Simple Biochemical Pathways far from Steady State Can Provide Switchlike and Integrated Responses

Covalent modification cycles (systems in which the activity of a substrate is regulated by the action of two opposing enzymes) and ligand/receptor interactions are ubiquitous in signaling systems and their steady-state properties are well understood. However, the behavior of such systems far from steady state remains unclear. Here, we analyze the properties of covalent modification cycles and ligand/receptor interactions driven by the accumulation of the activating enzyme and the ligand, respectively. We show that for a large range of parameters both systems produce sharp switchlike response and yet allow for temporal integration of the signal, two desirable signaling properties. Ultrasensitivity is observed also in a region of parameters where the steady-state response is hyperbolic. The temporal integration properties are tunable by regulating the levels of the deactivating enzyme and receptor, as well as by adjusting the rate of accumulation of the activating enzyme and ligand. We propose that this tunability is used to generate precise responses in signaling systems.     

Allosteric interactions and bifunctionality make the response of glutamine synthetase cascade system of Escherichia coli robust and ultrasensitive

Glutamine synthetase (GS) regulation in Escherichia coli by reversible covalent modification cycles is a prototype of signal transduction by enzyme cascades. Such enzyme cascades are known to exhibit ultrasensitive response to primary stimuli and act as signal integration systems. Here, we have quantified GS bicyclic cascade based on steady state analysis by evaluating Hill coefficient. We demonstrate that adenylylation of GS with glutamine as input is insensitive to total enzyme concentrations of GS, uridylyltransferase/uridylyl-removing enzyme, regulatory protein PII, and adenylyltransferase/adenylyl-removing enzyme. This robust response of GS adenylylation is also observed for change in system parameters. From numerical analyses, we show that the robust ultrasensitive response of bicyclic cascade is because of allosteric interactions of glutamine and 2-ketoglutarate, bifunctionality of converter enzymes, and closed loop bicyclic cascade structure. By system level quantification of the GS bicyclic cascade, we conclude that such a robust response may help the cell in adapting to different carbon and nitrogen status.     

Covalent Modification Cycles through the Spatial Prism

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.     

Covalent Modification Cycles through the Spatial Prism

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.     

Necessary conditions for a minimal model of receptor to show adaptive response over a wide range of levels of stimulus

Sensory systems respond to temporal changes in the stimulus and adapt to the new level when it persists, this pattern of response being maintained in a wide range of levels of stimulus. Here we use a simple model of adaptation developed by Segel et al. (J. Theor. Biol. 120 (1986) 151-179) and extended by Hauri and Ross (Biophys. J. 68 (1995) 708-722) to study the conditions in which it shows wide range of response. The model consists of a receptor that switches between a variable number of states, either by mass action law or by covalent modification. Using a global optimization procedure, we have optimized the adaptive response of the alternatives of the model with different number of states. We find that it is impossible to obtain a wide range of response if the receptor switches between states following mass-action laws, irrespective of the number of states. Instead, a wide range (of five orders of magnitude of ligand concentration) can be obtained if the receptor switches between several states by irreversible covalent modification, in agreement with previous models. Therefore, in this model, expenditure of energy to maintain a large number of covalent modification cycles operating outside equilibrium is necessary to achieve a wide range of response. The optimal values of the parameters present similar patterns to those reported for specific receptors, but there is no quantitative agreement. For instance, ligand affinity varies several orders of magnitude between the different states of the receptor, what is unlikely to be fulfilled by real systems. To see if the minimal model can show adaptive response and range with quantitatively plausible parameter values a sub-optimal receptor was studied, finding that adaptive response of high intensity can still be obtained in at least three orders of magnitude.     

EGF receptor signaling regulates pulses of cell delamination from the Drosophila ectoderm

Many different intercellular signaling pathways are known but, for most, it is unclear whether they can generate oscillating cell behaviors. Here we use time-lapse analysis of Drosophila embryogenesis to show that oenocytes delaminate from the ectoderm in discrete bursts of three. This pulsatile process has a 1 hour period, occurs without cell division, and requires a localized EGF receptor (EGFR) response. High-threshold EGFR targets are sequentially activated in rings of three cells, prefiguring the temporal pattern of delamination. Surprisingly, widespread misexpression of the relevant activating ligand, Spitz, is compatible with robust delamination pulses. Moreover, although Spitz ligand becomes limiting after only two pulses, artificially prolonging its secretion generates up to six additional cycles, revealing a rhythmic underlying mechanism. These findings illustrate how intercellular signaling and cell movements can generate multiple cycles of a cell behavior, despite individual cells experiencing only one cycle of receptor activation.     

A cellular perspective of bias at G protein‐coupled receptors

G protein‐coupled receptors (GPCRs) modulate cell function over short‐ and long‐term timescales. GPCR signaling depends on biochemical parameters that define the what, when, and where of receptor function: what proteins mediate and regulate receptor signaling, where within the cell these interactions occur, and how long these interactions persist. These parameters can vary significantly depending on the activating ligand. Collectivity, differential agonist activity at a GPCR is called bias or functional selectivity. Here we review agonist bias at GPCRs with a focus on ligands that show dramatically different cellular responses from their unbiased counterparts.     

Methyltransferase CheR binds to its chemoreceptor substrates independent of their signaling conformation yet modifies them differentially

Methylation of specific chemoreceptor glutamyl residues by methyltransferase CheR mediates sensory adaptation and gradient sensing in bacterial chemotaxis. Enzyme action is a function of chemoreceptor signaling conformation: kinase‐off receptors are more readily methylated than kinase‐on, a feature central to adaptational and gradient‐sensing mechanisms. Differential enzyme action could reflect differential binding, catalysis or both. We investigated by measuring CheR binding to kinase‐off and kinase‐on forms of Escherichia coli aspartate receptor Tar deleted of its CheR‐tethering, carboxyl terminus pentapeptide. This allowed characterization of the low‐affinity binding of enzyme to the substrate receptor body, otherwise masked by high‐affinity interaction with pentapeptide. We quantified the low‐affinity protein–protein interactions by determining kinetic rate constants of association and dissociation using bio‐layer interferometry and from those values calculating equilibrium constants. Whether Tar signaling conformations were shifted by ligand occupancy or adaptational modification, there was little or no difference between the two signaling conformations in kinetic or equilibrium parameters of enzyme‐receptor binding. Thus, differential methyltransferase action does not reflect differential binding. Instead, the predominant determinants of binding must be common to different signaling conformations. Characterization of the dependence of association rate constants on Deybe length, a measure of the influence of electrostatics, implicated electrostatic interactions as a common binding determinant. Taken together, our observations indicate that differential action of methyltransferase on kinase‐off and kinase‐on chemoreceptors is not the result of differential binding and suggest it reflects differential catalytic propensity. Differential catalysis rather than binding could well be central to other enzymes distinguishing alternative conformations of protein substrates.     

From ligand binding to gene expression: new insights into the regulation of G-protein-coupled receptors.

Transmembrane signaling systems relay information from the exterior to the interior of a cell, through a series of complex protein-protein interactions and second messenger cascades. One such system consists of the G-protein-coupled receptors, which interact with G proteins upon ligand binding, and in turn activate an effector molecule. The receptor is the first component in this signaling cascade and is subject to considerable regulation. Recent studies have shown that these regulatory events can occur at the levels of receptor protein modification and receptor gene expression. Interestingly, some of these processes appear to be mediated by the same second messenger systems that these receptors activate, which leads to various forms of positive and negative feedback regulation.     

Modeling of mechanisms and dynamics of pharmacological effects of psychotropic drugs in view of temporal organization of neuronal processes

Non-equilibrium kinetic models of ligand-receptor interaction are considered to describe the types and quantitative peculiarities of pharmacological effects of exogenous modulators, agonists, and antagonists of central neurotransmitter systems. Using the proposed model, we analyze synaptic ligand-receptor non-equilibrium (impulse) interactions against the background of steady-state interaction of a given ligand with postsynaptic receptors. The type of pharmacological effects of exogenous ligands is shown to be determined by temporal organization of specific synaptic processes (namely, the relation between the rates of receptor conformational transitions and elimination of the transmitter).     

Cell surface receptors for signal transduction and ligand transport: a design principles study

Receptors constitute the interface of cells to their external environment. These molecules bind specific ligands involved in multiple processes, such as signal transduction and nutrient transport. Although a variety of cell surface receptors undergo endocytosis, the systems-level design principles that govern the evolution of receptor trafficking dynamics are far from fully understood. We have constructed a generalized mathematical model of receptor–ligand binding and internalization to understand how receptor internalization dynamics encodes receptor function and regulation. A given signaling or transport receptor system represents a particular implementation of this module with a specific set of kinetic parameters. Parametric analysis of the response of receptor systems to ligand inputs reveals that receptor systems can be characterized as being: i) avidity-controlled where the response control depends primarily on the extracellular ligand capture efficiency, ii) consumption-controlled where the ability to internalize surface-bound ligand is the primary control parameter, and iii) dual-sensitivity where both the avidity and consumption parameters are important. We show that the transferrin and low-density lipoprotein receptors are avidity-controlled, the vitellogenin receptor is consumption-controlled, and the epidermal growth factor receptor is a dual-sensitivity receptor. Significantly, we show that ligand-induced endocytosis is a mechanism to enhance the accuracy of signaling receptors rather than merely serving to attenuate signaling. Our analysis reveals that the location of a receptor system in the avidity-consumption parameter space can be used to understand both its function and its regulation.     

Signaling complexes control the chemotaxis kinase by altering its apparent rate constant of autophosphorylation

Autophosphorylating histidine kinase CheA is central to signaling in bacterial chemotaxis. The kinase donates its phosphoryl group to two response regulators, CheY that controls flagellar rotation and thus motility and CheB, crucial for sensory adaptation. As measured by coupled CheY phosphorylation, incorporation into signaling complexes activates the kinase ～1000‐fold and places it under control of chemoreceptors. By the same assay, receptors modulate kinase activity ～100‐fold as a function of receptor ligand occupancy and adaptational modification. These changes are the essence of chemotactic signaling. Yet, the enzymatic properties affected by incorporation into signaling complexes, by chemoreceptor ligand binding or by receptor adaptational modification are largely undefined. To investigate, we performed steady‐state kinetic analysis of autophosphorylation using a liberated kinase phosphoryl‐accepting domain, characterizing kinase alone, in isolated core signaling complexes and in small arrays of core complexes assembled in vitro with receptors contained in isolated native membranes. Autophosphorylation in signaling complexes was measured as a function of ligand occupancy and adaptational modification. Activation by incorporation into signaling complexes and modulation in complexes by ligand occupancy and adaptational modification occurred largely via changes in the apparent catalytic rate constant (k_cat). Changes in the autophosphorylation k_cat accounted for most of the ～1000‐fold kinase activation in signaling complexes observed for coupled CheY phosphorylation, and the ～100‐fold inhibition by ligand occupancy or modulation by adaptational modification. Our results indicate no more than a minor role in kinase control for simple sequestration of the autophosphorylation substrate. Instead they indicate direct effects on the active site.     

Evidence that both ligand binding and covalent adaptation drive a two-state equilibrium in the aspartate receptor signaling complex.

The transmembrane aspartate receptor of bacterial chemotaxis regulates an associated kinase protein in response to both attractant binding to the receptor periplasmic domain and covalent modification of four adaptation sites on the receptor cytoplasmic domain. The existence of at least 16 covalent modification states raises the question of how many stable signaling conformations exist. In the simplest case, the receptor could have just two stable conformations ("on" and "off") yielding the two-state behavior of a toggle-switch. Alternatively, covalent modification could incrementally shift the receptor between many more than two stable conformations, thereby allowing the receptor to function as a rheostatic switch. An important distinction between these models is that the observed functional parameters of a toggle-switch receptor could strongly covary as covalent modification shifts the equilibrium between the on- and off-states, due to population-weighted averaging of the intrinsic on- and off-state parameters. By contrast, covalent modification of a rheostatic receptor would create new conformational states with completely independent parameters. To resolve the toggle-switch and rheostat models, the present study has generated all 16 homogeneous covalent modification states of the receptor adaptation sites, and has compared their effects on the attractant affinity and kinase activity of the reconstituted receptor-kinase signaling complex. This approach reveals that receptor covalent modification modulates both attractant affinity and kinase activity up to 100-fold, respectively. The regulatory effects of individual adaptation sites are not perfectly additive, indicating synergistic interactions between sites. The three adaptation sites at positions 295, 302, and 309 are more important than the site at position 491 in regulating attractant affinity and kinase activity, thereby explaining the previously observed dominance of the former three sites in in vivo studies. The most notable finding is that covalent modification of the adaptation sites alters the receptor attractant affinity and the receptor-regulated kinase activity in a highly correlated fashion, strongly supporting the toggle-switch model. Similarly, certain mutations that drive the receptor into the kinase activating state are found to have correlated effects on attractant affinity. Together these results provide strong evidence that chemotaxis receptors possess just two stable signaling conformations and that the equilibrium between these pure on- and off-states is modulated by both attractant binding and covalent adaptation. It follows that the attractant and adaptation signals drive the same conformational change between the two settings of a toggle. An approach that quantifies the fractional occupancy of the on- and off-states is illustrated.     

Direct and indirect interactions of the cytoplasmic region of CD244 (2B4) in mice and humans with FYN kinase

Engagement of the receptor CD244 (2B4) by its ligand CD48 has inhibitory and activating potential, and this differs depending on experimental systems in mouse and human. We show that, in both mouse and human upon engagement of its ligand CD48, CD244 can give a negative signal to natural killer cells, implying conservation of function between the two species. The signaling mechanisms used by CD244 in both human and mouse are conserved as shown by quantitative analyses of the direct molecular interactions of the SH2 domains of the adaptors SLAM-associated protein (SAP) and EAT-2 and of FYN kinase with CD244 together with the indirect interactions of the FYN SH2 domain with EAT-2. Functional experiments support the biochemical hierarchy of interactions and show that EAT-2 is not inhibitory per se. The data are consistent with a model in which the mechanism of signal transduction by CD244 is to regulate FYN kinase recruitment and/or activity and the outcome of CD48/CD244 interactions is determined by which other receptors are engaged.     

The complexity of complexes in signal transduction

Many activities of cells are controlled by cell-surface receptors, which in response to ligands, trigger intracellular signaling reactions that elicit cellular responses. A hallmark of these signaling reactions is the reversible nucleation of multicomponent complexes, which typically begin to assemble when ligand-receptor binding allows an enzyme, often a kinase, to create docking sites for signaling molecules through chemical modifications, such as tyrosine phosphorylation. One function of such docking sites is the co-localization of enzymes with their substrates, which can enhance both enzyme activity and specificity. The directed assembly of complexes can also influence the sensitivity of cellular responses to ligand-receptor binding kinetics and determine whether a cellular response is up- or downregulated in response to a ligand stimulus. The full functional implications of ligand-stimulated complex formation are difficult to discern intuitively. Complex formation is governed by conditional interactions among multivalent signaling molecules and influenced by quantitative properties of both the components in a system and the system itself. Even a simple list of the complexes that can potentially form in response to a ligand stimulus is problematic because of the number of ways signaling molecules can be modified and combined. Here, we review the role of multicomponent complexes in signal transduction and advocate the use of mathematical models that incorporate detail at the level of molecular domains to study this important aspect of cellular signaling.     

Spatio-temporal dependence of the signaling response in immune-receptor trafficking networks regulated by cell density: a theoretical model

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium ligand + surface receptor [Please see text] ligand - receptor complex. Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment.     

Mass-dependent signaling between G protein coupled receptors

The present study provides evidence that G protein coupled receptor (GPCR) signaling pathways participate in an interactive signaling network governed by the principles of mass action. Using an inducible thromboxane A2 receptor (TPR)/platelet activating factor receptor (PAFR) co-expressing cell model, TPR or PAFR expression was independently up-regulated. Immunostaining and radioligand binding experiments demonstrated that this receptor up-regulation resulted in increased GPCR:G protein mass ratios. This increase in mass ratio impacted both TPR and PAFR ligand affinity. Specifically, up-regulating TPR expression not only decreased TPR ligand affinity, but also decreased the ligand affinity of PAFRs. A similar effect on ligand affinities was observed when PAFRs were up-regulated. In addition, increasing the GPCR:G protein mass ratio for TPRs led to desensitization of the calcium mobilization response to PAFR activation, and increasing PAFR mass desensitized the TPR-mediated calcium response. Finally, it was observed that an increased TPR:G protein mass ratio was associated with a shift in the TPR signaling response, and revealed an additional TPR signaling pathway through G(S). Collectively, these results describe a novel mechanism, i.e., mass-dependent GPCR signaling, by which cells can modulate their GPCR signaling pathways and signaling priorities.     

Chemotaxis receptor complexes: from signaling to assembly

Complexes of chemoreceptors in the bacterial cytoplasmic membrane allow for the sensing of ligands with remarkable sensitivity. Despite the excellent characterization of the chemotaxis signaling network, very little is known about what controls receptor complex size. Here we use in vitro signaling data to model the distribution of complex sizes. In particular, we model Tar receptors in membranes as an ensemble of different sized oligomer complexes, i.e., receptor dimers, dimers of dimers, and trimers of dimers, where the relative free energies, including receptor modification, ligand binding, and interaction with the kinase CheA determine the size distribution. Our model compares favorably with a variety of signaling data, including dose-response curves of receptor activity and the dependence of activity on receptor density in the membrane. We propose that the kinetics of complex assembly can be measured in vitro from the temporal response to a perturbation of the complex free energies, e.g., by addition of ligand.     

Immobile ligands enhance FcγR-TLR2/1 crosstalk by promoting interface overlap of receptor clusters

Innate immune cells detect pathogens through simultaneous stimulation of multiple receptors, but how cells use the receptor crosstalk to elicit context-appropriate responses is unclear. Here, we reveal that the inflammatory response of macrophages from FcγR-TLR2/1 crosstalk inversely depends on the ligand mobility within a model pathogen membrane. The mechanism is that FcγR and TLR2/1 form separate nanoclusters that interact at their interfaces during crosstalk. Less mobile ligands induce stronger interactions and more overlap between the receptor nanoclusters, leading to enhanced signaling. Different from the prevailing view that immune receptors colocalize to synergize their signaling, our results show that FcγR-TLR2/1 crosstalk occurs through interface interactions between non-colocalizing receptor nanoclusters, which are modulated by ligand mobility. This suggests a mechanism by which innate immune cells could use physical properties of ligands to fine-tune host responses.