A universal thermodynamic approach to analyze biomolecular binding experiments

Binding processes of any kind can be characterized as an association of a given ligand with some binding factor. This includes macromolecules as well as supramolecular aggregates such as micelles or membranes. The underlying molecular binding mechanism may be more or less complicated due to various intermediate steps (involving for instance conformational changes, aggregation, cooperativity, etc.). A sensible discussion of possible binding models naturally calls for a model-independent access to basic thermodynamic properties. The present contribution will demonstrate how this can quite generally be accomplished by a pertinent processing of properly selected experimental data. The method requires a series of titration measurements comprising the use of variable amounts of both the ligand and the binding factor. It leads to a linear mass conservation plot (i.e. amount of the ligand vs. a matching amount of the binding factor) whose slope and ordinate intercept are equal to the binding ratio (i.e. bound ligand per binding factor) and the free ligand concentration, respectively. This establishes the specific binding isotherm. The approach also reveals latent structurally determined features of the applied physical measuring signal. A number of examples including specific binding, unspecific adsorption and insertion in two-dimensional molecular films will illustrate the methodology.     

Dissociation kinetics of bivalent ligand-immunoglobulin E aggregates in solution

We study the dissociation of preformed bivalent ligand-bivalent receptor aggregates in solution, where the ligand is a symmetric bivalent hapten with two identical 2,4-dinitrophenyl (DNP) groups and the receptor is a fluorescein-labeled monoclonal anti-DNP IgE. We promote dissociation in two ways: by the addition of high concentrations of a monovalent hapten that competes for IgE binding sites with the bivalent hapten and by the addition of high concentrations of unlabeled IgE that binds almost all ligand binding sites that dissociate from labeled IgE. We investigate both theoretically and experimentally the two types of dissociation and find them to be quite different. Theory predicts that their kinetics will depend differently on the fundamental rate constants that characterize binding and aggregation. Using monovalent ligand to promote dissociation, we find that the fraction of labeled IgE sites bound to bivalent ligand decays with a slow and fast component. The fast decay corresponds to the dissociation of a singly bound DNP hapten. The interpretation of the slow decay depends on the detailed way in which ligand-receptor aggregates break up. We show that one possible explanation of these data is that small stable rings form before the addition of monovalent ligand. Other possible explanations are also presented.     

Relative ligand binding to small or large aggregates measured by scanning correlation spectroscopy.

Cell surface receptors transduce signals, required to produce cellular activity, that may be mediated by ligand-induced receptor aggregation. Several receptor systems exhibit both low and high ligand affinities and some models of receptor activation associate receptor clusters with high or low ligand binding affinity. In the present work succinyl concanavalin A, which binds with both high and low affinity to receptors, was studied on 3T3 Swiss mouse fibroblasts, where preaggregation of receptors has been postulated. Scanning fluorescence correlation spectroscopy measurements were used to determine the relationship between the degree of ligand binding and the state of receptor aggregation. Correlation analysis of fluorescence fluctuations across the cell surface reveal that the variance of the fluctuations (quantitated by g[0]) increased when the ligand concentration was varied from 0.33 to 67 mg/L. The g(0) values reached a plateau at concentrations greater than approximately 10 mg/L. These data are incompatible with homogeneous receptor distributions or equal affinity receptor binding but are compatible with a partly aggregated receptor system with high affinity binding to small aggregates, and low affinity binding to large aggregates. Computer simulated scanning fluorescence correlation spectroscopy experiments confirm that background fluorescence from the cell does not account for the experimentally observed effects.     

Monte Carlo Simulation of Buffered Diffusion into and out of a Model Synapse

Buffered diffusion occurs when ligands enter or leave a restricted space, such as a chemical synapse, containing a high density of binding sites. This study used Monte Carlo simulations to determine the time and spatial dependences of buffered diffusion without a priori assumptions about kinetics. The synapse was modeled as a box with receptors on one inner face. The exterior was clamped to some ligand concentration and ligands diffused through two sides. Onset and recovery simulations were carried out and the effects of receptor density, ligand properties and synapse geometry were investigated. This study determined equilibration times for binding and the spatial gradient of unliganded receptors. Onset was characterized by a high spatial gradient; equilibration was limited by the time needed for sufficient ligands to enter the synapse. Recovery showed a low spatial gradient with receptor equilibration limited by ligand rebinding. Decreasing ligand association rate or increasing ligand diffusion coefficient reduced the role of buffered diffusion and decreased the spatial gradient. Simulations with irreversible ligands showed larger, persistent spatial gradients. These simulations identify characteristics that can be used to test whether a synaptic process is governed by buffered diffusion. They also indicate that fundamental differences in synapse function may occur with irreversible ligands.     

Modeling Multivalent Ligand-Receptor Interactions with Steric Constraints on Configurations of Cell-Surface Receptor Aggregates

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcεRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.     

The Berg-Purcell Limit Revisited

Biological systems often have to measure extremely low concentrations of chemicals with high precision. When dealing with such small numbers of molecules, the inevitable randomness of physical transport processes and binding reactions will limit the precision with which measurements can be made. An important question is what the lower bound on the noise would be in such measurements. Using the theory of diffusion-influenced reactions, we derive an analytical expression for the precision of concentration estimates that are obtained by monitoring the state of a receptor to which a diffusing ligand can bind. The variance in the estimate consists of two terms, one resulting from the intrinsic binding kinetics and the other from the diffusive arrival of ligand at the receptor. The latter term is identical to the fundamental limit derived by Berg and Purcell (Biophys. J., 1977), but disagrees with a more recent expression by Bialek and Setayeshgar. Comparing the theoretical predictions against results from particle-based simulations confirms the accuracy of the resulting expression and reaffirms the fundamental limit established by Berg and Purcell.     

The Berg-Purcell Limit Revisited

Biological systems often have to measure extremely low concentrations of chemicals with high precision. When dealing with such small numbers of molecules, the inevitable randomness of physical transport processes and binding reactions will limit the precision with which measurements can be made. An important question is what the lower bound on the noise would be in such measurements. Using the theory of diffusion-influenced reactions, we derive an analytical expression for the precision of concentration estimates that are obtained by monitoring the state of a receptor to which a diffusing ligand can bind. The variance in the estimate consists of two terms, one resulting from the intrinsic binding kinetics and the other from the diffusive arrival of ligand at the receptor. The latter term is identical to the fundamental limit derived by Berg and Purcell (Biophys. J., 1977), but disagrees with a more recent expression by Bialek and Setayeshgar. Comparing the theoretical predictions against results from particle-based simulations confirms the accuracy of the resulting expression and reaffirms the fundamental limit established by Berg and Purcell.     

Effects of free and macromolecular-bound TXA2 receptor antagonist BM 1..505 on U46619-induced platelet aggregation

The goal of this study was to synthesize a macromolecular probe of the TXA₂ receptor antagonist BM13.505 which is unable to penetrate the platelet membrane for localization and characterization of the TXA₂ receptor. The active NHS-ester of BM13.505 was synthesized and purified. It was used for covalent coupling of BM13.505 to bovine serum albumin, a macromolecular carrier. Inhibitory effects of free and macromolecular bound BM13.505 on aggregatory properties of U46619-stimulated platelets were measured and compared to TXA₂ generation in platelets, as determined by TXB₂ radioimmuno assay. No inhibitory effects of free and macromolecular-bound BM13.505 on ADP- or thrombin-induced platelet aggregation were observed. Equimolar concentrations of free or macromolecular bound BM13.505 inhibited U46619-induced platelet aggregation and TXA₂ generation with equal potency. IC₅₀-values for platelet aggregation inhibition by free and macromolecular bound BM13.505 were 64 nM and 96 nM respectively. It appears that the TXA₂ receptor ligand binding site is located close to the outer membrane surface of platelets. Interaction of macromolecular bound BM13.505 with the platelet thromboxane receptor does not depend on the availability of the free carboxyl residue in BM13.505. The method for coupling a TXA₂ receptor antagonist to a macromolecule will aid in constructing probes for the localization and characterization of the TXA₂ receptor.     

Novel use of an osmolyte to dissect multiple thermodynamic linkages in a chemokine ligand-receptor system

We have used trimethylamine N-oxide (TMAO), a protecting osmolyte, to dissect the complex thermodynamic linkages involved in the interaction between the chemokine interleukin-8 (IL-8) and the N-domain of its receptor CXCR1. Our results show that TMAO induces folding in the CXCR1 receptor N-domain and that the N-domain upon folding binds ligand with higher affinity. This represents, to our knowledge, the smallest domain that has been shown to be folded in osmolyte. Using the phase diagram method to analyze this thermodynamic relationship graphically, we also observe that TMAO favors ligand dimerization and that the dimeric ligand binds the receptor domain with lower affinity. We have thus been able to dissect coupling among three distinct processes, receptor domain folding, ligand dimerization, and ligand-receptor domain binding in this chemokine-receptor system. We also observe that the affinity of the related chemokine, melanoma growth stimulatory activity (MGSA), increases concurrent with N-domain folding similar to IL-8 but shows more profound differences on ligand dimerization. These studies establish a novel and innovative use of osmolytes to dissect linkages among different processes and exploit the phase diagram as a tool to graphically represent and dissect complex thermodynamic relationships in biological systems. On the basis of our observations and earlier work, we discuss the relevance of ligand dimerization in chemokine regulation.     

A simple theoretical model for fluorescence polarization binding assay development

Fluorescence polarization is a screening technology that is radioactivity free, homogeneous, and ratiometric. The signal measured with this technology is a weighted value of free and bound ligand. As a consequence, saturation curves are accessible only after calculation of the corresponding concentrations of free and bound ligand. To make this technology more accessible to assay development, the authors propose a simple mathematical model that predicts fluorescence polarization values from ligand and receptor total concentrations, depending on the corresponding dissociation constant. This model was validated using data of Bodipy-NDP-alphaMSH binding to MC(5), obtained after either ligand saturation of a receptor preparation or, conversely, receptor saturation of a ligand solution. These experimental data were also used to calculate the actual concentration of free and bound ligand and receptor and to obtain pharmacological constants by Scatchard analysis. A general method is proposed, which facilitates the design of fluorescence polarization binding assays by relying on the representation of theoretical polarization values. This approach is illustrated by the application to 2 systems of very different affinities.     

Cytoplasmic localization and the choice of ligand determine aggregate formation by androgen receptor with amplified polyglutamine stretch

Polyglutamine tract expansion in androgen receptor is a recognized cause of spinal and bulbar muscular atrophy (SBMA), an X-linked motor neuronopathy. Similar mutations have been identified in proteins associated with other neurodegenerative diseases. Recent studies have shown that amplified polyglutamine repeat stretches form cellular aggregates that may be markers for these neurodegenerative diseases. Here we describe conditions that lead to aggregate formation by androgen receptor with polyglutamine stretch amplification. In transfection experiments, the mutant, compared with the wild-type receptor, was delayed in its cytoplasmic-nuclear translocation and formed large cytoplasmic aggregates in the presence of androgen. The cytoplasmic environment appears crucial for this aggregation, since retention of both the wild-type and mutant receptors in this cellular compartment by the deletion of their nuclear localization signals resulted in massive aggregation. Conversely, rapid nuclear transport of both receptors brought about by deletion of their ligand binding domains did not result in aggregate formation. However, androgen antagonists that altered the conformation of the ligand binding domain and promoted varying rates of cytoplasmic-nuclear translocation all inhibited aggregate formation. This demonstrates that in addition to the cytoplasmic localization, a distinct contribution of the ligand binding domain of the receptor is necessary for the aggregation. The finding that antiandrogens inhibit aggregate formation may provide the basis for in vivo determination of the role of these structures in SBMA.     

Thermal Unfolding of a Mammalian Pentameric Ligand-gated Ion Channel Proceeds at Consecutive,Distinct Steps

Pentameric ligand-gated ion channels (LGICs) play an important role in fast synaptic signal transduction. Binding of agonists to the β-sheet-structured extracellular domain opens an ion channel in the transmembrane α-helical region of the LGIC. How the structurally distinct and distant domains are functionally coupled for such central transmembrane signaling processes remains an open question. To obtain detailed information about the stability of and the coupling between these different functional domains, we analyzed the thermal unfolding of a homopentameric LGIC, the 5-hydroxytryptamine receptor (ligand binding, secondary structure, accessibility of Trp and Cys residues, and aggregation), in plasma membranes as well as during detergent extraction, purification, and reconstitution into artificial lipid bilayers. We found a large loss in thermostability correlating with the loss of the lipid bilayer during membrane solubilization and purification. Thermal unfolding of the 5-hydroxytryptamine receptor occurred in consecutive steps at distinct protein locations. A loss of ligand binding was detected first, followed by formation of different transient low oligomeric states of receptor pentamers, followed by partial unfolding of helical parts of the protein, which finally lead to the formation receptor aggregates. Structural destabilization of the receptor in detergents could be partially reversed by reconstituting the receptor into lipid bilayers. Our results are important because they quantify the stability of LGICs during detergent extraction and purification and can be used to create stabilized receptor proteins for structural and functional studies.     

Free energy simulations for protein ligand binding and stability

Abstract

We summarize several computational techniques to determine relative free energies for condensed-phase systems. The focus is on practical considerations which are capable of making direct contact with experiments. Particular applications include the thermodynamic stability of apo- and holo-myoglobin, insulin dimerization free energy, ligand binding in lysozyme, and ligand diffusion in globular proteins. In addition to provide differential free energies between neighboring states, converged umbrella sampling simulations provide insight into migration barriers and ligand dissociation barriers and analysis of the trajectories yield additional insight into the structural dynamics of fundamental processes. Also, such simulations are useful tools to quantify relative stability changes for situations where experiments are difficult. This is illustrated for NO-bound myoglobin. For the dissociation of benzonitrile from lysozyme it is found that long umbrella sampling simulations are required to approximately converge the free energy profile. Then, however, the resulting differential free energy between the bound and unbound state is in good agreement with estimates from molecular mechanics with generalized Born surface area simulations. Furthermore, comparing the barrier height for ligand escape suggests that ligand dissociation contains a non-equilibrium component.     

Linked-function origins of cooperativity in a symmetrical dimer

The thermodynamic origins of substrate binding cooperativity in a dimeric enzyme that can bind one substrate (A) and one allosteric ligand (X) to each of two identical subunits are discussed. It is assumed that maximal activity is not subject to allosteric modification and that the substrates and allosteric ligands achieve binding equilibrium in the steady state. Each uniquely ligated form is assumed to be capable of exhibiting unique binding properties, and only the principles of thermodynamic linkage are used to constrain the system further. The explicit relationship between the Hill coefficient, the concentration of X, and the magnitudes of the relevant coupling free energies and dissociation constants is derived. In the absence of X only the homotropic coupling between substrate sites contributes to a nonhyperbolic substrate saturation profile. An allosteric ligand, X, can alter the cooperativity in two distinct ways, one mechanism being manifested when X is saturating and the only only when X is present at saturating concentrations. By evaluating the concentration of substrate required to produce half-maximal velocity as a function of [X], as well as the Hill coefficients when X is absent and fully saturating, the dissociation and coupling constants most important for understanding the mechanisms of allosteric action in an enzyme of this type can be determined.     

General thermodynamic considerations of receptor interactions.

Assuming that the biological response is directly proportional to the fractional degree of receptor occupancy, the mathematical relationships between free ligand concentration, receptor occupation and biological activity are developed for a number of equilibrium models. The models considered include simple 1:1 binding with and without conformational changes in the receptor, the coupled binding of two distinct effectors to a single macromolecule, and a system involving indirect coupling between two effectors that bind to two distinct components of the receptor system. This latter model is elaborated into the concept of a domain of receptor-enzyme pairs such that occupation of a single receptor may activate the entire domain of enzymes. This model can explain discrepancies between activation and binding isotherms as has been found with some beta-adrenergic agonist-sensitive adenylate cyclase systems.     

Chemoreceptors in signalling complexes: shifted conformation and asymmetric coupling

Bacterial chemotaxis is mediated by signalling complexes of chemoreceptors, histidine kinase CheA and coupling protein CheW. Interactions in complexes profoundly affect the kinase. We investigated effects of these interactions on chemoreceptors by comparing receptors alone and in complexes. Assays of initial rates of methylation indicated that signalling complexes shifted receptor conformation towards the methylation-on, higher-ligand-affinity, kinase-off state, tuning receptors for greater sensitivity. In contrast, transmembrane and conformational signalling within chemoreceptors was essentially unaltered, consistent with other evidence identifying receptor dimers as the fundamental units of such signalling. In signalling complexes, coupling of ligand binding to kinase activity is cooperative and the dynamic range of kinase control expanded > 100-fold by receptor adaptational modification. We observed no cooperativity in influence of ligand on receptor conformation, only on kinase activity. However, receptor modification generated increased dynamic range in a stepwise fashion, partly in coupling ligand to receptor conformation and partly in coupling receptor conformation to kinase activity. Thus, receptors and kinase were not equivalently affected by interactions in signalling complexes or by ligand binding and adaptational modification, indicating asymmetrical coupling between them. This has implications for mechanisms of precise adaptation. Coupling might vary, providing a previously unappreciated locus for sensory control.     

Aggregation of granulocyte colony stimulating factor under physiological conditions: characterization and thermodynamic inhibition

We have investigated the aggregation of recombinant human granulocyte colony stimulating factor (rhGCSF), a protein that rapidly aggregates and precipitates at pH 6.9 and 37 degrees C. We observed that native monomeric rhGCSF reversibly forms a dimer under physiological conditions and that this dimeric species does not participate in the irreversible aggregation process. Sucrose, a thermodynamic stabilizer, inhibits the aggregation of rhGCSF. We postulate that sucrose acts by reducing the concentration of structurally expanded species, consistent with the hypothesis that preferential exclusion favors most compact species in the native state ensemble. Thermodynamic stability data from unfolding curves and hydrogen-deuterium exchange experimental results support the above hypothesis. Thus, the strategy of stabilizing the native state of the protein under physiological conditions using thermodynamic stabilizers, especially ligands binding with high affinity to the native state, is expected to protect against protein aggregation occurring under such nonperturbing solution conditions.     

Structural activation pathways from dynamic olfactory receptor-odorant interactions

We have simulated an odor ligand's dynamic behavior in the binding region of an olfactory receptor (OR). Our short timescale computational studies (up to 200 ps) have helped identify unprecedented postdocking ligand behavior of ligands. From in vacuo molecular dynamics simulations of interactions between models of rat OR I7 and 10 aldehyde ligands, we have identified a dissociative pathway along which the ligand exits and enters the OR-binding pocket--a transit event. The ligand's transit through the receptor's binding region may mark the beginning of a signal transduction cascade leading to odor recognition. We have graphically traced the rotameric changes in key OR amino acid side chains during the transit. Our results have helped substantiate or refute previously held notions of amino acid contribution to ligand stability in the binding pocket. Our observations of ligand activity when compared to those of experimental (electroolfactogram response) OR-activation studies provide a view to predicting the stability of ligands in the binding pocket as a precursor to OR activation by the ligand.     

The reversible cross-linking of receptors by ligands: theory for the prediction of binding responses

The general concept of receptor aggregation through the action of a cross-linking ligand is considered, three models being examined in detail. In two, ligand self-interaction leads to the formation of receptor cross-links whereas, in the third, receptor cross-links are formed through a single ligand bridge. Binding equations in closed form are formulated for each case and are shown to predict both concave and convex Scatchard plots in binding studies conducted with such systems. The significant point which emerges is that while each of the systems gives rise to very different types of binding responses, the form of the binding response is always strongly dependent on the total concentration of receptor in the system.