Cooperativity of allosteric receptors

DNA binding reveals hidden interdomain allostery of a MazE antitoxin from Mycobacterium tuberculosis

Type II toxin-antitoxin (TA) systems are ubiquitously distributed genetic elements in prokaryotes and are crucial for cell maintenance and survival under environmental stresses. The antitoxin is a modular protein consisting of the disordered C-terminal region that physically contacts and neutralizes the cognate toxin and the well-folded N-terminal DNA binding domain responsible for autorepression of TA transcription. However, how the two functional domains communicate is largely unknown. Herein, we determined the crystal structure of the N-terminal domain of the type II antitoxin MazE-mt10 from Mycobacterium tuberculosis, revealing a homodimer of the ribbon-helix-helix (RHH) fold with distinct DNA binding specificity. NMR studies demonstrated that full-length MazE-mt10 forms the helical and coiled states in equilibrium within the C-terminal region, and that helical propensity is allosterically enhanced by the N-terminal binding to the cognate operator DNA. This coil-to-helix transition may promote toxin binding/neutralization of MazE-mt10 and further stabilize the TA-DNA transcription repressor. This is supported by many crystal structures of type II TA complexes in which antitoxins form an α-helical structure at the TA interface. The hidden helical state of free MazE-mt10 in solution, favored by DNA binding, adds a new dimension to the regulatory mechanism of type II TA systems. Furthermore, complementary approaches using X-ray crystallography and NMR allow us to study the allosteric interdomain interplay of many other full-length antitoxins of type II TA systems.

The bacterial magnesium transporter MgtA reveals highly selective interaction with specific cardiolipin species

The bacterial magnesium transporter A (MgtA) is a specialized P-type ATPase important for Mg2+ import into the cytoplasm; disrupted magnesium homeostasis is linked to intrinsic ribosome instability and antibacterial resistance in Salmonella strains. Here, we show that MgtA has functional specificity for cardiolipin 18:1. Still, it reaches maximum activity only in combination with cardiolipin 16:0, equivalent to the major components of native cardiolipin found in E. coli membranes. Native mass spectrometry indicates the presence of two binding sites for cardiolipin, agreeing with the kinetic studies revealing that a cooperative relationship likely exists between the two cardiolipin variants. This is the first experimental evidence of cooperative effects between lipids of the same class, with only minor variations in their acyl chain composition, acting on a membrane protein. In summary, our results reveal that MgtA exhibits a highly complex interaction with one cardiolipin 18:1 and one cardiolipin 16:0, affecting protein activity and stability, contributing to our understanding of the particular interactions between lipid environment and membrane proteins. Further, a better understanding of Mg2+ homeostasis in bacteria, due to its role as a virulence regulator, will provide further insights into the regulation and mechanism of bacterial infections.

A genetic platform for functionally profiling odorant receptors in olfactory cilia ex vivo

The molecular basis for odor perception in humans remains enigmatic because of the difficulty in studying odorant receptors (ORs) outside their native environment. Efforts toward OR expression and functional profiling have been met with limited success because of the poor efficiency of their cell surface expression in vitro. Structures protruding from the surface of olfactory sensory neurons called cilia contain all of the components of the olfactory signal transduction machinery and can be placed in an ex vivo plate assay to rapidly measure odor-specific responses. Here, we describe an approach using cilia isolated from the olfactory sensory neurons of mice expressing two human ORs, OR1A1 and OR5AN1, that showed 10- to 100-fold more sensitivity to ligands as compared to previous assays. A single mouse can produce enough olfactory cilia for up to 4000 384-well assay wells, and isolated cilia can be stored frozen and thus preserved. This pipeline offers a sensitive and highly scalable ex vivo odor-screening platform that has the potential to decode human olfaction.

Cooperativity as quantification and optimization paradigm for nuclear receptor modulators

A cooperativity framework describes the formation of nuclear receptor ternary complexes and deconvolutes ligand and cofactor binding into intrinsic affinities and a cooperativity factor, providing a conceptually new understanding of NR modulation.

Allosteric Cooperativity and Template-Directed Synthesis with Stacked Ligands in Porphyrin Nanorings

The link between allosteric cooperativity and template-directed synthesis has been investigated by studying complexes in which two oligopyridine ligands bind inside a zinc porphyrin nanoring in a stacked arrangement. The binding of a 6-porphyrin nanoring to two tridentate ligands (with s-triazine or benzene cores) occurs with high negative allosteric cooperativity (α ≈ 10^-3-10^-4). Formation constants for 1:1 and 1:2 complexes were determined by UV-vis-NIR denaturation titration, using pyridine as a competing ligand, and cooperativity factors were confirmed by NMR spectroscopy. The rate constants for formation of the 1:1 and 1:2 complexes are approximately equal, and the negative cooperativity can be attributed to faster dissociation of the 1:2 complex. These tridentate ligands are not effective templates for directing the synthesis of the 6-porphyrin nanoring, in keeping with their negative cooperativity of binding. In contrast, the binding of a 12-porphyrin nanoring to two hexadentate ligands occurs with high positive allosteric cooperativity (α > 40), and the ligand is an effective Vernier template for directing the synthesis of the 12-porphyrin nanoring. This stacked Vernier template approach creates the product in an open circular conformation, which is advantageous for preparing macrocycles that do not easily adopt a figure-of-eight geometry.

The role of cooperativity in a p53-miR34 dynamical mathematical model

The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.

Bohr equation and the lost allosteric Bohr effects in symmetry

Bohr, Hasselbalch and Krogh demonstrated a group of sigmoid curves under various carbon dioxide contents in 1904. Hill fitted these curves in 1910 with Hill equation without the physical meanings of Hill coefficient and dissociation constant. In 1965, Monod-Wyman-Changeux model (MWC) popularized the word “allostery” with 81 words of symmetry to define an orthosteric nature of cooperativity in a single and symmetric sigmoid curve. Paradoxically the MWC model didn’t quantify the homotropic Hill coefficient and confusingly described the symmetry of sigmoid shapes with three allosteric variables. A heterotropic Bohr equation, by clarifying the biophysical symmetry in allostery, suggests the solution of allosteric coefficients with only one Bohr variable. We reveal that the mathematical need of a fictional monomer by MWC model justify a symmetric logistic curve with a parabolic kernel of dissociation constant to model the 1904 sigmoid curves. The logistic-derived Bohr equation and its half-saturated P₅₀ equation successfully used the embedded P₅₀ values in the 1904 sigmoidal curves to quantify their hyperbolic conformational shifts and Hill coefficients (n) pending for a century. Both are the logarithmic functions of carbon dioxide. This truly quantitative Bohr equation digitizes the allosteric regulation of the orthosteric affinity by precisely cloning the original group of dissociation/association curves published in 1904. The Bohr equation honestly suggests that nature should have chosen the allosteric Bohr effects to modify hemoglobin to cope with the swift dynamic of gas exchange. The discovery of the Bohr function in Bohr equation challenges the feasibility of the orthosteric cooperativity of hemoglobin.

Phthalides serve as potent modulators to boost fetal hemoglobin induction therapy for β-hemoglobinopathies

Fetal hemoglobin (HbF) induction therapy has become the most promising strategy for treating β-hemoglobinopathies, including sickle-cell diseases and β-thalassemia. However, subtle but critical structural difference exists between HbF and normal adult hemoglobin (HbA), which inevitably leads to reduced binding of the endogenous modulator 2,3-bisphosphoglycerate (2,3-BPG) to HbF and thus increased oxygen affinity and decreased oxygen transport efficiency of HbF. We combined the oxygen equilibrium experiments, resonance Raman (RR) spectroscopy, and molecular docking modeling, and we discuss 2 phthalides, z-butylidenephthalide and z-ligustilide, that can effectively lower the oxygen affinity of HbF. They adjust it to a level closer to that of HbA and make it a more satisfactory oxygen carrier for adults. From the oxygen equilibrium curve measurements, we show that the 2 phthalides are more effective than 2,3-BPG for modulating HbF. The RR spectra show that phthalides allosterically stabilize the oxygenated HbF in the low oxygen affinity conformation, and the molecular docking modeling reveals that the 2 chosen phthalides interact with HbF via the cleft around the γ1/γ2 interface with a binding strength ∼1.6 times stronger than that of 2,3-BPG. We discuss the implications of z-butylidenephthalide and z-ligustilide in boosting the efficacy of HbF induction therapy to mitigate the clinical severities of β-hemoglobinopathies.

Stability estimation of autoregulated genes under Michaelis-Menten-type kinetics

Feedback loops are typical motifs appearing in gene regulatory networks. In some well-studied model organisms, including Escherichia coli, autoregulated genes, i.e., genes that activate or repress themselves through their protein products, are the only feedback interactions. For these types of interactions, the Michaelis-Menten (MM) formulation is a suitable and widely used approach, which always leads to stable steady-state solutions representative of homeostatic regulation. However, in many other biological phenomena, such as cell differentiation, cancer progression, and catastrophes in ecosystems, one might expect to observe bistable switchlike dynamics in the case of strong positive autoregulation. To capture this complex behavior we use the generalized family of MM kinetic models. We give a full analysis regarding the stability of autoregulated genes. We show that the autoregulation mechanism has the capability to exhibit diverse cellular dynamics including hysteresis, a typical characteristic of bistable systems, as well as irreversible transitions between bistable states. We also introduce a statistical framework to estimate the kinetics parameters and probability of different stability regimes given observational data. Empirical data for the autoregulated gene SCO3217 in the SOS system in Streptomyces coelicolor are analyzed. The coupling of a statistical framework and the mathematical model can give further insight into understanding the evolutionary mechanisms toward different cell fates in various systems.

Pharmacological characterisation of S 47445, a novel positive allosteric modulator of AMPA receptors

S 47445 is a novel positive allosteric modulator of alpha-amino-3-hydroxy-5-methyl-4-isoxazole-propionic acid (AMPA) receptors (AMPA-PAM). S 47445 enhanced glutamate’s action at AMPA receptors on human and rat receptors and was inactive at NMDA and kainate receptors. Potentiation did not differ among the different AMPA receptors subtypes (GluA1/2/4 flip and flop variants) (EC₅₀ between 2.5–5.4 μM), except a higher EC₅₀ value for GluA4 flop (0.7 μM) and a greater amount of potentiation on GluA1 flop. A low concentration of S 47445 (0.1 μM) decreased receptor response decay time of GluA1flop/GluA2flip AMPA receptors and increased the sensitivity to glutamate. Furthermore, S 47445 (0.1 and 0.3 μM) in presence of repetitive glutamate pulses induced a progressive potentiation of the glutamate-evoked currents from the second pulse of glutamate confirming a rapid-enhancing effect of S 47445 at low concentrations. The potentiating effect of S 47445 (1 μM) was concentration-dependently reversed by the selective AMPA receptor antagonist GYKI52466 demonstrating the selective modulatory effect of S 47445 on AMPA receptors. Using an AMPA-kainate chimera approach, it was confirmed that S 47445 binds to the common binding pocket of AMPA-PAMs. S 47445 did not demonstrate neurotoxic effect against glutamate-mediated excitotoxicity in vitro, in contrast significantly protected rat cortical neurons at 10 μM. S 47445 was shown to improve both episodic and spatial working memory in adult rodents at 0.3 mg/kg, as measured in the natural forgetting condition of object recognition and T-maze tasks. Finally, no deleterious effect on spontaneous locomotion and general behavior was observed up to 1000 mg/kg of S 47445 given acutely in rodents, neither occurrence of convulsion or tremors. Collectively, these results indicate that S 47445 is a potent and selective AMPA-PAM presenting procognitive and potential neuroprotective properties. This drug is currently evaluated in clinical phase 2 studies in Alzheimer’s disease and in Major Depressive Disorder.

Back to the future: Rational maps for exploring acetylcholine receptor space and time

Global functions of nicotinic acetylcholine receptors, such as subunit cooperativity and compatibility, likely emerge from a network of amino acid residues distributed across the entire pentameric complex. Identification of such networks has stymied traditional approaches to acetylcholine receptor structure and function, likely due to the cryptic interdependency of their underlying amino acid residues. An emerging evolutionary biochemistry approach, which traces the evolutionary history of acetylcholine receptor subunits, allows for rational mapping of acetylcholine receptor sequence space, and offers new hope for uncovering the amino acid origins of these enigmatic properties.

Cooperative binding mitigates the high-dose hook effect

Background

The high-dose hook effect (also called prozone effect) refers to the observation that if a multivalent protein acts as a linker between two parts of a protein complex, then increasing the amount of linker protein in the mixture does not always increase the amount of fully formed complex. On the contrary, at a high enough concentration range the amount of fully formed complex actually decreases. It has been observed that allosterically regulated proteins seem less susceptible to this effect. The aim of this study was two-fold: First, to investigate the mathematical basis of how allostery mitigates the prozone effect. And second, to explore the consequences of allostery and the high-dose hook effect using the example of calmodulin, a calcium-sensing protein that regulates the switch between long-term potentiation and long-term depression in neurons.

Results

We use a combinatorial model of a “perfect linker protein” (with infinite binding affinity) to mathematically describe the hook effect and its behaviour under allosteric conditions. We show that allosteric regulation does indeed mitigate the high-dose hook effect. We then turn to calmodulin as a real-life example of an allosteric protein. Using kinetic simulations, we show that calmodulin is indeed subject to a hook effect. We also show that this effect is stronger in the presence of the allosteric activator Ca ²⁺/calmodulin-dependent kinase II (CaMKII), because it reduces the overall cooperativity of the calcium-calmodulin system. It follows that, surprisingly, there are conditions where increased amounts of allosteric activator actually decrease the activity of a protein.

Conclusions

We show that cooperative binding can indeed act as a protective mechanism against the hook effect. This will have implications in vivo where the extent of cooperativity of a protein can be modulated, for instance, by allosteric activators or inhibitors. This can result in counterintuitive effects of decreased activity with increased concentrations of both the allosteric protein itself and its allosteric activators.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0447-8) contains supplementary material, which is available to authorized users.

Bidirectional allosteric interactions between cannabinoid receptor 1 (CB1) and dopamine receptor 2 long (D2L) heterotetramers

Type 1 cannabinoid (CB₁) and dopamine 2 long form (D_2L) receptors can physically interact to form heteromers that display unique pharmacology in vitro compared to homomeric complexes. Co-expression of CB₁ and D_2L and co-application of CB₁ and D₂ agonists increases cAMP levels while administration of either agonist alone decreases cAMP levels. To understand the observed co-agonist response, our first goal of the current study was to define the stoichiometry of CB₁/D_2L/Gα protein complexes. Using bioluminescence resonance energy transfer 2 (BRET²), we confirmed that, CB₁ homodimers, D_2L homodimers, and CB₁/D_2L heteromers are formed. By using sequential resonance energy transfer 2 (SRET²) combined with bimolecular fluorescence complementation (BiFC), we were able to demonstrate that CB₁/D_2L form heterotetramers consisting of CB₁ and D_2L homodimers. We demonstrated that CB₁/D_2L heterotetramers are coupled to at least two Gα proteins. The second aim of the study was to investigate allosteric effects of a D_2L agonist (quinpirole) on CB₁ receptor function and to investigate the effects of a CB₁ agonist [arachidonyl-2-chloroethylamide (ACEA)] on D_2L receptor function within CB₁/D_2L heterotetramers. Treating cells co-expressing CB₁ and D_2L with both ACEA and quinpirole switched CB₁ and D_2L receptor coupling and signaling from Gα_i to Gα_s proteins, enhanced β-arrestin1 recruitment and receptor co-internalization. The concept of bidirectional allosteric interaction within CB₁/D₂ heterotetramers has important implications for understanding the activity of receptor complexes in native tissues and under pathological conditions.

Cooperativity: a competition of definitions

Cooperativity as a concept is easy to grasp intuitively, but surprisingly hard to define. Two recent papers shed light on the issue and continue the debate on how best to define cooperative binding.

Leveraging allostery to improve G protein-coupled receptor (GPCR)-directed therapeutics: cannabinoid receptor 1 as discovery target

INTRODUCTION

Allosteric modulators of G-protein coupled receptors (GPCRs) hold the promise of improved pharmacology and safety over typical orthosteric GPCR ligands. These features are particularly relevant to the cannabinoid receptor 1 (CB1R) GPCR, since typical orthosteric CB1R ligands are associated with adverse events that limit their translational potential. Areas covered: The contextual basis for applying allostery to CB1R is considered from pharmacological, drug-discovery, and medicinal standpoints. Rational design of small-molecule CB1R allosteric modulators as potential pharmacotherapeutics would be greatly facilitated by direct experimental characterization of structure-function correlates underlying the biological activity of chemically-diverse CB1R allosteric modulators, CB1R allosteric ligand-binding binding pockets, and amino acid contact residues critical to allosteric ligand engagement and activity. In these regards, designer covalent probes exhibiting well-characterized molecular pharmacology as CB1R allosteric modulators are emerging as valuable molecular reporters enabling experimental interrogation of CB1R allosteric site(s) and informing the design of new CB1R agents as drugs. Expert opinion: Synthesis and pharmacological profiling of CB1R allosteric ligands will continue to provide valuable insights into CB1R structure-function correlates. The resulting data should expand the repertoire of novel agents capable of exerting therapeutic benefit by modulating CB1R-dependent signaling.

Looking for the Origin of Allosteric Cooperativity in Metallopolymers

The basic concept of allosteric cooperativity used in biology, chemistry and physics states that any change in the intermolecular host-guest interactions operating in multisite receptors can be assigned to intersite interactions. Using lanthanide metals as guests and linear multi-tridentate linear oligomers of variable lengths and geometries as hosts, this work shows that the quantitative modeling of metal loadings requires the consideration of a novel phenomenon originating from solvation processes. It stepwise modulates the intrinsic affinity of each isolated site in multisite receptors, and this without resorting to allosteric cooperativity. An easy-to-handle additive model predicts a negative power law dependence of the intrinsic affinity on the length of the linear metallopolymer. Applied to lanthanidopolymers, the latter common analysis overestimates cooperativity factors by more than two orders of magnitude.

Cooperativity in Binding Processes: New Insights from Phenomenological Modeling

Cooperative binding is one of the most interesting and not fully understood phenomena involved in control and regulation of biological processes. Here we analyze the simplest phenomenological model that can account for cooperativity (i.e. ligand binding to a macromolecule with two binding sites) by generating equilibrium binding isotherms from deterministically simulated binding time courses. We show that the Hill coefficients determined for cooperative binding, provide a good measure of the Gibbs free energy of interaction among binding sites, and that their values are independent of the free energy of association for empty sites. We also conclude that although negative cooperativity and different classes of binding sites cannot be distinguished at equilibrium, they can be kinetically differentiated. This feature highlights the usefulness of pre-equilibrium time-resolved strategies to explore binding models as a key complement of equilibrium experiments. Furthermore, our analysis shows that under conditions of strong negative cooperativity, the existence of some binding sites can be overlooked, and experiments at very high ligand concentrations can be a valuable tool to unmask such sites.

Structural and Biochemical Analysis of a Single Amino-Acid Mutant of WzzBSF That Alters Lipopolysaccharide O-Antigen Chain Length in Shigella flexneri

Lipopolysaccharide (LPS), a surface polymer of Gram-negative bacteria, helps bacteria survive in different environments and acts as a virulence determinant of host infection. The O-antigen (Oag) component of LPS exhibits a modal chain-length distribution that is controlled by polysaccharide co-polymerases (PCPs). The molecular basis of the regulation of Oag chain-lengths remains unclear, despite extensive mutagenesis and structural studies of PCPs from Escherichia coli and Shigella. Here, we identified a single mutation (A107P) of the Shigella flexneri WzzBSF, by a random mutagenesis approach, that causes a shortened Oag chain-length distribution in bacteria. We determined the crystal structures of the periplasmic domains of wild-type WzzBSF and the A107P mutant. Both structures form a highly similar open trimeric assembly in the crystals, and show a similar tendency to self-associate in solution. Binding studies by bio-layer interferometry reveal cooperative binding of very short (VS)-core-plus-O-antigen polysaccharide (COPS) to the periplasmic domains of both proteins, but with decreased affinity for the A107P mutant. Our studies reveal that subtle and localized structural differences in PCPs can have dramatic effects on LPS chain-length distribution in bacteria, for example by altering the affinity for the substrate, which supports the role of the structure of the growing Oag polymer in this process.

Uncoupling PIP2-calmodulin regulation of Kv7.2 channels by an assembly destabilizing epileptogenic mutation

We show that the combination of an intracellular bi-partite calmodulin (CaM)-binding site and a distant assembly region affect how an ion channel is regulated by a membrane lipid. Our data reveal that regulation by phosphatidylinositol(4,5)bisphosphate (PIP2) and stabilization of assembled Kv7.2 subunits by intracellular coiled-coil regions far from the membrane are coupled molecular processes. Live-cell fluorescence energy transfer measurements and direct binding studies indicate that remote coiled-coil formation creates conditions for different CaM interaction modes, each conferring different PIP2 dependency to Kv7.2 channels. Disruption of coiled-coil formation by epilepsy-causing mutation decreases apparent CaM-binding affinity and interrupts CaM influence on PIP2 sensitivity.

An allosteric receptor by simultaneous "casting" and "molding" in a dynamic combinatorial library

Allosteric synthetic receptors are difficult to access by design. Herein we report a dynamic combinatorial strategy towards such systems based on the simultaneous use of two different templates. Through a process of simultaneous casting (the assembly of a library member around a template) and molding (the assembly of a library member inside the binding pocket of a template), a Russian-doll-like termolecular complex was obtained with remarkable selectivity. Analysis of the stepwise formation of the complex indicates that binding of the two partners by the central macrocycle exhibits significant positive cooperativity. Such allosteric systems represent hubs that may have considerable potential in systems chemistry.

Novel RANK antagonists for the treatment of bone-resorptive disease: theoretical predictions and experimental validation

Receptor activator of nuclear factor-κB (RANK) and RANK ligand (RANKL) play a pivotal role in bone metabolism, and selective targeting of RANK signaling has become a promising therapeutic strategy in the management of resorptive bone diseases. Existing antibody-based therapies and novel inhibitors currently in development were designed to target the ligand, rather than the membrane receptor expressed on osteoclast precursors. We describe here an alternative approach to designing small peptides able to specifically bind to the hinge region of membrane RANK responsible for the conformational change upon RANKL association. A nonapeptide generated by this method was validated for its biological activity in vitro and in vivo and served as a lead compound for the generation of a series of peptide RANK antagonists derived from the original sequence. Our study presents a structure- and knowledge-based strategy for the design of novel effective and affordable small peptide inhibitors specifically targeting the receptor RANK and opens a new therapeutic opportunity for the treatment of resorptive bone disease.

Integration of methods in cheminformatics and biocalorimetry for the design of trypanosomatid enzyme inhibitors

Background: The enzyme GAPDH, which acts in the glycolytic pathway, is seen as a potential target for pharmaceutical intervention of Chagas disease. Results: Herein, we report the discovery of new Trypanosoma cruzi GAPDH (TcGAPDH) inhibitors from target- and ligand-based virtual screening protocols using isothermal titration calorimetry (ITC) and molecular dynamics. Molecular dynamics simulations were used to gain insight on the binding poses of newly identified inhibitors acting at the TcGAPDH substrate (G3P) site. Conclusion: Nequimed125, the most potent inhibitor to act upon TcGAPDH so far, which sits on the G3P site without any contact with the co-factor (NAD+) site, underpins the result obtained by ITC that it is a G3P-competitive inhibitor. Molecular dynamics simulation provides biding poses of TcGAPDH inhibitors that correlate with mechanisms of inhibition observed by ITC. Overall, a new class of dihydroindole compounds that act upon TcGAPDH through a competitive mechanism of inhibition as proven by ITC measurements also kills T. cruzi.

Measuring positive cooperativity using the direct ESI-MS assay. Cholera toxin B subunit homopentamer binding to GM1 pentasaccharide

Direct electrospray ionization mass spectrometry (ESI-MS) assay was used to investigate the stepwise binding of the GM1 pentasaccharide β-D-Galp-(1→3)-β-D-GalpNAc-(1→4)[α-D-Neu5Ac-(2→3)]-β-D-Galp-(1→4)-β-D-Glcp (GM1os) to the cholera toxin B subunit homopentamer (CTB5) and to establish conclusively whether GM1os binding is cooperative. Apparent association constants were measured for the stepwise addition of one to five GM1os to CTB5 at pH 6.9 and 22 °C. The intrinsic association constant, which was established from the apparent association constant for the addition of a single GM1os to CTB5, was found to be (3.2 ± 0.2) × 106 M(–1). This is in reasonable agreement with the reported value of (6.4 ± 0.3) × 106 M(–1), which was measured at pH 7.4 and 25 °C using isothermal titration calorimetry (ITC). Analysis of the apparent association constants provides direct and unambiguous evidence that GM1os binding exhibits small positive cooperativity. Binding was found to be sensitive to the number of ligand-bound nearest neighbor subunits, with the affinities enhanced by a factor of 1.7 and 2.9 when binding occurs next to one or two ligand-bound subunits, respectively. These findings, which provide quantitative support for the binding model proposed by Homans and coworkers [14], highlight the unique strengths of the direct ESI-MS assay for measuring cooperative ligand binding.

A novel equation for cooperativity of the allosteric state function

The MWC (Monod–Wyman–Changeux) allosteric model postulates concerted conformational changes between two states: the intrinsically more stable T state with relatively weak ligand binding and the R state with relatively strong ligand binding. The model distinguishes between Y¯ (the fractional occupation of the binding sites) and R¯ (the fraction of molecules in the R state). Cooperativity (measured by the Hill coefficient) has strikingly different properties for Y¯ and R¯. For the latter, cooperativity depends only on the relative affinities of the two states, not on their relative intrinsic stabilities, as demonstrated here with a simple new equation relating the Hill coefficient to R¯.

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A simple new equation relating the Hill coefficient to R¯ is presented.

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This equation shows that cooperativity (measured by the Hill coefficient) for R¯ depends only on the relative affinities of the two states, not on their relative intrinsic stabilities.

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The curves for R¯ may be characterized by Hill coefficients < 1, even under conditions of positive cooperativity.

The Goodwin model: behind the Hill function

The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathematically shown that to obtain limit-cycle oscillations, the Hill coefficient must be larger than 8, a value often considered unrealistic. It is indeed difficult to explain such a high coefficient with simple cooperative dynamics. We present here molecular models of the standard Goodwin model, based on single or multisite phosphorylation/dephosphorylation processes of a transcription factor, which have been previously shown to generate switch-like responses. We show that when the phosphorylation/dephosphorylation processes are fast enough, the limit-cycle obtained with a multisite phosphorylation-based mechanism is in very good quantitative agreement with the oscillations observed in the Goodwin model. Conditions in which the detailed mechanism is well approximated by the Goodwin model are given. A variant of the Goodwin model which displays sharp thresholds and relaxation oscillations is also explained by a double phosphorylation/dephosphorylation-based mechanism through a bistable behavior. These results not only provide rational support for the Goodwin model but also highlight the crucial role of the speed of post-translational processes, whose response curve are usually established at a steady state, in biochemical oscillators.