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.     

A mechanism for exact sensory adaptation based on receptor modification

We provide a theoretical explanation for the observation that in many sensory systems a step increase in stimulus triggers a response that goes through a maximum and then returns to the basal level. Considered here is a receptor molecule that in the absence of ligand can be found in either of two states R and D. Two more states, RL and DL, are formed upon the addition of ligand L. It is assumed that the receptor triggers activity in a sensory system, and that the activity is proportional to a weighted combination of the fractions of molecules that are in each of the four states. It is shown that judicious choice of the weights can provide both an adequate response and exact adaptation to step increases in stimuli. The interconversion between states may operate without energy expenditure or through covalent modification. In both cases, adaptation is associated with receptor modification that acts as a counterweight to changed external conditions. Application to cAMP secretion in Dictyostelium discoideum and to chemotaxis in bacteria is discussed.     

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.     

Adaptation Dynamics in Densely Clustered Chemoreceptors

In many sensory systems, transmembrane receptors are spatially organized in large clusters. Such arrangement may facilitate signal amplification and the integration of multiple stimuli. However, this organization likely also affects the kinetics of signaling since the cytoplasmic enzymes that modulate the activity of the receptors must localize to the cluster prior to receptor modification. Here we examine how these spatial considerations shape signaling dynamics at rest and in response to stimuli. As a model system, we use the chemotaxis pathway of Escherichia coli, a canonical system for the study of how organisms sense, respond, and adapt to environmental stimuli. In bacterial chemotaxis, adaptation is mediated by two enzymes that localize to the clustered receptors and modulate their activity through methylation-demethylation. Using a novel stochastic simulation, we show that distributive receptor methylation is necessary for successful adaptation to stimulus and also leads to large fluctuations in receptor activity in the steady state. These fluctuations arise from noise in the number of localized enzymes combined with saturated modification kinetics between the localized enzymes and the receptor substrate. An analytical model explains how saturated enzyme kinetics and large fluctuations can coexist with an adapted state robust to variation in the expression levels of the pathway constituents, a key requirement to ensure the functionality of individual cells within a population. This contrasts with the well-mixed covalent modification system studied by Goldbeter and Koshland in which mean activity becomes ultrasensitive to protein abundances when the enzymes operate at saturation. Large fluctuations in receptor activity have been quantified experimentally and may benefit the cell by enhancing its ability to explore empty environments and track shallow nutrient gradients. Here we clarify the mechanistic relationship of these large fluctuations to well-studied aspects of the chemotaxis system, precise adaptation and functional robustness.     

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.     

Variable sizes of Escherichia coli chemoreceptor signaling teams

Like many sensory receptors, bacterial chemotaxis receptors form clusters. In bacteria, large‐scale clusters are subdivided into signaling teams that act as ‘antennas’ allowing detection of ligands with remarkable sensitivity. The range of sensitivity is greatly extended by adaptation of receptors to changes in concentrations through covalent modification. However, surprisingly little is known about the sizes of receptor signaling teams. Here, we combine measurements of the signaling response, obtained from in vivo fluorescence resonance energy transfer, with the statistical method of principal component analysis, to quantify the size of signaling teams within the framework of the previously successful Monod–Wyman–Changeux model. We find that size of signaling teams increases 2‐ to 3‐fold with receptor modification, indicating an additional, previously unrecognized level of adaptation of the chemotaxis network. This variation of signaling‐team size shows that receptor cooperativity is dynamic and likely optimized for sensing noisy ligand concentrations.     

Functional Suppression of HAMP Domain Signaling Defects in the E. coli Serine Chemoreceptor

HAMP domains play key signaling roles in many bacterial receptor proteins. The four-helix HAMP bundle of the homodimeric Escherichia coli serine chemoreceptor (Tsr) interacts with an adjoining four-helix sensory adaptation bundle to regulate the histidine autokinase CheA bound to the cytoplasmic tip of the Tsr molecule. The adaptation helices undergo reversible covalent modifications that tune the stimulus-responsive range of the receptor: unmodified E residues promote kinase-off output, and methylated E residues or Q replacements at modification sites promote kinase-on output. We used mutationally imposed adaptational modification states and cells with various combinations of the sensory adaptation enzymes, CheR and CheB, to characterize the signaling properties of mutant Tsr receptors that had amino acid replacements in packing layer 3 of the HAMP bundle and followed in vivo CheA activity with an assay based on Förster resonance energy transfer. We found that an alanine or a serine replacement at HAMP residue I229 effectively locked Tsr output in a kinase-on state, abrogating chemotactic responses. A second amino acid replacement in the same HAMP packing layer alleviated the I229A and I229S signaling defects. Receptors with the suppressor changes alone mediated chemotaxis in adaptation-proficient cells but exhibited altered sensitivity to serine stimuli. Two of the suppressors (S255E and S255A) shifted Tsr output toward the kinase-off state, but two others (S255G and L256F) shifted output toward a kinase-on state. The alleviation of locked-on defects by on-shifted suppressors implies that Tsr-HAMP has several conformationally distinct kinase-active output states and that HAMP signaling might involve dynamic shifts over a range of bundle conformations.     

Carboxyl-terminal extensions beyond the conserved pentapeptide reduce rates of chemoreceptor adaptational modification

Sensory adaptation in bacterial chemotaxis is mediated by covalent modification of chemoreceptors. Specific glutamyl residues are methylated and demethylated in reactions catalyzed by methyltransferase CheR and methylesterase CheB. In the well-characterized chemosensory systems of Escherichia coli and Salmonella spp., efficient modification by either enzyme is dependent on a conserved pentapeptide sequence, NWETF or NWESF, present at the extreme carboxyl terminus of high-abundance chemoreceptors. To what extent is position at the extreme carboxyl terminus important for pentapeptide-mediated enhancement of adaptational modification? Is this position equally important for enhancement of both enzyme activities? To address these questions, we created forms of high-abundance receptor Tsr or Tar carrying one, six, or eight additional amino acids extending beyond the pentapeptide at their carboxyl termini and assayed methylation, demethylation, deamidation, and ability to mediate chemotaxis. In vitro and in vivo, all three carboxyl-terminal extensions reduced pentapeptide-mediated enhancement of rates of adaptational modification. CheB-catalyzed reactions were more affected than CheR-catalyzed reactions. Effects were less severe for the complete sensory system in vivo than for the minimal system of receptor and modification enzymes in vitro. Notably, extended receptors mediated chemotaxis as efficiently as wild-type receptors, providing a striking example of robustness in chemotactic systems. This could reflect compensatory reductions of rates for both modification reactions, mitigation of effects of slower reactions by the intertwined circuitry of signaling and adaptation, or tolerance of a range of reactions rates for adaptational modification. No matter what the mechanism, the observations provide a challenging test for mathematical models of chemotaxis.     

On the information received by sensory receptors

It is hypothesized that a sensory neuron, a neuron issuing from a sensory receptor, encodes the rate at which entropy or uncertainty is removed at the receptor level. This hypothesis is tested for the case of the entropy associated with the magnitude of a signal (stimulus) applied at the sensory receptor. A simple mathematical model of the process is presented and a number of well-known stimulus-response relationships are seen to emerge. For example, the adaptation of a receptor may be seen to occur as a consequence of reduced uncertainty regarding stimulus intensity. A general equation relating stimulus and response is developed, and this equation will simplify, depending upon the ratio of signal power to noise power, to either a logarithmic or a power law.     

Imprecision of Adaptation in Escherichia coli Chemotaxis

Adaptability is an essential property of many sensory systems, enabling maintenance of a sensitive response over a range of background stimulus levels. In bacterial chemotaxis, adaptation to the preset level of pathway activity is achieved through an integral feedback mechanism based on activity-dependent methylation of chemoreceptors. It has been argued that this architecture ensures precise and robust adaptation regardless of the ambient ligand concentration, making perfect adaptation a celebrated property of the chemotaxis system. However, possible deviations from such ideal adaptive behavior and its consequences for chemotaxis have not been explored in detail. Here we show that the chemotaxis pathway in Escherichia coli shows increasingly imprecise adaptation to higher concentrations of attractants, with a clear correlation between the time of adaptation to a step-like stimulus and the extent of imprecision. Our analysis suggests that this imprecision results from a gradual saturation of receptor methylation sites at high levels of stimulation, which prevents full recovery of the pathway activity by violating the conditions required for precise adaptation. We further use computer simulations to show that limited imprecision of adaptation has little effect on the rate of chemotactic drift of a bacterial population in gradients, but hinders precise accumulation at the peak of the gradient. Finally, we show that for two major chemoeffectors, serine and cysteine, failure of adaptation at concentrations above 1 mM might prevent bacteria from accumulating at toxic concentrations of these amino acids.     

Attractant regulation of the aspartate receptor-kinase complex: limited cooperative interactions between receptors and effects of the receptor modification state

The manner by which the bacterial chemotaxis system responds to a wide range of attractant concentrations remains incompletely understood. In principle, positive cooperativity between chemotaxis receptors could explain the ability of bacteria to respond to extremely low attractant concentrations. By utilizing an in vitro receptor-coupled kinase assay, the attractant-dependent response curve has been measured for the Salmonella typhimurium aspartate chemoreceptor. The attractant chosen, alpha-methyl aspartate, was originally used to quantitate high receptor sensitivity at low attractant concentrations by Segall, Block, and Berg [(1986) Proc. Natl. Acad. Sci. U.S.A. 83, 8987-8991]. The attractant response curve exhibits limited positive cooperativity, yielding a Hill coefficient of 1.7-2.4, and this Hill coefficient is relatively independent of both the receptor modification state and the mole ratio of CheA to receptor. These results disfavor models in which there are strong cooperative interactions between large numbers of receptor dimers in an extensive receptor array. Instead, the results are consistent with cooperative interactions between a small number of coupled receptor dimers. Because the in vitro receptor-coupled kinase assay utilizes higher than native receptor densities arising from overexpression, the observed positive cooperativity may overestimate that present in native receptor populations. Such positive cooperativity between dimers is fully compatible with the negative cooperativity previously observed between the two symmetric ligand binding sites within a single dimer. The attractant affinity of the aspartate receptor is found to depend on the modification state of its covalent adaptation sites. Increasing the the level of modification decreases the apparent attractant affinity at least 10-fold in the in vitro receptor-coupled kinase assay. This observation helps explain the ability of the chemotaxis pathway to respond to a broad range of attractant concentrations in vivo.     

Nonadaptive Fluctuation in an Adaptive Sensory System: Bacterial Chemoreceptor

Background

Sensory systems often exhibit an adaptation or desensitization after a transient response, making the system ready to receive a new signal over a wide range of backgrounds. Because of the strong influence of thermal stochastic fluctuations on the biomolecules responsible for the adaptation, such as many membrane receptors and channels, their response is inherently noisy, and the adaptive property is achieved as a statistical average.

Methodology/Principal Findings

Here, we study a simple kinetic model characterizing the essential aspects of these adaptive molecular systems and show theoretically that, while such an adaptive sensory system exhibits a perfect adaptation property on average, its temporal stochastic fluctuations are able to be sensitive to the environmental conditions. Among the adaptive sensory systems, an extensively studied model system is the bacterial receptor responsible for chemotaxis. The model exhibits a nonadaptive fluctuation sensitive to the environmental ligand concentration, while perfect adaptation is achieved on average. Furthermore, we found that such nonadaptive fluctuation makes the bacterial behavior dependent on the environmental chemoattractant concentrations, which enhances the chemotactic performance.

Conclusions/Significance

This result indicates that adaptive sensory systems can make use of such stochastic fluctuation to carry environmental information, which is not possible by means of the average, while keeping responsive to the changing stimulus.     

Bacterial chemoreceptors: recent progress in structure and function.

The behavior of a bacterial cell is determined by the interplay between transmembrane receptor molecules and a cytoplasmic kinase that is linked to the flagellar apparatus. In the absence of external stimulus, a balance exists between stresses in the periplasmic region of receptor molecules, and compensating cytoplasmic forces. A response, positive or negative, is due to a temporary disturbance in this balance, with corresponding alterations in kinase activity, and ultimately, of swimming behavior. Methylation acts to restore the balance by changing the properties of the receptor. Because methylation is slow, a response will continue for a period of time following stimulation. The mechanisms by which these processes occur are now being elucidated at the molecular level, and should soon make bacterial chemotaxis the first available picture of a complete sensory system.     

Neither methylating nor demethylating enzymes are required for bacterial chemotaxis

Clarification of the information processing system in bacterial sensing has been obtained by studying mutants that lack the capacity to modify receptors covalently. The remaining part of the system is able to receive signals from the receptor, to respond with partial adaptation, and to exhibit a chemotactic response. A cycle of chemical reactions analogous to the rhodopsin-transducin cycle in the visual system is shown to provide the proper characteristics to serve as the bridge between receptor and chemotactic output, which allows adaptation in the absence of covalent protein modifications.     

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.     

Psychophysical and behavioral characteristics of olfactory adaptation

Sensory adaptation allows organisms to reach behavioral equilibrium with the ambient environment and respond primarily to changes in stimulation. Given its functional significance, it is not surprising that adaptation in the olfactory system exhibits many of the same characteristics as adaptation in other sensory systems, including vision. Repeated or prolonged exposure to an odorant typically leads to stimulus-specific decreases in olfactory sensitivity to that odorant, but sensitivity recovers over time in the absence of further exposure. Psychophysical analysis shows that olfactory adaptation results in elevations in odor thresholds and in reduced responsiveness to suprathreshold stimulation. Further, the magnitude of the decrease and the time course of adaptation and recovery are dependent on the concentration of the odor and on the duration of exposure. It is generally agreed that olfactory adaptation can occur at multiple levels in the olfactory system and can involve both peripheral (receptor level) and more central (post-receptor) components. Evidence for peripheral and central involvement comes from studies showing that monorhinal stimulation results in adaptation in both the ipsilateral and contralateral nostril, although the degree of adaptation in the ipsilateral nostril is more profound and recovery is slower. Additional evidence for central involvement comes from studies that have found relatively small decreases in peripheral response following repeated stimulation despite substantial reductions in perceived intensity. Most psychophysical studies of adaptation, however, have not differentiated the peripheral and central processes. Although relatively few in number, studies of the parametric features of olfactory adaptation in both vertebrate (e.g. rat) and invertebrate (e.g. Drosophila, Caenorhabditis elegans) animal models appear to replicate the findings in psychophysical studies of adult humans. Despite the broad overall similarity of olfactory adaptation to adaptation in other sensory systems, olfactory adaptation exhibits some unique features. Adaptation in olfaction has been shown to be very long-lasting in some cases and may be modulated by the contribution of pre-neural events and physico-chemical properties of the odorant molecules that govern diffusion to receptor sites and post-receptor clearance.     

Sites of deamidation and methylation in Tsr, a bacterial chemotaxis sensory transducer

The sensory transducer proteins in bacterial chemotaxis undergo two covalent modifications, deamidation and reversible methylation, in response to attractants and repellents. Oligonucleotide-directed mutagenesis was used to alter putative methylation and deamidation sites in one of the transducers to further define these sites and their role in chemotaxis. The mutations, in combination with peptide maps and Edman analysis, have clarified the sites of covalent modification in Tsr. Tsr contains six specific glutamates and glutamines that serve as methyl-accepting sites. An arginine-containing tryptic peptide (R1) has two sites, one at glutamate 493 and a newly located site at glutamate 502. A lysine-containing peptide (K1) has four methyl-accepting sites. Two of the lysine peptide sites are glutamates and can accept methyl groups without deamidation. The other two sites are glutamines and two methyl-accepting sites are created by two distinct deamidations. Both deamidations can occur on the same polypeptide chain. Single glutamate mutants have shown that one deamidation (at glutamine 311) proceeds rapidly, while the other deamidation (at glutamine 297) has a half-life of approximately 60 min under our experimental conditions.     

The three adaptation systems of Bacillus subtilis chemotaxis

Adaptation has a crucial role in the gradient-sensing mechanism that underlies bacterial chemotaxis. The Escherichia coli chemotaxis pathway uses a single adaptation system involving reversible receptor methylation. In Bacillus subtilis, the chemotaxis pathway seems to use three adaptation systems. One involves reversible receptor methylation, although quite differently than in E. coli. The other two involve CheC, CheD and CheV, which are chemotaxis proteins not found in E. coli. Remarkably, no one system is absolutely required for adaptation or is independently capable of generating adaptation. In this review, we discuss these three novel adaptation systems in B. subtilis and propose a model for their integration.     

SENSORY ADAPTATION AND THE STATIONARY STATE

1. Experiments are described which measure the sensitivity of animals exposed to continued illumination to which they have become adapted. It is shown that the amount of outside light energy necessary to stimulate an adapted animal increases with the intensity of the adapting illumination. 2. The data are analyzed quantitatively in terms of the reversible reaction S ⇌ P + A shown previously to account for the photic sensitivity of these animals. This analysis demonstrates that, though the amount of incident energy necessary for a minimal response varies with the adapting intensity, the actual amount of photochemical decomposition required to set off the sensory mechanism is a constant quantity. 3. The ability of these animals to come into sensory equilibrium with any sustained illumination is accounted for quantitatively by the presence of a stationary state in the reversible photochemical reaction S ⇌ P + A during which the concentrations of the three components are constant. 4. It is shown that the concentrations of these substances at the stationary state are automatically controlled by the outside intensity. Therefore, given the sensory mechanism as a basis, the adaptation of the animals to light and the consequent changes in sensitivity, are determined entirely by the light to which the animals are exposed. 5. Because of the properties of the stationary state, and of the constancy of photochemical decomposition for a minimal effect, it is suggested that the sensory system is not only the traditional receptor system, but is also a protecting layer which stabilizes and buffers the relation between the nervous system and the environment.     

Interactions among the three adaptation systems of Bacillus subtilis chemotaxis as revealed by an in vitro receptor‐kinase assay

The Bacillus subtilis chemotaxis pathway employs three systems for sensory adaptation: the methylation system, the CheC/CheD/CheYp system, and the CheV system. Little is known in general about how these three adaptation systems contribute to chemotaxis in B. subtilis and whether they interact with one another. To further understand these three adaptation systems, we employed a quantitative in vitro receptor‐kinase assay. Using this assay, we were able to determine how CheD and CheV affect receptor‐kinase activity as a function of the receptor modification state. CheD was found to increase receptor‐kinase activity, where the magnitude of the increase depends on the modification state of the receptor. The principal new findings concern CheV. Little was known about this protein before now. Our data suggest that this protein has two roles depending on the modification state of the receptor, one for sensory adaptation when the receptors are modified (methylated) and the other for signal amplification when they are unmodified (unmethylated). In addition, our data suggest that methylation of site 630 tunes the strength of the CheV adaptation system. Collectively, our results provide new insight regarding the integrated function of the three adaptation systems in B. subtilis.