Ligand depletion in vivo modulates the dynamic range and cooperativity of signal transduction

GroEL Allostery Illuminated by a Relationship between the Hill Coefficient and the MWC Model

A fundamental problem that has hindered the use of the classic Monod-Wyman-Changuex (MWC) allosteric model since its introduction is that it has been difficult to determine the values of its parameters in a reliable manner because they are correlated with each other and sensitive to the data-fitting method. Consequently, experimental data are often fitted to the Hill equation, which provides a measure of cooperativity but no insights into its origin. In this work, we derived a general relationship between the value of the Hill coefficient and the parameters of the MWC model. It is shown that this relationship can be used to select the best estimate of the true combination of the MWC parameter values from all the possible ones found to fit the data. Here, this approach was applied to fits to the MWC model of curves of the fraction of GroEL molecules in the high-affinity (R) state for ATP as a function of ATP concentration. Such curves were collected at different temperatures, thereby providing insight into the hydrophobic effect associated with the ATP-promoted allosteric switch of GroEL. More generally, the relationship derived here should facilitate future thermodynamic analysis of other MWC-type allosteric systems.

Mechanistic insight into activation of MAPK signaling by pro-angiogenic factors

Background

Angiogenesis is important in physiological and pathological conditions, as blood vessels provide nutrients and oxygen needed for tissue growth and survival. Therefore, targeting angiogenesis is a prominent strategy in both tissue engineering and cancer treatment. However, not all of the approaches to promote or inhibit angiogenesis lead to successful outcomes. Angiogenesis-based therapies primarily target pro-angiogenic factors such as vascular endothelial growth factor-A (VEGF) or fibroblast growth factor (FGF) in isolation. However, pre-clinical and clinical evidence shows these therapies often have limited effects. To improve therapeutic strategies, including targeting FGF and VEGF in combination, we need a quantitative understanding of the how the promoters combine to stimulate angiogenesis.

Results

In this study, we trained and validated a detailed mathematical model to quantitatively characterize the crosstalk of FGF and VEGF intracellular signaling. This signaling is initiated by FGF binding to the FGF receptor 1 (FGFR1) and heparan sulfate glycosaminoglycans (HSGAGs) or VEGF binding to VEGF receptor 2 (VEGFR2) to promote downstream signaling. The model focuses on FGF- and VEGF-induced mitogen-activated protein kinase (MAPK) signaling and phosphorylation of extracellular regulated kinase (ERK), which promotes cell proliferation. We apply the model to predict the dynamics of phosphorylated ERK (pERK) in response to the stimulation by FGF and VEGF individually and in combination. The model predicts that FGF and VEGF have differential effects on pERK. Additionally, since VEGFR2 upregulation has been observed in pathological conditions, we apply the model to investigate the effects of VEGFR2 density and trafficking parameters. The model predictions show that these parameters significantly influence the response to VEGF stimulation.

Conclusions

The model agrees with experimental data and is a framework to synthesize and quantitatively explain experimental studies. Ultimately, the model provides mechanistic insight into FGF and VEGF interactions needed to identify potential targets for pro- or anti-angiogenic therapies.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0668-5) contains supplementary material, which is available to authorized users.

Competitive tuning: Competition's role in setting the frequency-dependence of Ca2+-dependent proteins

A number of neurological disorders arise from perturbations in biochemical signaling and protein complex formation within neurons. Normally, proteins form networks that when activated produce persistent changes in a synapse’s molecular composition. In hippocampal neurons, calcium ion (Ca²⁺) flux through N-methyl-D-aspartate (NMDA) receptors activates Ca²⁺/calmodulin signal transduction networks that either increase or decrease the strength of the neuronal synapse, phenomena known as long-term potentiation (LTP) or long-term depression (LTD), respectively. The calcium-sensor calmodulin (CaM) acts as a common activator of the networks responsible for both LTP and LTD. This is possible, in part, because CaM binding proteins are “tuned” to different Ca²⁺ flux signals by their unique binding and activation dynamics. Computational modeling is used to describe the binding and activation dynamics of Ca²⁺/CaM signal transduction and can be used to guide focused experimental studies. Although CaM binds over 100 proteins, practical limitations cause many models to include only one or two CaM-activated proteins. In this work, we view Ca²⁺/CaM as a limiting resource in the signal transduction pathway owing to its low abundance relative to its binding partners. With this view, we investigate the effect of competitive binding on the dynamics of CaM binding partner activation. Using an explicit model of Ca²⁺, CaM, and seven highly-expressed hippocampal CaM binding proteins, we find that competition for CaM binding serves as a tuning mechanism: the presence of competitors shifts and sharpens the Ca²⁺ frequency-dependence of CaM binding proteins. Notably, we find that simulated competition may be sufficient to recreate the in vivo frequency dependence of the CaM-dependent phosphatase calcineurin. Additionally, competition alone (without feedback mechanisms or spatial parameters) could replicate counter-intuitive experimental observations of decreased activation of Ca²⁺/CaM-dependent protein kinase II in knockout models of neurogranin. We conclude that competitive tuning could be an important dynamic process underlying synaptic plasticity.

Learning and memory formation are likely associated with dynamic fluctuations in the connective strength of neuronal synapses. These fluctuations, called synaptic plasticity, are regulated by calcium ion (Ca²⁺) influx through ion channels localized to the post-synaptic membrane. Within the post-synapse, the dominant Ca²⁺ sensor protein, calmodulin (CaM), may activate a variety of downstream binding partners, each contributing to synaptic plasticity outcomes. The conditions at which certain binding partners most strongly activate are increasingly studied using computational models. Nearly all computational studies describe these binding partners in combinations of only one or two CaM binding proteins. In contrast, we combine seven well-studied CaM binding partners into a single model wherein they simultaneously compete for access to CaM. Our dynamic model suggests that competition narrows the window of conditions for optimal activation of some binding partners, mimicking the Ca²⁺-frequency dependence of some proteins in vivo. Further characterization of CaM-dependent signaling dynamics in neuronal synapses may benefit our understanding of learning and memory formation. Furthermore, we propose that competitive binding may be another framework, alongside feedback and feed-forward loops, signaling motifs, and spatial localization, that can be applied to other signal transduction networks, particularly second messenger cascades, to explain the dynamical behavior of protein activation.

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.

Biased Allostery

G-protein-coupled receptors (GPCRs) constitute a large group of integral membrane proteins that transduce extracellular signals from a wide range of agonists into targeted intracellular responses. Although the responses can vary depending on the category of G-proteins activated by a particular receptor, responses were also found to be triggered by interactions of the receptor with β-arrestins. It was subsequently discovered that for the same receptor molecule (e.g., the β-adrenergic receptor), some agonists have a propensity to specifically favor responses by G-proteins, others by β-arrestins, as has now been extensively studied. This feature of the GPCR system is known as biased agonism and is subject to various interpretations, including agonist-induced conformational change versus selective stabilization of preexisting active conformations. Here, we explore a complete allosteric framework for biased agonism based on alternative preexisting conformations that bind more strongly, but nonexclusively, either G-proteins or β-arrestins. The framework incorporates reciprocal effects among all interacting molecules. As a result, G-proteins and β-arrestins are in steric competition for binding to the cytoplasmic surface of either the G-protein-favoring or β-arrestin-favoring GPCR conformation. Moreover, through linkage relations, the strength of the interactions of G-proteins or β-arrestins with the corresponding active conformation potentiates the apparent affinity for the agonist, effectively equating these two proteins to allosteric modulators. The balance between response alternatives can also be influenced by the physiological concentrations of either G-proteins or β-arrestins, as well as by phosphorylation or interactions with positive or negative allosteric modulators. The nature of the interactions in the simulations presented suggests novel experimental tests to distinguish more fully among alternative mechanisms.

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.

Modulation of calmodulin lobes by different targets: an allosteric model with hemiconcerted conformational transitions

Calmodulin is a calcium-binding protein ubiquitous in eukaryotic cells, involved in numerous calcium-regulated biological phenomena, such as synaptic plasticity, muscle contraction, cell cycle, and circadian rhythms. It exibits a characteristic dumbell shape, with two globular domains (N- and C-terminal lobe) joined by a linker region. Each lobe can take alternative conformations, affected by the binding of calcium and target proteins. Calmodulin displays considerable functional flexibility due to its capability to bind different targets, often in a tissue-specific fashion. In various specific physiological environments (e.g. skeletal muscle, neuron dendritic spines) several targets compete for the same calmodulin pool, regulating its availability and affinity for calcium. In this work, we sought to understand the general principles underlying calmodulin modulation by different target proteins, and to account for simultaneous effects of multiple competing targets, thus enabling a more realistic simulation of calmodulin-dependent pathways. We built a mechanistic allosteric model of calmodulin, based on an hemiconcerted framework: each calmodulin lobe can exist in two conformations in thermodynamic equilibrium, with different affinities for calcium and different affinities for each target. Each lobe was allowed to switch conformation on its own. The model was parameterised and validated against experimental data from the literature. In spite of its simplicity, a two-state allosteric model was able to satisfactorily represent several sets of experiments, in particular the binding of calcium on intact and truncated calmodulin and the effect of different skMLCK peptides on calmodulin's saturation curve. The model can also be readily extended to include multiple targets. We show that some targets stabilise the low calcium affinity T state while others stabilise the high affinity R state. Most of the effects produced by calmodulin targets can be explained as modulation of a pre-existing dynamic equilibrium between different conformations of calmodulin's lobes, in agreement with linkage theory and MWC-type models.

Cooperative substrate binding by a diguanylate cyclase

XAC0610, from Xanthomonas citri subsp. citri, is a large multi-domain protein containing one GAF (cGMP-specific phosphodiesterases, adenylyl cyclases and FhlA) domain, four PAS (Per-Arnt-Sim) domains and one GGDEF domain. This protein has a demonstrable in vivo and in vitro diguanylate cyclase (DGC) activity that leads to the production of cyclic di-GMP (c-di-GMP), a ubiquitous bacterial signaling molecule. Analysis of a XacΔ0610 knockout strain revealed that XAC0610 plays a role in the regulation of Xac motility and resistance to H2O2. Site-directed mutagenesis of a conserved DGC lysine residue (Lys759 in XAC0610) resulted in a severe reduction in XAC0610 DGC activity. Furthermore, experimental and in silico analyses suggest that XAC0610 is not subject to allosteric product inhibition, a common regulatory mechanism for DGC activity control. Instead, steady-state kinetics of XAC0610 DGC activity revealed a positive cooperative effect of the GTP substrate with a dissociation constant for the binding of the first GTP molecule (K1) approximately 5× greater than the dissociation constant for the binding of the second GTP molecule (K2). We present a general kinetics scheme that should be used when analyzing DGC kinetics data and propose that cooperative GTP binding could be a common, though up to now overlooked, feature of these enzymes that may in some cases offer a physiologically relevant mechanism for regulation of DGC activity in vivo.

Utilization of extracellular information before ligand-receptor binding reaches equilibrium expands and shifts the input dynamic range

Cell signaling systems sense and respond to ligands that bind cell surface receptors. These systems often respond to changes in the concentration of extracellular ligand more rapidly than the ligand equilibrates with its receptor. We demonstrate, by modeling and experiment, a general "systems level" mechanism cells use to take advantage of the information present in the early signal, before receptor binding reaches a new steady state. This mechanism, pre-equilibrium sensing and signaling (PRESS), operates in signaling systems in which the kinetics of ligand-receptor binding are slower than the downstream signaling steps, and it typically involves transient activation of a downstream step. In the systems where it operates, PRESS expands and shifts the input dynamic range, allowing cells to make different responses to ligand concentrations so high as to be otherwise indistinguishable. Specifically, we show that PRESS applies to the yeast directional polarization in response to pheromone gradients. Consideration of preexisting kinetic data for ligand-receptor interactions suggests that PRESS operates in many cell signaling systems throughout biology. The same mechanism may also operate at other levels in signaling systems in which a slow activation step couples to a faster downstream step.

On the origin of the stereoselective affinity of Nutlin-3 geometrical isomers for the MDM2 protein

The stereoselective affinity of small-molecule binding to proteins is typically broadly explained in terms of the thermodynamics of the final bound complex. Using Brownian dynamics simulations, we show that the preferential binding of the MDM2 protein to the geometrical isomers of Nutlin-3, an effective anticancer lead that works by inhibiting the interaction between the proteins p53 and MDM2, can be explained by kinetic arguments related to the formation of the MDM2:Nutlin-3 encounter complex. This is a diffusively bound state that forms prior to the final bound complex. We find that the MDM2 protein stereoselectivity for the Nutlin-3a enantiomer stems largely from the destabilization of the encounter complex of its mirror image enantiomer Nutlin-3b, by the K70 residue that is located away from the binding site. On the other hand, the trans-Nutlin-3a diastereoisomer exhibits a shorter residence time in the vicinity of MDM2 compared with Nutlin-3a due to destabilization of its encounter complex by the collective interaction of pairs of charged residues on either side of the binding site: Glu25 and Lys51 on one side, and Lys94 and Arg97 on the other side. This destabilization is largely due to the electrostatic potential of the trans-Nutlin-3a isomer being largely positive over extended continuous regions around its structure, which are otherwise well-identified into positive and negative regions in the case of the Nutlin-3a isomer. Such rich insight into the binding processes underlying biological selectivity complements the static view derived from the traditional thermodynamic analysis of the final bound complex. This approach, based on an explicit consideration of the dynamics of molecular association, suggests new avenues for kinetics-based anticancer drug development and discovery.

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.

Cooperativity of allosteric receptors

Cooperativity of ligand binding to allosteric receptors can be quantified using the Hill coefficient (nH) to measure the sigmoidal character of the binding curve. However, for measurements of the transition between conformational states, nH values can be misleading due to ambiguity of the reference state. For cooperative ligand binding, the reference state is a hyperbolic curve for a monomer with a single binding site characterized by nH=1. Therefore, binding curves with nH>1 provide a direct measure of cooperativity. For the dependence of the conformational state on ligand concentration, curves with nH>1 are observed, but in virtually all cases, the equivalent allosteric monomer has a value of nH<1. The ratio of the two nH values defines the effective cooperativity and always corresponds to nH=N (the number of protomers in the oligomer) for concerted transitions as specified by the Monod-Wyman-Changeux model. Dose-response curves for homopentameric α7 nicotinic receptors illustrate this relationship for both wild-type and mutant forms. For functional allosteric monomers such as G-protein-coupled receptors, normalization stretches the dose-response curve along the y-axis, thereby masking the "allosteric range" and increasing the apparent cooperativity to a limit for monomers of nH =1. The concepts of equivalent monomer and allosteric range were originally proposed in 1965 by Crick and Wyman in a manuscript circulated among the proponents of allostery, but only now published for the first time in this special issue.

Coarsening and accelerated equilibration in mass-conserving heterogeneous nucleation

We propose a model of mass-conserving heterogeneous nucleation to describe the dynamics of ligand-receptor binding in closed cellular compartments. When the ligand dissociation rate is small, competition among receptors for free ligands gives rise to two very different long-time ligand-receptor cluster-size distributions. Cluster sizes first plateau to a long-lived, initial-condition-dependent, "metastable" distribution, and coarsen only much later to a qualitatively different equilibrium one. Surprisingly, we also find parameters for which a very special subset of clusters have equal metastable and equilibrium sizes, appearing to equilibrate much faster than the rest. Our results provide a quantitative framework for ligand-binding kinetics and suggest a mechanism by which different clusters can approach their equilibrium sizes in unexpected ways.