Reconstruction of the chemotaxis receptor-kinase assembly

In bacterial chemotaxis, an assembly of transmembrane receptors, the CheA histidine kinase and the adaptor protein CheW processes environmental stimuli to regulate motility. The structure of a Thermotoga maritima receptor cytoplasmic domain defines CheA interaction regions and metal ion-coordinating charge centers that undergo chemical modification to tune receptor response. Dimeric CheA-CheW, defined by crystallography and pulsed ESR, positions two CheWs to form a cleft that is lined with residues important for receptor interactions and sized to clamp one receptor dimer. CheW residues involved in kinase activation map to interfaces that orient the CheW clamps. CheA regulatory domains associate in crystals through conserved hydrophobic surfaces. Such CheA self-contacts align the CheW receptor clamps for binding receptor tips. Linking layers of ternary complexes with close-packed receptors generates a lattice with reasonable component ratios, cooperative interactions among receptors and accessible sites for modification enzymes.     

Receptor-mediated protein kinase activation and the mechanism of transmembrane signaling in bacterial chemotaxis.

Chemotaxis responses of Escherichia coli and Salmonella are mediated by type I membrane receptors with N-terminal extracytoplasmic sensing domains connected by transmembrane helices to C-terminal signaling domains in the cytoplasm. Receptor signaling involves regulation of an associated protein kinase, CheA. Here we show that kinase activation by a soluble signaling domain construct involves the formation of a large complex, with approximately 14 receptor signaling domains per CheA dimer. Electron microscopic examination of these active complexes indicates a well defined bundle composed of numerous receptor filaments. Our findings suggest a mechanism for transmembrane signaling whereby stimulus-induced changes in lateral packing interactions within an array of receptor-sensing domains at the cell surface perturb an equilibrium between active and inactive receptor-kinase complexes within the cytoplasm.     

Covalent modification regulates ligand binding to receptor complexes in the chemosensory system of Escherichia coli

In the Escherichia coli chemosensory pathway, receptor modification mediates adaptation to ligand. Evidence is presented that covalent modification influences ligand binding to receptors in complexes with CheW and the kinase CheA. Kinase inhibition was measured with serine receptor complexes in different modification levels; Ki for serine-mediated inhibition increased 10,000-fold from the lowest to the highest level. Without CheA and CheW, ligand binding is unaffected by covalent modification; thus, the influence of covalent modification is mediated only in the receptor complex, a conclusion supported by an analogy to allosteric enzymes and the observation of cooperative kinase inhibition. Also, the finding that a subsaturating serine concentration accelerates active receptor-kinase complex assembly implies that the assembly/disassembly process may also contribute to kinase regulation.     

Mapping out regions on the surface of the aspartate receptor that are essential for kinase activation

The aspartate receptor of bacterial chemotaxis is representative of a large family of taxis receptors widespread in prokaryotes. The homodimeric receptor associates with cytoplasmic components to form a receptor-kinase signaling complex. Within this complex the receptor is known to directly contact the histidine kinase CheA, the coupling protein CheW, and other receptor dimers. However, the locations and extents of the contact regions on the receptor surface remain ambiguous. The present study applies the protein-interactions-by-cysteine-modification (PICM) method to map out surfaces on the aspartate receptor that are essential for kinase stimulation in the assembled receptor-kinase complex. The approach utilizes 52 engineered cysteine positions scattered over the surface of the receptor periplasmic and cytoplasmic domains. When the bulky, anionic probe 5-fluorescein-maleimide is coupled to these positions, large effects on receptor-mediated kinase stimulation are observed at eight cytoplasmic locations. By contrast, no large effects are observed for probe attachment at exposed positions in the periplasmic domain. The results indicate that essential receptor surface regions are located near the hairpin turn at the distal end of the cytoplasmic domain and in the cytoplasmic adaptation site region. These surface regions include the docking sites for CheA, CheW, and other receptor dimers, as well as surfaces that transmit information from the receptor adaptation sites to the kinase. Smaller effects observed in the cytoplasmic linker or HAMP region suggest this region may also play a role in kinase regulation. A comparison of the activity perturbations caused by a dianionic, bulky probe (5-fluorescein-maleimide), a zwitterionic, bulky probe (5-tetramethyl-rhodamine-maleimide), and a nonionic, smaller probe (N-ethyl-maleimide) reveals the roles of probe size and charge in generating the observed effects on kinase activity. Overall, the results indicate that interactions between the periplasmic domains of different receptor dimers are not required for kinase activation in the signaling complex. By contrast, the observed spatial distribution of protein contact surfaces on the cytoplasmic domain is consistent with both (i) distinct docking sites for cytoplasmic proteins and (ii) interactions between the cytoplasmic domains of different dimers to form a trimer-of-dimers.     

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.     

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.     

A fragment liberated from the Escherichia coli CheA kinase that blocks stimulatory, but not inhibitory, chemoreceptor signaling.

CheA, a cytoplasmic histidine autokinase, in conjunction with the CheW coupling protein, forms stable ternary complexes with the cytoplasmic signaling domains of transmembrane chemoreceptors. These signaling complexes induce chemotactic movements by stimulating or inhibiting CheA autophosphorylation activity in response to chemoeffector stimuli. To explore the mechanisms of CheA control by chemoreceptor signaling complexes, we examined the ability of various CheA fragments to interfere with receptor coupling control of CheA. CheA[250-654], a fragment carrying the catalytic domain and an adjacent C-terminal segment previously implicated in stimulatory control of CheA activity, interfered with the production of clockwise flagellar rotation and with chemotactic ability in wild-type cells. Epistasis tests indicated that CheA[250-654] blocked clockwise rotation by disrupting stimulatory coupling of CheA to receptors. In vitro coupling assays confirmed that a stoichiometric excess of CheA[250-654] fragments could exclude CheA from stimulatory receptor complexes, most likely by competing for CheW binding. However, CheA[250-654] fragments, even in vast excess, did not block receptor-mediated inhibition of CheA, suggesting that CheA[250-654] lacks an inhibitory contact site present in native CheA. This inhibitory target is most likely in the N-terminal P1 domain, which contains His-48, the site of autophosphorylation. These findings suggest a simple allosteric model of CheA control by ternary signaling complexes in which the receptor signaling domain conformationally regulates the interaction between the substrate and catalytic domains of CheA.     

Regulation of Fas-associated death domain interactions by the death effector domain identified by a modified reverse two-hybrid screen

The adapter protein FADD consists of two protein interaction domains and is an essential component of the death inducing signaling complex (DISC) that is formed by activated death receptors of the tumor necrosis factor (TNF) receptor family. The FADD death domain binds to activated receptors such as Fas or other adapters such as TRADD, whereas the FADD death effector domain binds to procaspase 8. Each domain can interact with its target in the absence of the other domain, and this has led to the idea that the two domains function independently. FADD death domain interactions with Fas and TRADD are thought to occur on the same surface; however, the regulation of these interactions is poorly understood. We developed a modified reverse two-hybrid method that can identify mutations, which inhibit some protein-protein interactions without affecting other interactions. Using this method, we identified mutations in FADD that prevent binding to Fas but do not affect binding to TRADD. Surprisingly, these mutations were in the death effector domain rather than the death domain. To test whether the mutants function in mammalian cells, we expressed wild type or mutant FADD molecules in FADD-deficient cells. Wild type FADD rescued both Fas ligand- and TNF-dependent signaling, whereas the FADD death effector domain mutants rescued only TNF signaling. These data indicate that in contrast to current models, the death effector domain of FADD is involved in interaction with Fas.     

CheA Kinase of bacterial chemotaxis: chemical mapping of four essential docking sites

The chemotaxis pathway of Escherichia coli and Salmonella typhimurium is the paradigm for the ubiquitous class of 2-component signaling pathways in prokaryotic organisms. Chemosensing begins with the binding of a chemical attractant to a transmembrane receptor on the cell surface. The resulting transmembrane signal regulates a cytoplasmic, multiprotein signaling complex that controls cellular swimming behavior by generating a diffusible phosphoprotein. The minimal functional unit of this signaling complex, termed the core complex, consists of the transmembrane receptor, the coupling protein CheW, and the histidine kinase CheA. Though the structures of individual components are largely known and the core complex can be functionally reconstituted, the architecture of the assembled core complex has remained elusive. To probe this architecture, the present study has utilized an enhanced version of the protein-interactions-by-cysteine-modification method (PICM-beta) to map out docking surfaces on CheA essential for kinase activity and for core complex assembly. The approach employed a library of 70 single, engineered cysteine residues, scattered uniformly over the surfaces of the five CheA domains in a cysteine-free CheA background. These surface Cys residues were further modified by the sulfhydryl-specific alkylating agent, 5-fluorescein-maleimide (5FM). The functional effects of individual Cys and 5FM-Cys surface modifications were measured by kinase assays of CheA activity in both the free and core complex-associated states, and by direct binding assays of CheA associations with CheW and the receptor. The results define (i) two mutual docking surfaces on the CheA substrate and catalytic domains essential for the association of these domains during autophosphorylation, (ii) a docking surface on the CheA regulatory domain essential for CheW binding, and (iii) a large docking surface encompassing regions of the CheA dimerization, catalytic, and regulatory domains proposed to bind the receptor. To test the generality of these findings, a CheA sequence alignment was analyzed, revealing that the newly identified docking surfaces are highly conserved among CheA homologues. These results strongly suggest that the same docking sites are widely utilized in prokaryotic sensory pathways. Finally, the results provide new structural constraints allowing the development of improved models for core complex architecture.     

CheA-Receptor Interaction Sites in Bacterial Chemotaxis

In bacterial chemotaxis, transmembrane chemoreceptors, the CheA histidine kinase, and the CheW coupling protein assemble into signaling complexes that allow bacteria to modulate their swimming behavior in response to environmental stimuli. Among the protein-protein interactions in the ternary complex, CheA-CheW and CheW-receptor interactions were studied previously, whereas CheA-receptor interaction has been less investigated. Here, we characterize the CheA-receptor interaction in Thermotoga maritima by NMR spectroscopy and validate the identified receptor binding site of CheA in Escherichia coli chemotaxis. We find that CheA interacts with a chemoreceptor in a manner similar to that of CheW, and the receptor binding site of CheA's regulatory domain is homologous to that of CheW. Collectively, the receptor binding sites in the CheA-CheW complex suggest that conformational changes in CheA are required for assembly of the CheA-CheW-receptor ternary complex and CheA activation.     

Constitutively signaling fragments of Tsr, the Escherichia coli serine chemoreceptor.

Tsr, the serine chemoreceptor of Escherichia coli, has two signaling modes. One augments clockwise (CW) flagellar rotation, and the other augments counterclockwise (CCW) rotation. To identify the portion of the Tsr molecule responsible for these activities, we isolated soluble fragments of the Tsr cytoplasmic domain that could alter the flagellar rotation patterns of unstimulated wild-type cells. Residues 290 to 470 from wild-type Tsr generated a CW signal, whereas the same fragment with a single amino acid replacement (alanine 413 to valine) produced a CCW signal. The soluble components of the chemotaxis phosphorelay system needed for expression of these Tsr fragment signals were identified by epistasis analysis. Like full-length receptors, the fragments appeared to generate signals through interactions with the CheA autokinase and the CheW coupling factor. CheA was required for both signaling activities, whereas CheW was needed only for CW signaling. Purified Tsr fragments were also examined for effects on CheA autophosphorylation activity in vitro. Consistent with the in vivo findings, the CW fragment stimulated CheA, whereas the CCW fragment inhibited CheA. CheW was required for stimulation but not for inhibition. These findings demonstrate that a 180-residue segment of the Tsr cytoplasmic domain can produce two active signals. The CCW signal involves a direct contact between the receptor and the CheA kinase, whereas the CW signal requires participation of CheW as well. The correlation between the in vitro effects of Tsr signaling fragments on CheA activity and their in vivo behavioral effects lends convincing support to the phosphorelay model of chemotactic signaling.     

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.     

Distributed subunit interactions in CheA contribute to dimer stability: a sedimentation equilibrium study

The structural domains of the Escherichia coli CheA protein resemble 'beads on a string', since the N-terminal phosphate-accepting (P) domain is joined to the CheY/CheB-binding (B) domain through a flexible linker, and the B domain is in turn joined to the C-terminal dimerization/catalytic/regulatory domains by a second intervening linker. Dimerization occurs primarily via interactions between two dimerization domains, which is required for CheA trans-autophosphorylation. In this study, sedimentation equilibrium was used to demonstrate significant subunit interactions at secondary sites in the two naturally occurring (full-length and short) forms of CheA (CheA(1-654) or CheA(L), and CheA(98-654) or CheA(S)) by contrasting the dimerization of CheA(L) and CheA(S) to CheA(T), an engineered form that lacked the P domain entirely. The estimated dimer dissociation constant (K(1,2)) for CheA(T) (3.1 microM) was weaker than K(1,2) for CheA(L) (0.49 microM), which was attributed to the P domain-catalytic domain interactions that were present in CheA(L) but not CheA(T). In contrast, CheA(S) dimerization was unexpectedly stronger (K(1,2) approximately 20 nM), which arose through interactions between two P domain remnants in the CheA(S) dimer. This conclusion was supported by the results of sedimentation equilibrium experiments conducted with P domains and P domain remnants expressed in the absence of the dimerization/catalytic/regulatory domains. The P domain remnant had a measurable tendency to self-associate; the full-length P domain did not. Hydrophobic forces probably drive this interaction, since hydrophobic amino acids buried in the intact P domain are solvent-exposed in CheA(S). Also, the nascent N-terminus of CheA(S) bound to the phosphatase (CheZ) more effectively, a conclusion based on the demonstrably greater ability of the P domain remnant to co-sediment CheZ, compared to the intact P domain.     

Mutational analysis of the chemoreceptor-coupling domain of the Escherichia coli chemotaxis signaling kinase CheA

During chemotactic signaling by Escherichia coli, autophosphorylation of the histidine kinase CheA is coupled to chemoreceptor control by the CheW protein, which interacts with the C-terminal P5 domain of CheA. To identify P5 determinants important for CheW binding and receptor coupling control, we isolated and characterized a series of P5 missense mutants. The mutants fell into four phenotypic groups on the basis of in vivo behavioral and protein stability tests and in vitro assays with purified mutant proteins. Group 1 mutants exhibited autophosphorylation and receptor-coupling defects, and their CheA proteins were subject to relatively rapid degradation in vivo. Group 1 mutations were located at hydrophobic residues in P5 subdomain 2 and most likely caused folding defects. Group 2 mutants made stable CheA proteins with normal autophosphorylation ability but with defects in CheW binding and in receptor-mediated activation of CheA autophosphorylation. Their mutations affected residues in P5 subdomain 1 near the interface with the CheA dimerization (P3) and ATP-binding (P4) domains. Mutant proteins of group 3 were normal in all tests yet could not support chemotaxis, suggesting that P5 has one or more important but still unknown signaling functions. Group 4 mutant proteins were specifically defective in receptor-mediated deactivation control. The group 4 mutations were located in P5 subdomain 1 at the P3/P3' interface. We conclude that P5 subdomain 1 is important for CheW binding and for receptor coupling control and that these processes may require substantial motions of the P5 domain relative to the neighboring P3 and P4 domains of CheA.     

Structural determinants for phosphatidic acid regulation of phospholipase C-beta1

Signaling from G protein-coupled receptors to phospholipase C-beta (PLC-beta) is regulated by coordinate interactions among multiple intracellular signaling molecules. Phosphatidic acid (PA), a signaling phospholipid, binds to and stimulates PLC-beta(1) through a mechanism that requires the PLC-beta(1) C-terminal domain. PA also modulates Galpha(q) stimulation of PLC-beta(1). These data suggest that PA may have a key role in the regulation of PLC-beta(1) signaling in cells. The present studies addressed the structural requirements and the mechanism for PA regulation of PLC-beta(1). We used a combination of enzymatic assays, PA-binding assays, and circular dichroism spectroscopy to evaluate the interaction of PA with wild-type and mutant PLC-beta(1) proteins and with fragments of the Galpha(q) binding domain. The results identify a region that includes the alphaA helix and flexible loop of the Galpha(q)-binding domain as necessary for PA regulation. A mutant PLC-beta(1) with multiple alanine/glycine replacements for residues (944)LIKEHTTKYNEIQN(957) was markedly impaired in PA regulation. The high affinity and low affinity component of PA stimulation was reduced 70% and PA binding was reduced 45% in this mutant. Relative PLC stimulation by PA increased with PLC-beta(1) concentration in a manner suggesting cooperative binding to PA. Similar concentration dependence was observed in the PLC-beta(1) mutant. These data are consistent with a model for PA regulation of PLC-beta(1) that involves cooperative interactions, probably PLC homodimerization, that require the flexible loop region, as is consistent with the dimeric structure of the Galpha(q)-binding domain. PA regulation of PLC-beta(1) requires unique residues that are not required for Galpha(q) stimulation or GTPase-activating protein activity.     

Different signaling roles of two conserved residues in the cytoplasmic hairpin tip of Tsr, the Escherichia coli serine chemoreceptor

Bacterial chemoreceptors form ternary signaling complexes with the histidine kinase CheA through the coupling protein CheW. Receptor complexes in turn cluster into cellular arrays that produce highly sensitive responses to chemical stimuli. In Escherichia coli, receptors of different types form mixed trimer-of-dimers signaling teams through the tips of their highly conserved cytoplasmic domains. To explore the possibility that the hairpin loop at the tip of the trimer contact region might promote interactions with CheA or CheW, we constructed and characterized mutant receptors with amino acid replacements at the two nearly invariant hairpin charged residues of Tsr: R388, the most tip-proximal trimer contact residue, and E391, the apex residue of the hairpin turn. Mutant receptors were subjected to in vivo tests for the assembly and function of trimers, ternary complexes, and clusters. All R388 replacements impaired or destroyed Tsr function, apparently through changes in trimer stability or geometry. Large-residue replacements locked R388 mutant ternary complexes in the kinase-off (F, H) or kinase-on (W, Y) signaling state, suggesting that R388 contributes to signaling-related conformational changes in the trimer. In contrast, most E391 mutants retained function and all formed ternary signaling complexes efficiently. Hydrophobic replacements of any size (G, A, P, V, I, L, F, W) caused a novel phenotype in which the mutant receptors produced rapid switching between kinase-on and -off states, indicating that hairpin tip flexibility plays an important role in signal state transitions. These findings demonstrate that the receptor determinants for CheA and CheW binding probably lie outside the hairpin tip of the receptor signaling domain.     

Assembly of an MCP receptor, CheW, and kinase CheA complex in the bacterial chemotaxis signal transduction pathway.

We examined the binding interactions of the methylation-dependent chemotaxis receptors Tsr and Tar with the chemotaxis-specific protein kinase CheA and the coupling factor CheW. Receptor directly bound CheW, but receptor-CheA binding was dependent upon the presence of CheW. These observations in combination with our previous identification of a CheW-CheA complex suggest that CheW physically links the kinase to the receptor. The ternary complex of receptor, CheW, and CheA is both kinetically and thermodynamically stable at physiological concentrations. Stability is not significantly altered by changes associated with attractant or repellent binding to the receptor. Such binding greatly modulates the kinase activity of CheA. Our results demonstrate that modulation of the kinase activity does not require association-dissociation of the ternary complex. This suggests that the receptor signal is transduced through conformational changes in the ternary complex rather than through changes in the association of the kinase CheA with receptor and/or CheW.     

Crystal Structure of the Mineralocorticoid Receptor DNA Binding Domain in Complex with DNA

The steroid hormone receptors regulate important physiological functions such as reproduction, metabolism, immunity, and electrolyte balance. Mutations within steroid receptors result in endocrine disorders and can often drive cancer formation and progression. Despite the conserved three-dimensional structure shared among members of the steroid receptor family and their overlapping DNA binding preference, activation of individual steroid receptors drive unique effects on gene expression. Here, we present the first structure of the human mineralocorticoid receptor DNA binding domain, in complex with a canonical DNA response element. The overall structure is similar to the glucocorticoid receptor DNA binding domain, but small changes in the mode of DNA binding and lever arm conformation may begin to explain the differential effects on gene regulation by the mineralocorticoid and glucocorticoid receptors. In addition, we explore the structural effects of mineralocorticoid receptor DNA binding domain mutations found in type I pseudohypoaldosteronism and multiple types of cancer.     

Determinants of chemoreceptor cluster formation in Escherichia coli

Chemotactic stimuli in bacteria are sensed by large sensory complexes, or receptor clusters, that consist of tens of thousands of proteins. Receptor clusters appear to play a key role in signal processing, but their structure remains poorly understood. Here we used fluorescent protein fusions to study in vivo formation of the cluster core, which consists of receptors, a kinase CheA and an assisting protein CheW. We show that receptors aggregate through their cytoplasmic domains even in the absence of other chemotaxis proteins. Clustering is further enhanced by the binding of CheW. Surprisingly, we observed that some fragments of CheA bind receptor clusters well in the absence of CheW, although the latter does assist the binding of full-length CheA. The resulting mode of receptor cluster formation is consistent with an experimentally observed flexible stoichiometry of chemosensory complexes and with assumptions of recently proposed computer models of signal processing in chemotaxis.