SCORE: A New Empirical Method for Estimating the Binding Affinity of a Protein-Ligand Complex

A new method is presented to estimate the binding affinity of a protein-ligand complex with known three-dimensional structure. The method, SCORE, uses an empirical scoring function to describe the binding free energy, which includes terms to account for van der Waals contact, metal-ligand bonding, hydrogen bonding, desolvation effect, and deformation penalty upon the binding process. The coefficients of each term are obtained by multivariate regressional analysis of a diverse training set of 170 protein-ligand complexes. The final scoring function reproduces the binding free energies of the whole training set with a cross-validated deviation of 6.3 kJ/mol. The predictive ability of the function is further tested by a set of 11 endothiapepsin complexes and the internal consistency of the function is demonstrated in a stepwise procedure named Evolutionary Test. A major innovation of this method is the introduction of an atomic binding score which allows the researcher to inspect and optimize the lead compound rationally in a structure-based drug design scheme.     

Probabilistic Prediction of Contacts in Protein-Ligand Complexes

We introduce a statistical method for evaluating atomic level 3D interaction patterns of protein-ligand contacts. Such patterns can be used for fast separation of likely ligand and ligand binding site combinations out of all those that are geometrically possible. The practical purpose of this probabilistic method is for molecular docking and scoring, as an essential part of a scoring function. Probabilities of interaction patterns are calculated conditional on structural x-ray data and predefined chemical classification of molecular fragment types. Spatial coordinates of atoms are modeled using a Bayesian statistical framework with parametric 3D probability densities. The parameters are given distributions a priori, which provides the possibility to update the densities of model parameters with new structural data and use the parameter estimates to create a contact hierarchy. The contact preferences can be defined for any spatial area around a specified type of fragment. We compared calculated contact point hierarchies with the number of contact atoms found near the contact point in a reference set of x-ray data, and found that these were in general in a close agreement. Additionally, using substrate binding site in cathechol-O-methyltransferase and 27 small potential binder molecules, it was demonstrated that these probabilities together with auxiliary parameters separate well ligands from decoys (true positive rate 0.75, false positive rate 0). A particularly useful feature of the proposed Bayesian framework is that it also characterizes predictive uncertainty in terms of probabilities, which have an intuitive interpretation from the applied perspective.     

The Affinity of DNA-Microtubule Protein Complexes and their Disruption by Tubulin Binding Drugs

Abstract

Using the gel shift assay system, we have measured the apparent affinity constant for the interaction of two different DNAs with MAP proteins found in both total calf brain microtubules and heat stable brain preparations. Both DNAs studied contained centromere/kinetochore sequences- one was enriched in the calf satellite DNA; the other was a large restriction fragment containing the yeast CEN11 DNA sequence. Complexes formed using both DNAs had similar K_app values in the range of 2.1×10⁷ M^?1 to 2.0×10⁸ M^?1. CEN11 DNA-MTP complexes had by far the highest K_app value of 2.0×10⁸ M^?1. The CEN11 DNA sequence is where the yeast kinetochore of chromosome 11 is formed and where the single yeast microtubule is bound in vivo. The CEN11 conserved region II known binding sites -(dA/dT)n runs- for mammalian MAP2 protein, are in good agreement with this higher K_app value. The effects of the classical tubulin binding drugs colchicine, podophyllotoxin and vinblastine on the DNA-MAP protein complex stability were investigated by determining the drug concentrations where the complexes were destabilized. Only the complexes formed from total microtubule protein (tubulin containing) were destabilized over a wide drug concentration range. Heat stable brain protein complexes (no tubulin) were largely unaffected. Furthermore, it took 10–100 fold higher drug concentrations to disrupt the CEN 11 DNA complexes compared to the calf thymus satellite DNA enriched complexes. These data support our previous results suggesting that there is a DNA sequence dependent interaction with MAP proteins that appears to be conserved in evolution (Marx et. al., Biochim. Biophys. Acta. 783, 383–392,1984; Marx and Denial, Molecular Basis of Cancer 172B,65-15 1985). In addition, these results imply that the classical tubulin binding drugs may exert their biological effects in cells at least in part by disrupting DNA-Protein complexes of the type we have studied here.     

Accounting for Ligand Conformational Restriction in Calculations of Protein-Ligand Binding Affinities

The conformation adopted by a ligand on binding to a receptor may differ from its lowest-energy conformation in solution. In addition, the bound ligand is more conformationally restricted, which is associated with a configurational entropy loss. The free energy change due to these effects is often neglected or treated crudely in current models for predicting binding affinity. We present a method for estimating this contribution, based on perturbation theory using the quasi-harmonic model of Karplus and Kushick as a reference system. The consistency of the method is checked for small model systems. Subsequently we use the method, along with an estimate for the enthalpic contribution due to ligand-receptor interactions, to calculate relative binding affinities. The AMBER force field and generalized Born implicit solvent model is used. Binding affinities were estimated for a test set of 233 protein-ligand complexes for which crystal structures and measured binding affinities are available. In most cases, the ligand conformation in the bound state was significantly different from the most favorable conformation in solution. In general, the correlation between measured and calculated ligand binding affinities including the free energy change due to ligand conformational change is comparable to or slightly better than that obtained by using an empirically-trained docking score. Both entropic and enthalpic contributions to this free energy change are significant.     

Entropic Enhancement of Protein-DNA Affinity by Oxygen-to-Sulfur Substitution in DNA Phosphate

Dithioation of DNA phosphate is known to enhance binding affinities, at least for some proteins. We mechanistically characterized this phenomenon for the Antennapedia homeodomain-DNA complex by integrated use of fluorescence, isothermal titration calorimetry, NMR spectroscopy, and x-ray crystallography. By fluorescence and isothermal titration calorimetry, we found that this affinity enhancement is entropy driven. By NMR, we investigated the ionic hydrogen bonds and internal motions of lysine side-chain NH₃⁺ groups involved in ion pairs with DNA. By x-ray crystallography, we compared the structures of the complexes with and without dithioation of the phosphate. Our NMR and x-ray data show that the lysine side chain in contact with the DNA phosphate becomes more dynamic upon dithioation. Our thermodynamic, structural, and dynamic investigations collectively suggest that the affinity enhancement by the oxygen-to-sulfur substitution in DNA phosphate is largely due to an entropic gain arising from mobilization of the intermolecular ion pair at the protein-DNA interface.     

Determining the Binding Affinity of Therapeutic Monoclonal Antibodies towards Their Native Unpurified Antigens in Human Serum

Monoclonal antibodies (mAbs) are a growing segment of therapeutics, yet their in vitro characterization remains challenging. While it is essential that a therapeutic mAb recognizes the native, physiologically occurring epitope, the generation and selection of mAbs often rely on the use of purified recombinant versions of the antigen that may display non-native epitopes. Here, we present a method to measure both, the binding affinity of a therapeutic mAb towards its native unpurified antigen in human serum, and the antigen’s endogenous concentration, by combining the kinetic exclusion assay and Biacore’s calibration free concentration analysis. To illustrate the broad utility of our method, we studied a panel of mAbs raised against three disparate soluble antigens that are abundant in the serum of healthy donors: proprotein convertase subtilisin/kexin type 9 (PCSK9), progranulin (PGRN), and fatty acid binding protein (FABP4). We also determined the affinity of each mAb towards its purified recombinant antigen and assessed whether the interactions were pH-dependent. Of the six mAbs studied, three did not appear to discriminate between the serum and recombinant forms of the antigen; one mAb bound serum antigen with a higher affinity than recombinant antigen; and two mAbs displayed a different affinity for serum antigen that could be explained by a pH-dependent interaction. Our results highlight the importance of taking pH into account when measuring the affinities of mAbs towards their serum antigens, since the pH of serum samples becomes increasingly alkaline upon aerobic handling.     

Computational Assessment of Protein–protein Binding Affinity by Reversely Engineering the Energetics in Protein Complexes

The cellular functions of proteins are maintained by forming diverse complexes. The stability of these complexes is quantified by the measurement of binding affinity, and mutations that alter the binding affinity can cause various diseases such as cancer and diabetes. As a result, accurate estimation of the binding stability and the effects of mutations on changes of binding affinity is a crucial step to understanding the biological functions of proteins and their dysfunctional consequences. It has been hypothesized that the stability of a protein complex is dependent not only on the residues at its binding interface by pairwise interactions but also on all other remaining residues that do not appear at the binding interface. Here, we computationally reconstruct the binding affinity by decomposing it into the contributions of interfacial residues and other non-interfacial residues in a protein complex. We further assume that the contributions of both interfacial and non-interfacial residues to the binding affinity depend on their local structural environments such as solvent-accessible surfaces and secondary structural types. The weights of all corresponding parameters are optimized by Monte-Carlo simulations. After cross-validation against a large-scale dataset, we show that the model not only shows a strong correlation between the absolute values of the experimental and calculated binding affinities, but can also be an effective approach to predict the relative changes of binding affinity from mutations. Moreover, we have found that the optimized weights of many parameters can capture the first-principle chemical and physical features of molecular recognition, therefore reversely engineering the energetics of protein complexes. These results suggest that our method can serve as a useful addition to current computational approaches for predicting binding affinity and understanding the molecular mechanism of protein–protein interactions.     

Low Affinity and Slow Na+ Binding Precedes High Affinity Aspartate Binding in the Secondary-active Transporter GltPh

Glt_Ph from Pyrococcus horikoshii is a homotrimeric Na⁺-coupled aspartate transporter. It belongs to the widespread family of glutamate transporters, which also includes the mammalian excitatory amino acid transporters that take up the neurotransmitter glutamate. Each protomer in Glt_Ph consists of a trimerization domain involved in subunit interactions and a transport domain containing the substrate binding site. Here, we have studied the dynamics of Na⁺ and aspartate binding to Glt_Ph. Tryptophan fluorescence measurements on the fully active single tryptophan mutant F273W revealed that Na⁺ binds with low affinity to the apoprotein (K_d 120 mm), with a particularly low k_on value (5.1 m⁻¹s⁻¹). At least two sodium ions bind before aspartate. The binding of Na⁺ requires a very high activation energy (E_a 106.8 kJ mol⁻¹) and consequently has a large Q₁₀ value of 4.5, indicative of substantial conformational changes before or after the initial binding event. The apparent affinity for aspartate binding depended on the Na⁺ concentration present. Binding of aspartate was not observed in the absence of Na⁺, whereas in the presence of high Na⁺ concentrations (above the K_d for Na⁺) the dissociation constants for aspartate were in the nanomolar range, and the aspartate binding was fast (k_on of 1.4 × 10⁵ m⁻¹s⁻¹), with low E_a and Q₁₀ values (42.6 kJ mol⁻¹ and 1.8, respectively). We conclude that Na⁺ binding is most likely the rate-limiting step for substrate binding.     

Statistics and Physical Origins of pK and Ionization State Changes upon Protein-Ligand Binding

This work investigates statistical prevalence and overall physical origins of changes in charge states of receptor proteins upon ligand binding. These changes are explored as a function of the ligand type (small molecule, protein, and nucleic acid), and distance from the binding region. Standard continuum solvent methodology is used to compute, on an equal footing, pK changes upon ligand binding for a total of 5899 ionizable residues in 20 protein-protein, 20 protein-small molecule, and 20 protein-nucleic acid high-resolution complexes. The size of the data set combined with an extensive error and sensitivity analysis allows us to make statistically justified and conservative conclusions: in 60% of all protein-small molecule, 90% of all protein-protein, and 85% of all protein-nucleic acid complexes there exists at least one ionizable residue that changes its charge state upon ligand binding at physiological conditions (pH = 6.5). Considering the most biologically relevant pH range of 4-8, the number of ionizable residues that experience substantial pK changes (ΔpK > 1.0) due to ligand binding is appreciable: on average, 6% of all ionizable residues in protein-small molecule complexes, 9% in protein-protein, and 12% in protein-nucleic acid complexes experience a substantial pK change upon ligand binding. These changes are safely above the statistical false-positive noise level. Most of the changes occur in the immediate binding interface region, where approximately one out of five ionizable residues experiences substantial pK change regardless of the ligand type. However, the physical origins of the change differ between the types: in protein-nucleic acid complexes, the pK values of interface residues are predominantly affected by electrostatic effects, whereas in protein-protein and protein-small molecule complexes, structural changes due to the induced-fit effect play an equally important role. In protein-protein and protein-nucleic acid complexes, there is a statistically significant number of substantial pK perturbations, mostly due to the induced-fit structural changes, in regions far from the binding interface.     

AutoDockFR: Advances in Protein-Ligand Docking with Explicitly Specified Binding Site Flexibility

Automated docking of drug-like molecules into receptors is an essential tool in structure-based drug design. While modeling receptor flexibility is important for correctly predicting ligand binding, it still remains challenging. This work focuses on an approach in which receptor flexibility is modeled by explicitly specifying a set of receptor side-chains a-priori. The challenges of this approach include the: 1) exponential growth of the search space, demanding more efficient search methods; and 2) increased number of false positives, calling for scoring functions tailored for flexible receptor docking. We present AutoDockFR–AutoDock for Flexible Receptors (ADFR), a new docking engine based on the AutoDock4 scoring function, which addresses the aforementioned challenges with a new Genetic Algorithm (GA) and customized scoring function. We validate ADFR using the Astex Diverse Set, demonstrating an increase in efficiency and reliability of its GA over the one implemented in AutoDock4. We demonstrate greatly increased success rates when cross-docking ligands into apo receptors that require side-chain conformational changes for ligand binding. These cross-docking experiments are based on two datasets: 1) SEQ17 –a receptor diversity set containing 17 pairs of apo-holo structures; and 2) CDK2 –a ligand diversity set composed of one CDK2 apo structure and 52 known bound inhibitors. We show that, when cross-docking ligands into the apo conformation of the receptors with up to 14 flexible side-chains, ADFR reports more correctly cross-docked ligands than AutoDock Vina on both datasets with solutions found for 70.6% vs. 35.3% systems on SEQ17, and 76.9% vs. 61.5% on CDK2. ADFR also outperforms AutoDock Vina in number of top ranking solutions on both datasets. Furthermore, we show that correctly docked CDK2 complexes re-create on average 79.8% of all pairwise atomic interactions between the ligand and moving receptor atoms in the holo complexes. Finally, we show that down-weighting the receptor internal energy improves the ranking of correctly docked poses and that runtime for AutoDockFR scales linearly when side-chain flexibility is added.     

Ion Channel Selectivity through Stepwise Changes in Binding Affinity

Voltage-gated Ca²⁺ channels select Ca²⁺ over competing, more abundant ions by means of a high affinity binding site in the pore. The maximum off rate from this site is ∼1,000× slower than observed Ca²⁺ current. Various theories that explain how high Ca²⁺ current can pass through such a sticky pore all assume that flux occurs from a condition in which the pore''s affinity for Ca²⁺ transiently decreases because of ion interactions. Here, we use rate theory calculations to demonstrate a different mechanism that requires no transient changes in affinity to quantitatively reproduce observed Ca²⁺ channel behavior. The model pore has a single high affinity Ca²⁺ binding site flanked by a low affinity site on either side; ions permeate in single file without repulsive interactions. The low affinity sites provide steps of potential energy that speed the exit of a Ca²⁺ ion off the selectivity site, just as potential energy steps accelerate other chemical reactions. The steps could be provided by weak binding in the nonselective vestibules that appear to be a general feature of ion channels, by specific protein structures in a long pore, or by stepwise rehydration of a permeating ion. The previous ion-interaction models and this stepwise permeation model demonstrate two general mechanisms, which might well work together, to simultaneously generate high flux and high selectivity in single file pores.     

Binding Specificity and Affinity of Acriflavine for Nucleic Acids

A set of conditions was developed for the specific binding of acriflavine to the DNA of intact squamous cells. This was achieved through a series of studies into the relative affinities for dye between DNA and various biopolymers by an agar gel diffusion technique. Specificity was ascertained by DNase and RNase treatment of the cells. The final conditions, based on an estimated DNA-to-dye ratio of 4:1, required a constant cell count of 100,000 and dye at a concentration of 0.0025 μg per ml in 10 ml of phosphate buffer, pH 6.0-7.4. These quantities were dictated by the sensitivity limitations of the analytical apparatus. To make use of standard fluorometric instrumentation, the whole cell population method for determining average values was followed. Free dye was analyzed after cell samples were stained, and the difference between this value and that of an aliquot of working dye was taken as the amount of bound dye. To ensure cell-free residues of dye, cells were removed by centrifugation through Teflon membrane filters. The average amount of dye which was bound to the DNA of normal squamous cells was 1.6 × 10^-7 μg (0.7 × 10^-15 mole) per cell, and the amount bound to HeLa cells was 2.3 × 10^-7 μg (1 × 10^-15 mole). These values were highly replicable, making it possible to use them as an expression of the DNA content of the cells. The mildness of the staining conditions, and the preservation of cellular integrity in this technique may permit quantitative measurements of the DNA content of living cells.     

Non-additivity of Functional Group Contributions in Protein-Ligand Binding: A Comprehensive Study by Crystallography and Isothermal Titration Calorimetry

Additivity of functional group contributions to protein-ligand binding is a very popular concept in medicinal chemistry as the basis of rational design and optimized lead structures. Most of the currently applied scoring functions for docking build on such additivity models. Even though the limitation of this concept is well known, case studies examining in detail why additivity fails at the molecular level are still very scarce. The present study shows, by use of crystal structure analysis and isothermal titration calorimetry for a congeneric series of thrombin inhibitors, that extensive cooperative effects between hydrophobic contacts and hydrogen bond formation are intimately coupled via dynamic properties of the formed complexes. The formation of optimal lipophilic contacts with the surface of the thrombin S3 pocket and the full desolvation of this pocket can conflict with the formation of an optimal hydrogen bond between ligand and protein. The mutual contributions of the competing interactions depend on the size of the ligand hydrophobic substituent and influence the residual mobility of ligand portions at the binding site. Analysis of the individual crystal structures and factorizing the free energy into enthalpy and entropy demonstrates that binding affinity of the ligands results from a mixture of enthalpic contributions from hydrogen bonding and hydrophobic contacts, and entropic considerations involving an increasing loss of residual mobility of the bound ligands. This complex picture of mutually competing and partially compensating enthalpic and entropic effects determines the non-additivity of free energy contributions to ligand binding at the molecular level.     

Engineering of Bispecific Affinity Proteins with High Affinity for ERBB2 and Adaptable Binding to Albumin

The epidermal growth factor receptor 2, ERBB2, is a well-validated target for cancer diagnostics and therapy. Recent studies suggest that the over-expression of this receptor in various cancers might also be exploited for antibody-based payload delivery, e.g. antibody drug conjugates. In such strategies, the full-length antibody format is probably not required for therapeutic effect and smaller tumor-specific affinity proteins might be an alternative. However, small proteins and peptides generally suffer from fast excretion through the kidneys, and thereby require frequent administration in order to maintain a therapeutic concentration. In an attempt aimed at combining ERBB2-targeting with antibody-like pharmacokinetic properties in a small protein format, we have engineered bispecific ERBB2-binding proteins that are based on a small albumin-binding domain. Phage display selection against ERBB2 was used for identification of a lead candidate, followed by affinity maturation using second-generation libraries. Cell surface display and flow-cytometric sorting allowed stringent selection of top candidates from pools pre-enriched by phage display. Several affinity-matured molecules were shown to bind human ERBB2 with sub-nanomolar affinity while retaining the interaction with human serum albumin. Moreover, parallel selections against ERBB2 in the presence of human serum albumin identified several amino acid substitutions that dramatically modulate the albumin affinity, which could provide a convenient means to control the pharmacokinetics. The new affinity proteins competed for ERBB2-binding with the monoclonal antibody trastuzumab and recognized the native receptor on a human cancer cell line. Hence, high affinity tumor targeting and tunable albumin binding were combined in one small adaptable protein.     

High Affinity Binding of Indium and Ruthenium Ions by Gastrins

The peptide hormone gastrin binds two ferric ions with high affinity, and iron binding is essential for the biological activity of non-amidated forms of the hormone. Since gastrins act as growth factors in gastrointestinal cancers, and as peptides labelled with Ga and In isotopes are increasingly used for cancer diagnosis, the ability of gastrins to bind other metal ions was investigated systematically by absorption spectroscopy. The coordination structures of the complexes were characterized by extended X-ray absorption fine structure (EXAFS) spectroscopy. Changes in the absorption of gastrin in the presence of increasing concentrations of Ga³⁺ were fitted by a 2 site model with dissociation constants (K_d) of 3.3 x 10⁻⁷ and 1.1 x 10⁻⁶ M. Although the absorption of gastrin did not change upon the addition of In³⁺ ions, the changes in absorbance on Fe³⁺ ion binding in the presence of indium ions were fitted by a 2 site model with K_d values for In³⁺ of 6.5 x 10⁻¹⁵ and 1.7 x 10⁻⁷ M. Similar results were obtained with Ru³⁺ ions, although the K_d values for Ru³⁺ of 2.6 x 10⁻¹³ and 1.2 x 10⁻⁵ M were slightly larger than observed for In³⁺. The structures determined by EXAFS all had metal:gastrin stoichiometries of 2:1 but, while the metal ions in the Fe, Ga and In complexes were bridged by a carboxylate and an oxygen with a metal-metal separation of 3.0–3.3 Å, the Ru complex clearly demonstrated a short range Ru—Ru separation, which was significantly shorter, at 2.4 Å, indicative of a metal-metal bond. We conclude that gastrin selectively binds two In³⁺ or Ru³⁺ ions, and that the affinity of the first site for In³⁺ or Ru³⁺ ions is higher than for ferric ions. Some of the metal ion-gastrin complexes may be useful for cancer diagnosis and therapy.     

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy methods.