Protonation changes upon ligand binding to trypsin and thrombin: structural interpretation based on pK(a) calculations and ITC experiments

The protonation states of a protein and a ligand can be altered upon complex formation. Such changes can be detected experimentally by isothermal titration calorimetry (ITC). For a series of ligands binding to the serine proteases trypsin and thrombin, we previously performed an extensive ITC and crystallographic study and were able to identify protonation changes for four complexes. However, since ITC measures only the overall proton exchange, it does not provide structural insights into the functional groups involved in the proton transfer. Using Poisson-Boltzmann calculations based on our recently developed PEOE_PB charges, we compute pK(a) values for all complexes of our former study in order to reveal the residues with altered protonation states. The results indicate that His57, a member of the catalytic triad, is responsible for the most relevant pK(a) shifts leading to the experimentally detected protonation changes. This finding is in contrast to our previous assumption that the observed protonation changes occur at the carboxylic group of the ligands. The newly detected proton acceptor is used for a revised factorization of the ITC data, which is necessary whenever the protonation inventory changes upon complexation. The pK(a) values of complexes showing no protonation change in the ITC experiment are reliably predicted in most cases, whereas predictions of strongly coupled systems remain problematic.     

Estimating binding affinities by docking/scoring methods using variable protonation states

To investigate the effects of multiple protonation states on protein-ligand recognition, we generated alternative protonation states for selected titratable groups of ligands and receptors. The selection of states was based on the predicted pK(a) of the unbound receptor and ligand and the proximity of titratable groups of the receptor to the binding site. Various ligand tautomer states were also considered. An independent docking calculation was run for each state. Several protocols were examined: using an ensemble of all generated states of ligand and receptor, using only the most probable state of the unbound ligand/receptor, and using only the state giving the most favorable docking score. The accuracies of these approaches were compared, using a set of 176 protein-ligand complexes (15 receptors) for which crystal structures and measured binding affinities are available. The best agreement with experiment was obtained when ligand poses from experimental crystal structures were used. For 9 of 15 receptors, using an ensemble of all generated protonation states of the ligand and receptor gave the best correlation between calculated and measured affinities.     

Estimating protein-ligand binding free energy: atomic solvation parameters for partition coefficient and solvation free energy calculation

Solvation energy calculation is one of the main difficulties for the estimation of protein-ligand binding free energy and the correct scoring in docking studies. We have developed a new solvation energy estimation method for protein-ligand binding based on atomic solvation parameter (ASP), which has been shown to improve the power of protein-ligand binding free energy predictions. The ASP set, designed to handle both proteins and organic compounds and derived from experimental n-octanol/water partition coefficient (log P) data, contains 100 atom types (united model that treats hydrogen atoms implicitly) or 119 atom types (all-atom model that treats hydrogen atoms explicitly). By using this unified ASP set, an algorithm was developed for solvation energy calculation and was further integrated into a score function for predicting protein-ligand binding affinity. The score function reproduced the absolute binding free energies of a test set of 50 protein-ligand complexes with a standard error of 8.31 kJ/mol. As a byproduct, a conformation-dependent log P calculation algorithm named ASPLOGP was also implemented. The predictive results of ASPLOGP for a test set of 138 compounds were r = 0.968, s = 0.344 for the all-atom model and r = 0.962, s = 0.367 for the united model, which were better than previous conformation-dependent approaches and comparable to fragmental and atom-based methods. ASPLOGP also gave good predictive results for small peptides. The score function based on the ASP model can be applied widely in protein-ligand interaction studies and structure-based drug design.     

Who cares for the protons?

It is tempting to use standard protonation states for the analysis of protein-ligand interactions. Two different pK(a) calculation methods, PROPKA (protein pK(a)) and MCCE (multi conformation continuum electrostatics), were applied to challenge this convenient behavior. As data basis, we selected five recently approved drugs for which structural information of the protein-drug complex is available. We analyzed the pK(a) calculations in terms of a measure termed BIPS (binary protonation states) recently introduced by us. Both methods agree in detecting the majority of the sites with atypical BIPS values. However, when using only one method, some of the atypcial BIPS value would have been missed. Therefore, we recommend using both methods to set such an interpretation on a solid basis.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.     

An evaluation of Poisson-Boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

For systems involving highly and oppositely charged proteins, electrostatic forces dominate association and contribute to biomolecular complex stability. Using experimental or theoretical alanine-scanning mutagenesis, it is possible to elucidate the contribution of individual ionizable amino acids to protein association. We evaluated our electrostatic free energy calculations by comparing calculated and experimental data for alanine mutants of five protein complexes. We calculated Poisson-Boltzmann electrostatic free energies based on a thermodynamic cycle, which incorporates association in a reference (Coulombic) and solvated (solution) state, as well as solvation effects. We observe that Coulombic and solvation free energy values correlate with experimental data in highly and oppositely charged systems, but not in systems comprised of similarly charged proteins. We also observe that correlation between solution and experimental free energies is dependent on dielectric coefficient selection for the protein interior. Free energy correlations improve as protein dielectric coefficient increases, suggesting that the protein interior experiences moderate dielectric screening, despite being shielded from solvent. We propose that higher dielectric coefficients may be necessary to more accurately predict protein-protein association. Additionally, our data suggest that Coulombic potential calculations alone may be sufficient to predict relative binding of protein mutants.     

Theoretical prediction of relative and absolute pKa values of aminopyridines

This work presents a study aimed at the theoretical prediction of pK(a) values of aminopyridines, as a factor responsible for the activity of these compounds as blockers of the voltage-dependent K(+) channels. To cover a large range of pK(a) values, a total of seven substituted pyridines is considered as a calibration set: pyridine, 2-aminopyridine, 3-aminopyridine, 4-aminopyridine, 2-chloropyridine, 3-chloropyridine, and 4-methylpirydine. Using ab initio G1, G2 and G3 extrapolation methods, and the CPCM variant of the Polarizable Continuum Model for solvation, we calculate gas phase and solvation free energies. pK(a) values are obtained from these data using a thermodynamic cycle for describing protonation in aqueous and gas phases. The results show that the relatively inexpensive G1 level of theory is the most accurate at predicting pK(a) values in aminopyridines. The highest standard deviation with respect to the experimental data is 0.69 pK(a) units for absolute values calculations. The difference increases slightly to 0.74 pK(a) units when the pK(a) is computed relative to the pyridine molecule. Considering only compounds at least as basic as pyridine (the values of interest for bioactive aminopyridines) the error falls to 0.10 and 0.12 pK(a) units for the absolute and relative computations, respectively. The technique can be used to predict the effect of electronegative substituents in the pK(a) of 4-AP, the most active aminopyridine considered in this work. Thus, 2-chloro and 3-chloro-4-aminopyridine are taken into account. The results show a decrease of the pK(a), suggesting that these compounds are less active than 4-AP at blocking the K(+) channel.     

Optimizing the hydrogen-bond network in Poisson-Boltzmann equation-based pK(a) calculations

pK(a) calculation methods that are based on finite difference solutions to the Poisson-Boltzmann equation (FDPB) require that energy calculations be performed for a large number of different protonation states of the protein. Normally, the differences between these protonation states are modeled by changing the charges on a few atoms, sometimes the differences are modeled by adding or removing hydrogens, and in a few cases the positions of these hydrogens are optimized locally. We present an FDPB-based pK(a) calculation method in which the hydrogen-bond network is globally optimized for every single protonation state used. This global optimization gives a significant improvement in the accuracy of calculated pK(a) values, especially for buried residues. It is also shown that large errors in calculated pK(a) values are often due to structural artifacts induced by crystal packing. Optimization of the force fields and parameters used in pK(a) calculations should therefore be performed with X-ray structures that are corrected for crystal artifacts.     

Computational method for relative binding energies of enzyme-substrate complexes.

A computational method for estimating the relative binding free energies of enzyme-substrate complexes is described that combines electrostatic and solvation models and X-ray crystallographic data. The polar contribution is evaluated by the Poisson-Boltzman equation. The nonpolar contribution is evaluated by solvent transfer data and surface area calculations. This algorithm was used to calculate the relative binding energies of 63 pairs of nine different mutant proteins with seven different substituted R-malate substrates of Escherichia coli isocitrate dehydrogenase. Comparison of calculated values with the experimentally observed values shows a high degree of correlation.     

Complexity in modeling and understanding protonation states: computational titration of HIV-1-protease-inhibitor complexes

The computational-titration (CT) algorithm based on the 'natural' Hydropathic INTeractions (HINT) force field is described. The HINT software model is an empirical, non-Newtonian force field derived from experimentally measured partition coefficients for solvent transfer between octanol and H(2)O (log P(o/w)). The CT algorithm allows the identification, modeling, and optimization of multiple protonation states of residues and ligand functional groups at the protein-ligand active site. The importance of taking into account pH and ionization states of residues, which strongly affect the process of ligand binding, for correctly predicting binding free energies is discussed. The application of the CT protocol to a set of six cyclic inhibitors in their complexes with HIV-1 protease is presented, and the advance of HINT as a virtual-screening tool is outlined.     

Ligand solvation in molecular docking

Solvation plays an important role in ligand‐protein association and has a strong impact on comparisons of binding energies for dissimilar molecules. When databases of such molecules are screened for complementarity to receptors of known structure, as often occurs in structure‐based inhibitor discovery, failure to consider ligand solvation often leads to putative ligands that are too highly charged or too large. To correct for the different charge states and sizes of the ligands, we calculated electrostatic and non‐polar solvation free energies for molecules in a widely used molecular database, the Available Chemicals Directory (ACD). A modified Born equation treatment was used to calculate the electrostatic component of ligand solvation. The non‐polar component of ligand solvation was calculated based on the surface area of the ligand and parameters derived from the hydration energies of apolar ligands. These solvation energies were subtracted from the ligand‐receptor interaction energies. We tested the usefulness of these corrections by screening the ACD for molecules that complemented three proteins of known structure, using a molecular docking program. Correcting for ligand solvation improved the rankings of known ligands and discriminated against molecules with inappropriate charge states and sizes. Proteins 1999;34:4–16. © 1999 Wiley‐Liss, Inc.     

Analysis of knowledge-based protein-ligand potentials using a self-consistent method

We propose a self-consistent approach to analyze knowledge-based atom-atom potentials used to calculate protein-ligand binding energies. Ligands complexed to actual protein structures were first built using the SMoG growth procedure (DeWitte & Shakhnovich, 1996) with a chosen input potential. These model protein-ligand complexes were used to construct databases from which knowledge-based protein-ligand potentials were derived. We then tested several different modifications to such potentials and evaluated their performance on their ability to reconstruct the input potential using the statistical information available from a database composed of model complexes. Our data indicate that the most significant improvement resulted from properly accounting for the following key issues when estimating the reference state: (1) the presence of significant nonenergetic effects that influence the contact frequencies and (2) the presence of correlations in contact patterns due to chemical structure. The most successful procedure was applied to derive an atom-atom potential for real protein-ligand complexes. Despite the simplicity of the model (pairwise contact potential with a single interaction distance), the derived binding free energies showed a statistically significant correlation (approximately 0.65) with experimental binding scores for a diverse set of complexes.     

SuperStar: comparison of CSD and PDB-based interaction fields as a basis for the prediction of protein-ligand interactions.

SuperStar is an empirical method for identifying interaction sites in proteins, based entirely on the experimental information about non-bonded interactions, present in the IsoStar database. The interaction information in IsoStar is contained in scatterplots, which show the distribution of a chosen probe around structure fragments. SuperStar breaks a template molecule (e.g. a protein binding site) into structural fragments which correspond to those in the scatterplots. The scatterplots are then superimposed on the corresponding parts of the template and converted into a composite propensity map.The original version of SuperStar was based entirely on scatterplots from the CSD. Here, scatterplots based on protein-ligand interactions are implemented in SuperStar, and validated on a test set of 122 X-ray structures of protein-ligand complexes. In this validation, propensity maps are compared with the experimentally observed positions of ligand atoms of comparable types. Although non-bonded interaction geometries in small molecule structures are similar to those found in protein-ligand complexes, their relative frequencies of occurrence are different. Polar interactions are more common in the first class of structures, while interactions between hydrophobic groups are more common in protein crystals. In general, PDB and CSD-based SuperStar maps appear equally successful in the prediction of protein-ligand interactions. PDB-based maps are more suitable to identify hydrophobic pockets, and inherently take into account the experimental uncertainties of protein atomic positions. If the protonation state of a histidine, aspartate or glutamate protein side-chain is known, specific CSD-based maps for that protonation state are preferred over PDB-based maps which represent an ensemble of protonation states.     

Computational approach to the basicity of a series of alpha1-adrenoceptor ligands in aqueous solution

In order to design any new potential drug, it is crucial to know their corresponding pK(a) since their protonation state will be critical in the ligand-receptor interaction and it will play an essential role in their pharmacokinetic profile. Several authors have developed approaches for the computational determination of pK(a) which involve the use of a thermodynamic cycle relating pK(a) to the gas-phase proton basicity via the solvation energies of the products and the reactants. Such methods are very dependent on the solvation model used and the nature of the system. The theoretical pK(a) of a number of agonists and antagonists of the alpha1A-adrenoceptor has been computed and the performance of this approach has been tested through comparison with the available and/or measured experimental pK(a) values.     

Knowledge-based scoring function to predict protein-ligand interactions

The development and validation of a new knowledge-based scoring function (DrugScore) to describe the binding geometry of ligands in proteins is presented. It discriminates efficiently between well-docked ligand binding modes (root-mean-square deviation <2.0 A with respect to a crystallographically determined reference complex) and those largely deviating from the native structure, e.g. generated by computer docking programs. Structural information is extracted from crystallographically determined protein-ligand complexes using ReLiBase and converted into distance-dependent pair-preferences and solvent-accessible surface (SAS) dependent singlet preferences for protein and ligand atoms. Definition of an appropriate reference state and accounting for inaccuracies inherently present in experimental data is required to achieve good predictive power. The sum of the pair preferences and the singlet preferences is calculated based on the 3D structure of protein-ligand binding modes generated by docking tools. For two test sets of 91 and 68 protein-ligand complexes, taken from the Protein Data Bank (PDB), the calculated score recognizes poses generated by FlexX deviating <2 A from the crystal structure on rank 1 in three quarters of all possible cases. Compared to FlexX, this is a substantial improvement. For ligand geometries generated by DOCK, DrugScore is superior to the "chemical scoring" implemented into this tool, while comparable results are obtained using the "energy scoring" in DOCK. None of the presently known scoring functions achieves comparable power to extract binding modes in agreement with experiment. It is fast to compute, regards implicitly solvation and entropy contributions and produces correctly the geometry of directional interactions. Small deviations in the 3D structure are tolerated and, since only contacts to non-hydrogen atoms are regarded, it is independent from assumptions of protonation states.     

Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Interaction Energy (LIE) method (Aqvist et. al., Prot Eng 1994;7:385-391). The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The examination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 1992;5:215-228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both the LRA and LIE methods. The difference is, however, that the LIE method neglects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the "non-polar" ligand, l;, where all the residual charges are set to zero. It is shown that the LIE term, which involves the scaling of the van der Waals interaction by a constant beta (usually in the order of 0.15 to 0.25), corresponds to this part of the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant beta, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, DeltaG(bind,l;). Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate DeltaG(bind,l;) by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contributions that make up the total DeltaG(bind,l;). The sum of these contributions is scaled by a factor straight theta and it is argued that obtaining a quantitative balance between these contributions should result in straight theta = 1. By doing so we should have a reliable estimate of the value of the LIE beta and a way to understand its origin. The present approach gives straight theta values between 0.5 and 0.73, depending on the approximation used. This is encouraging but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the change of the LIE straight theta between different protein active sites. It is pointed out that the LIE method is quite similar to our original approach where the electrostatic term was evaluated by the LRA method and the non-electrostatic term by the PDLD method (with its vdw, solvation,     

Theoretical studies on solvation contribution to the thermodynamic stability of mutants of lysozyme T4

Atomic solvation parameters (ASPs) are widely used to estimate the solvation contribution to the thermodynamic stability of proteins as well as the free energy of association for protein-ligand complexes. In view of discrepancies in the results of free energies of solvation of folding for various proteins obtained using different atomic solvation parameter sets, systematic studies have been carried out for the calculation of accessible surface area and the changes in free energy of solvation of folding (deltaG(s,f)) for mutants of lysozyme T4 where threonine 157 is replaced by amino acids: cysteine, aspartate, glutamate, phenylalanine, glycine, histidine, isoleucine, leucine, asparagine, arginine, serine and valine. The deviations of the calculated results from the experimental results are discussed to highlight the discrepancies in the atomic solvation parameter sets and possible reasons for them. The results are also discussed to throw light on the effect of chain free energy and hydrogen bonding on the stability of mutants. The octanol to water-based ASP sets 'Sch1' and 'EM' perform better than the vacuum to water-based ASP sets. The vacuum to water-based ASP sets 'Sch3' and 'WE' can be used to predict the stability of mutants if a proper method to calculate the hydrogen bond contribution to overall stability is in place.     

Protonation states and pH titration in the photocycle of photoactive yellow protein

Photoactive yellow protein (PYP) undergoes a light-driven cycle of color and protonation states that is part of a mechanism of bacterial phototaxis. This article concerns functionally important protonation states of PYP and the interactions that stabilize them, and changes in the protonation state during the photocycle. In particular, the chromophore pK(a) is known to be shifted down so that the chromophore is negatively charged in the ground state (dark state) even though it is buried in the protein, while nearby Glu46 has an unusually high pK(a). The photocycle involves changes of one or both of these protonation states. Calculations of pK(a) values and protonation states using a semi-macroscopic electrostatic model are presented for the wild-type and three mutants, in both the ground state and the bleached (I(2)) intermediate state. Calculations allowing multiple H-bonding arrangements around the chromophore also have been carried out. In addition, ground-state pK(a) values of the chromophore have been measured by UV-visible spectroscopy for the wild-type and the same three mutants. Because of the unusual protonation states and strong electrostatic interactions, PYP represents a severe test of the ability of theoretical models to yield correct calculations of electrostatic interactions in proteins. Good agreement between experiment and theory can be obtained for the ground state provided the protein interior is assumed to have a relatively low dielectric constant, but only partial agreement between theory and experiment is obtained for the bleached state. We also present a reinterpretation of previously published data on the pH-dependence of the recovery of the ground state from the bleached state. The new analysis implies a pK(a) value of 6.37 for Glu46 in the bleached state, which is consistent with other available experimental data, including data that only became available after this analysis. The new analysis suggests that signal transduction is modulated by the titration properties of the bleached state, which are in turn determined by electrostatic interactions. Overall, the results of this study provide a quantitative picture of the interactions responsible for the unusual protonation states of the chromophore and Glu46, and of protonation changes upon bleaching.     

Comparison of atomic solvation parametric sets: applicability and limitations in protein folding and binding.

Atomic solvation parameters (ASP) are widely used to estimate the solvation contribution to the thermodynamic stability of proteins as well as the free energy of association for protein-ligand complexes. They are also included in several molecular mechanics computer programs. In this work, a total of eight atomic solvation parametric sets has been employed to calculate the solvation contribution to the free energy of folding delta Gs for 17 proteins. A linear correlation between delta Gs and the number of residues in each protein was found for each ASP set. The calculations also revealed a great variety in the absolute value and in the sign of delta Gs values such that certain ASP sets predicted the unfolded state to be more stable than the folded, whereas others yield precisely the opposite. Further, the solvation contribution to the free energy of association of helix pairs and to the disassociation of loops (connection between secondary structural elements in proteins) from the protein tertiary structures were computed for each of the eight ASP sets and discrepancies were evident among them.