On the nature of the multivalency effect: a thermodynamic model

A quantitative model is proposed for the analysis of the thermodynamic parameters of multivalent interactions in dilute solutions or with immobilized multimeric receptor. The model takes into account all bound species and describes multivalent binding via two microscopic binding energies corresponding to inter- and intramolecular interactions (Delta G(o)inter and Delta G(o)intra), the relative contributions of which depend on the distribution of complexes with different numbers of occupied binding sites. The third component of the overall free energy, which we call the "avidity entropy" term, is a function of the degeneracy of bound states, Omega(i), which is calculated on the basis of the topology of interaction and the distribution of all bound species. This term grows rapidly with the number of receptor sites and ligand multivalency, it always favors binding, and explains why multivalency can overcome the loss of conformational entropy when ligands displayed at the ends of long tethers are bound. The microscopic parameters and may be determined from the observed binding energies for a set of oligovalent ligands by nonlinear fitting with the theoretical model. Here binding data obtained from two series of oligovalent carbohydrate inhibitors for Shiga-like toxins were used to verify the theory. The decavalent and octavalent inhibitors exhibit subnanomolar activity and are the most active soluble inhibitors yet seen that block Shiga-like toxin binding to its native receptor. The theory developed here in conjunction with our protocol for the optimization of tether length provides a predictive approach to design and maximize the avidity of multivalent ligands.     

Nonspanning bivalent ligands as improved surface receptor binding inhibitors of the cholera toxin B pentamer

A series of bivalent ligands of varying length were synthesized to inhibit the receptor-binding process of cholera toxin. Competitive surface receptor binding assays showed that significant potency gains relative to the constituent monovalent ligands were achieved independently from the ability of the extended bivalent ligands to span binding sites within the toxin pentamer. Several models that could account for the unexpected improvement in IC(50) values are examined, taking into account crystallographic analysis of each ligand in complex with the toxin pentamer. Evidence is presented that steric blocking at the receptor binding surface may play a role. The results of our study suggest that the use of relatively short, "nonspanning" bivalent ligands, or monovalent ligands of similar topology and bulk may be an effective way of blocking the interaction of multimeric proteins with their cell surface receptors.     

Multivalency effects in protein--carbohydrate interaction: the binding of the Shiga-like toxin 1 binding subunit to multivalent C-linked glycopeptides

A series of monovalent and bivalent glycopeptides displaying a C-linked analogue of the Pk trisaccharide, the in vivo ligand for the pentavalent Shiga-like toxin binding subunit (SLT-1B), were prepared and evaluated as ligands for SLT-1B by isothermal titration microcalorimetry and competitive enzyme-linked immunosorbent assay (ELISA). Although none of the monovalent ligands showed any enhancement in affinity compared to O-methyl glycoside, two bivalent ligands show significant enhancements in affinity in assays. This observation represents the first calorimetric observation of an enhancement in affinity for this system. In contrast, only one of the two ligands shows an enhancement in the competitive ELISA. Together, these data signal a difference in the means by which the two ligands achieve affinity, apparently triggered by a change in the nature of the linker domain. These results provide a rationalization for apparently contradictory reports from the recent literature and again emphasize the importance of investigating complex binding phenomena by multiple techniques.     

A computational analysis of the binding model of MDM2 with inhibitors

Abstract  

It is a new and promising strategy for anticancer drug design to block the MDM2-p53 interaction using a non-peptide small-molecule inhibitor. We carry out molecular dynamics simulations to study the binding of a set of six non-peptide small-molecule inhibitors with the MDM2. The relative binding free energies calculated using molecular mechanics Poisson–Boltzmann surface area method produce a good correlation with experimentally determined results. The study shows that the van der Waals energies are the largest component of the binding free energy for each complex, which indicates that the affinities of these inhibitors for MDM2 are dominated by shape complementarity. The A-ligands and the B-ligands are the same except for the conformation of 2,2-dimethylbutane group. The quantum mechanics and the binding free energies calculation also show the B-ligands are the more possible conformation of ligands. Detailed binding free energies between inhibitors and individual protein residues are calculated to provide insights into the inhibitor-protein binding model through interpretation of the structural and energetic results from the simulations. The study shows that G1, G2 and G3 group mimic the Phe19, Trp23 and Leu26 residues in p53 and their interactions with MDM2, but the binding model of G4 group differs from the original design strategy to mimic Leu22 residue in p53.     

Large-scale millisecond intersubunit dynamics in the B subunit homopentamer of the toxin derived from Escherichia coli O157

We report here solution NMR relaxation measurements that show millisecond time-scale intersubunit dynamics in the homopentameric B subunit (VTB) of the toxin derived from Escherichia coli O157. These data are consistent with interconversion between an axially symmetric form and a low-abundance ( approximately 10%, 45 degrees C) higher energy form. The higher energy state is depopulated on binding of a novel bivalent analogue (P(k) dimer) of the natural carbohydrate acceptor globotriaosylceramide. The isothermal titration calorimetry isotherm for the binding of P(k) dimer to VTB is consistent with a five-site sequential binding model which assumes that cooperative effects arise through communication only between neighboring binding sites. The resulting thermodynamic parameters (K(a1) = 114 +/- 2.2 M(-1), K(a2) = 283 +/- 4.5 M(-1), DeltaH(1) degrees = -116.3 +/- 0.55 kJ/mol, and DeltaH(2) degrees = -50.3 +/- 0.11 kJ/mol) indicate favorable entropic cooperativity that has not previously been observed in multivalent systems.     

Photoswitchable multivalent sugar ligands: synthesis, isomerization, and lectin binding studies of azobenzene-glycopyranoside derivatives

Coating of azobenzene chromophore with multivalent sugar ligands has been accomplished. Such sugar coating allows the study of the isomerization properties of this chromophore in aqueous solutions. The predominantly cis-isomer-containing photostationary state (PS) mixture of these azobenzene derivatives is found to be stable for hours. The rate constants for their isomerization, as well as the Arrhenius activation energies, are determined experimentally. An assessment of the lectin binding properties of the lactoside bearing isomeric azobenzene derivatives, by isothermal calorimetric methods, reveals the existence of an unusual cooperativity in their binding to lectin peanut agglutinin. Thermodynamic parameters evaluated for the trans and the PS mixture are discussed, in detail, for the lactoside bearing bivalent azobenzene derivative.     

Grand canonical Monte Carlo simulation of ligand-protein binding

A new application of the grand canonical thermodynamics ensemble to compute ligand-protein binding is described. The described method is sufficiently rapid that it is practical to compute ligand-protein binding free energies for a large number of poses over the entire protein surface, thus identifying multiple putative ligand binding sites. In addition, the method computes binding free energies for a large number of poses. The method is demonstrated by the simulation of two protein-ligand systems, thermolysin and T4 lysozyme, for which there is extensive thermodynamic and crystallographic data for the binding of small, rigid ligands. These low-molecular-weight ligands correspond to the molecular fragments used in computational fragment-based drug design. The simulations correctly identified the experimental binding poses and rank ordered the affinities of ligands in each of these systems.     

A model of the human M2 muscarinic acetylcholine receptor

The M₂ muscarinic acetylcholine receptor belongs to the family of rhodopsin like G-Protein Coupled Receptors. This subtype of muscarinic receptors is of special interest because it bears, aside from an orthosteric binding site, also an allosteric binding site. Based on the X-ray structure of bovine rhodopsin a complete homology model of the human M₂ receptor was developed. For the orthosteric binding site point mutations and binding studies with different agonists and antagonists are available. This knowledge was utilized for an initial verification of the M₂ model. Allosteric modulation of activity is mediated by structurally different ligands such as gallamine, caracurine V salts or W84 (a hexamethonium-derivative). Caracurine V derivatives with different affinities to M₂ were docked using GRID-fields. Subsequent molecular dynamics simulations yielded different binding energies based on diverse electrostatic and lipophilic interactions. The calculated affinities are in good agreement to experimentally determined affinities.     

Classification of water molecules in protein binding sites

Water molecules play a crucial role in mediating the interaction between a ligand and a macromolecular receptor. An understanding of the nature and role of each water molecule in the active site of a protein could greatly increase the efficiency of rational drug design approaches: if the propensity of a water molecule for displacement can be determined, then synthetic effort may be most profitably applied to the design of specific ligands with the displacement of this water molecule in mind. In this paper, a thermodynamic analysis of water molecules in the binding sites of six proteins, each complexed with a number of inhibitors, is presented. Two classes of water molecules were identified: those conserved and not displaced by any of the ligands, and those that are displaced by some ligands. The absolute binding free energies of 54 water molecules were calculated using the double decoupling method, with replica exchange thermodynamic integration in Monte Carlo simulations. It was found that conserved water molecules are on average more tightly bound than displaced water molecules. In addition, Bayesian statistics is used to calculate the probability that a particular water molecule may be displaced by an appropriately designed ligand, given the calculated binding free energy of the water molecule. This approach therefore allows the numerical assessment of whether or not a given water molecule should be targeted for displacement as part of a rational drug design strategy.     

Accurate predictions of nonpolar solvation free energies require explicit consideration of binding-site hydration

Continuum solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the nonpolar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz., the polarized continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate nonpolar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though the simulations and experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure because they lack a microscopic picture of binding-site hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuum solvation methods by adding information about the solvent exposure of the binding site or the hydration of the binding site, and the results are promising at least for this small set of complexes.     

Solid-phase synthesis for the identification of high-affinity bivalent lectin ligands

The development of carbohydrate-based therapeutics has been frustrated by the low affinities that characterize protein-carbohydrate complexation. Because of the oligomeric nature of most lectins, the use of multivalency may offer a successful strategy for the creation of high-affinity ligands. The solid-phase evaluation of libraries of peptide-linked multivalent ligands facilitates rapid examination of a large fraction of linker structure space. If such solid-phase assays are to replicate solution binding behavior, the potential for intermolecular bivalent binding on bead surfaces must be eliminated. Here we report the solid-phase synthesis and analysis of peptide-linked, spatially segregated mono- and bivalent ligands for the legume lectin concanavalin A. Bead shaving protocols were used for the creation of beads displaying spatially segregated binding sequences on the surface of Tentagel resins. The same ligands were also synthesized on PEGA resin to determine the effect of ligand presentation on solid-phase binding. While we set out to determine the lower limit of assay sensitivity, the unexpected observation that intermolecular bivalent ligand binding is enhanced for bivalent ligands relative to monovalent ligands allowed direct observation of the level of surface blocking required to prevent intermolecular bivalent ligand binding. For a protein with binding sites separated by 65 A, approximately 99.9% of Tentagel(1) surface sites and 99.99% of the total sites on a PEGA bead must be blocked to prevent intermolecular bivalent binding. We also report agglutination and calorimetric solution-phase binding studies of mono- and bivalent peptide-linked ligands.     

Dissecting the thermodynamics and cooperativity of ligand binding in cytochrome P450eryF

Conformational flexibility and cooperativity in ligand recognition are two key aspects of the catalytic diversity of cytochrome P450 enzymes. In this study, we dissect the ligand binding stoichiometry and energetics of the soluble bacterial P450eryF by isothermal titration calorimetry (ITC) using three allosteric and two non-allosteric ligands of diverse chemistry. Complementary spectral binding studies and sequential, two-ligand docking simulations were performed to help assign the binding sites. Binding of 4-phenylpyridine (4-PP) or 4-(4-chlorophenyl)imidazole (4-CPI) showed 1:1 stoichiometry in ITC, consistent with the lack of cooperativity observed in spectral binding studies. The larger ligands 9-aminophenanthrene (9-AP), 1-pyrenebutanol (1-PB), and alpha-naphthoflavone (ANF) show cooperative spectral binding and yielded 2:1 stoichiometry. The associated thermodynamic parameters for the sites were calculated using a sequential binding mechanism. The binding constant (KD) for the first site was almost two times lower than that of the second site for all three compounds. Ligand binding at site 1 was entropically favored, whereas binding at site 2 was weak and entropically unfavorable. Simulations showed that two molecules of 9-AP, ANF or 1-PB can be adequately docked to two individual sub-sites within a large binding pocket. The absence of hydrophobic tethering and ligand stacking are consistent with the single low affinity binding site observed for 4-CPI and 4-PP. Competitive binding studies with P450eryF preloaded with either 1-PB or ANF showed a decrease in the affinities for 9-AP at both the sites, with large entropy-enthalpy compensation, indicating the ability of the binding pocket to accommodate two ligands of diverse chemistry and enable cooperativity.     

Towards a rational spacer design for bivalent inhibition of estrogen receptor

Estrogen receptors are known drug targets that have been linked to several kinds of cancer. The structure of the estrogen receptor ligand binding domain is available and reveals a homodimeric layout. In order to improve the binding affinity of known estrogen receptor inhibitors, bivalent compounds have been developed that consist of two individual ligands linked by flexible tethers serving as spacers. So far, binding affinities of the bivalent compounds do not surpass their monovalent counterparts. In this article, we focus our attention on the molecular spacers that are used to connect the individual ligands to form bivalent compounds, and describe their thermodynamic contribution during the ligand binding process. We use computational methods to predict structural and entropic parameters of different spacer structures. We find that flexible spacers introduce a number of effects that may interfere with ligand binding and possibly can be connected to the low binding affinities that have been reported in binding assays. Based on these findings, we try to provide guidelines for the design of novel molecular spacers.     

Fluorescence Anisotropy Assays Reveal Affinities of C- and O-Glycosides for Concanavalin A(1)

The free energies of binding of various C- and O-glycosides to the lectin concanavalin A were measured using fluorescence anisotropy. Fluorescein derivatives of mannose and glucose were synthesized and were shown to bind to concanavalin A with free energies of -5.1 and -4.3 kcal mol(-)(1), respectively. Competition experiments were performed to determine the binding energies of different nonfluorescent carbohydrates, and the results were in excellent agreement with the binding energies determined by microcalorimetry. The minimum carbohydrate epitope that fills the lectin carbohydrate binding site, methyl 3,6-di-O-(alpha-mannopyranosyl)-alpha-mannopyranoside, competes directly for the site with the fluorescent ligands, indicating that the fluorescent ligands bind specifically. The binding affinities of C-glycosides to concanavalin A were compared with those of O-glycosides. The free energies of binding for corresponding C- and O-glycosides differed by less than 0.5 kcal mol(-)(1), indicating that recognition properties of C- and O-glycosides are very similar. It was found that for some ligands the use of a carbon linkage rather than an oxygen linkage caused the specificity of binding to decrease slightly.     

Relative energies of binding for antibody-carbohydrate-antigen complexes computed from free-energy simulations

Free-energy perturbation (FEP) simulations have been applied to a series of analogues of the natural trisaccharide epitope of Salmonella serotype B bound to a fragment of the monoclonal anti-Salmonella antibody Se155-4. This system was selected in order to assess the ability of free-energy perturbation (FEP) simulations to predict carbohydrate-protein interaction energies. The ultimate goal is to use FEP simulations to aid in the design of synthetic high affinity ligands for carbohydrate-binding proteins. The molecular dynamics (MD) simulations were performed in the explicit presence of water molecules, at room temperature. The AMBER force field, with the GLYCAM parameter set for oligosaccharides, was employed. In contrast to many modeling protocols, FEP simulations are capable of including the effects of entropy, arising from differential ligand flexibilities and solvation properties. The experimental binding affinities are all close in value, resulting in small relative free energies of binding. Many of the DeltaDeltaG values are on the order of 0-1 kcal mol(-1), making their accurate calculation particularly challenging. The simulations were shown to reasonably reproduce the known geometries of the ligands and the ligand-protein complexes. A model for the conformational behavior of the unbound antigen is proposed that is consistent with the reported NMR data. The best agreement with experiment was obtained when histidine 97H was treated as fully protonated, for which the relative binding energies were predicted to well within 1 kcal mol(-1). To our knowledge this is the first report of FEP simulations applied to an oligosaccharide-protein complex.     

Calculation of binding free energies of inhibitors to plasmepsin II

An understanding at the atomic level of the driving forces of inhibitor binding to the protein plasmepsin (PM) II would be of interest to the development of drugs against malaria. To this end, three state of the art computational techniques to compute relative free energies-thermodynamic integration (TI), Hamiltonian replica-exchange (H-RE) TI, and comparison of bound versus unbound ligand energy and entropy-were applied to a protein-ligand system of PM II and several exo-3-amino-7-azabicyclo[2.2.1]heptanes and the resulting relative free energies were compared with values derived from experimental IC(50) values. For this large and flexible protein-ligand system, the simulations could not properly sample the relevant parts of the conformational space of the bound ligand, resulting in failure to reproduce the experimental data. Yet, the use of Hamiltonian replica exchange in conjunction with thermodynamic integration resulted in enhanced convergence and computational efficiency compared to standard thermodynamic integration calculations. The more approximate method of calculating only energetic and entropic contributions of the ligand in its bound and unbound states from conventional molecular dynamics (MD) simulations reproduced the major trends in the experimental binding free energies, which could be rationalized in terms of energetic and entropic characteristics of the different structural and physico-chemical properties of the protein and ligands.     

Force-induced de-adhesion of specifically bound vesicles: strong adhesion in competition with tether extraction

A theoretical study of the thermodynamic equilibrium between force-induced tether formation and the adhesion of vesicles mediated by specific ligand-receptor interactions has been performed. The formation of bonds between mobile ligands in the vesicle and immobile receptors on the substrate is examined within a thermodynamic approximation. The shape of a vesicle pulled with a point force is calculated within a continuous approach. The two approaches are merged self-consistently by the use of the effective adhesion potential produced by the collective action of the bonds. As a result, the shapes of the vesicle and the tether, as well as the number of formed bonds in the contact zone, are determined as a function of the force, and approximate analytic expressions for them are provided. The de-adhesion process is characterized by the construction of a phase diagram that is a function of the density of the ligands in the vesicle, the surface coverage by receptors, the ligand-receptor binding affinity, and the reduced volume of the vesicle. In all cases, the phase diagram contains three regions separated by two nonintersecting lines of critical forces. The first is the line of onset forces associated with a second-order shape transition from a spherical cap to a tethered vesicle. The second line is attributed to the detachment forces at which a first-order unbinding transition from a tethered shape to a free vesicle occurs.     

Converging free energies of binding in cucurbit[7]uril and octa-acid host–guest systems from SAMPL4 using expanded ensemble simulations

Molecular containers such as cucurbit[7]uril (CB7) and the octa-acid (OA) host are ideal simplified model test systems for optimizing and analyzing methods for computing free energies of binding intended for use with biologically relevant protein–ligand complexes. To this end, we have performed initially blind free energy calculations to determine the free energies of binding for ligands of both the CB7 and OA hosts. A subset of the selected guest molecules were those included in the SAMPL4 prediction challenge. Using expanded ensemble simulations in the dimension of coupling host–guest intermolecular interactions, we are able to show that our estimates in most cases can be demonstrated to fully converge and that the errors in our estimates are due almost entirely to the assigned force field parameters and the choice of environmental conditions used to model experiment. We confirm the convergence through the use of alternative simulation methodologies and thermodynamic pathways, analyzing sampled conformations, and directly observing changes of the free energy with respect to simulation time. Our results demonstrate the benefits of enhanced sampling of multiple local free energy minima made possible by the use of expanded ensemble molecular dynamics and may indicate the presence of significant problems with current transferable force fields for organic molecules when used for calculating binding affinities, especially in non-protein chemistries.     

Can the calculation of ligand binding free energies be improved with continuum solvent electrostatics and an ideal‐gas entropy correction?

The prediction of a ligand binding constant requires generating three-dimensional structures of the complex concerned and reliably scoring these structures. Here, the scoring problem is investigated by examining benzamidine-like inhibitors of trypsin, a system for which errors in the structures are small. Precise and consistent binding free energies for the inhibitors are determined experimentally for this test system. To examine possible improvement of scoring methods, we test the suitability of continuum electrostatics to account for solvation effects and use an ideal-gas entropy correction to account for the changes in the degrees of freedom of the ligand. The small observed root-mean-square deviation of 0.55 kcal/mol of the calculated relative to the experimental values indicates that the essentials of the binding process have been captured. Even though all six ligands make the same salt bridge and H-bonds to the protein, the electrostatic contribution varies among the ligands by as much as 2 kcal/mol. Moreover, although the ligands are rigid and similar in size, the entropic terms also significantly affect the relative binding affinities (by up to 2.7 kcal/mol). The present approach to solvation and entropy may allow the ranking of the ligands to be considerably improved at a cost that makes the method applicable to the optimization of lead compounds or to the screening of small collections of ligands.     

Studying how different terminal groups change the motion of H2NSO2C6H4CONH(EG)3R when bound to the active site of human carbonic anhydrase II

Molecular dynamics simulations have been used to explore the motions of series of ligands containing coupled benzenesulfonamide and oligoethylene glycol moieties (H2NSO2C6H4CONH(CH2-CH2OCH2CH2OCH2CH2)R+; R+ = NH3+, NHCOCH2NH3+, NHCOCH(CH2Ph)NH3+) bound at the active site of human carbonic anhydrase II (HCAII; E.C. 4.2.1.1). These complexes have been examined previously by X-ray crystallography; the locations of the terminal groups of these ligands were not defined in the crystal structures. These stimulations, carried out in the presence of water, provide dynamic information about the motion of the bound ligand that supplements the quasistatic information from crystallography. Our results suggested that the Gly and Phe groups of these ligands interacted weakly with the protein adjacent to the active site. Quantitative estimates of energies of binding did not correlate usefully with observed free energies of binding, but in the absence of information about entropies, it is not possible to tell if the lack of correlation between calculated energies and observed free energies represents inaccuracies in the energies, or a compensation between enthalpies and entropies. When the terminal Phe group was placed near a previously identified hydrophobic patch in the active site (Phe20 and Pro202) the average conformation of the ligand inferred from this simulation was inconsistent with that from the crystal structure; this result illustrates the problems of misleading local minima in these types of simulations.