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This article addresses calculations of the standard free energy of binding from molecular simulations in which a bound ligand is extracted from its binding site by steered molecular dynamics (MD) simulations or equilibrium umbrella sampling (US). Host-guest systems are used as test beds to examine the requirements for obtaining the reversible work of ligand extraction. We find that, for both steered MD and US, marked irreversibilities can occur when the guest molecule crosses an energy barrier and suddenly jumps to a new position, causing dissipation of energy stored in the stretched molecule(s). For flexible molecules, this occurs even when a stiff pulling spring is used, and it is difficult to suppress in calculations where the spring is attached to the molecules by single, fixed attachment points. We, therefore, introduce and test a method, fluctuation-guided pulling, which adaptively adjusts the spring's attachment points based on the guest's atomic fluctuations relative to the host. This adaptive approach is found to substantially improve the reversibility of both steered MD and US calculations for the present systems. The results are then used to estimate standard binding free energies within a comprehensive framework, termed attach-pull-release, which recognizes that the standard free energy of binding must include not only the pulling work itself, but also the work of attaching and then releasing the spring, where the release work includes an accounting of the standard concentration to which the ligand is discharged., (Copyright © 2013 Wiley Periodicals, Inc.)

Continuum solvation models are widely used to estimate the hydration free energies of small molecules and proteins, in applications ranging from drug design to protein engineering, and most such models are based on the approximation of a linear dielectric response by the solvent. We used explicit-water molecular dynamics simulations with the TIP3P water model to probe this linear response approximation in the case of neutral polar molecules, using miniature cucurbituril and cyclodextrin receptors and protein side-chain analogs as model systems. We observe supralinear electrostatic solvent responses, and this nonlinearity is found to result primarily from waters' being drawn closer and closer to the solutes with increased solute-solvent electrostatic interactions; i.e., from solute electrostriction. Dielectric saturation and changes in the water-water hydrogen bonding network, on the other hand, play little role. Thus, accounting for solute electrostriction may be a productive approach to improving the accuracy of continuum solvation models.

Molecular dynamics simulations of unprecedented duration now can provide new insights into biomolecular mechanisms. Analysis of a 1-ms molecular dynamics simulation of the small protein bovine pancreatic trypsin inhibitor reveals that its main conformations have different thermodynamic profiles and that perturbation of a single geometric variable, such as a torsion angle or interresidue distance, can select for occupancy of one or another conformational state. These results establish the basis for a mechanism that we term entropy-enthalpy transduction (EET), in which the thermodynamic character of a local perturbation, such as enthalpic binding of a small molecule, is camouflaged by the thermodynamics of a global conformational change induced by the perturbation, such as a switch into a high-entropy conformational state. It is noted that EET could occur in many systems, making measured entropies and enthalpies of folding and binding unreliable indicators of actual thermodynamic driving forces. The same mechanism might also account for the high experimental variance of measured enthalpies and entropies relative to free energies in some calorimetric studies. Finally, EET may be the physical mechanism underlying many cases of entropy-enthalpy compensation.

The design of ligands with high affinity and specificity remains a fundamental challenge in understanding molecular recognition and developing therapeutic interventions. Charge optimization theory addresses this problem by determining ligand charge distributions that produce the most favorable electrostatic contribution to the binding free energy. The theory has been applied to the design of binding specificity as well. However, the formulations described only treat a rigid ligand-one that does not change conformation upon binding. Here, we extend the theory to treat induced-fit ligands for which the unbound ligand conformation may differ from the bound conformation. We develop a thermodynamic pathway analysis for binding contributions relevant to the theory, and we illustrate application of the theory using HIV-1 protease with our previously designed and validated subnanomolar inhibitor. Direct application of rigid charge optimization approaches to nonrigid cases leads to very favorable intramolecular electrostatic interactions that are physically unreasonable, and analysis shows the ligand charge distribution massively stabilizes the preconformed (bound) conformation over the unbound. After analyzing this case, we provide a treatment for the induced-fit ligand charge optimization problem that produces physically realistic results. The key factor is introducing the constraint that the free energy of the unbound ligand conformation be lower or equal to that of the preconformed ligand structure, which corresponds to the notion that the unbound structure is the ground unbound state. Results not only demonstrate the applicability of this methodology to discovering optimized charge distributions in an induced-fit model, but also provide some insights into the energetic consequences of ligand conformational change on binding. Specifically, the results show that, from an electrostatic perspective, induced-fit binding is not an adaptation designed to enhance binding affinity; at best, it can only achieve the same affinity as optimized rigid binding.

The Human Proteome Organisation Proteomics Standards Initiative (HUPO-PSI) was established in 2002 with the aim of defining community standards for data representation in proteomics and facilitating data comparison, exchange and verification. Over the last 10 years significant advances have been made, with common data standards now published and implemented in the field of both mass spectrometry and molecular interactions. The 2012 meeting further advanced this work, with the mass spectrometry groups finalising approaches to capturing the output from recent developments in the field, such as quantitative proteomics and SRM. The molecular interaction group focused on improving the integration of data from multiple resources. Both groups united with a guest work track, organized by the HUPO Technology/Standards Committee, to formulate proposals for data submissions from the HUPO Human Proteome Project and to start an initiative to collect standard experimental protocols., (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The displacement of perturbed water upon binding is believed to play a critical role in the thermodynamics of biomolecular recognition, but it is nontrivial to unambiguously define and answer questions about this process. We address this issue by introducing grid inhomogeneous solvation theory (GIST), which discretizes the equations of inhomogeneous solvation theory (IST) onto a three-dimensional grid situated in the region of interest around a solute molecule or complex. Snapshots from explicit solvent simulations are used to estimate localized solvation entropies, energies, and free energies associated with the grid boxes, or voxels, and properly summing these thermodynamic quantities over voxels yields information about hydration thermodynamics. GIST thus provides a smoothly varying representation of water properties as a function of position, rather than focusing on hydration sites where solvent is present at high density. It therefore accounts for full or partial displacement of water from sites that are highly occupied by water, as well as for partly occupied and water-depleted regions around the solute. GIST can also provide a well-defined estimate of the solvation free energy and therefore enables a rigorous end-states analysis of binding. For example, one may not only use a first GIST calculation to project the thermodynamic consequences of displacing water from the surface of a receptor by a ligand, but also account, in a second GIST calculation, for the thermodynamics of subsequent solvent reorganization around the bound complex. In the present study, a first GIST analysis of the molecular host cucurbit[7]uril is found to yield a rich picture of hydration structure and thermodynamics in and around this miniature receptor. One of the most striking results is the observation of a toroidal region of high water density at the center of the host's nonpolar cavity. Despite its high density, the water in this toroidal region is disfavored energetically and entropically, and hence may contribute to the known ability of this small receptor to bind guest molecules with unusually high affinities. Interestingly, the toroidal region of high water density persists even when all partial charges of the receptor are set to zero. Thus, localized regions of high solvent density can be generated in a binding site without strong, attractive solute-solvent interactions.

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.

We used the second-generation mining minima method (M2) to compute the binding affinities of the novel host-guest complexes in the SAMPL3 blind prediction challenge. The predictions were in poor agreement with experiment, and we conjectured that much of the error might derive from the force field, CHARMm with Vcharge charges. Repeating the calculations with other generalized force-fields led to no significant improvement, and we observed that the predicted affinities were highly sensitive to the choice of force-field. We therefore embarked on a systematic evaluation of a set of generalized force fields, based upon comparisons with PM6-DH2, a fast yet accurate semi-empirical quantum mechanics method. In particular, we compared gas-phase interaction energies and entropies for the host-guest complexes themselves, as well as for smaller chemical fragments derived from the same molecules. The mean deviations of the force field interaction energies from the quantum results were greater than 3 kcal/mol and 9 kcal/mol, for the fragments and host-guest systems respectively. We further evaluated the accuracy of force-fields for computing the vibrational entropies and found the mean errors to be greater than 4 kcal/mol. Given these errors in energy and entropy, it is not surprising in retrospect that the predicted binding affinities deviated from the experiment by several kcal/mol. These results emphasize the need for improvements in generalized force-fields and also highlight the importance of systematic evaluation of force-field parameters prior to evaluating different free-energy methods.

The computational prediction of protein-ligand binding affinities is of central interest in early-stage drug-discovery, and there is a widely recognized need for improved methods. Low molecular weight receptors and their ligands--i.e., host-guest systems--represent valuable test-beds for such affinity prediction methods, because their small size makes for fast calculations and relatively facile numerical convergence. The SAMPL3 community exercise included the first ever blind prediction challenge for host-guest binding affinities, through the incorporation of 11 new host-guest complexes. Ten participating research groups addressed this challenge with a variety of approaches. Statistical assessment indicates that, although most methods performed well at predicting some general trends in binding affinity, overall accuracy was not high, as all the methods suffered from either poor correlation or high RMS errors or both. There was no clear advantage in using explicit versus implicit solvent models, any particular force field, or any particular approach to conformational sampling. In a few cases, predictions using very similar energy models but different sampling and/or free-energy methods resulted in significantly different results. The protonation states of one host and some guest molecules emerged as key uncertainties beyond the choice of computational approach. The present results have implications for methods development and future blind prediction exercises.

Two new peptidic proteasome inhibitors were isolated as trace components from a Curaçao collection of the marine cyanobacterium Symploca sp. Carmaphycin A (1) and carmaphycin B (2) feature a leucine-derived α,β-epoxyketone warhead directly connected to either methionine sulfoxide or methionine sulfone. Their structures were elucidated on the basis of extensive NMR and MS analyses and confirmed by total synthesis, which in turn provided more material for further biological evaluations. Pure carmaphycins A and B were found to inhibit the β5 subunit (chymotrypsin-like activity) of the S. cerevisiae 20S proteasome in the low nanomolar range. Additionally, they exhibited strong cytotoxicity to lung and colon cancer cell lines, as well as exquisite antiproliferative effects in the NCI60 cell-line panel. These assay results as well as initial structural biology studies suggest a distinctive binding mode for these new inhibitors., (Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The field of host-guest chemistry provides computationally tractable yet informative model systems for biomolecular recognition. We applied molecular dynamics simulations to study the forces and mechanical stresses associated with forced dissociation of aqueous cucurbituril-guest complexes with high binding affinities. First, the unbinding transitions were modeled with constant velocity pulling (steered dynamics) and a soft spring constant, to model atomic force microscopy (AFM) experiments. The computed length-force profiles yield rupture forces in good agreement with available measurements. We also used steered dynamics with high spring constants to generate paths characterized by a tight control over the specified pulling distance; these paths were then equilibrated via umbrella sampling simulations and used to compute time-averaged mechanical stresses along the dissociation pathways. The stress calculations proved to be informative regarding the key interactions determining the length-force profiles and rupture forces. In particular, the unbinding transition of one complex is found to be a stepwise process, which is initially dominated by electrostatic interactions between the guest's ammoniums and the host's carbonyl groups, and subsequently limited by the extraction of the guest's bulky bicyclooctane moiety; the latter step requires some bond stretching at the cucurbituril's extraction portal. Conversely, the dissociation of a second complex with a more slender guest is mainly driven by successive electrostatic interactions between the different guest's ammoniums and the host's carbonyl groups. The calculations also provide information on the origins of thermodynamic irreversibilities in these forced dissociation processes.

Non-covalent molecular association underlies a diverse set of biologically and technologically relevant phenomena, including the action of drugs on their biomolecular targets and self- and supra-molecular assembly processes. Computer models employed to model binding frequently use interaction potentials with atomistic detail while neglecting the thermal molecular motions of the binding species. However, errors introduced by this simplification and, more broadly, the thermodynamic consequences of molecular flexibility on binding, are little understood. Here, we isolate the fundamental relationship of molecular flexibility to binding thermodynamics via simulations of simplified molecules with a wide range of flexibilities but the same interaction potential. Disregarding molecular motion is found to generate large errors in binding entropy, enthalpy and free energy, even for molecules that are nearly rigid. Indeed, small decreases in rigidity markedly reduce affinity for highly rigid molecules. Remarkably, precisely the opposite occurs for more flexible molecules, for which increasing flexibility leads to stronger binding affinity. We also find that differences in flexibility suffice to generate binding specificity: for example, a planar surface selectively binds rigid over flexible molecules. Intriguingly, varying molecular flexibility while keeping interaction potentials constant leads to near-linear enthalpy-entropy compensation over a wide range of flexibilities, with the unexpected twist that increasing flexibility produces opposite changes in entropy and enthalpy for molecules in the flexible versus the rigid regime. Molecular flexibility is thus a crucial determinant of binding affinity and specificity and variations in flexibility can lead to strong yet non-intuitive consequences.

There are at least two good reasons for the on-going interest in drug-target interactions: first, drug-effects can only be fully understood by considering a complex network of interactions to multiple targets (so-called off-target effects) including metabolic and signaling pathways; second, it is crucial to consider drug-target-pathway relations for the identification of novel targets for drug development. To address this on-going need, we have developed a web-based data warehouse named SuperTarget, which integrates drug-related information associated with medical indications, adverse drug effects, drug metabolism, pathways and Gene Ontology (GO) terms for target proteins. At present, the updated database contains >6000 target proteins, which are annotated with >330,000 relations to 196,000 compounds (including approved drugs); the vast majority of interactions include binding affinities and pointers to the respective literature sources. The user interface provides tools for drug screening and target similarity inclusion. A query interface enables the user to pose complex queries, for example, to find drugs that target a certain pathway, interacting drugs that are metabolized by the same cytochrome P450 or drugs that target proteins within a certain affinity range. SuperTarget is available at http://bioinformatics.charite.de/supertarget.

The free energy of a molecular system can, at least in principle, be computed by thermodynamic perturbation from a reference system whose free energy is known. The convergence of such a calculation depends critically on the conformational overlap between the reference and the physical systems. One approach to defining a suitable reference system is to construct it from the one-dimensional marginal probability distribution functions (PDFs) of internal coordinates observed in a molecular simulation. However, the conformational overlap of this reference system tends to decline steeply with increasing dimensionality, due to the neglect of correlations among the coordinates. Here, we test a reference system that can account for pairwise correlations among the internal coordinates, as captured by their two-dimensional marginal PDFs derived from a molecular simulation. Incorporating pairwise correlations in the reference system is found to dramatically improve the convergence of the free energy estimates relative to the first-order reference system, due to increased conformational overlap with the physical distribution.

A dicationic ferrocene derivative has previously been shown to bind cucurbit[7]uril (CB[7]) in water with ultrahigh affinity (ΔG(o) = -21 kcal/mol). Here, we describe new compounds that bind aqueous CB[7] equally well, validating our prior suggestion that they, too, would be ultrahigh affinity CB[7] guests. The present guests, which are based upon either a bicyclo[2.2.2]octane or adamantane core, have no metal atoms, so these results also confirm that the remarkably high affinities of the ferrocene-based guest need not be attributed to metal-specific interactions. Because we used the M2 method to compute the affinities of several of the new host-guest systems prior to synthesizing them, the present results also provide for the first blinded evaluation of this computational method. The blinded calculations agree reasonably well with experiment and successfully reproduce the observation that the new adamantane-based guests achieve extremely high affinities, despite the fact that they position a cationic substituent at only one electronegative portal of the CB[7] host. However, there are also significant deviations from experiment, and these lead to the correction of a procedural error and an instructive evaluation of the sensitivity of the calculations to physically reasonable variations in molecular energy parameters. The new experimental and computational results presented here bear on the physical mechanisms of molecular recognition, the accuracy of the M2 method, and the usefulness of host-guest systems as test-beds for computational methods.

The use of molecular simulations and ab initio calculations to predict thermodynamic properties of molecules has become routine. Such methods rely upon an accurate representation of the molecular partition function or configurational integral, which in turn often includes a rotational symmetry number. However, the reason for including the symmetry number is unclear to many practitioners, and there is also a need for a general prescription for evaluating the symmetry numbers of flexible molecules, i.e., for molecules with thermally active internal degrees of freedom, such as internal rotors. Surprisingly, we have been unable to find any complete and convincing explanations of these important issues in textbooks or the journal literature. The present paper aims to explain why symmetry numbers are needed and how their values should be determined. Both classical and quantum approaches are provided.

We present the first application of the mining minima algorithm to protein-small molecule binding. This end-point approach use an empirical force field and implicit solvent models, treats the protein binding-site as fully flexible and estimates free energies as sums over local energy wells. The calculations are found to yield encouraging agreement with experiment for three sets of HIV-1protease inhibitors and a set of phosphodiesterase 10a inhibitors. The contributions of various aspects of the model to its accuracy are examined, and the Poisson-Boltzmann correction is found to be the most critical. Interestingly, the computed changes in configurational entropy upon binding fall roughly along the same entropy-energy correlation previously observed for smaller host-guest systems. Strengths and weaknesses of the method are discussed, as are the prospects for enhancing accuracy and speed.

Drug resistance mutations in HIV-1 protease selectively alter inhibitor binding without significantly affecting substrate recognition and cleavage. This alteration in molecular recognition led us to develop the substrate-envelope hypothesis which predicts that HIV-1 protease inhibitors that fit within the overlapping consensus volume of the substrates are less likely to be susceptible to drug-resistant mutations, as a mutation impacting such inhibitors would simultaneously impact the processing of substrates. To evaluate this hypothesis, over 130 HIV-1 protease inhibitors were designed and synthesized using three different approaches with and without substrate-envelope constraints. A subset of 16 representative inhibitors with binding affinities to wild-type protease ranging from 58 nM to 0.8 pM was chosen for crystallographic analysis. The inhibitor-protease complexes revealed that tightly binding inhibitors (at the picomolar level of affinity) appear to "lock" into the protease active site by forming hydrogen bonds to particular active-site residues. Both this hydrogen bonding pattern and subtle variations in protein-ligand van der Waals interactions distinguish nanomolar from picomolar inhibitors. In general, inhibitors that fit within the substrate envelope, regardless of whether they are picomolar or nanomolar, have flatter profiles with respect to drug-resistant protease variants than inhibitors that protrude beyond the substrate envelope; this provides a strong rationale for incorporating substrate-envelope constraints into structure-based design strategies to develop new HIV-1 protease inhibitors.

The differential Shannon entropy of information theory can change under a change of variables (coordinates), but the thermodynamic entropy of a physical system must be invariant under such a change. This difference is puzzling, because the Shannon and Gibbs entropies have the same functional form. We show that a canonical change of variables can, indeed, alter the spatial component of the thermodynamic entropy just as it alters the differential Shannon entropy. However, there is also a momentum part of the entropy, which turns out to undergo an equal and opposite change when the coordinates are transformed, so that the total thermodynamic entropy remains invariant. We furthermore show how one may correctly write the change in total entropy for an isothermal physical process in any set of spatial coordinates.

Changes in mechanical stresses in a tight-binding host-guest system were computed and visualized as the cationic was computationally pulled out of the cucurbituril host in a series of steps. A sharp conformational transition was observed as one of the guest's ammonium groups jumped through the center of the host to the opposite portal. The conformation immediately prior to this transition was found to possess high levels of Lennard-Jones and electrostatic stress. This observation, along with the specific distribution of Lennard-Jones stress around the portals, suggested that the conformational transition resulted from steric constriction, which had been expected, and electrostatics, which was not expected. An important role for electrostatics, at least at the level of these calculations, was confirmed by a comparative computational pulling study of another guest molecule lacking the critical ammonium group. These calculations suggest that the binding kinetics of diammonium guests that position an ammonium at each cucurbituril portal will be found to be slower than the kinetics of monoammonium guests. More generally, the results suggest that computational stress analysis can provide mechanistic insight into supramolecular systems. It will be of considerable interest to extend such applications to biomolecules, for which the mechanisms of conformational change are of great scientific and practical interest.

Previous studies have shown the usefulness of the substrate envelope concept in the analysis and prediction of drug resistance profiles for human immunodeficiency virus protease mutants. This study tests its applicability to several other therapeutic targets: Abl kinase, chitinase, thymidylate synthase, dihydrofolate reductase, and neuraminidase. For the targets where many (> or =6) mutation data are available to compute the average mutation sensitivity of inhibitors, the total volume of an inhibitor molecule that projects outside the substrate envelope V(out), is found to correlate with average mutation sensitivity. Analysis of a locally computed volume suggests that the same correlation would hold for the other targets, if more extensive mutation data sets were available. It is concluded that the substrate envelope concept offers a promising and easily implemented computational tool for the design of drugs that will tend to resist mutations. Software implementing these calculations is provided with the 'Supporting Information'.

Configurational entropy is thought to influence biomolecular processes, but there are still many open questions about this quantity, including its magnitude, its relationship to molecular structure, and the importance of correlation. The mutual information expansion (MIE) provides a novel and systematic approach to extracting configurational entropy changes due to correlated motions from molecular simulations. We present the first application of the MIE method to protein-ligand binding using multiple molecular dynamics simulations to study the association of the ubiquitin E2 variant domain of the protein Tsg101 and an HIV-derived nonapeptide. This investigation utilizes the second-order MIE approximation, which accounts for correlations between all pairs of degrees of freedom. The computed change in configurational entropy is large and has a major contribution from changes in pairwise correlation. The results also reveal intricate structure-entropy relationships. Thus, the present analysis suggests that in order for a model of binding to be accurate, it must include a careful accounting of configurational entropy changes.

We present an approximation to a molecule's N-dimensional conformational probability density function (pdf) in terms of marginal pdfs of highest order l, where l is much less than N. The approximation is constructed as a product of conditional pdfs derived by recursive application of the generalized Kirkwood superposition approximation. Furthermore, an algorithm is presented to sample conformations from the approximate full-dimensional pdf based upon all input marginal pdfs. The sampling algorithm is tested for three small molecule systems by using the algorithm to sample conformations at levels l=1, 2, or 3 and comparing the distributions of sampled conformations with those from the molecular dynamics (MD) simulations. The distributions of conformations sampled at third (l=3) order resemble the MD distributions rather well and significantly better than those sampled at second (l=2) or first (l=1) order. In addition to highlighting the importance of correlations among internal degrees of freedom, these results suggest that low-order correlations suffice to describe most of the conformational fluctuations of molecules in a thermal environment.

It has recently been discovered that guests combining a nonpolar core with cationic substituents bind cucurbit[7]uril (CB[7]) in water with ultrahigh affinities. The present study uses the Mining Minima algorithm to study the physics of these extraordinary associations and to computationally test a new series of CB[7] ligands designed to bind with similarly high affinity. The calculations reproduce key experimental observations regarding the affinities of ferrocene-based guests with CB[7] and beta-cyclodextrin and provide a coherent view of the roles of electrostatics and configurational entropy as determinants of affinity in these systems. The newly designed series of compounds is based on a bicyclo[2.2.2]octane core, which is similar in size and polarity to the ferrocene core of the existing series. Mining Minima predicts that these new compounds will, like the ferrocenes, bind CB[7] with extremely high affinities.

Proteins can be influenced strongly by the electrolyte in which they are dissolved, and we wish to model, understand, and ultimately control such ionic effects. Relatively detailed Monte Carlo (MC) ion simulations are needed to capture biologically important properties of ion channels, but a simpler treatment of ions, the linearized Poisson-Boltzmann (LPB) theory, is often used to model processes such as binding and folding, even in settings where the LPB theory is expected to be inaccurate. This study uses MC simulations to assess the reliability of the LPB theory for such a system, the constrained, anionic active site of HIV protease. We study the distributions of ions in and around the active site, as well as the energetics of displacing ions when a protease inhibitor is inserted into the active site. The LPB theory substantially underestimates the density of counterions in the active site when divalent cations are present. It also underestimates the energy cost of displacing these counterions, but the error is not consequential because the energy cost is less than kBT, according to the MC calculations. Thus, the LPB approach will often be suitable for studying energetics, but the more detailed MC approach is critical when ionic distributions and fluxes are at issue.

We explore the applicability of an additive treatment of substituent effects to the analysis and design of HIV protease inhibitors. Affinity data for a set of inhibitors with a common chemical framework were analyzed to provide estimates of the free energy contribution of each chemical substituent. These estimates were then used to design new inhibitors whose high affinities were confirmed by synthesis and experimental testing. Derivations of additive models by least-squares and ridge-regression methods were found to yield statistically similar results. The additivity approach was also compared with standard molecular descriptor-based QSAR; the latter was not found to provide superior predictions. Crystallographic studies of HIV protease-inhibitor complexes help explain the perhaps surprisingly high degree of substituent additivity in this system, and allow some of the additivity coefficients to be rationalized on a structural basis.

Changes in the configurational entropies of molecules make important contributions to the free energies of reaction for processes such as protein-folding, noncovalent association, and conformational change. However, obtaining entropy from molecular simulations represents a long-standing computational challenge. Here, two recently introduced approaches, the nearest-neighbor (NN) method and the mutual-information expansion (MIE), are combined to furnish an efficient and accurate method of extracting the configurational entropy from a molecular simulation to a given order of correlations among the internal degrees of freedom. The resulting method takes advantage of the strengths of each approach. The NN method is entirely nonparametric (i.e., it makes no assumptions about the underlying probability distribution), its estimates are asymptotically unbiased and consistent, and it makes optimum use of a limited number of available data samples. The MIE, a systematic expansion of entropy in mutual information terms of increasing order, provides a well-characterized approximation for lowering the dimensionality of the numerical problem of calculating the entropy of a high-dimensional system. The combination of these two methods enables obtaining well-converged estimations of the configurational entropy that capture many-body correlations of higher order than is possible with the simple histogramming that was used in the MIE method originally. The combined method is tested here on two simple systems: an idealized system represented by an analytical distribution of six circular variables, where the full joint entropy and all the MIE terms are exactly known, and the R,S stereoisomer of tartaric acid, a molecule with seven internal-rotation degrees of freedom for which the full entropy of internal rotation has been already estimated by the NN method. For these two systems, all the expansion terms of the full MIE of the entropy are estimated by the NN method and, for comparison, the MIE approximations up to third order are also estimated by simple histogramming. The results indicate that the truncation of the MIE at the two-body level can be an accurate, computationally nondemanding approximation to the configurational entropy of anharmonic internal degrees of freedom. If needed, higher-order correlations can be estimated reliably by the NN method without excessive demands on the molecular-simulation sample size and computing time., ((c) 2008 Wiley Periodicals, Inc. J Comput Chem, 2008.)

The acquisition of drug-resistant mutations by infectious pathogens remains a pressing health concern, and the development of strategies to combat this threat is a priority. Here we have applied a general strategy, inverse design using the substrate envelope, to develop inhibitors of HIV-1 protease. Structure-based computation was used to design inhibitors predicted to stay within a consensus substrate volume in the binding site. Two rounds of design, synthesis, experimental testing, and structural analysis were carried out, resulting in a total of 51 compounds. Improvements in design methodology led to a roughly 1000-fold affinity enhancement to a wild-type protease for the best binders, from a Ki of 30-50 nM in round one to below 100 pM in round two. Crystal structures of a subset of complexes revealed a binding mode similar to each design that respected the substrate envelope in nearly all cases. All four best binders from round one exhibited broad specificity against a clinically relevant panel of drug-resistant HIV-1 protease variants, losing no more than 6-13-fold affinity relative to wild type. Testing a subset of second-round compounds against the panel of resistant variants revealed three classes of inhibitors: robust binders (maximum affinity loss of 14-16-fold), moderate binders (35-80-fold), and susceptible binders (greater than 100-fold). Although for especially high-affinity inhibitors additional factors may also be important, overall, these results suggest that designing inhibitors using the substrate envelope may be a useful strategy in the development of therapeutics with low susceptibility to resistance.

The molecular host cucurbit[7]uril forms an extremely stable inclusion complex with the dicationic ferrocene derivative bis(trimethylammoniomethyl)ferrocene in aqueous solution. The equilibrium association constant for this host-guest pair is 3 x 10(15) M(-1) (K(d) = 3 x 10(-16) M), equivalent to that exhibited by the avidin-biotin pair. Although purely synthetic systems with larger association constants have been reported, the present one is unique because it does not rely on polyvalency. Instead, it achieves its extreme affinity by overcoming the compensatory enthalpy-entropy relationship usually observed in supramolecular complexes. Its disproportionately low entropic cost is traced to extensive host desolvation and to the rigidity of both the host and the guest.

Crystallographic data show that various substrates of HIV protease occupy a remarkably uniform region within the binding site; this region has been termed the substrate envelope. It has been suggested that an inhibitor that fits within the substrate envelope should tend to evade viral resistance because a protease mutation that reduces the affinity of the inhibitor will also tend to reduce the affinity of substrate, and will hence decrease the activity of the enzyme. Accordingly, inhibitors that fit the substrate envelope better should be less susceptible to clinically observed resistant mutations, since these must also allow substrates to bind. The present study describes a quantitative measure of the volume of a bound inhibitor falling outside the substrate envelope, and observes that this quantity correlates with the inhibitor's losses in affinity to clinically relevant mutants. This measure may thus be useful as a penalty function in the design of robust HIV protease inhibitors., ((c) 2007 Wiley-Liss, Inc.)

A method is presented for extracting the configurational entropy of solute molecules from molecular dynamics simulations, in which the entropy is computed as an expansion of multidimensional mutual information terms, which account for correlated motions among the various internal degrees of freedom of the molecule. The mutual information expansion is demonstrated to be equivalent to estimating the full-dimensional configurational probability density function (PDF) using the generalized Kirkwood superposition approximation (GKSA). While the mutual information expansion is derived to the full dimensionality of the molecule, the current application uses a truncated form of the expansion in which all fourth- and higher-order mutual information terms are neglected. Truncation of the mutual information expansion at the nth order is shown to be equivalent to approximating the full-dimensional PDF using joint PDFs with dimensionality of n or smaller by successive application of the GKSA. The expansion method is used to compute the absolute (classical) configurational entropy in a basis of bond-angle-torsion internal coordinates for several small molecules as well as the change in entropy upon binding for a small host-guest system. Convergence properties of the computed entropy values as a function of simulation time are investigated and comparisons are made with entropy values from the second generation Mining Minima software. These comparisons demonstrate a deviation in -TS of no more than about 2 kcal/mol for all cases in which convergence has been obtained.

There is a clinical need for HIV protease inhibitors that can evade resistance mutations. One possible approach to designing such inhibitors relies upon the crystallographic observation that the substrates of HIV protease occupy a rather constant region within the binding site. In particular, it has been hypothesized that inhibitors which lie within this region will tend to resist clinically relevant mutations. The present study offers the first prospective evaluation of this hypothesis, via computational design of inhibitors predicted to conform to the substrate envelope, followed by synthesis and evaluation against wild-type and mutant proteases, as well as structural studies of complexes of the designed inhibitors with HIV protease. The results support the utility of the substrate envelope hypothesis as a guide to the design of robust protease inhibitors.

Low-molecular-weight receptors that bind targeted guest molecules have a wide range of potential applications but are difficult to design. This paper describes an evolutionary method for computer-aided design of such receptors that works by linking together chemical components from a user-defined library around a stable conformation of the targeted ligand. The software can operate in three modes: de novo design, in which it builds a wide variety of receptors from small components; macrocycle design, in which it builds homopolymeric macrocycles around the ligand; and elaboration of an existing receptor structure. The top candidates generated by the automatic construction process are further studied with detailed affinity calculations whose validity is supported by prior studies of experimentally characterized host-guest systems. All three modes of operation are illustrated here through the design of novel adenine receptors.

The restriction of a small molecule's motion on binding to a protein causes a loss of configurational entropy, and thus a penalty in binding affinity. Some energy models used in computer-aided ligand design neglect this entropic penalty, whereas others account for it based on an expected drop in the number of accessible rotamers upon binding. However, the validity of the physical assumptions underlying the various approaches is largely unexamined. The present study addresses this issue by using Mining Minima calculations to analyze the association of amprenavir with HIV protease. The computed loss in ligand configurational entropy is large, contributing approximately 25 kcal/mol (4.184 kJ/kcal) to DeltaG degrees. Most of this loss results from narrower energy wells in the bound state, rather than a drop in the number of accessible rotamers. Coupling among rotation/translation and internal degrees of freedom complicates the decomposition of the entropy change into additive terms. The results highlight the potential to gain affinity by designing conformationally restricted ligands and have implications for the formulation of energy models for ligand scoring.

BindingDB (http://www.bindingdb.org) is a publicly accessible database currently containing approximately 20,000 experimentally determined binding affinities of protein-ligand complexes, for 110 protein targets including isoforms and mutational variants, and approximately 11,000 small molecule ligands. The data are extracted from the scientific literature, data collection focusing on proteins that are drug-targets or candidate drug-targets and for which structural data are present in the Protein Data Bank. The BindingDB website supports a range of query types, including searches by chemical structure, substructure and similarity; protein sequence; ligand and protein names; affinity ranges and molecular weight. Data sets generated by BindingDB queries can be downloaded in the form of annotated SDfiles for further analysis, or used as the basis for virtual screening of a compound database uploaded by the user. The data in BindingDB are linked both to structural data in the PDB via PDB IDs and chemical and sequence searches, and to the literature in PubMed via PubMed IDs.

Accurate methods of computing the affinity of a small molecule with a protein are needed to speed the discovery of new medications and biological probes. This paper reviews physics-based models of binding, beginning with a summary of the changes in potential energy, solvation energy, and configurational entropy that influence affinity, and a theoretical overview to frame the discussion of specific computational approaches. Important advances are reported in modeling protein-ligand energetics, such as the incorporation of electronic polarization and the use of quantum mechanical methods. Recent calculations suggest that changes in configurational entropy strongly oppose binding and must be included if accurate affinities are to be obtained. The linear interaction energy (LIE) and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) methods are analyzed, as are free energy pathway methods, which show promise and may be ready for more extensive testing. Ultimately, major improvements in modeling accuracy will likely require advances on multiple fronts, as well as continued validation against experiment.

Homology modeling is a computational methodology to assign a 3-D structure to a target protein when experimental data are not available. The methodology uses another protein with a known structure that shares some sequence identity with the target as a template. The crudest approach is to thread the target protein backbone atoms over the backbone atoms of the template protein, but necessary refinement methods are needed to produce realistic models. In this mini-review anchored within the scope of drug design, we show the validity of using homology models of proteins in the discovery of binders for potential therapeutic targets. We also report several different approaches to homology model refinement, going from very simple to the most elaborate. Results show that refinement approaches are system dependent and that more elaborate methodologies do not always correlate with better performances from built homology models.

Synthetic receptors have a wide range of potential applications, but it has been difficult to design low molecular weight receptors that bind ligands with high, "proteinlike" affinities. This study uses novel computational methods to understand why it is hard to design a high-affinity receptor and to explore the limits of affinity, with the bioactive peptide RGD as a model ligand. The M2 modeling method is found to yield excellent agreement with experiment for a known RGD receptor and then is used to analyze a series of receptors generated in silico with a de novo design algorithm. Forces driving binding are found to be systematically opposed by proportionate repulsions due to desolvation and entropy. In particular, strong correlations are found between Coulombic attractions and the electrostatic desolvation penalty and between the mean energy change on binding and the cost in configurational entropy. These correlations help explain why it is hard to achieve high affinity. The change in surface area upon binding is found to correlate poorly with affinity within this series. Measures of receptor efficiency are formulated that summarize how effectively a receptor uses surface area, total energy, and Coulombic energy to achieve affinity. Analysis of the computed efficiencies suggests that a low molecular weight receptor can achieve proteinlike affinity. It is also found that macrocyclization of a receptor can, unexpectedly, increase the entropy cost of binding because the macrocyclic structure further restricts ligand motion.

Sensitivity analysis and charge-optimization have been suggested as methods to guide the optimization of lead compounds in early-stage drug discovery. However, applications to date have been restricted by the simplifying assumption of a rigid ligand. The present study applies both formalisms to the case of a flexible ligand in a model application to an HIV-protease inhibitor. The results suggest that sensitivity analysis is a fast and robust method for guiding charge changes in both a rigid and a flexible ligand, although its accuracy is limited by the fact that it represents a linear approximation. The more complete quadratic analysis provided by charge-optimization produces unexpected results when the ligand is considered to be flexible. For example, it can yield atomic charges which powerfully stabilize the bound conformation of the ligand relative to the conformation assumed for the free state, thus markedly destabilizing the assumed free conformation. Such results are traceable to the fact that the energy matrix possesses negative eigenvalues. However, optimizing charges under the assumption that the ligand does not change conformation upon binding leads to a set of charges that robustly improve affinity, even when the free conformation is later allowed to vary. Thus, both sensitivity analysis and charge-optimization appear to be useful techniques.

In the absence of an experimentally solved structure, a homology model of a protein target can be used instead for virtual screening of drug candidates by docking and scoring. This approach poses a number of questions regarding the choice of the template to use in constructing the model, the accuracy of the screening results, and the importance of allowing for protein flexibility. The present study addresses such questions with compound screening calculations for multiple homology models of five drug targets. A central result is that docking to homology models frequently yields enrichments of known ligands as good as that obtained by docking to a crystal structure of the actual target protein. Interestingly, however, standard measures of the similarity of the template used to build the homology model to the targeted protein show little correlation with the effectiveness of the screening calculations, and docking to the template itself often is as successful as docking to the corresponding homology model. Treating key side chains as mobile produces a modest improvement in the results. The reasons for these sometimes unexpected results, and their implications for future methodologic development, are discussed.

The quasiharmonic approximation (QH) allows the configurational entropy of a molecule to be estimated on the basis of a molecular dynamics simulation, through construction of a Gaussian probability distribution of conformations with variances equal to those provided by the simulation. At its introduction in 1981, the QH method was successfully applied to simple molecular systems with only one highly occupied energy well, and fluctuations were analyzed in a system of internal bond-angle-torsion coordinates. However, more recent studies have applied the QH method to complex biomolecular systems and have relied upon Cartesian coordinates. The present study evaluates the accuracy of the QH method through comparisons with more detailed methods. The chief findings are that the QH method can markedly overestimate the configurational entropy for systems with multiple occupied energy wells and that such errors tend to be magnified by the use of Cartesian coordinates instead of bond-angle-torsion coordinates.

The Support Vector Machine (SVM) is an algorithm that derives a model used for the classification of data into two categories and which has good generalization properties. This study applies the SVM algorithm to the problem of virtual screening for molecules with a desired activity. In contrast to typical applications of the SVM, we emphasize not classification but enrichment of actives by using a modified version of the standard SVM function to rank molecules. The method employs a simple and novel criterion for picking molecular descriptors and uses cross-validation to select SVM parameters. The resulting method is more effective at enriching for active compounds with novel chemistries than binary fingerprint-based methods such as binary kernel discrimination.

Standard uses of ligand-receptor docking typically focus on the association of candidate ligands with a single targeted receptor, but actual applications increasingly require comparisons across multiple receptors. This study demonstrates that comparative docking to multiple receptors can help to select homology models for virtual compound screening and to discover ligands that bind to one set of receptors but not to another, potentially similar, set. A serial docking algorithm is furthermore described that reduces the computational costs of such calculations by testing compounds against a series of receptor structures and discarding a compound as soon as it fails to satisfy specified bind/no bind criteria for each receptor. The algorithm also realizes substantial efficiencies by taking advantage of the fact that a ligand typically binds in similar conformations to similar receptors. Thus, once detailed docking has been used to fit a ligand into the first of a series of similar receptors, much less extensive calculations can be used for the remaining structures.

The second generation Mining Minima method yields binding affinities accurate to within 0.8 kcal/mol for the associations of alpha-, beta-, and gamma-cyclodextrin with benzene, resorcinol, flurbiprofen, naproxen, and nabumetone. These calculations require hours to a day on a commodity computer. The calculations also indicate that the changes in configurational entropy upon binding oppose association by as much as 24 kcal/mol and result primarily from a narrowing of energy wells in the bound versus the free state, rather than from a drop in the number of distinct low-energy conformations on binding. Also, the configurational entropy is found to vary substantially among the bound conformations of a given cyclodextrin-guest complex. This result suggests that the configurational entropy must be accounted for to reliably rank docked conformations in both host-guest and ligand-protein complexes. In close analogy with the common experimental observation of entropy-enthalpy compensation, the computed entropy changes show a near-linear relationship with the changes in mean potential plus solvation energy.

This study applies a novel computational method to study molecular recognition for three sets of synthetic hosts: molecular clips, molecular tweezers, and a synthetic barbiturate receptor. The computed standard free energies of binding for the 12 binding reactions agree closely with experiment and provide insight into the roles of configurational entropy, preorganization, and induced fit in the systems studied. The computed changes in configurational entropy are comparable in magnitude to the changes in mean potential plus solvation energy, and they result primarily from changes in the average width of the energy wells upon binding. A strong correlation is observed between the changes in configurational energy and configurational entropy upon binding, resulting in near-linear compensation analogous to classical entropy-enthalpy compensation.

It is widely accepted that the binding constant of a receptor and ligand can be written as a two-body integral involving the interaction energy of the receptor and the ligand. Interestingly, however, three different theories of binding in the literature dictate three distinct integrals. The present study uses theory, as well as simulations of binding experiments, to test the validity of the three integrals. When binding is measured by a signal that detects the ligand in the binding site, the most accurate results are obtained by an integral of the Boltzmann factor, where the bound complex is defined in terms of an exclusive binding region. A novel prediction of this approach, that expanding a ligand can increase its binding constant, is borne out by the simulations. The simulations also show that abnormal binding isotherms can be obtained when the region over which the signal is detected deviates markedly from the exclusion zone. Interestingly, the binding constant measured by equilibrium dialysis, rather than by monitoring a localized signal, can yield a binding constant that differs from that obtained from a signal measurement, and that is matched best by the integral of the Mayer factor.