A Monte Carlo study of the dynamics of G-protein activation.

To link quantitatively the cell surface binding of ligand to receptor with the production of cellular responses, it may be necessary to explore early events in signal transduction such as G-protein activation. Two different model frameworks relating receptor/ligand binding to G-protein activation are examined. In the first framework, a simple ordinary differential equation model is used to describe receptor/ligand binding and G-protein activation. In the second framework, the events leading to G-protein activation are simulated using a dynamic Monte Carlo model. In both models, reactions between ligand-bound receptors and G-proteins are assumed to be diffusion-limited. The Monte Carlo model predicts two regimes of G-protein activation, depending upon whether the lifetime of a receptor/ligand complex is long or short compared with the time needed for diffusional encounters of complexes and G-proteins. When the lifetime of a complex is relatively short compared with the diffusion time, the movement of ligand among free receptors by binding and unbinding ("switching") significantly enhances G-protein activation. Receptor antagonists dramatically reduce G-protein activation and, thus, signal transduction in this case, and significant clustering of active G-proteins near receptor/ligand complexes results. The simple ordinary differential equation model poorly predicts G-protein activation for this situation. In the alternative case, when diffusion is relatively fast, ligand movement among receptors is less important and the simple ordinary differential equation model and Monte Carlo model results are similar. In this case, there is little clustering of active G-proteins near receptor/ligand complexes. Results also indicate that as the GTPase activity of the alpha-subunit decreases, the steady-state level of alpha-GTP increases, although temporal sensitivity is compromised.     

Affinity regulates spatial range of EGF receptor autocrine ligand binding

Proper spatial localization of EGFR signaling activated by autocrine ligands represents a critical factor in embryonic development as well as tissue organization and function, and ligand/receptor binding affinity is among the molecular and cellular properties suggested to play a role in governing this localization. We employ a computational model to predict how receptor-binding affinity affects local capture of autocrine ligand vis-a-vis escape to distal regions, and provide experimental test by constructing cell lines expressing EGFR along with either wild-type EGF or a low-affinity mutant, EGF(L47M). The model predicts local capture of a lower affinity autocrine ligand to be less efficient when the ligand production rate is small relative to receptor appearance rate. Our experimental data confirm this prediction, demonstrating that cells can use ligand/receptor binding affinity to regulate ligand spatial distribution when autocrine ligand production is limiting for receptor signaling.     

A Mathematical Model for BRASSINOSTEROID INSENSITIVE1-Mediated Signaling in Root Growth and Hypocotyl Elongation

Brassinosteroid (BR) signaling is essential for plant growth and development. In Arabidopsis (Arabidopsis thaliana), BRs are perceived by the BRASSINOSTEROID INSENSITIVE1 (BRI1) receptor. Root growth and hypocotyl elongation are convenient downstream physiological outputs of BR signaling. A computational approach was employed to predict root growth solely on the basis of BRI1 receptor activity. The developed mathematical model predicts that during normal root growth, few receptors are occupied with ligand. The model faithfully predicts root growth, as observed in bri1 loss-of-function mutants. For roots, it incorporates one stimulatory and two inhibitory modules, while for hypocotyls, a single inhibitory module is sufficient. Root growth as observed when BRI1 is overexpressed can only be predicted assuming that a decrease occurred in the BRI1 half-maximum response values. Root growth appears highly sensitive to variation in BR concentration and much less to reduction in BRI1 receptor level, suggesting that regulation occurs primarily by ligand availability and biochemical activity.     

Negative co-operativity in clustered receptors as a possible basis for membrane action

A model for the interaction of a membrane receptor with a stimulating ligand is presented. It is assumed that (a) the receptor macromolecules are embedded in the membrane as a close packed two-dimensional cluster and (b) strong negative co-operative interaction occurs among the receptor molecules. The model explains the existence of (a) strong membrane stimulation by fractional ligand occupancy of the receptor; (b) the absence of positively co-operative binding curves for ligand to membrane receptors and (c) it provides a molecular explanation for the existence of “spare receptor”.     

The effect of multiple binding modes on empirical modeling of ligand docking to proteins.

A popular approach to the computational modeling of ligand/receptor interactions is to use an empirical free energy like model with adjustable parameters. Parameters are learned from one set of complexes, then used to predict another set. To improve these empirical methods requires an independent way to study their inherent errors. We introduce a toy model of ligand/receptor binding as a workbench for testing such errors. We study the errors incurred from the two state binding assumption--the assumption that a ligand is either bound in one orientation, or unbound. We find that the two state assumption can cause large errors in free energy predictions, but it does not affect rank order predictions significantly. We show that fitting parameters using data from high affinity ligands can reduce two state errors; so can using more physical models that do not use the two state assumption. We also find that when using two state models to predict free energies, errors are more severe on high affinity ligands than low affinity ligands. And we show that two state errors can be diagnosed by systematically adding new binding modes when predicting free energies: if predictions worsen as the modes are added, then the two state assumption in the fitting step may be at fault.     

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations, this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.Send offprint requests to:Markus R. Owen     

Stacking-interactions in the control-gear binding of kynurenic acid with NR2A- and GluR2-subunits of glutamate ionotropic receptors

Kynurenine products in tryptophan metabolism are of crucial importance in modulation of neurodegenerative processes in the CNS. Kynurenic acid (KYNA): the endogenous antagonist of ionotropic glutamate receptors, displays specific affinity towards glycine site ofNMDA-receptor NR1 subunit. Mechanisms for the selective interaction of KYNA and its derivatives with other glutamate receptor subtypes are studied insufficiently. Ab initio quantum chemical calculations for KYNA-imidazole dimer, as a model for ligand interaction with His88 fragment of NR2A-subunit, along with KYNA-phenol dimer, as a model for ligand interaction with Tyr61 fragment of GluR2-subunit, were carried out in order to investigate stacking-interaction role of KYNA binding by NR2A subunit of NMDA-receptor and GluR2 subunit of AMPA-receptor. Stacking-interaction energy of KYNA-H88 for the assumed ligand orientation in the binding site is 3.0-5.0 kcal/mol and 102. kcal/mol for the optimized dimer KYNA-imidazole geometry. Stacking-interaction energy of KYNA-Tyr61 for the assumed ligand orientation in the binding site is 6.7-8.5 kcal/mol. The obtained values are comparable with the energies of hydrogen bonds. Thus, stacking-interaction should be taken into account while studing ligand glutamate receptor binding mechanisms. Stacking-interaction is evidently important for the initial ligand orientation inside the receptor binding site after which the delicate tuning of hydrogen bonding pattern is realized. On the other hand, the specific affinity of KYNA derivatives to the receptor subunits could be explained by ligand-aromatic receptor aminoacid stacking-interaction geometry difference.     

A molecular model for singlet/singlet energy transfer of monovalent ligand/receptor interactions

A stochastic model is described that predicts the degree of singlet/singlet energy transfer in complexes formed between monovalent ligands and monovalent receptors. The modeling approach is intended to serve as an analytical tool for approximating the level of fluorescence quenching that can be expected to occur in fluorescently labeled monovalent ligands and receptors that are bound together in complexes. This approach has utility in areas such as modeling protein/protein interactions and designing fluorescence energy transfer assays.Using the crystallographic data for papain (monovalent ligand ) and concanavalin A (monovalent receptor ) along with a molecular graphics computational package the ligand and receptor were docked together to form a ligand/receptor complex. The intermolecular distances between the lysine resides of the ligand and receptor were then estimated, receptor complex was calculated assuming a value for the characteristic length R(0) of the donor/acceptor pair. Results from the stochastic model were used to calculate the level of fluorescence quenching one would expect for a resonance energy transfer competition assay based on the monovalent ligand/pair.Three key assumptions were made during the model development. First, all lysine resides for the ligand and receptor were equally reactive with the dye molecules so the stoichiometry of the donor and acceptor chromophores was governed by a binomial distribution. Second, the dye molecules were located at the alpha-carbon position for each reactive lysine residue. Finally, in the energy transfer competition assay, it was assumed that equilibrium existed between the ligand, receptor, and competing hapten at all times. Based on these assumptions, results are presented that indicate the maximum energy transfer for the monovalent papain/concanavalin. A complex is strongly dependent on the number of acceptor chromophores and on the value of R(0). Results are also presented on the approximate level of fluorescence quenching that may occur in a competition assay based on the papin/pConA complex. Lastly, a strategy is discussed for maximizing the dynamic range and linearity of energy transfer assays by optimizing several key design variables.     

Multi-random binding molecular interactions: a general kinetic model

A kinetic model is suggested to account for the interactions of several ligands with a target whose molecule possesses several independent equivalent receptor sites for each ligand (multiligand multisite model). To analyse the problem, we shall derive solutions for three elementary situations: (a) interactions of a ligand with a mono-receptor site target molecule (monosite model); (b) interactions of several ligands with a target whose molecule possesses one receptor site for each ligand involved (multiligand model); (c) interactions of a ligand with a target whose molecule possesses several receptor sites of the same kind for this ligand (multisite model). Throughout this study, every ligand molecule is assumed to offer one binding site to the target. The main implications of the corresponding analytical solutions are discussed from a molecular point of view. The results cover a great many well-known aspects of the molecular interactions in various fields such as enzymology, endocrinology, radio-immunology and saturation analysis. As suggested by the inhibition patterns obtained, this model may therefore provide a new point of view to interpret the relevant phenomena. Furthermore, a kinetic approach to the generalized mass action law can be deduced from this model, and experimental conditions in which the isotopic dilution law applies are examined.     

Elucidation of direct competition and allosteric modulation of small‐molecular‐weight protein ligands using surface plasmon resonance methods

The present work introduces a surface plasmon resonance‐based method for the discrimination of direct competition and allosteric effects that occur in ternary systems comprising a receptor protein and two small‐molecular‐weight ligands that bind to it. Fatty acid binding protein 4, fructose‐1,6‐bisphosphatase and human serum albumin were used as model receptor molecules to demonstrate the performance of the method. For each of the receptor molecules, pairs of ligand molecules were selected for which either direct competition or an allosteric effect had already been determined by other methods. The method of discrimination introduced here is based on the surface plasmon resonance responses observed at equilibrium when an immobilized receptor protein is brought into contact with binary mixtures of interacting ligands. These experimentally determined responses are compared with the responses calculated using a theoretical model that considers both direct competition and allosteric ligand interaction modes. This study demonstrates that the allosteric ternary complex model, which enables calculation of the fractional occupancy of the protein by each ligand in such ternary systems, is well suited for the theoretical calculation of these types of responses. For all of the ternary systems considered in this work, the experimental and calculated responses in the chosen concentration ratio range were identical within a five‐σ confidence interval when the calculations considered the correct interaction mode of the ligands (direct competition or different types of allosteric regulation), and in case of allosteric modulation, also the correct strength of this effect. This study also demonstrates that the allosteric ternary complex model‐based calculations are well suited to predict the ideal concentration ratio range or even single concentration ratios that can serve as hot spots for discrimination, and such hot spots can drastically reduce the numbers of measurements needed for discrimination between direct competition and distinct modulation modes (neutral, positive or negative allostery). Copyright © 2015 John Wiley & Sons, Ltd.     

De novo ligand design to an ensemble of protein structures

We describe a combinatorial method for de novo ligand design to an ensemble of receptor structures. Receptor conformations, protonation states, and structural water molecules are considered consistently within the framework of de novo ligand design. The method relies on Monte Carlo optimization to search the space of ligand structures, conformations, and rigid-body movements as well as receptor models. The method is applied to an ensemble of HIV protease and human collagenase receptor models. Ligand structures generated de novo exhibit the correct hydrogen-bonding pattern in the core of the active site, with hydrophobic groups extending into the receptor S1 and S1' pocket space. Furthermore, it is shown that known ligands are recovered in the correct binding mode and in the native, most tightly binding receptor model.     

A Model for the Effect of Estrogen Antagonists on Cooperative Estradiol Binding

Abstract

Partial agonists such as estriol and estrone have been reported to diminish or even eliminate the upward convexity of the Scatchard plot of the binding of labeled estradiol to estrogen receptor. This has been interpreted as agonist interference with the receptor dimerization induced by estradiol. In order to investigate how a partial agonist or antagonist might interfere with dimerization we have developed a theoretical mass-action law model, where soluble receptors can dimerize and bind to two different ligands. Special attention was devoted to manifestations of positive cooperativity to determine whether they could be modified by competition with a second ligand. This was done using a computer program that evaluated a large set of combinations of affinity constants in an effort to explore all possible situations. The model could reproduce the effect of a second ligand on the cooperative binding of estradiol to the estrogen receptor but only if the second ligand was anticooperative, which is not the case of estriol, estrone and tamoxifen. Furthermore, even when the Scatchard plot was linear, the model still required dimerization of the receptor in most of the cases, showing that the addition of an antagonist may eliminate the upward curvature of the Scatchard without truly eliminating dimerization or cooperativity. We conclude that the effect of a second ligand on the binding of labeled estradiol to estrogen receptor is not necessarily due to interference with dimerization and/or cooperativity. The inability of this model to fully explain the published data for estriol, estrone, clomiphene, and tamoxifen suggests that a more complex mechanism is involved.     

Analysis of receptor binding displacement curves by a nonhomologous ligand, on the basis of an equivalent competition principle

An exact method for the analysis of receptor-ligand binding data when labeled bound ligand is displaced by a nonhomologous ligand with a different dissociation constant is described. The present method, which is based on an equivalent competition principle for the homologous and the nonhomologous ligand, converts displacement curves into a linear form and is also applicable to situations in which free concentrations of ligand are significantly smaller than the added concentrations as a result of ligand binding. It is shown that the dissociation constant of the nonhomologous ligand is given directly by the concentration of this nonhomologous ligand added and the free concentration of unlabeled homologous ligand required to give the same level of displacement of labeled bound ligand. On the basis of these displacement characteristics, all binding parameters for receptor interaction of the nonhomologous ligand can be obtained and expressed, for example, in a Scatchard plot. The present method, which is referred to as the equivalent competition method, is also evaluated in this study with respect to the effects of nonspecific ligand binding and the presence of multiple receptor classes.     

Current noise of a protein-selective biological nanopore

1/f current noise is ubiquitous in protein pores, porins, and channels. We have previously shown that a protein-selective biological nanopore with an external protein receptor can function as a 1/f noise generator when a high-affinity protein ligand is reversibly captured by the receptor. Here, we demonstrate that the binding affinity and concentration of the ligand are key determinants for the nature of current noise. For example, 1/f was absent when a protein ligand was reversibly captured at a much lower concentration than its equilibrium dissociation constant against the receptor. Furthermore, we also analyzed the composite current noise that resulted from mixtures of low-affinity and high-affinity ligands against the same receptor. This study highlights the significance of protein recognition events in the current noise fluctuations across biological membranes.     

Multiple receptor states are required to describe both kinetic binding and activation of neutrophils via N-formyl peptide receptor ligands

It is well-established that the binding of N-formyl peptides to the N-formyl peptide receptor on neutrophils can be described by a kinetic scheme that involves two ligand-bound receptor states, both a low affinity ligand-receptor complex and a high affinity ligand-receptor complex, and that the rate constants describing ligand-receptor binding and receptor affinity state interconversion are ligand-specific. Here we examine whether differences due to these rate constants, i.e. differences in the numbers and lifetimes of particular receptor states, are correlated with neutrophil responses, namely actin polymerization and oxidant production. We find that an additional receptor state, one not discerned from kinetic binding assays, is required to account for these responses. This receptor state is interpreted as the number of low affinity bound receptors that are capable of activating G proteins; in other words, the accumulation of these active receptors correlates with the extent of both responses. Furthermore, this analysis allows for the quantification of a parameter that measures the relative strength of a ligand to bias the receptor into the active conformation. A model with this additional receptor state is sufficient to describe response data when two ligands (agonist/agonist or agonist/antagonist pairs) are added simultaneously, suggesting that cells respond to the accumulation of active receptors regardless of the identity of the ligand(s).     

Steric effects on multivalent ligand-receptor binding: exclusion of ligand sites by bound cell surface receptors.

Steric effects can influence the binding of a cell surface receptor to a multivalent ligand. To account for steric effects arising from the size of a receptor and from the spacing of binding sites on a ligand, we extend a standard mathematical model for ligand-receptor interactions by introducing a steric hindrance factor. This factor gives the fraction of unbound ligand sites that are accessible to receptors, and thus available for binding, as a function of ligand site occupancy. We derive expressions for the steric hindrance factor for various cases in which the receptor covers a compact region on the ligand surface and the ligand expresses sites that are distributed regularly or randomly in one or two dimensions. These expressions are relevant for ligands such as linear polymers, proteins, and viruses. We also present numerical algorithms that can be used to calculate steric hindrance factors for other cases. These theoretical results allow us to quantify the effects of steric hindrance on ligand-receptor kinetics and equilibria.     

An NMR-based scoring function improves the accuracy of binding pose predictions by docking by two orders of magnitude

Low-affinity ligands can be efficiently optimized into high-affinity drug leads by structure based drug design when atomic-resolution structural information on the protein/ligand complexes is available. In this work we show that the use of a few, easily obtainable, experimental restraints improves the accuracy of the docking experiments by two orders of magnitude. The experimental data are measured in nuclear magnetic resonance spectra and consist of protein-mediated NOEs between two competitively binding ligands. The methodology can be widely applied as the data are readily obtained for low-affinity ligands in the presence of non-labelled receptor at low concentration. The experimental inter-ligand NOEs are efficiently used to filter and rank complex model structures that have been pre-selected by docking protocols. This approach dramatically reduces the degeneracy and inaccuracy of the chosen model in docking experiments, is robust with respect to inaccuracy of the structural model used to represent the free receptor and is suitable for high-throughput docking campaigns.