Receptor methylation controls the magnitude of stimulus-response coupling in bacterial chemotaxis

Motile prokaryotes employ a chemoreceptor-kinase array to sense changes in the media and properly adjust their swimming behavior. This array is composed of a family of Type I membrane receptors, a histidine protein kinase (CheA), and an Src homology 3-like protein (CheW). Binding of an attractant to the chemoreceptors inhibits CheA, which results in decreased phosphorylation of the chemotaxis response regulator (CheY). Sensitivity of the system to stimuli is modulated by a protein methyltransferase (CheR) and a protein methylesterase (CheB) that catalyze the methylation and demethylation of specific glutamyl residues in the cytoplasmic domain of the receptors. One of the most fundamental unanswered questions concerning the bacterial chemotaxis mechanism is the quantitative relationship between ligand binding to receptors and CheA inhibition. We show that the receptor glutamyl modifications cause adaptation by changing the gain (magnitude amplification) between attractant binding and kinase inhibition without substantially affecting ligand binding affinity. The mechanism adjusts receptor sensitivity to background stimulus intensity over several orders of magnitude of attractant concentrations. The cooperative effects of ligand binding appear to be minimal with Hill coefficients for kinase inhibition less than 2, independent of the state of glutamyl modification.     

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.     

Cooperative signaling among bacterial chemoreceptors

Four chemoreceptors in Escherichia coli mediate responses to chemicals in the environment. The receptors self-associate and localize to the cell poles. This aggregation implies that interactions among receptors are important parameters of signal processing during chemotaxis. We examined this phenomenon using a receptor-coupled in vitro assay of CheA kinase activity. The ability of homogeneous populations of the serine receptor Tsr and the aspartate receptor Tar to stimulate CheA was directly proportional to the ratio of the receptor to total protein in cell membranes up to a fraction of 50%. Membranes containing mixed populations of Tar and Tsr supported an up to 4-fold greater stimulation of CheA than expected on the basis of the contributions of the individual receptors. Peak activity was seen at a Tar:Tsr ratio of 1:4. This synergy was observed only when the two proteins were expressed simultaneously, suggesting that, under our conditions, the fundamental "cooperative receptor unit" is relatively static, even in the absence of CheA and CheW. Finally, we observed that inhibition of receptor-stimulated CheA activity by serine or aspartate required significantly higher concentrations of ligand for membranes containing mixed Tsr and Tar populations than for membranes containing only Tsr (up to 10(2)-fold more serine) or Tar (up to 10(4)-fold more aspartate). Together with recent analyses of the interactions of Tsr and Tar in vivo, our results reveal the emergent properties of mixed receptor populations and emphasize their importance in the integrated signal processing that underlies bacterial chemotaxis.     

Adaptation of human neutrophil responsiveness to the chemoattractant N-formylmethionylleucylphenylalanine. Heterogeneity and/or negative cooperative interaction of receptors

The dose-response characteristics of the neutrophil 3-3'-dipentyloxacarbocyanine (di-O-C5(3)) fluorescence response to repetitive stimulation with the chemoattractant N-formylmethionylleucylphenylalanine (fMet-Leu-Phe) were studied. Neutrophils exposed to the chemoattractant fMet-Leu-Phe at less than 5 X 10(-8) M subsequently responded only to higher concentrations of fMet-Leu-Phe. This stimulus-induced modification of neutrophil responsiveness involved a reversible fMet-Leu-Phe-induced shift in response Km (the concentration of fMet-Leu-Phe producing a half-maximal response) to higher values which occurred 1 to 2 min after exposure to fMet-Leu-Phe and represented a form of adaptation. A Hill coefficient of 0.68 +/- 0.07 was determined from analysis of the data indicating that the di-O-C5(3) fluorescence response behavior is compatible with functional negatively cooperative interaction and/or heterogeneity of fMet-Leu-Phe receptors. In related studies, analysis of the binding of fMet-Leu-[3H]Phe to intact cells and cell-free plasma membrane preparations resulted in Hill coefficients of 0.64 +/- 0.06 and 0.69 +/- 0.07, respectively, indicating that fMet-Leu-Phe binding exhibits properties similar to the fMet-Leu-Phe-elicited di-O-C5(3) fluorescence response. Modulation of receptor affinity, through either negative cooperativity or changing populations of heterogeneous receptors, may be an important mechanism by which neutrophils adapt and respond to a gradient of chemoattractant during the process of chemotaxis.     

Chemoreceptors in signalling complexes: shifted conformation and asymmetric coupling

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

Quantitative analysis of aspartate receptor signaling complex reveals that the homogeneous two-state model is inadequate: development of a heterogeneous two-state model

The two-state model of receptor activation, in which a receptor population exists in equilibrium between a single on-state and a single off-state, has long been considered a viable model for the signaling behavior of bacterial chemoreceptors. Here, we show that this simple, homogeneous two-state model is adequate for a pure receptor population with just one adaptation state, but fails to account quantitatively for the observed linear relationship between the apparent attractant affinity (K(1/2)) and kinase activity (V(obs)(apo)) as the adaptation state is varied. Further analysis reveals that the available data are instead consistent with a heterogeneous two-state model in which covalent modification of receptor adaptation sites changes the microscopic properties of the on-state or off-state. In such a system, each receptor molecule retains a single on-state and off-state, but covalent adaptation generates a heterogeneous population of receptors exhibiting a range of different on-states or off-states with different microscopic parameters and conformations. It follows that covalent adaptation transforms the receptor from a simple, two-state toggle switch into a variable switch. In order to identify the microscopic parameters most sensitive to covalent adaptation, six modified, two-state models were examined in which covalent adaptation alters a different microscopic parameter. The analysis suggests that covalent adaptation primarily alters the ligand-binding affinity of the receptor off-state (K(D1)). By contrast, models in which covalent adaptation alters the ligand-binding affinity of the receptor on-state, the maximal kinase stimulation of the on-state or off-state, cooperative interactions between receptors, or the assembly of the receptor-kinase signaling complex are inconsistent with the available evidence. Overall, the findings support a heterogeneous two-state model in which modification of the receptor adaptation sites generates a population of receptors with heterogeneous off-states differing in their attractant affinities.In the process of testing the effects of covalent adaptation on the assembly of the receptor-kinase signaling complex, a new method for estimating the stoichiometric ratio of receptor and CheA in the ternary signaling complex was devised. This method suggests that the ratio of receptor dimers to CheA dimers in the assembled complex is 6:1 or less.     

Control of chemotactic signal gain via modulation of a pre-formed receptor array

The remarkably wide dynamic range of the chemotactic pathway of Escherichia coli, a model signal transduction system, is achieved by methylation/amidation of the transmembrane chemoreceptors that regulate the histidine kinase CheA in response to extracellular stimuli. The chemoreceptors cluster at a cell pole together with CheA and the adaptor CheW. Several lines of evidence have led to models that assume high cooperativity and sensitivity via collaboration of receptor dimers within a cluster. Here, using in vivo disulfide cross-linking assays, we have demonstrated a well defined arrangement of the aspartate chemoreceptor (Tar). The differential effects of amidation on cross-linking at different positions indicate that amidation alters the relative orientation of Tar dimers to each other (presumably inducing rotational displacements) without much affecting the conformation of the periplasmic domains. Interestingly, the effect of aspartate on cross-linking at any position tested was roughly opposite to that of receptor amidation. Furthermore, amidation attenuated the effects of aspartate by several orders of magnitude. These results suggest that receptor covalent modification controls signal gain by altering the arrangement or packing of receptor dimers in a pre-formed cluster.     

Tuning the responsiveness of a sensory receptor via covalent modification.

Down-regulation or adaptation of receptors is an essential part of the chemotaxis mechanism to sense gradients. Using localized mutagenesis it is shown that the covalent modification of the receptors makes a slight change in the binding constant (factor of 2) which is far too small to explain the adaptation. The modification does, however, alter the signaling dramatically, an increasing tumbling signal being correlated with increased covalent modification. Responses in the two extreme cases, namely, completely unmodified and completely modified receptor, occur at attractant concentrations separated by 2 orders of magnitude. Amidation of the regulatory glutamate residues causes essentially the same signaling change as methylation. Thus, adaptation in chemotaxis is due to modulation of the receptor's signaling properties, not its affinity for the chemoeffector.     

Hydrophobic agaroses: basis for a model of multivalent effector-receptor interactions.

An increase in the density of butyl residues bound to Sepharose 4B leads to an enhancement of the affinity of these gels for phosphorylase b in the presence of 1.1M ammonium sulfate. A Hill coefficient of 2.9 indicates that a minimum of ca. 3 binding sites is involved in the positive cooperative adsorption of this enzyme. Binding studies of phosphorylase b on butyl-Sepharose of a specific degree of substitution demonstrate that the affinity of the gel for this ligand decreases as a function of fractional saturation. A Hill coefficient of 0.44 indicates negative cooperativity as a result of multivalent binding. From these observations a multivalent, mobile receptor model is derived which can explain such characteristics of effector-receptor interactions as: positive and negative cooperativity, high binding constants and low dissociation rate constants. The application of this model to experiments taken from the literature on the binding of the multivalent effectors concanavalin A and cholera toxin to fat cells shows that the postulated mode of interactions is probably realized in nature.     

Adaptation mechanism of the aspartate receptor: electrostatics of the adaptation subdomain play a key role in modulating kinase activity

The aspartate receptor of the Escherichia coli and Salmonella typhimurium chemotaxis pathway generates a transmembrane signal that regulates the activity of the cytoplasmic kinase CheA. Previous studies have identified a region of the cytoplasmic domain that is critical to receptor adaptation and kinase regulation. This region, termed the adaptation subdomain, contains a high density of acidic residues, including specific glutamate residues that serve as receptor adaptation sites. However, the mechanism of signal propagation through this region remains poorly understood. This study uses site-directed mutagenesis to neutralize each acidic residue within the subdomain to probe the hypothesis that electrostatics in this region play a significant role in the mechanism of kinase activation and modulation. Each point mutant was tested for its ability to regulate chemotaxis in vivo and kinase activity in vitro. Four point mutants (D273N, E281Q, D288N, and E477Q) were found to superactivate the kinase relative to the wild-type receptor, and all four of these kinase-activating substitutions are located along the same intersubunit interface as the adaptation sites. These activating substitutions retained the wild-type ability of the attractant-occupied receptor to inhibit kinase activity. When combined in a quadruple mutant (D273N/E281Q/D288N/E477Q), the four charge-neutralizing substitutions locked the receptor in a kinase-superactivating state that could not be fully inactivated by the attractant. Similar lock-on character was observed for a charge reversal substitution, D273R. Together, these results implicate the electrostatic interactions at the intersubunit interface as a major player in signal transduction and kinase regulation. The negative charge in this region destabilizes the local structure in a way that enhances conformational dynamics, as detected by disulfide trapping, and this effect is reversed by charge neutralization of the adaptation sites. Finally, two substitutions (E308Q and E463Q) preserved normal kinase activation in vitro but blocked cellular chemotaxis in vivo, suggesting that these sites lie within the docking site of an adaptation enzyme, CheR or CheB. Overall, this study highlights the importance of electrostatics in signal transduction and regulation of kinase activity by the cytoplasmic domain of the aspartate receptor.     

A mechanism for simultaneous sensing of aspartate and maltose by the Tar chemoreceptor of Escherichia coli

The Tar chemoreceptor of Escherichia coli exhibits partial sensory additivity. Tar can mediate simultaneous responses to two disparate ligands, aspartate and substrate-loaded maltose-binding protein (MBP). To investigate how one receptor generates concurrent signals to two stimuli, ligand-binding asymmetry was imposed on the rotationally symmetric Tar homodimer. Mutations causing specific defects in aspartate or maltose chemotaxis were introduced pairwise into plasmid-borne tar genes. The doubly mutated tar genes did not restore aspartate or maltose chemotaxis in a strain containing a chromosomal deletion of tar (Δ tar ). However, when Tar proteins with complementing sets of mutations were co-expressed from compatible plasmids, the resulting heterodimeric receptors enabled Δ tar cells to respond to aspartate or maltose. The effect of one attractant on the response to the other depended on the relative orientations of the functional binding sites for aspartate and MBP. When the sites were in the 'same' orientation, saturating levels of one attractant strongly inhibited chemotaxis to the other. In the 'opposite' orientation, such inhibitory effects were negligible. These data demonstrate that opposing subunits of Tar can transmit signals to aspartate and maltose independently if the ligands are restricted to the 'opposite' binding orientation. When aspartate and MBP bind in the 'same' orientation, they compete for signalling through one subunit. In the wild-type Tar dimer, aspartate and MBP can bind in either the 'same' or the 'opposite' orientation, a freedom that can explain the partial additivity of the aspartate and maltose responses that is seen with tar ⁺ cells.     

Study of the interaction between rabbit cardiac contractile and regulatory proteins. An <Emphasis Type="Italic">in vitro</Emphasis> motility assay

A series of experiments was performed in an in vitro motility assay with reconstructed thin filaments to obtain pCa-force relationships for cardiac isomyosins V1 and V3. Two concentrations of each isomyosin (200 and 300 microg/ml) on the surface of a flow cell were tested. Isometric force was estimated as the amount of actin-binding protein, alpha-actinin, stopping thin filament movement. It was found that the amount of alpha-actinin stopping the movement at saturating calcium concentration for V3 was twice higher than for V1 at both concentrations of isoforms. Hill coefficients of cooperativity (h) were determined for pCa-force relationships. The value of h did not differ significantly for isoforms at 300 microg/ml of protein (h was 1.56 for V1 and 1.54 for V3). However, the Hill coefficient was higher for V3 isoform at 200 microg/ml (h = 2.00 and 1.76 for V3 and V1, respectively). Importantly, the Hill coefficient increased for both isoenzymes when their concentrations were decreased. The connection between Hill coefficient and cooperative interactions between cardiac contractile and regulatory proteins is analyzed in detail.     

Changing the specificity of a bacterial chemoreceptor

The methyl-accepting chemotaxis proteins are a family of receptors in bacteria that mediate chemotaxis to diverse signals. To explore the plasticity of these proteins, we have developed a simple method for selecting cells that swim to target attractants. The procedure is based on establishing a diffusive gradient in semi-soft agar plates and does not require that the attractant be metabolized or degraded. We have applied this method to select for variants of the Escherichia coli aspartate receptor, Tar, that have a new or improved response to different amino acids. We found that Tar can be readily mutated to respond to new chemical signals. However, the overall change in specificity depended on the target compound. A Tar variant that could detect cysteic acid still showed a strong sensitivity to aspartate, indicating that the new receptor had a broadened specificity relative to wild-type Tar. Tar variants that responded to phenylalanine or N-methyl aspartate, or that had an increased sensitivity to glutamate showed a strong decrease in their response to aspartate. In at least some of the cases, the maximal level of sensitivity that was obtained could not be attributed solely to substitutions within the binding pocket. The new tar alleles and the techniques described here provide a new approach for exploring the relationship between ligand binding and signal transduction by chemoreceptors and for engineering new receptors for applications in biotechnology.     

Discrimination between nucleotide effector responses of aspartate transcarbamoylase due to a single site substitution in the allosteric binding site

The substitution of alanine for lysine at position 56 of the regulatory polypeptide of aspartate transcarbamoylase affected both homotropic and heterotropic characteristics. In the absence of effectors, the ALAr56-substituted holoenzyme lost the homotropic cooperativity observed for aspartate in the wild-type holoenzyme. Under conditions of allosteric inhibition in the presence of 2mM CTP, the cooperative character of ATCase was restored, and the Hill coefficient increased from 1.0 to 1.7. In contrast to the native enzyme, the altered enzyme did not respond to ATP; however, ATP could still bind to the enzyme as demonstrated by its direct competition with CTP. Furthermore, the recently observed CTP-UTP synergism of the wild-type enzyme was not detectable. The site-directed mutant enzyme could not be activated by low levels of the bisubstrate analogue, N-(phosphonacetyl)-L-aspartate, and the rate of association of pHMB with the cysteine residues located at the interface of the catalytic and regulatory chains was slightly altered. These characteristics suggested that the mutant holoenzyme assumed a relaxed (or abnormal T state) conformation. Thus, this single substitution differentially affected the heterotropic responses to the various allosteric effectors of ATCase and eliminated the homotropic characteristics in response to aspartate in the absence of CTP.     

Reconstitution of the bacterial chemotaxis signal transduction system from purified components.

In bacterial chemotaxis, transmembrane receptor proteins detect attractants and repellents in the medium and send intracellular signals that control motility. The cytoplasmic proteins that transduce information from the receptors to the flagellar motor have previously been purified and many of their enzymatic activities have been identified. Here we report the reconstitution of the complete signal transduction system from purified components. The protein kinase, CheA, plays a central role in both the initial excitation response to stimuli as well as subsequent events associated with adaptation. This kinase provides phosphoryl groups to two acceptor proteins, CheY, which interacts with the flagellar motor, and CheB, which demethylates the receptors. The purified aspartate receptor, Tar, reconstituted into phospholipid vesicles, acts in conjunction with an auxiliary protein, CheW, to stimulate the rate of kinase autophosphorylation greater than 10-fold. This stimulation is inhibited by aspartate. The activity of the kinase is increased by increased levels of receptor methylation. This effect provides a mechanism that explains how changes in receptor methylation mediate adaptive responses to attractant and repellant stimuli.     

Virus-receptor interaction in the adenovirus system: characterization of the positive cooperative binding of virions on HeLa cells.

The established positive cooperativity of adenovirus 2 binding to HeLa cells revealed a strong temperature dependence. The degree of cooperativity, quantified by means of Hill coefficients, progressively increased from 10 degrees C to reach a maximum level, which was maintained between 20 and 37 degrees C. On the other hand, negative cooperativity of virion attachment was apparent at 3.0 degrees C and on glutaraldehyde-stabilized cells. The corresponding monovalent ligand of the system, the fiber antigen, demonstrated only weak-positive cooperativity of the binding at 37.0 degrees C, which was absent at 3.0 degrees C. Dithiothreitol and dansylcadaverine, reagents inhibiting clustering of ligand-receptor complexes in the plasma membrane, markedly reduced the degree of positive cooperative binding at 37.0 degrees C. Evidently, the positive cooperative binding of adenovirus to HeLa cells at 37.0 degrees C is a consequence of both the multivalency of virus attachment proteins, i.e., fibers, on the virion and of the capacity of the receptor sites to migrate in the plane of the plasma membrane, forming local aggregates of virus-receptor site complexes.     

An allosteric model for transmembrane signaling in bacterial chemotaxis

Bacteria are able to sense chemical gradients over a wide range of concentrations. However, calculations based on the known number of receptors do not predict such a range unless receptors interact with one another in a cooperative manner. A number of recent experiments support the notion that this remarkable sensitivity in chemotaxis is mediated by localized interactions or crosstalk between neighboring receptors. A number of simple, elegant models have proposed mechanisms for signal integration within receptor clusters. What is a lacking is a model, based on known molecular mechanisms and our accumulated knowledge of chemotaxis, that integrates data from multiple, heterogeneous sources. To address this question, we propose an allosteric mechanism for transmembrane signaling in bacterial chemotaxis based on the "trimer of dimers" model, where three receptor dimers form a stable complex with CheW and CheA. The mechanism is used to integrate a diverse set of experimental data in a consistent framework. The main predictions are: (1) trimers of receptor dimers form the building blocks for the signaling complexes; (2) receptor methylation increases the stability of the active state and retards the inhibition arising from ligand-bound receptors within the signaling complex; (3) trimer of dimer receptor complexes aggregate into clusters through their mutual interactions with CheA and CheW; (4) cooperativity arises from neighboring interaction within these clusters; and (5) cluster size is determined by the concentration of receptors, CheA, and CheW. The model is able to explain a number of seemingly contradictory experiments in a consistent manner and, in the process, explain how bacteria are able to sense chemical gradients over a wide range of concentrations by demonstrating how signals are integrated within the signaling complex.     

Engineered single‐ and multi‐cell chemotaxis pathways in E. coli

We have engineered the chemotaxis system of Escherichia coli to respond to molecules that are not attractants for wild‐type cells. The system depends on an artificially introduced enzymatic activity that converts the target molecule into a ligand for an E. coli chemoreceptor, thereby enabling the cells to respond to the new attractant. Two systems were designed, and both showed robust chemotactic responses in semisolid and liquid media. The first incorporates an asparaginase enzyme and the native E. coli aspartate receptor to produce a response to asparagine; the second uses penicillin acylase and an engineered chemoreceptor for phenylacetic acid to produce a response to phenylacetyl glycine. In addition, by taking advantage of a ‘hitchhiker’ effect in which cells producing the ligand can induce chemotaxis of neighboring cells lacking enzymatic activity, we were able to design a more complex system that functions as a simple microbial consortium. The result effectively introduces a logical ‘AND’ into the system so that the population only swims towards the combined gradients of two attractants.     

Ligand Depletion in vivo Modulates the Dynamic Range and Cooperativity of Signal Transduction

Biological signal transduction commonly involves cooperative interactions in the binding of ligands to their receptors. In many cases, ligand concentrations in vivo are close to the value of the dissociation constant of their receptors, resulting in the phenomenon of ligand depletion. Using examples based on rotational bias of bacterial flagellar motors and calcium binding to mammalian calmodulin, we show that ligand depletion diminishes cooperativity and broadens the dynamic range of sensitivity to the signaling ligand. As a result, the same signal transducer responds to different ranges of signal with various degrees of cooperativity according to its effective cellular concentration. Hence, results from in vitro dose-response analyses cannot be applied directly to understand signaling in vivo. Moreover, the receptor concentration is revealed to be a key element in controlling signal transduction and we propose that its modulation constitutes a new way of controlling sensitivity to signals. In addition, through an analysis of the allosteric enzyme aspartate transcarbamylase, we demonstrate that the classical Hill coefficient is not appropriate for characterizing the change in conformational state upon ligand binding to an oligomeric protein (equivalent to a dose-response curve), because it ignores the cooperativity of the conformational change for the corresponding equivalent monomers, which are generally characterized by a Hill coefficient . Therefore, we propose a new index of cooperativity based on the comparison of the properties of oligomers and their equivalent monomers.