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1.
Chemotaxis by cells of Escherichia coli and Salmonella typhimurium depends upon the ability of chemoreceptors called transducers to communicate with switch components of flagellar motors to modulate swimming behavior. This communication requires an excitatory pathway composed of the cytoplasmic signal transduction proteins, CheAL, CheAS, CheW, CheY, and CheZ. Of these, the autokinase CheAL is most central. Modifications or mutations that affect the rate at which CheAL autophosphorylates result in profound chemotactic defects. Here we demonstrate that pH can affect CheAL autokinase activity in vitro. This activity exhibits a bell-shaped dependence upon pH within the range 6.5 to 10.0, consistent with the notion that two proton dissociation events affect CheAL autophosphorylation kinetics: one characterized by a pKa of about 8.1 and another exhibiting a pKa of about 8.9. These in vitro results predict a decrease in the rate of CheAL autophosphorylation in response to a reduction in intracellular pH, a decrease that should cause increased counterclockwise flagellar rotation. We observed such a response in vivo for cells containing a partially reconstituted chemotaxis system. Benzoate (10 mM, pH 7.0), a weak acid that when undissociated readily traverses the cytoplasmic membrane, causes a reduction of cytoplasmic pH from 7.6 to 7.3. In response to this reduction, cells expressing CheAL, CheAS, and CheY, but not transducers, exhibited a small but reproducible increase in the fraction of time that they spun their flagellar motors counterclockwise. The added presence of CheW and the transducers Tar and Trg resulted in a more dramatic response. The significance of our in vitro results, their relationships to regulation of swimming behavior, and the mechanisms by which transducers might affect the pH dependence of CheA autokinase activity are discussed.  相似文献   

2.
If cells of Escherichia coli deleted for genes that specify transducers and all known cytoplasmic chemotaxis proteins are reconstituted with CheA, CheW, and CheY, they spin their flagella alternately clockwise and counterclockwise. If the aspartate receptor also is present, clockwise rotation is suppressed upon addition of aspartate. If either CheA or CheW is absent, the fraction of time that the flagella spin clockwise is reduced and responses to aspartate do not occur.  相似文献   

3.
The signal transduction system that mediates bacterial chemotaxis allows cells to moduate their swimming behavior in response to fluctuations in chemical stimuli. Receptors at the cell surface receive information from the surroundings. Signals are then passed from the receptors to cytoplasmic chemotaxis components: CheA, CheW, CheZ, CheR, and CheB. These proteins function to regulate the level of phosphorylation of a response regulator designated CheY that interacts with the flagellar motor switch complex to control swimming behavior. The structure of CheY has been determined. Magnesium ion is essential for activity. The active site contains highly conserved Asp residues that are required for divalent metal ion binding and CheY phosphorylation. Another residue-at the active site, Lys109, is important in the phosphorylation-induced conformational change that facilitates communication with the switch complex and another chemotaxis component, CheZ. CheZ facilitates the dephosphorylation of phospho-CheY. Defects in CheY and CheZ can be suppressed by mutations in the flagellar switch complex. CheZ is thought to modulate the switch bias by varying the level of phospho-CheY. © 1993 Wiley-Liss, Inc.  相似文献   

4.
We prepared fusions of yellow fluorescent protein [the YFP variant of green fluorescent protein (GFP)] with the cytoplasmic chemotaxis proteins CheY, CheZ and CheA and the flagellar motor protein FliM, and studied their localization in wild-type and mutant cells of Escherichia coli. All but the CheA fusions were functional. The cytoplasmic proteins CheY, CheZ and CheA tended to cluster at the cell poles in a manner similar to that observed earlier for methyl-accepting chemotaxis proteins (MCPs), but only if MCPs were present. Co-localization of CheY and CheZ with MCPs was CheA dependent, and co-localization of CheA with MCPs was CheW dependent, as expected. Co-localization with MCPs was confirmed by immunofluorescence using an anti-MCP primary antibody. The motor protein FliM appeared as discrete spots on the sides of the cell. These were seen in wild-type cells and in a fliN mutant, but not in flhC or fliG mutants. Co-localization with flagellar structures was confirmed by immunofluorescence using an antihook primary antibody. Surprisingly, we did not observe co-localization of CheY with motors, even under conditions in which cells tumbled.  相似文献   

5.
The Escherichia coli chemotaxis signal transduction pathway has: CheA, a histidine protein kinase; CheW, a linker between CheA and sensory proteins; CheY, the effector; and CheZ, a signal terminator. Rhodobacter sphaeroides has multiple copies of these proteins (2 x CheA, 3 x CheW and 3 x CheY, but no CheZ). In this study, we found a fourth cheY and expressed these R. sphaeroides proteins in E. coli. CheA2 (but not CheA1) restored swarming to an E. coli cheA mutant (RP9535). CheW3 (but not CheW2) restored swarming to a cheW mutant of E. coli (RP4606). R. sphaeroides CheYs did not affect E. coli lacking CheY, but restored swarming to a cheZ strain (RP1616), indicating that they can act as signal terminators in E. coli. An E. coli CheY, which is phosphorylated but cannot bind the motor (CheY109KR), was expressed in RP1616 but had no effect. Overexpression of CheA2, CheW2, CheW3, CheY1, CheY3 and CheY4 inhibited chemotaxis of wild-type E. coli (RP437) by increasing its smooth-swimming bias. While some R. sphaeroides proteins restore tumbling to smooth-swimming E. coli mutants, their activity is not controlled by the chemosensory receptors. R. sphaeroides possesses a phosphorelay cascade compatible with that of E. coli, but has additional incompatible homologues.  相似文献   

6.
The dynamics of protein phosphorylation in bacterial chemotaxis   总被引:30,自引:0,他引:30  
K A Borkovich  M I Simon 《Cell》1990,63(6):1339-1348
The chemotaxis signal transduction pathway allows bacteria to respond to changes in concentration of specific chemicals (ligands) by modulating their swimming behavior. The pathway includes ligand binding receptors, and the CheA, CheY, CheW, and CheZ proteins. We showed previously that phosphorylation of CheY is activated in reactions containing receptor, CheW, CheA, and CheY. Here we demonstrate that this activation signal results from accelerated autophosphorylation of the CheA kinase. Evidence for a second signal transmitted by a ligand-bound receptor, which corresponds to inhibition of CheA autophosphorylation, is also presented. We postulate that CheA can exist in three forms: a "closed" form in the absence of receptor and CheW; an "open" form that results from activation of CheA by receptor and CheW; and a "sequestered" form in reactions containing ligand-bound receptor and CheW. The system's dynamics depends on the relative distribution of CheA among these three forms at any time.  相似文献   

7.
Bacterial chemotaxis is a colonization factor for the ulcer-causing pathogen Helicobacter pylori. H. pylori contains genes encoding the chemotaxis signalling proteins CheW, CheA and CheY; CheW couples chemoreceptors to the CheA kinase and is essential for chemotaxis. While characterizing a cheW mutant, we isolated a spontaneous, chemotactic variant (Che+). We determined that this phenotype was caused by a genetic change unlinked to the original cheW mutation. To locate the underlying Che+ mutation, we compared total protein profiles of the non-chemotactic mutant (cheW) with those from the cheW Che+ variant by two-dimensional differential in-gel electrophoresis. One protein was found only in the cheW Che+ variant. This protein was identified by MS/MS as HP0170, a hypothetical protein with no known function. DNA sequencing verified that hp0170 was mutated in the cheW Che+ suppressor, and deletion of this open reading frame in the cheW background nearly recapitulated the Che+ suppressor phenotype. Using hidden Markov models, we found that HP0170 is a remote homologue of E. coli CheZ. CheZ interacts with phosphorylated CheY and stimulates its autodephosphorylation. CheZ was not predicted to be present in epsilon-proteobacteria. We found that chemotaxis in the cheW Che+ suppressor depended on both cheY and cheA. We hypothesize that a small amount of phosphorylated CheY is generated via CheA in the cheW mutant, and this amount is sufficient to affect flagellar rotation when HP0170 is removed. Our results suggest that HP0170 is a remote homologue of CheZ, and that CheZ homologues are found in a broader range of bacteria than previously supposed.  相似文献   

8.
The sensory transduction pathways between the transducing proteins and the switch on the flagellar motors have been investigated in Escherichia coli and Salmonella typhimurium. ATP, not GTP, is required for normal chemotaxis. A site of ATP action appears to be the conversion of an inactive form of the CheY protein to an active form, designated CheY*, that binds to the motor switch and initiates clockwise rotation. The methylation-dependent and methylation-independent pathways for chemotaxis have a common requirement for the CheA, CheW, and CheY proteins in addition to the switch and flagellar motor. It is concluded that the receptor/transducing proteins and the adaptation mechanism differ in the two types of pathway, but that other components of the transduction pathway are common to the methylation-dependent and methylation-independent pathways.  相似文献   

9.
Protein phosphorylation in the bacterial chemotaxis system   总被引:2,自引:0,他引:2  
M I Simon  K A Borkovich  R B Bourret  J F Hess 《Biochimie》1989,71(9-10):1013-1019
Bacterial chemotaxis involves the detection of changes in concentration of specific chemicals in the environment of the cell as a function of time. This process is mediated by a series of cell surface receptors that interact with and activate intracellular protein phosphorylation. Five cytoplasmic proteins essential for chemotaxis have been shown to be involved in a coupled system of protein phosphorylation. Ligand binding to cell surface receptors affects the rate of autophosphorylation of the CheA protein. In the absence of an attractant bound to receptor and in the presence of the CheW protein, the rate of CheA autophosphorylation is markedly increased. Phosphorylated CheA can transfer phosphate to the CheY or CheB proteins; phosphorylation of these "effector" proteins may increase their activity. The CheY protein is thought to regulate flagellar rotation and thus control swimming behavior. The CheB protein modifies the cell surface receptor and thus regulates receptor function. Finally, another chemotaxis protein, CheZ, acts to specifically dephosphorylate CheY-phosphate. This system shows marked similarity to the 2-component sensor-regulator systems found to control specific gene expression in a variety of bacteria.  相似文献   

10.
Most motile bacteria are capable of directing their movement in response to chemical gradients, a behavior known as chemotaxis. The signal transduction system that mediates chemotaxis in enteric bacteria consists of a set of six cytoplasmic proteins that couple stimuli sensed by a family of transmembrane receptors to behavioral responses generated by the flagellar motors. Signal transduction occurs via a phosphotransfer pathway involving a histidine protein kinase, CheA, and a response regulator protein, CheY, that in its phosphorylated state, modulates the direction of flagellar rotation. Two auxiliary proteins, CheW and CheZ, and two receptor modification enzymes, methylesterase CheB and methyltransferase CheR, influence the flux of phosphoryl groups within this central pathway. This paper focuses on structural characteristics of the four signaling proteins (CheA, CheY, CheB, and CheR) for which NMR or x-ray crystal structures have been determined. The proteins are examined with respect to their signaling activities that involve reversible protein modifications and transient assembly of macromolecular complexes. A variety of data suggest conformational flexibility of these proteins, a feature consistent with their multiple roles in a dynamic signaling pathway.  相似文献   

11.
Chemical signals sensed on the periplasmic side of bacterial cells by transmembrane chemoreceptors are transmitted to the flagellar motors via the histidine kinase CheA, which controls the phosphorylation level of the effector protein CheY. Chemoreceptor arrays comprise remarkably stable supramolecular structures in which thousands of chemoreceptors are networked through interactions between their cytoplasmic tips, CheA, and the small coupling protein CheW. To explore the conformational changes that occur within this protein assembly during signalling, we used in vivo cross‐linking methods to detect close interactions between the coupling protein CheW and the serine receptor Tsr in intact Escherichia coli cells. We identified two signal‐sensitive contacts between CheW and the cytoplasmic tip of Tsr. Our results suggest that ligand binding triggers changes in the receptor that alter its signalling contacts with CheW (and/or CheA).  相似文献   

12.
CheY, a small cytoplasmic response regulator, plays an essential role in the chemotaxis pathway. The concentration of phospho-CheY is thought to determine the swimming behaviour of the cell: high levels of phospho-CheY cause bacteria to rotate their flagella clockwise and tumble, whereas low levels of the phos-phorylated form of the protein allow counter-ciockwise rotation of the flagella and smooth swimming. The phosphorylation state of CheY in vivo is determined by the activity of the phosphoryl donor CheA, and by the antagonistic effect of dephosphorylation of phospho-CheY. The dephosphorylation rate is controlled by the intrinsic autohydrolytic activity of phospho-CheY and by the CheZ protein, which accelerates dephosphorylation. We have analysed the effect of CheZ on the dephosphorylation rates of several mutant CheY proteins. Two point mutations were identified which were 50-fold and 5-fold less sensitive to the activity of CheZ than was the wild-type protein. Nonetheless, the phosphorylation and autodephos-phorylation rates of these mutants, CheY23ND and CheY26KE, were observed to be identical to those of wild-type CheY in the absence of CheZ. These are the first examples of CheY mutations that reduce sensitivity to the phosphatase activity of CheZ without being altered in terms of their intrinsic phosphorylation and autodephospborylation rates, interestingly, the residues Asn-23 and Lys-26 are located on a face of CheY far from the phosphorylation site (Asp-57), distinct from the previously described site of inter-action with the histidine kinase CheA, and partially overlapping with a region implicated in interaction with the flagellar switch.  相似文献   

13.
A well-characterized protein phosphorelay mediates Escherichia coli chemotaxis towards the amino acid attractant aspartate. The protein CheY shuttles between flagellar motors and methyl-accepting chemoreceptor (MCP) complexes containing the linker CheW and the kinase CheA. CheA-CheY phosphotransfer generates phospho-CheY, CheY-P. Aspartate triggers smooth swim responses by inactivation of the CheA bound to the target MCP, Tar; but this mechanism alone cannot explain the observed response sensitivity. Here, we used behavioral analysis of mutants deleted for CheZ, a catalyst of CheY-P dephosphorylation, or the methyltransferase CheR and/or the methylesterase CheB to examine the roles of accelerated CheY-P dephosphorylation and MCP methylation in enhancement of the chemotactic response. The extreme motile bias of the mutants was adjusted towards wild-type values, while preserving much of the aspartate response sensitivity by expressing fragments of the MCP, Tsr, that either activate or inhibit CheA. We then measured responses to small jumps of aspartate, generated by flash photolysis of photo-labile precursors. The stimulus-response relation for Delta cheZ mutants overlapped that for the host strains. Delta cheZ excitation response times increased with stimulus size consistent with formation of an occluded CheA state. Thus, neither CheZ-dependent or independent increases in CheY-P dephosphorylation contribute to the excitation response. In Delta cheB Delta cheR or Delta cheR mutants, the dose for a half-maximal response, [Asp](50), was ca 10 microM; but was elevated to 100 microM in Delta cheB mutants. In addition, the stimulus-response relation for these mutants was linear, consistent with stoichiometric inactivation, in contrast to the non-linear relation for wild-type E. coli. These data suggest that response sensitivity is controlled by differential binding of CheR and/or CheB to distinct MCP signaling conformations.  相似文献   

14.
CheY, a response regulator of the chemotaxis system in Escherichia coli, can be activated by either phosphorylation or acetylation to generate clockwise rotation of the flagellar motor. Both covalent modifications are involved in chemotaxis, but the function of the latter remains obscure. To understand why two different modifications apparently activate the same function of CheY, we studied the effect that each modification exerts on the other. The phosphodonors of CheY, the histidine kinase CheA and acetyl phosphate, each strongly inhibited both the autoacetylation of the acetylating enzyme, acetyl-CoA synthetase (Acs), and the acetylation of CheY. CheZ, the enzyme that enhances CheY dephosphorylation, had the opposite effect and enhanced Acs autoacetylation and CheY acetylation. These effects of the phosphodonors and CheZ were not caused by their respective activities. Rather, they were caused by their interactions with Acs and, possibly, with CheY. In addition, the presence of Acs elevated the phosphorylation levels of both CheA and CheY, and acetate repressed this stimulation. These observations suggest that CheY phosphorylation and acetylation are linked and co-regulated. We propose that the physiological role of these mutual effects is at two levels: linking chemotaxis to the metabolic state of the cell, and serving as a tuning mechanism that compensates for cell-to-cell variations in the concentrations of CheA and CheZ.  相似文献   

15.
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.  相似文献   

16.
Defects in the chemotaxis proteins CheY and CheZ of Salmonella typhimurium can be suppressed by mutations in the flagellar switch, such that swarming of a pseudorevertant on semisolid plates is significantly better than that of its parent. cheY suppressors contribute to a clockwise switch bias, and cheZ suppressors contribute to a counterclockwise bias. Among the three known switch genes, fliM contributes most examples of such suppressor mutations. We have investigated the changes in FliM that are responsible for suppression, as well as the changes in CheY or CheZ that are being compensated for. Ten independently isolated parental cheY mutations represented nine distinct mutations, one an amino acid duplication and the rest missense mutations. Several of the altered amino acids lie on one face of the three-dimensional structure of CheY (A. M. Stock, J. M. Mottonen, J. B. Stock, and C. E. Schutt, Nature (London) 337:745-749, 1989; K. Volz and P. Matsumura, J. Biol. Chem. 266:15511-15519, 1991); this face may constitute the binding site for the switch. All 10 cheZ mutations were distinct, with several of them resulting in premature termination. cheY and cheZ suppressors in FliM occurred in clusters, which in general did not overlap. A few cheZ suppressors and one cheY suppressor involved changes near the N terminus of FliM, but neither cheY nor cheZ suppressors involved changes near the C terminus. Among the strongest cheY suppressors were changes from Arg to a neutral amino acid or from Val to Glu, suggesting that electrostatic interactions may play an important role in switching. A given cheY or cheZ mutation could be suppressed by many different fliM mutations; conversely, a given fliM mutation was often encountered as a suppressor of more than one cheY or cheZ mutation. The data suggest that an important factor in suppression is a balancing of the shift in switch bias introduced by alteration of CheY or CheZ with an appropriate opposing shift introduced by alteration of FliM. For strains with a severe parental mutation, such as the cheZ null mutations, adjustment of switch bias is essentially the only factor in suppression, since the attractant L-aspartate caused at most a slight further enhancement of the swarming rate over that occurring in the absence of a chemotactic stimulus. We discuss a model for switching in which there are distinct interactions for the counterclockwise and clockwise states, with suppression occurring by impairment of one of the states and hence by relative enhancement of the other state. FliM can also undergo amino acid changes that result in a paralyzed (Mot-) phenotype; these changes were confined to a very few residues in the protein.  相似文献   

17.
The CheA kinase is a central protein in the signal transduction network that controls chemotaxis in Escherichia coli. CheA receives information from a transmembrane receptor (e.g., Tar) and CheW proteins and relays it to the CheB and CheY proteins. The biochemical activities of CheA proteins truncated at various distances from the carboxy terminus were examined. The carboxy-terminal portion of CheA regulates autophosphorylation in response to environmental signals transmitted through Tar and CheW. The central portion of CheA is required for autophosphorylation and is also presumably involved in dimer formation. The amino-terminal portion of CheA was previously shown to contain the site of autophosphorylation and to be able to transfer the phosphoryl group to CheB and CheY. These studies further delineate three functional domains of the CheA protein.  相似文献   

18.
Escherichia coli responds to its environment by means of a network of intracellular reactions which process signals from membrane-bound receptors and relay them to the flagellar motors. Although characterization of the reactions in the chemotaxis signaling pathway is sufficiently complete to construct computer simulations that predict the phenotypes of mutant strains with a high degree of accuracy, two previous experimental investigations of the activity remaining upon genetic deletion of multiple signaling components yielded several contradictory results (M. P. Conley, A. J. Wolfe, D. F. Blair, and H. C. Berg, J. Bacteriol. 171:5190–5193, 1989; J. D. Liu and J. S. Parkinson, Proc. Natl. Acad. Sci. USA 86:8703–8707, 1989). For example, “building up” the pathway by adding back CheA and CheY to a gutted strain lacking chemotaxis genes resulted in counterclockwise flagellar rotation whereas “breaking down” the pathway by deleting chemotaxis genes except cheA and cheY resulted in alternating episodes of clockwise and counterclockwise flagellar rotation. Our computer simulation predicts that trace amounts of CheZ expressed in the gutted strain could account for this difference. We tested this explanation experimentally by constructing a mutant containing a new deletion of the che genes that cannot express CheZ and verified that the behavior of strains built up from the new deletion does in fact conform to both the phenotypes observed for breakdown strains and computer-generated predictions. Our findings consolidate the present view of the chemotaxis signaling pathway and highlight the utility of molecularly based computer models in the analysis of complex biochemical networks.  相似文献   

19.
Chemotaxis, the environment-specific swimming behavior of a bacterial cell is controlled by flagellar rotation. The steady-state level of the phosphorylated or activated form of the response regulator CheY dictates the direction of flagellar rotation. CheY phosphorylation is regulated by a fine equilibrium of three phosphotransfer activities: phosphorylation by the kinase CheA, its auto-dephosphorylation and dephosphorylation by its phosphatase CheZ. Efficient dephosphorylation of CheY by CheZ requires two spatially distinct protein-protein contacts: tethering of the two proteins to each other and formation of an active site for dephosphorylation. The former involves interaction of phosphorylated CheY with the small highly conserved C-terminal helix of CheZ (CheZ(C)), an indispensable structural component of the functional CheZ protein. To understand how the CheZ(C) helix, representing less than 10% of the full-length protein, ascertains molecular specificity of binding to CheY, we have determined crystal structures of CheY in complex with a synthetic peptide corresponding to 15 C-terminal residues of CheZ (CheZ(200-214)) at resolutions ranging from 2.0 A to 2.3A. These structures provide a detailed view of the CheZ(C) peptide interaction both in the presence and absence of the phosphoryl analog, BeF3-. Our studies reveal that two different modes of binding the CheZ(200-214) peptide are dictated by the conformational state of CheY in the complex. Our structures suggest that the CheZ(C) helix binds to a "meta-active" conformation of inactive CheY and it does so in an orientation that is distinct from the one in which it binds activated CheY. Our dual binding mode hypothesis provides implications for reverse information flow in CheY and extends previous observations on inherent resilience in CheY-like signaling domains.  相似文献   

20.
The chemotactic sensory system of Escherichia coli comprises membrane-embedded chemoreceptors and six soluble chemotaxis (Che) proteins. These components form signaling complexes that mediate sensory excitation and adaptation. Previous determinations of cellular content of individual components provided differing and apparently conflicting values. We used quantitative immunoblotting to perform comprehensive determinations of cellular amounts of all components in two E. coli strains considered wild type for chemotaxis, grown in rich and minimal media. Cellular amounts varied up to 10-fold, but ratios between proteins varied no more than 30%. Thus, cellular stoichiometries were almost constant as amounts varied substantially. Calculations using those cellular stoichiometries and values for in vivo proportions of core components in complexes yielded an in vivo stoichiometry for core complexes of 3.4 receptor dimers and 1.6 CheW monomers for each CheA dimer and 2.4 CheY, 0.5 CheZ dimers, 0.08 CheB, and 0.05 CheR per complex. The values suggest a core unit of a trimer of chemoreceptor dimers, a dimer (or two monomers) of kinase CheA, and two CheW. These components may interact in extended arrays and, thus, stoichiometries could be nonintegral. In any case, cellular stoichiometries indicate that CheY could be bound to all signaling complexes and this binding would recruit essentially the entire cellular complement of unphosphorylated CheY, and also that phosphatase CheZ, methylesterase CheB, and methyltransferase CheR would be present at 1 per 2, per 14, and per 20 core complexes, respectively. These characteristic ratios will be important in quantitative treatments of chemotaxis, both experimental and theoretical.  相似文献   

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