved approach to the simulation of strongly fluctuating Coulomb gases, based on a local lattice technique introduced by Maggs and Rossetto [A.C. Maggs and V. Rossetto, Phys. Rev. Lett. 88, 196402 (2002)], is described and then tested in a problem of biophysical interest. The low acceptance rates for charged particle moves in regimes of physical interest are increased to a serviceable level by use of a coupled particle-field update procedure in the new method. Sensitivity of the results to lattice discretization effects is also studied using asymmetric lattices.

Free energy calculations for the relative binding affinity between DNA and lambda-repressor

The change in the binding free energy between DNA and lambda-repressor resulting from a base substitution, thymine (T)-->deoxyuracil (abbreviated as U), was evaluated by the free energy perturbation method on the basis of molecular dynamics simulations for the DNA-lambda-repressor complex in water with all degrees of freedom and including long-range Coulomb interactions. The binding free energy change that we calculated (1.47 +/- 0.40 kcal/mol) was in good agreement with an experimental value (1.8 kcal/mol). We clarified why the small difference between T and U (CH(3) in T is replaced with H in U) caused such a significant change in the binding free energy: The substitution of CH(3) in T with H in U lowered the dissociated-state free energy level due to the gain of the hydration free energy. Furthermore, the T-->U substitution raised the free energy level in the associated state due to the loss of the favored van der Waals (vdW) interactions with the lambda-repressor amino acid residues. In other words, the amino acid residues of lambda-repressor can recognize the CH(3) in T through the vdW interactions with the CH(3). This recognition is enhanced in a water environment, because the hydrophobic CH(3) prefers the amino acid residues of lambda-repressor to water molecules.

Protein-protein docking with a reduced protein model accounting for side-chain flexibility

A protein-protein docking approach has been developed based on a reduced protein representation with up to three pseudo atoms per amino acid residue. Docking is performed by energy minimization in rotational and translational degrees of freedom. The reduced protein representation allows an efficient search for docking minima on the protein surfaces within. During docking, an effective energy function between pseudo atoms has been used based on amino acid size and physico-chemical character. Energy minimization of protein test complexes in the reduced representation results in geometries close to experiment with backbone root mean square deviations (RMSDs) of approximately 1 to 3 A for the mobile protein partner from the experimental geometry. For most test cases, the energy-minimized experimental structure scores among the top five energy minima in systematic docking studies when using both partners in their bound conformations. To account for side-chain conformational changes in case of using unbound protein conformations, a multicopy approach has been used to select the most favorable side-chain conformation during the docking process. The multicopy approach significantly improves the docking performance, using unbound (apo) binding partners without a significant increase in computer time. For most docking test systems using unbound partners, and without accounting for any information about the known binding geometry, a solution within approximately 2 to 3.5 A RMSD of the full mobile partner from the experimental geometry was found among the 40 top-scoring complexes. The approach could be extended to include protein loop flexibility, and might also be useful for docking of modeled protein structures.

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 degrees C in 0.1M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge-dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds.A primary objective in this study was to investigate the influence of charge-charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the alpha-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge-dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge-charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pK(Sa)-pK(5K)) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson-Boltzmann equation, which considers desolvation and charge-dipole interactions in addition to charge-charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge-charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.

The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology

Electrostatics plays a fundamental role in virtually all processes involving biomolecules in solution. The Poisson-Boltzmann equation constitutes one of the most fundamental approaches to treat electrostatic effects in solution. The theoretical basis of the Poisson-Boltzmann equation is reviewed and a wide range of applications is presented, including the computation of the electrostatic potential at the solvent-accessible molecular surface, the computation of encounter rates between molecules in solution, the computation of the free energy of association and its salt dependence, the study of pKa shifts and the combination with classical molecular mechanics and dynamics. Theoretical results may be used for rationalizing or predicting experimental results, or for suggesting working hypotheses. An ever-increasing body of successful applications proves that the Poisson-Boltzmann equation is a useful tool for structural biology and complementary to other established experimental and theoretical methodologies.

Pattern recognition strategies for molecular surfaces. I. Pattern generation using fuzzy set theory

A new method for the characterization of molecules based on the model approach of molecular surfaces is presented. We use the topographical properties of the surface as well as the electrostatic potential, the local lipophilicity/hydrophilicity, and the hydrogen bond density on the surface for characterization. The definition and the calculation method for these properties are reviewed shortly. The surface is segmented into overlapping patches with similar molecular properties. These patches can be used to represent the characteristic local features of the molecule in a way that is beyond the atomistic resolution but can nevertheless be applied for the analysis of partial similarities of different molecules as well as for the identification of molecular complementarity in a very general sense. The patch representation can be used for different applications, which will be demonstrated in subsequent articles.

Protein-protein association kinetics and protein docking

Rigid body protein docking methods frequently yield false positive structures that have good surface complementarity, but are far from the native complex. The main reason for this is the uncertainty of the protein structures to be docked, including the positions of solvent-exposed sidechains. Substantial efforts have been devoted to finding near-native structures by rescoring the docked conformations and employing various filters. An alternative approach emulates the process of protein-protein association, that is, first finding the region in which binding is likely to occur and then refining the complex while allowing for flexibility.

Binding mode prediction for a flexible ligand in a flexible pocket using multi-conformation simulated annealing pseudo crystallographic refinement

We describe multi-conformation simulated annealing-pseudo-crystallographic refinement (MCSA-PCR), a technique developed for predicting the binding mode of a flexible ligand in a flexible binding pocket. To circumvent the local-minimum problem efficiently, this method performs multiple independent cycles of simulated annealing with explicit solvent, "growing" the ligand in the binding pocket each time. From the ensemble of structures, a pseudo-crystallographic electron density map is calculated, and then conventional crystallographic refinement methods are used to best fit a single, optimal structure into the density map. The advantage of the MCSA-PCR method is that it provides a direct means to evaluate the accuracy and uniqueness of the calculated solution, provides a measure of ligand and protein dynamics from the refined B-factors, and facilitates comparison with X-ray crystallographic data. Here, we show that our MCSA-PCR method succeeds in predicting the correct binding mode of the VSV8 peptide to the major histocompatibility complex (MHC) receptor. Importantly, there is a significant correlation between the experimentally determined crystallographic water molecules and water density observed in the pseudo map by MCSA-PCR. Furthermore, comparison of different approaches for extracting a single, most probable structure from the calculated ensemble reveals the power of the PCR method and provides insights into the nature of the energetic landscape.

Structure-based ligand design for flexible proteins: application of new F-DycoBlock

A method of structure-based ligand design - DycoBlock - has been proposed and tested by Liu et al. It was further improved by Zhu et al. and applied to design new selective inhibitors of cyclooxygenase 2. In the current work, we present a new methodology - F-DycoBlock that allows for the incorporation of receptor flexibility. During the designing procedure, both the receptor and molecular building blocks are subjected to the multiple-copy stochastic molecular dynamics (MCSMD) simulation, while the protein moves in the mean field of all copies. It is tested for two enzymes studied previously - cyclooxygenase 2 (COX-2) and human immunodeficiency type 1 (HIV-1) protease. To identify the applicability of F-DycoBlock, the binding protein structure was used as starting point to explore the conformational space around the bound state. This method can be easily extended to accommodate the flexibility in different degree. Four types of treatment of the receptor flexibility - all-atom restrained, backbone restrained, intramolecular hydrogen-bond restrained and active-site flexible - were tested with or without the grid approximation. Two inhibitors, SC-558 for COX-2 and L700417 for HIV-1 protease, are used in this testing study for comparison with previous results. The accuracy of recovery, binding energy, solvent accessible surface area (SASA) and positional root-mean-square (RMS) deviation are used as criteria. The results indicate that F-DycoBlock is a robust methodology for flexible drug design. It is particularly notable that the protein flexibility has been perfectly associated with each stage of drug design - search for the binding sites, dynamic assembly and optimization of candidate compounds. When all protein atoms were restrained, F-DycoBlock yielded higher accuracy of recovery than DycoBlock (100%). If backbone atoms were restrained, the same ratio of accuracy was achieved. Moreover, with the intramolecular hydrogen bonds restrained, reasonable conformational changes were observed for HIV- 1 protease during the long-time MCSMD simulation and L700417 was reassembled at the active site. It makes it possible to study the receptor motion in the binding process.

Nuclear receptor-DNA binding specificity: A COMBINE and Free-Wilson QSAR analysis

Specific binding of transcription factors to DNA is crucial for gene regulation. We derived models for the binding specificity of transcription factors of the nuclear receptor family to DNA using two QSAR methods: a Free-Wilson-like method and COMparative BINding Energy (COMBINE) analysis. The analysis is based on experimental data for the interaction of 20 mutant glucocorticoid receptor DNA-binding domains with 16 different response elements in a total of 320 complexes (Zilliacus, J.; Wright, A. P.; Carlstedt-Duke, J.; Nilsson, L.; Gustafsson, J. A. Proteins 1995, 21, 57-67). The predictive abilities of the models obtained by the two methods are similar. The COMBINE analysis indicates that the most important properties for determining binding specificity for this dataset are the changes upon binding of the solvation free energies of the bases that are mutated in the dataset and the electrostatic interactions of the mutated nucleotides with certain charged amino acids. Further important descriptors are the changes of solvation free energy and surface area of the side chain of the mutated residue. It is clear, however, that there are additional features important for the specificity of binding that are not included in the models, such as differences in interfacial hydration of the complexes.

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr-Lys-Pro-Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson-Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed.

Determinants of ligand binding to cAMP-dependent protein kinase

Protein kinases are essential for the regulation of cellular growth and metabolism. Since their dysfunction leads to debilitating diseases, they represent key targets for pharmaceutical research. The rational design of kinase inhibitors requires an understanding of the determinants of ligand binding to these proteins. In the present study, a theoretical model based on continuum electrostatics and a surface-area-dependent nonpolar term is used to calculate binding affinities of balanol derivatives, H-series inhibitors, and ATP analogues toward the catalytic subunit of cAMP-dependent protein kinase (cAPK or protein kinase A). The calculations reproduce most of the experimental trends and provide insight into the driving forces responsible for binding. Nonpolar interactions are found to govern protein-ligand affinity. Hydrogen bonds represent a negligible contribution, because hydrogen bond formation in the complex requires the desolvation of the interacting partners. However, the binding affinity is decreased if hydrogen-bonding groups of the ligand remain unsatisfied in the complex. The disposition of hydrogen-bonding groups in the ligand is therefore crucial for binding specificity. These observations should be valuable guides in the design of potent and specific kinase inhibitors.

Electrostatic contributions to heat capacity changes of DNA-ligand binding

Significant heat capacity changes (DeltaCp) often accompany protein unfolding, protein binding, and specific DNA-ligand binding reactions. Such changes are widely used to analyze contributions arising from hydrophobic and polar hydration. Current models relate the magnitude of DeltaCp to the solvent accessible surface area (ASA) of the molecule. However, for many binding systems-particularly those involving non-peptide ligands-these models predict a DeltaCp that is significantly different from the experimentally measured value. Electrostatic interactions provide a potential source of heat capacity changes and do not scale with ASA. Using finite-difference Poisson-Boltzmann methods (FDPB), we have determined the contribution of electrostatics to the DeltaCp associated with binding for DNA binding reactions involving the ligands DAPI, netropsin, lexitropsin, and the lambda repressor binding domain.

Analysis of the stability of looped-out and stacked-in conformations of an adenine bulge in DNA using a continuum model for solvent and ions

A combination of conformational search, energy minimization, and energetic evaluation using a continuum solvent treatment has been employed to study the stability of various conformations of the DNA fragment d(CGCAGAA)/d(TTCGCG) containing a single adenine bulge. The extra-helical (looped-out) bulge conformation derived from a published x-ray structure and intra-helical (stacked bulge base) model structures partially based on nuclear magnetic resonance (NMR) data were used as start structures for the conformational search. Solvent-dependent contributions to the stability of the conformations were calculated from the solvent exposed molecular surface area and by using the finite difference Poisson-Boltzmann approach. Three classes (I-III) of bulge conformations with calculated low energies can be distinguished. The lowest-energy conformations were found in class I, corresponding to structures with the bulge base stacked between flanking helices, and class II, composed of structures forming a triplet of the bulge base and a flanking base pair. All extra-helical bulge structures, forming class III, were found to be less stable compared with the lowest energy structures of class I and II. The results are consistent with NMR data on an adenine bulge in the same sequence context indicating an intra-helical or triplet bulge conformation in solution. Although the total energies and total electrostatic energies of the low-energy conformations show only relatively modest variations, the energetic contributions to the stability were found to vary significantly among the classes of bulge structures. All intra-helical bulge structures are stabilized by a more favorable Coulomb charge-charge interaction but destabilized by a larger electrostatic reaction field contribution compared with all extra-helical and most triplet bulge structures. Van der Waals packing interactions and nonpolar surface-area-dependent contributions appear to favor triplet class II structures and to a lesser degree also the intra-helical stacked bulge conformations. The large conformational variation found for class III conformers might add a favorable entropic contribution to the stability of the extra-helical bulge form.

Solvation effects are responsible for the reduced inhibitor affinity of some HIV-1 PR mutants

The formulation of HIV-1 PR inhibitors as anti-viral drugs has been hindered by the appearance of protease strains that present drug resistance to these compounds. The mechanism by which the HIV-1 PR mutants lower their affinity for the inhibitor is not yet fully understood. We have applied a modified Poisson-Boltzmann method to the evaluation of the molecular interactions that contribute to the lowering of the inhibitor affinity to some polar mutants at position 82. These strains present drug resistance behavior and hence are ideally suited for these studies. Our results indicate that the reduction in binding affinity is due to the solvation effects that penalize the binding to the more polar mutants. The inhibitor binding ranking of the different mutants can be explained from the analysis of the different components of our free energy scoring function.

Structure-based drug design: computational advances

Structure-based computational methods continue to enhance progress in the discovery and refinement of therapeutic agents. Several such methods and their applications are described. These include molecular visualization and molecular modeling, docking, fragment methods, 3-D database techniques, and free-energy perturbation. Related issues that are discussed include the use of simplified potential energy functions and the determination of the positions of tightly bound waters. Strengths and weaknesses of the various methods are described.

Electrostatics of a simple membrane model using Green's functions formalism

The electrostatics of a simple membrane model picturing a lipid bilayer as a low dielectric constant slab immersed in a homogeneous medium of high dielectric constant (water) can be accurately computed using the exact Green's functions obtainable for this geometry. We present an extensive discussion of the analysis and numerical aspects of the problem and apply the formalism and algorithms developed to the computation of the energy profiles of a test charge (e.g., ion) across the bilayer and a molecular model of the acetylcholine receptor channel embedded in it. The Green's function approach is a very convenient tool for the computer simulation of ionic transport across membrane channels and other membrane problems where a good and computationally efficient first-order treatment of dielectric polarization effects is crucial.

Exploring the energy landscapes of molecular recognition by a genetic algorithm: analysis of the requirements for robust docking of HIV-1 protease and FKBP-12 complexes

Energy landscapes of molecular recognition are explored by performing "semi-rigid" docking of FK-506 and rapamycin with the Fukisawa binding protein (FKBP-12), and flexible docking simulations of the Ro-31-8959 and AG-1284 inhibitors with HIV-1 protease by a genetic algorithm. The requirements of a molecular recognition model to meet thermodynamic and kinetic criteria of ligand-protein docking simultaneously are investigated using a family of simple molecular recognition energy functions. The critical factor that determines the success rate in predicting the structure of ligand-protein complexes is found to be the roughness of the binding energy landscape, in accordance with a minimal frustration principle. The results suggest that further progress in structure prediction of ligand-protein complexes can be achieved by designing molecular recognition energy functions that generate binding landscapes with reduced frustration.

A refined model of the thyrotropin-releasing hormone (TRH) receptor binding pocket. Novel mixed mode Monte Carlo/stochastic dynamics simulations of the complex between TRH and TRH receptor

Previous mutational and computational studies of the thyrotropin-releasing hormone (TRH) receptor identified several residues in its binding pocket [see accompanying paper, Perlman et al. (1996) Biochemistry 35, 7643-7650]. On the basis of the initial model constructed with standard energy minimization techniques, we have conducted 15 mixed mode Monte Carlo/stochastic dynamics (MC-SD) simulations to allow for extended sampling of the conformational states of the ligand and the receptor in the complex. A simulated annealing protocol was adopted in which the complex was cooled from 600 to 310 K in segments of 30 ps of the MC-SD simulations for each change of 100 K. Analysis of the simulation results demonstrated that the mixed mode MC-SD protocol maintained the desired temperature in the constant temperature simulation segments. The elevated temperature and the repeating simulations allowed for adequate sampling of the torsional space of the complex with successful conservation of the general structure and good helicity of the receptor. For the analysis of the interaction between TRH and the binding pocket, TRH was divided into four groups consisting of pyroGlu, His, ProNH2, and the backbone. The pairwise interaction energies of the four separate portions of TRH with the corresponding residues in the receptor provide a physicochemical basis for the understanding of ligand-receptor complexes. The interaction of pyroGlu with Tyr106 shows a bimodal distribution that represents two populations: one with a H-bond and another without it. Asp195 was shown to compete with pyroGlu for the H-bond to Tyr106. Simulations in which Asp195 was interacting with Arg283, thus removing it from the vicinity of Tyr106, resulted in a stable H-bond to pyroGlu. In all simulations His showed a van der Waals attraction to Tyr282 and a weak electrostatic repulsion from Arg 306. The ProNH2 had a strong and frequent H-bonding interaction with Arg306. The backbone carbonyls show a frequent H-bonding interaction with the OH group of Tyr282 and strong, often multiple, interactions with Arg306. Three structures, which maintained these interactions simultaneously, were selected as candidates for ligand-receptor complexes. These show persistent interactions of TRH with Ile 109 and Ile 116 in HX 3 and with Tyr310 and Ser313 in HX 7, which will be tested to refine the structure of the ligand-receptor complex. The superposition of the three structures shows the extent of structural flexibility of the receptor and the ligand in the complex. The backbone of TRH inside the receptor is in an alpha-helical conformation, suggesting that the receptor, through its interaction with the ligand, provides the energy required for the conformational change in the ligand from an extended to the folded form.

Calculations of nucleic acid conformations

The present computational power and sophistication of theoretical approaches to nucleic acid structural investigation are sufficient for the realization of static and dynamic models that correlate accurately with current crystallographic, NMR and solution-probing structural data, and consequently are able to provide valuable insights and predictions for a variety of nucleic acid conformational families. In molecular dynamics simulations, the year 1995 was marked by the foray of fast Ewald methods, an accomplishment resulting from several years' work in the search for an adequate treatment of the electrostatic long-range forces so primordial in nucleic acid behavior. In very large systems, and particularly in the RNA-folding field, techniques originating from artificial intelligence research, like constraint satisfaction programming or genetic algorithms, have established their utility and potential.

Modeling protein-ligand complexes

Increasing the rate at which new biologically active compounds are found is a major goal in pharmaceutical chemistry. Recently, several computational methods have been proposed with this intent. For some time, algorithms have been used to direct ligand evolution on the basis of complementarity to the three-dimensional structure of a selected protein. Current research focuses on enhancements to methods for searching chemical databases, proposing sensible modifications to known active compounds, and construction of novel ligands from theoretical principles.

New approaches in molecular structure prediction

In the past years, much effort has been put on the development of new methodologies and algorithms for the prediction of protein secondary and tertiary structures from (sequence) data; this is reviewed in detail. New approaches for these predictions such as neural network methods, genetic algorithms, machine learning, and graph theoretical methods are discussed. Secondary structure prediction algorithms were improved mostly by considering families of related proteins; however, for the reliable tertiary structure modeling of proteins, knowledge-based techniques are still preferred. Methods and examples with more or less successful results are described. Also, programs and parameterizations for energy minimisations, molecular dynamics, and electrostatic interactions have been improved, especially with respect to their former limits of applicability. Other topics discussed in this review include the use of traditional and on-line databases, the docking problem and surface properties of biomolecules, packing of protein cores, de novo design and protein engineering, prediction of membrane protein structures, the verification and reliability of model structures, and progress made with currently available software and computer hardware. In summary, the prediction of the structure, function, and other properties of a protein is still possible only within limits, but these limits continue to be moved.

A mean field model of ligand-protein interactions: implications for the structural assessment of human immunodeficiency virus type 1 protease complexes and receptor-specific binding

We propose a general mean field model of ligand-protein interactions to determine the thermodynamic equilibrium of a system at finite temperature. The method is employed in structural assessments of two human immuno-deficiency virus type 1 protease complexes where the gross effects of protein flexibility are incorporated by utilizing a data base of crystal structures. Analysis of the energy spectra for these complexes has revealed that structural and thermo-dynamic aspects of molecular recognition can be rationalized on the basis of the extent of frustration in the binding energy landscape. In particular, the relationship between receptor-specific binding of these ligands to human immunodeficiency virus type 1 protease and a minimal frustration principle is analyzed.

Salt effects on polyelectrolyte-ligand binding: comparison of Poisson-Boltzmann, and limiting law/counterion binding models

The theory for salt dependence of the free energy, entropy, and enthalpy of a polyelectrolyte in the PB (PB) model is extended to treat the nonspecific salt dependence of polyelectrolyte-ligand binding reactions. The salt dependence of the binding constant (K) is given by the difference in osmotic pressure terms between the reactants and products. For simple 1-1 salts it is shown that this treatment is equivalent to the general preferential interaction model for the salt dependence of binding [C. Anderson and M. Record (1993) Journal of Physical Chemistry, Vol. 97, pp. 7116-7126]. The salt dependence, entropy, and enthalpy are compared for the PB model and one specific form of the preferential interaction coefficient model that uses counterion condensation/limiting law (LL) behavior. The PB and LL models are applied to three ligand-polyelectrolyte systems with the same net ligand charge: a model sphere-cylinder binding reaction, a drug-DNA binding reaction, and a protein-DNA binding reaction. For the small ligands both the PB and limiting law models give (In K vs. In[salt]) slopes close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the predominant ion cratic (release) entropy in the limiting law model. The relative contributions of these three terms in the PB model depends on the ligand: For the protein, ion release entropy is the smallest contribution to the salt dependence of binding. The effect of three approximations made in the LL model is examined: These approximations are (1) the ligand behaves ideally, (2) the preferential interaction coefficient of the polyelectrolyte is unchanged upon ligand binding, and (3) the polyelectrolyte preferential interaction coefficient is given by the limiting law/counterion-condensation value. Analysis of the PB model shows that assumptions 2 and 3 break down at finite salt concentrations. For the small ligands the effects on the slope cancel, however, giving net slopes that are similar in the PB and LL models, but with a different entropy/enthalpy breakdown. For the protein ligand the errors from assumptions 2 and 3 in the LL models do not cancel.

Salt effects on nucleic acids

Salt-dependent electrostatic effects are a major factor in determining the stability, structure, reactivity, and binding behavior of nucleic acids. Increasingly detailed theoretical methods, especially those based on Monte Carlo and Poisson-Boltzmann methodologies, combined with powerful computational algorithms are being used to examine how the shape, charge distribution and dielectric properties of the molecules affect the ion distribution in the surrounding aqueous solution, and how they play a role in ligand binding, structural transitions and other biologically important reactions. These studies indicate that inclusion of detailed structural information about the nucleic acid and its ligands is crucial for improving models of nucleic acid electrostatics, and that better treatment of the ion atmosphere and dielectric effects is also of major importance.

Molecular recognition of the inhibitor AG-1343 by HIV-1 protease: conformationally flexible docking by evolutionary programming

BACKGROUND

An important prerequisite for computational structure-based drug design is prediction of the structures of ligand-protein complexes that have not yet been experimentally determined by X-ray crystallography or NMR. For this task, docking of rigid ligands is inadequate because it assumes knowledge of the conformation of the bound ligand. Docking of flexible ligands would be desirable, but requires one to search an enormous conformational space. We set out to develop a strategy for flexible docking by combining a simple model of ligand-protein interactions for molecular recognition with an evolutionary programming search technique.

RESULTS

We have developed an intermolecular energy function that incorporates steric and hydrogen-bonding terms. The parameters in this function were obtained by docking in three different protein systems. The effectiveness of this method was demonstrated by conformationally flexible docking of the inhibitor AG-1343, a potential new drug against AIDS, into HIV-1 protease. For this molecule, which has nine rotatable bonds, the crystal structure was reproduced within 1.5 A root-mean-square deviation 34 times in 100 simulations, each requiring eight minutes on a Silicon Graphics R4400 workstation. The energy function correctly evaluates the crystal structure as the global energy minimum.

CONCLUSIONS

We believe that a solution of the docking problem may be achieved by matching a simple model of molecular recognition with an efficient search procedure. The necessary ingredients of a molecular recognition model include only steric and hydrogen-bond interaction terms. Although these terms are not necessarily sufficient to predict binding affinity, they describe ligand-protein interactions faithfully enough to enable a docking program to predict the structure of the bound ligand. This docking strategy thus provides an important tool for the interdisciplinary field of rational drug design.

Theory of electrostatic interactions in macromolecules

In the past year, substantial progress has been made in the modeling of electrostatic interactions in biomolecules. This review highlights advances in the following areas: first, the efficient computation of long-range electrostatic interactions in detailed molecular simulations; second, the application of the Poisson-Boltzmann electrostatic model in conformational analysis; third, the application of the Poisson-Boltzmann model in quantum chemistry calculations; fourth, the development of atomic parameters; and finally, the modeling of ionization equilibria in proteins.

Ligand-protein docking and rational drug design

Over the past year there have been some interesting and significant advances in computer-based ligand-protein docking techniques and related rational drug-design tools, including flexible ligand docking and better estimation of binding free energies and solvation energies. As a result, the successful use of computational tools to help generate interesting new guide (lead) compounds for targeted receptors is becoming more commonplace.