Free-energy relationships in ion channels activated by voltage and ligand

Many ion channels are modulated by multiple stimuli, which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part because of the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained by measuring the charge-voltage (Q-V) relationship in zero ligand condition and the ligand binding curve at highly depolarizing membrane voltages. Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the Q-V curves at multiple ligand concentrations. When a single reference ligand binding curve is available, this relationship allows us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the Q-V curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand- and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in a polymodal ion channel.     

On the importance of van der Waals interaction in the groove binding of DNA with ligands: restrained molecular dynamics study

Comparison of interaction energy between an oligonucleotide and a DNA-binding ligand in the minor and major groove modes was made by use of restrained molecular dynamics. Distortion in DNA was found for the major groove mode whereas less significant changes for both ligand and DNA were detected for the minor groove binding after molecular dynamics simulation. The conformation of the ligand obtained from the major groove mode resembles that computed with the ligand soaked in water. The van der Waals contact energy was found to be as significant as electrostatic energy and more important for difference in binding energy between these two binding modes. The importance of van der Waals force in groove binding was supported by computations on the complex formed by the repressor peptide fragment from the bacteriophage 434 and its operator oligonucleotide.     

Co-operative ligand binding in a protein composed of subunits

The mechanism of the co-operative ligand binding in a protein composed of subunits is studied on a realistic assumption that the strain energy due to the ligand binding is stored in weak contacts between the subunits. In a pair of subunits, which is the minimum co-operative unit, two competitive mechanisms operate; the expansion or contraction of the weak contacts results in negative co-operativity, and positive co-operativity can be produced by the alternation of the contacts.Emphasizing the above role of the weak contacts, and taking into account the widespread interaction which correlates the alternation of the contacts in one interface of subunits with that in another interface, we construct a general partition function to describe the co-operative effects in proteins composed of more than two subunits. The partition function thus obtained includes those of the two allosteric models (Monod, Wyman & Changeux, 1965; Koshland, Nemethy & Filmer, 1966) in the two extreme cases of the strength of the widespread interaction.The partition function is applied to the analysis of the molecular mechanism of heme-heme interaction by the curve fitting to the experimental data for hemoglobin solution under various conditions. The comparison of the parameter values thus determined with the molecular structure leads us to one interpretation that the widespread interaction originates from contact connecting three subunits. This interpretation suggests that the strength of the widespread interaction can be changed by modification of an amino acid residue in the intermediate subunit, and that this interaction plays an essential role in the manifestation of the co-operativity. The reduced co-operativity in mutant hemoglobins can also be explained along these lines.     

Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.     

The concentration dependence of active K+ transport in the turkey erythrocyte. Hill analysis and evidence for positive cooperativity between ion binding sites

A mathematical model is presented which describes the theoretical relationship between ligand concentration and physiological response for systems in which the response is dependent upon simultaneous occupancy of two receptor ligand-binding sites. The treatment considers both the possibility of intrinsic differences between the binding sites with regard to ligand affinity, as well as the possibility of mutually induced changes in affinity resulting from allosteric interactions. Unlike the Monod-Wyman-Changeux formulation for allosteric enzymes, the general model put forward here makes double occupancy an absolute requirement for enzymatic function. It is shown that such a model leads to the prediction of a curvilinear Hill plot from which one can obtain an explicit estimate of the degree of allosteric interaction between the two ligand binding sites as well as the Gibbs standard free energy change for the overall binding reaction. It is then shown that, in the specific instance of Na, K-ATPase-mediated K+ transport by the turkey erythrocyte, the configuration of the Hill curve describing the rate of ouabain-sensitive K+ transport as a function of external K+ concentration conforms closely to that predicted by the model described above. The results are of particular interest because they indicate a strongly cooperative interaction between the two K+ binding sites on the transport protein such that occupancy of one site results in an enhancement of the affinity of the other site for K+ by a minimum of 15- to 20-fold. Finally, we consider in detail a model of the Monod-Wyman- Changeux type in which, by contrast, both singly and doubly occupied forms of the enzyme are assumed to be catalytically active, and which we analogously extend to allow for the possibility of asymmetry between the two ligand binding sites. Although it is shown that the two models can not be differentiated from each other in the present experimental system, they yield virtually identical estimates for the degree of positive cooperativity between the two K+ binding sites.     

Ligand-dependent aggregation and cooperativity: a critique

Ligand-dependent site-site (or subunit-subunit) interactions provide the basis for explaining cooperativity in chemical reactions. Even in the simplest possible nonaggregating system, interpretation of the interactions in terms of structural details requires an explicit assumption (or model) for the binding of the ligand to the sites when there are no interactions. This paper develops in detail the processes by which aggregation will yield ligand-dependent cooperativity. Two conceptually distinct free energy differences may contribute to cooperativity in an aggregation reaction. One is the free energy difference in ligand binding between the monomer and the aggregate. The other is derived from ligand-dependent interactions between the sites of the aggregate. In this analysis an explicit distinction is made between the experimentally accessible constants and those derived from assumed models. Experimental measurements of an aggregation cycle in which all of the species in equilibrium are defined do not allow for an evaluation of the energies of interaction without some model (or assumption). In the analysis presented, an explicit assumption is employed relating the constant for binding of the ligand to the isolated monomer and the constant for the binding of the ligand to aggregate under conditions where there are no ligand-dependent interactions.     

On the theory of noncovalent binding

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.     

Free energy coupling within macromolecules. The chemical work of ligand binding at the individual sites in co-operative systems

Individual-site binding curves such as those obtainable from techniques of DNase footprinting or nuclear magnetic resonance spectroscopy can be used to monitor structurally localized events within biopolymers. This paper discusses thermodynamic aspects of individual-site ligand binding for co-operative systems where the binding of ligand at a local site is coupled to binding of the same ligand species at other sites within the macromolecule. Individual-site binding isotherms have the following properties. (1) They provide a direct indication of the role played by the particular site in the overall binding reaction. (2) They can be used to determine the energetic contribution of loading the site regardless of the complexity of the system. (3) They can be used to resolve microscopic equilibrium constants and co-operativity constants in cases where the classical isotherm is incapable of such resolution. The microscopic constants bear a complex relation to the chemical work of loading each individual site. For a system with two interacting sites we derive analytical relationships between the individual-site loading energies and the microscopic constants. These relationships prescribe, for any values of the microscopic constants, how the co-operative energy is partitioned between events at the two sites. At fixed ligand activity the binding free energy can be estimated directly from an individual-site isotherm. This quantity, which is also a composite of the microscopic constants, provides a useful measure of site--site interaction. Several examples and applications are discussed for these properties of individual-site binding reactions.     

The role of backbone motions in ligand binding to the c-Src SH3 domain.

The Src homology 3 (SH3) domain of pp60(c-src) (Src) plays dual roles in signal transduction, through stabilizing the repressed form of the Src kinase and through mediating the formation of activated signaling complexes. Transition of the Src SH3 domain between a variety of binding partners during progression through the cell cycle requires adjustment of a delicate free energy balance. Although numerous structural and functional studies of SH3 have provided an in-depth understanding of structural determinants for binding, the origins of binding energy in SH3-ligand interactions are not fully understood. Considering only the protein-ligand interface, the observed favorable change in standard enthalpy (DeltaH=-9.1 kcal/mol) and unfavorable change in standard entropy (TDeltaS=-2.7 kcal/mol) upon binding the proline-rich ligand RLP2 (RALPPLPRY) are inconsistent with the predominantly hydrophobic interaction surface. To investigate possible origins of ligand binding energy, backbone dynamics of free and RLP2-bound SH3 were performed via (15)N NMR relaxation and hydrogen-deuterium (H/(2)H) exchange measurements. On the ps-ns time scale, assuming uncorrelated motions, ligand binding results in a significant reduction in backbone entropy (-1.5(+/-0.6) kcal/mol). Binding also suppresses motions on the micros-ms time scale, which may additionally contribute to an unfavorable change in entropy. A large increase in protection from H/(2)H exchange is observed upon ligand binding, providing evidence for entropy loss due to motions on longer time scales, and supporting the notion that stabilization of pre-existing conformations within a native state ensemble is a fundamental paradigm for ligand binding. Observed changes in motion on all three time scales occur at locations both near and remote from the protein-ligand interface. The propagation of ligand binding interactions across the SH3 domain has potential consequences in target selection through altering both free energy and geometry in intact Src, and suggests that looking beyond the protein-ligand interface is essential in understanding ligand binding energetics.     

Stacking interaction and its role in kynurenic acid binding to glutamate ionotropic receptors

Stacking interaction is known to play an important role in protein folding, enzyme-substrate and ligand-receptor complex formation. It has been shown to make a contribution into the aromatic antagonists binding with glutamate ionotropic receptors (iGluRs), in particular, the complex of NMDA receptor NR1 subunit with the kynurenic acid (KYNA) derivatives. The specificity of KYNA binding to the glutamate receptors subtypes might partially result from the differences in stacking interaction. We have calculated the optimal geometry and binding energy of KYNA dimers with the four types of aromatic amino acid residues in Rattus and Drosophila ionotropic iGluR subunits. All ab initio quantum chemical calculations were performed taking into account electron correlations at MP2 and MP4 perturbation theory levels. We have also investigated the potential energy surfaces (PES) of stacking and hydrogen bonds (HBs) within the receptor binding site and calculated the free energy of the ligand-receptor complex formation. The energy of stacking interaction depends both on the size of aromatic moieties and the electrostatic effects. The distribution of charges was shown to determine the geometry of polar aromatic ring dimers. Presumably, stacking interaction is important at the first stage of ligand binding when HBs are weak. The freedom of ligand movements and rotation within receptor site provides the precise tuning of the HBs pattern, while the incorrect stacking binding prohibits the ligand-receptor complex formation.     

Effects of heterogeneity and cooperativity on the forms of binding curves for multivalent ligands

An exploratory investigation is made of the binding behavior that is likely to be encountered with multivalent ligands under circumstances where a single intrinsic binding constant does not suffice to describe all acceptor-ligand interactions. Numerical simulations of theoretical binding behavior have established that current criteria for recognizing heterogeneity and cooperativity of acceptor sites on the basis of the deviation of the binding curve from rectangular hyperbolic form for univalent ligands also apply to the interpretation of the corresponding binding curves for multivalent ligands. However, for systems in which the source of the departure from equivalence and independence of binding sites resides in the ligand, these criteria are reversed. On the basis of these observations a case is then made for attributing results of an experimental binding study of the interaction between pyruvate kinase and muscle myofibrils to positive cooperativity of enzyme sites rather than to heterogeneity or negative cooperativity of the myofibrillar sites.     

Probing the interaction mechanism of small molecule inhibitors with matriptase based on molecular dynamics simulation and free energy calculations

Matriptase is a serine protease associated with a wide variety of human tumors and carcinoma progression. Up to now, many promising anti-cancer drugs have been developed. However, the detailed structure–function relationship between inhibitors and matriptase remains elusive. In this work, molecular dynamics simulation and binding free energy studies were performed to investigate the biochemistry behaviors of two class inhibitors binding to matriptase. The binding free energies predicted by MM/GBSA methods are in good agreement with the experimental bioactivities, and the analysis of the individual energy terms suggests that the van der Waals interaction is the major driving force for ligand binding. The key residues responsible for achieving strong binding have been identified by the MM/GBSA free energy decomposition analysis. Especially, Trp215 and Phe99 had an important impact on active site architecture and ligand binding. The results clearly identify the two class inhibitors exist different binding modes. Through summarizing the two different modes, we have mastered some important and favorable interaction patterns between matriptase and inhibitors. Our findings would be helpful for understanding the interaction mechanism between the inhibitor and matriptase and afford important guidance for the rational design of potent matriptase inhibitors.     

Interaction of monoclonal anti-peptide antibodies with lysozyme

The interaction of monoclonal anti-peptide antibodies with the free peptide and its protein counterpart has been evaluated for hen egg white lysozyme and the peptide constituting residues 38 to 45. Fluorescence methodology has been developed for the measurement of association constants based on resonance energy transfer between the excited tryptophan of antibody and bound peptide ligand conjugated to a fluorescent probe. Five antibodies, four IgM and one IgG, have been assayed by ELISA, and have demonstrated binding to the adsorbed peptide alone, to the adsorbed lysozyme alone, or to both. Multivalent interaction with the adsorbed ligand is a key factor in the efficacy of binding. Measurement of binding constants in homogeneous solution, by equilibrium dialysis and energy transfer, demonstrated that lysozyme was bound to an IgG antipeptide antibody with an association constant (4 X 10(2) M-1) 200-fold less than that for the free peptide (8 X 10(4) M-1). It was also inferred for IgM that an association constant of the order of 10(2) M-1 was sufficient to effect selective interaction in a system providing multivalent interaction. The shared conformations between protein and peptide, implied by the specific reactivity of the anti-peptide antibody with the protein, points to structural fluctuations of the surface regions and residues of globular proteins.     

Comparative molecular dynamics simulation analysis of G20 and C92 mutations in c-di-GMP I riboswitch and the wild type with docked c-di-GMP ligand

Riboswitch, a bacterial regulatory RNA consists of an aptamer (specific ligand binding unit) and an expression platform (gene expression modulation unit), which act as a potential drug target as it regulates critical genes. Therefore, it is of interest to glean information on the binding of c-di-GMP ligand to mutated conserved G20 and C92 residues of cyclic diguanosine monophosphate I (c-di-GMP I) riboswitch using molecular dynamics simulation. The result shows that the binding energy of wild/native type riboswitch-ligand complex (3IRW) is lower than the mutant complexes suggesting that the binding affinity for c-di-GMP ligand decreases in case of mutant riboswitches. The hydrogen bonding interactions analysis also showed a high number of hydrogen bonds formation in the wild type riboswitch-ligand complex as compared to the mutant complexes illustrating stronger interaction of ligand to wild type riboswitch than the mutants. The simulation result shows that the mutations affected riboswitch-ligand interactions. The residues G14, G21, C46, A47, and U92 were identified as the key residues which contributed effectively to the binding of c-di-GMP I riboswitch with the natural ligand.     

Insight into estrogenicity of phytoestrogens using in silico simulation

Phytoestrogens, including miroestrol and deoxymiroestrol, have the ability to act through competition with estrogen for binding to the estrogen receptor (ER). Here, we utilize manual ligand docking followed by molecular dynamics simulations and binding free energy calculations with the linear interaction energy method to predict the binding modes and the binding affinities of phytoestrogens on the ligand binding domain of ER (ERα-LBD). The calculations brought about the good correlation between the calculated binding free energy and the bioassays. Furthermore, consideration of Lennard-Jones and Coulomb interaction energies of miroestrol and deoxymiroestrol on ERα-LBD provided the information to develop the phytoestrogen derivatives as the preferred drug for ER positive breast cancer treatment.     

Analysis of ligand binding curves in terms of species fractions

The ligand binding curve for a macromolecular system presents the average number or ligand molecules bound per macromolecule as a function of the chemical potential or the logarithm of the ligand concentration. We show that various observable properties of this curve, for example its asymptotes and derivatives, are expressible in terms of linear combinations of the mole fractions α_i of macromolecules binding i molecules of ligand. Whenever enough such properties of the binding curve are known, the linear equations in α_i can be solved to give the mole fractions of each of the various macromolecular species. An application of these results is that a Hill plot for hemoglobin-ligand equilibrium where the asymptotes approach unit slope can be made to yield the four Adair constants by a simple algebraic method. A second use is that a knowledge of the first and second derivatives of the binding curve at points along the curve can yield the species fractions as functions of the degree of saturation without direct knowledge of the ligand binding constants. These methods are illustrated by some numerical examples.     

Energetics of the cleft closing transition and the role of electrostatic interactions in conformational rearrangements of the glutamate receptor ligand binding domain

The ionotropic glutamate receptors are localized in the pre- and postsynaptic membrane of neurons in the brain. Activation by the principal excitatory neurotransmitter glutamate allows the ligand binding domain to change conformation, communicating opening of the channel for ion conduction. The free energy of the GluR2 S1S2 ligand binding domain (S1S2) closure transition was computed using a combination of thermodynamic integration and umbrella sampling modeling methods. A path that involves lowering the charge on E705 was chosen to clarify the role of this binding site residue. A continuum electrostatics approach in S1S2 is used to show E705, located in the ligand binding cleft, stabilizes the closed conformation of S1S2 via direct interactions with other protein residues, not through the ligand. In the closed conformation, in the absence of a ligand, S1S2 is somewhat more closed than what has been reported in X-ray structures. A semiopen conformation has been identified which is characterized by disruption of a single cross-cleft interaction and differs only slightly in energy from the fully closed S1S2. The fully open S1S2 conformation exhibits a wide energy well and shares structural similarity with the apo S1S2 crystal structure. Hybrid continuum electrostatics/MD calculations along the chosen closure transition pathway reveal solvation energies, and electrostatic interaction energies between two lobes of the protein increase the relative energetic difference between the open and closed conformational states. By analyzing the role of several cross-cleft contacts as well as other binding site residues, we demonstrate how S1S2 interactions facilitate formation of the closed conformation of the GluR2 ligand binding domain.     

Thermodynamic dissection of the binding energetics of proline-rich peptides to the Abl-SH3 domain: implications for rational ligand design

The inhibition of the interactions between SH3 domains and their targets is emerging as a promising therapeutic strategy. To date, rational design of potent ligands for these domains has been hindered by the lack of understanding of the origins of the binding energy. We present here a complete thermodynamic analysis of the binding energetics of the p41 proline-rich decapeptide (APSYSPPPPP) to the SH3 domain of the c-Abl oncogene. Isothermal titration calorimetry experiments have revealed a thermodynamic signature for this interaction (very favourable enthalpic contributions opposed by an unfavourable binding entropy) inconsistent with the highly hydrophobic nature of the p41 ligand and the Abl-SH3 binding site. Our structural and thermodynamic analyses have led us to the conclusion, having once ruled out any possible ionization events or conformational changes coupled to the association, that the establishment of a complex hydrogen-bond network mediated by water molecules buried at the binding interface is responsible for the observed thermodynamic behaviour. The origin of the binding energetics for proline-rich ligands to the Abl-SH3 domain is further investigated by a comparative calorimetric analysis of a set of p41-related ligands. The striking effects upon the enthalpic and entropic contributions provoked by conservative substitutions at solvent-exposed positions in the ligand confirm the complexity of the interaction. The implications of these results for rational ligand design are discussed.