Signal Transduction In Bacterial Chemotaxis. Bioessays

Citation: Hamadeh A, Roberts MAJ, August E, McSharry PE, Maini PK, Armitage JP, et al. (2011) Feedback Control Architecture and the Bacterial Chemotaxis Network. PLoS Comput Biol 7(5): e1001130. https://doi.org/10.1371/journal.pcbi.1001130

Editor: Jason M. Haugh, North Carolina State University, United States of America

Received: August 12, 2010; Accepted: April 1, 2011; Published: May 5, 2011

Copyright: © 2011 Hamadeh et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This work was funded by the EPSRC [www.epsrc.ac.uk], project E05708X. PKM was partially supported by a Royal Society-Wolfson Merit Award. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Living organisms respond to changes in their internal and external environment in order to survive. The sensing, signalling and response mechanisms often consist of complicated pathways the dynamical behaviour of which is often difficult to understand without mathematical models [1]. Considering the structure and dynamics of these signalling pathways as integrated dynamical systems can help us understand how the pathway architecture and parameter values result in the performance and robustness in the response dynamics [2].

One extensively studied sensory pathway is bacterial chemotaxis. This pathway controls changes in bacterial motion in response to environmental stimuli, biasing movement towards regions of higher concentration of beneficial or lower concentration of toxic chemicals. The chemotaxis signalling pathway in the bacterium Escherichia coli is a simple network with one feedback loop [3] which has been extensively studied and used as a paradigm for the mechanism of chemotaxis signalling networks [4]. In E. coli, chemical ligands bind to methyl-accepting chemotaxis protein (MCP) receptors that span the cell membrane and alter the activity of a cytoplasmic histidine kinase called CheA. When attractant ligands stimulate the chemotaxis pathway by binding to MCP, there is a decrease in the autophosphorylation rate of CheA; conversely, repellent binding or lack of attractant binding increase CheA autophosphorylation activity. CheA, when phosphorylated, can transfer the phosphoryl group to two possible response regulators: CheY and CheB. CheY-P (where ‘-P’ denotes phosphorylation) interacts with FliM in the multiple E. coli flagellar motors resulting in a change in the direction of rotation of the motor. At the same time, a negative feedback loop allows the system to sense temporal gradients and react to a wide ligand concentration range: the MCP receptors, which are constantly methylated by the action of a methyltransferase CheR, are de-methylated by CheB-P. This negative feedback loop restores the CheA autophosphorylation rate and the flagellar activity to the pre-stimulus equilibrium state [5], [6].

Describing this pathway mathematically as a dynamical system can be facilitated by using tools from control theory. For example, it has been shown that the adaptation mechanism in the E. coli model [7], [8] is a particular example of integral control, a feedback system design principle used in control engineering to ensure the elimination of offset errors between a system's desired and actual signals, irrespective of the levels of other signals [9].

Many species have chemotaxis pathways that are much more complicated than that of E. coli[10], [11], either containing chemotaxis proteins not found in E. coli, e.g. in the case of Bacillus subtilis[12]; or containing multiple homologues of the proteins found in the E. coli pathway, as in the case of Rhodobacter sphaeroides[11], [13]. Furthermore, in R. sphaeroides there are two receptor clusters containing sensory proteins which localize to different parts of the cell, one located at the cell pole and the other in the cytoplasm [14]. Although the purpose of the two clusters is unclear, in vitro phosphotransfer experiments [15], [16] show that the CheA homologues located at the two clusters can phosphotransfer to different CheY and CheB homologues: at the cell pole CheA2-P phosphotransfers to CheY3, CheY4, CheY6, CheB1 and CheB2, while at the cytoplasm CheA3A4-P phosphotransfers to CheY6 and CheB2. The two methylesterase proteins, CheB1 and CheB2, which are homologues of CheB in E. coli, are responsible for the adaptation mechanism in R. sphaeroides[13], [17]. Past localization studies have shown that CheB1 and CheB2 are found diffuse throughout the cytoplasm [14]. This is different to E. coli where the CheB protein is localized at the cell pole, and could potentially mean that the two proteins de-methylate either receptor cluster [14].

As a system featuring an adaptation mechanism similar to that in E. coli, but with multiple homologues of the E. coli chemotaxis proteins, it is useful to examine the R. sphaeroides chemotaxis pathway from a control engineering perspective. In this way, we can suggest structures for the R. sphaeroides chemotaxis pathway that integrate the control mechanisms thought to be responsible for adaptation in E. coli along with the possible feedback architectures that arise from the dual sensory modules present in R. sphaeroides. The relative evolutionary advantages of the different architectures can then be compared from both control engineering and biological points of view. The fact that there are two endogenous ‘measurements’ available to the feedback mechanism (CheB1-P and CheB2-P) which can be used to regulate two signals (CheA2 and CheA3A4) makes the whole chemotaxis feedback pathway a multi-input, multi-output control system (as opposed to possessing only one CheB and one CheA as in the E. coli models [7], [18]). This introduces extra degrees of freedom in the feedback control mechanism of the system and, thus, the potential for better regulation.

However, the different conceivable connectivity configurations between the two CheB-P proteins and the two receptor clusters actually correspond to different feedback control architectures, each with different properties. Some of these configurations, as will be demonstrated, could allow the bacterium to integrate information from both internal and external sources and to function more efficiently, e.g., by varying how strongly it reacts to external attractants depending on its internal state. At the same time, the additional receptor cluster not found in E. coli has the potential of introducing extra sources of performance degradation such as noise (both intrinsic and extrinsic) and variations in quantities internal to the cell such as protein copy numbers and phosphorylation rates: the feedback signalling pathway may be required to remedy this, and in this regard, some of these feedback architectures perform better than others.

One of the different pathway configurations that is possible in this system has similarities to a feedback architecture commonly found in engineering control systems termed cascade control[19], which is usually employed when the process to be controlled can be split into a slow ‘primary’ sub-process ( in Figure 1) and a faster, secondary sub-process ( in Figure 1). Without the internal feedback shown dashed in Figure 1 the primary module maintains a set-point for the secondary module to follow and the output of the secondary module is fed back to the primary. A cascade control design places an additional feedback loop around the fast secondary process (shown dashed). This has been known to improve system performance in several ways: it reduces the sensitivity of the output of the secondary module to changes in the parameters (thus improving robustness), it attenuates the effects of disturbance signals, it makes the step response of the control system to inputs and disturbances less oscillatory and, since the secondary process is relatively fast, the effects of unwanted disturbances are corrected before they affect the system output. Including this additional internal feedback also allows the control system designer more flexibility in increasing the feedback gain to achieve higher bandwidth and faster system responses without losing stability. In fact, cascade control is employed as a design principle in several engineering systems such as aircraft pitch control and industrial heat exchangers (see Text S1 for further details).

Figure 1. A cascade control system.

The subsystem is slow relative to . Cascade control involves placing a negative feedback loop (dashed line) around the fast secondary module. This scheme helps reduce the sensitivity of the system's output to uncertainties in the subsystems and .

https://doi.org/10.1371/journal.pcbi.1001130.g001

In our previous work [20], we used a model invalidation technique to arrive at a possible pathway architecture that allows the R. sphaeroides chemotaxis system to convey, via a signalling cascade, sensed changes in ligand concentration outside the cell to the flagellar motor. In that model, proteins CheY3-P and CheY4-P act together to promote autophosphorylation of CheA3A4 (schematically illustrated in Figure 2(A)) whilst CheY6-P binds with the FliM rotor switch to increase the frequency of motor switching (and hence reduce the motor rotation frequency). This stimulation of CheA3A4 need not be a direct interaction [20].

Figure 2. Chemotaxis in R. sphaeroides.

(A) The chemotaxis pathway in R. sphaeroides as currently understood, including the forward chemotaxis pathway previously proposed [20]. MCP: transmembrane methyl accepting chemotaxis protein, Tlp: cytoplasmic methyl accepting chemotaxis protein, A: CheA histidine protein kinase, W: CheW a linker protein between receptors and CheA, Y: the response regulator CheY, B: the response regulator CheB, R: the methyltransferase CheR. P indicates a phosphoryl group. The number in subscript denotes one of the multiple homologues in R. sphaeroides. The flagella motor is shown at the right of the figure. (B) The possible de-methylation feedback structures for the phosphorylated proteins CheB1-P and CheB2-P in R. sphaeroides. Each possible connection is denoted by a (red) thick solid, dashed or dotted line. Possible models involve combinations of these four lines. Interactions from the phosphotransfer network are shown in (black) thin dashed arrows, receptor activation/de-activation is denoted by (black) thin solid lines.

https://doi.org/10.1371/journal.pcbi.1001130.g002

In this paper, we assume that the chemotaxis pathway has the same forward signalling pathway of [20] and then suggest four plausible interconnection structures for the feedback pathway between the two CheB-P proteins and the two receptor clusters. Following this, we present the results of experiments that are used to invalidate all but one of these structures. We then discuss the results of in silico experiments that highlight the differences in chemotactic performance between the different models with particular focus on the robustness of chemotaxis to parametric variations in the chemotaxis pathway and noise [21], [22]. Using analytical techniques from control theory, we demonstrate that the model not invalidated by our experiments is structurally similar to the cascade control architecture, and we use the structural properties of this interconnection, which are commonly used to reduce the effects of uncertainty and disturbances in various engineering applications, to explain the robustness features of the suggested model.

Results

Chemotaxis model creation

Given the structure of the forward path of the chemotaxis pathway from [20], illustrated in Figure 2(A), and given the rates previously measured in [15], [16] for the phosphotransfer reactions also shown in Figure 2(A), we constructed a generic ordinary differential equation model of the R. sphaeroides chemotaxis pathway, detailed in Materials and Methods. With this forward signalling pathway, the model makes the following assumptions:

  • Polar and cytoplasmic cluster receptors are either methylated or un-methylated.
  • Only a subset of methylated receptors is active, as in [23].
  • CheR2/CheR3 act to methylate inactive receptors whilst proteins CheB1-P/CheB2-P de-methylate active polar and cytoplasmic receptors with unknown connectivity, as in [23].
  • A sensed increase in ligand concentration causes a reduction in the number of active receptors.
  • Active polar and cytoplasmic receptors promote the auto-phosphorylation of CheA2 and CheA3A4 respectively.
  • CheY3-P and CheY4-P act together to promote autophosphorylation of CheA3A4 (Figure 3) whilst CheY6-P binds the FliM rotor switch to increase the frequency of motor switching.
  • Through the phosphotransfer network, a decrease in the number of active receptors due to a sensed increase in ligand concentration results in a subsequent decrease in the amount of CheY3-P, CheY4-P, CheY6-P, CheB1-P and CheB2-P.

Figure 3. The speed of response of each cluster to input signals.

The response of the normalized CheY6-P concentration to a step decrease, at time 10 seconds, in the number of active receptors at the polar cluster (from  = 1 µM to  = 0 µM, dashed) and at the cytoplasmic cluster (from  = 1 µM to  = 0 µM, solid). Such a decrease in active receptors can be due to a step increase in sensed ligand. A step decrease in active polar cluster receptors results in a slower fall in the normalized CheY6-P concentration (90%-10% fall time: 50.57 sec) than would an identical change in the number of active cytoplasmic cluster receptors (90%-10% fall time: 21.98 sec).

https://doi.org/10.1371/journal.pcbi.1001130.g003

One effect of a sensed increase in ligand concentration is a decrease in the flagellar switching frequency due to decreased amounts of CheY6-P binding with FliM. Figure 3 shows the result of a simulation of the signalling pathway that demonstrates the fall in the concentration of CheY6-P in response to a step decrease in the number of active receptors at the polar or at the cytoplasmic clusters. The reaction rates of the phosphotransfer network are such that a change in the number of active receptors at the cytoplasmic cluster causes a faster fall in CheY6-P concentration than does a similar change in the number of active receptors at the polar cluster.

Qualitatively, the adaptation mechanism in the generic ODE model presented in Materials and Methods functions as follows: CheB1-P and CheB2-P are assumed to de-methylate active receptors, and the phosphotransfer network responds to a sensed increase in ligand concentration by reducing the concentration of CheB1-P, CheB2-P, CheY3-P, CheY4-P and CheY6-P. This results in a reduction in the de-methylation rate of active receptors in the two receptor clusters, and also results in a decrease in the flagellar stopping frequency (which corresponds to an increase in the flagellar rotation rate). The constant methylation of inactive receptors by CheR2 and CheR3 then causes the number of methylated receptors, and, it is assumed, of active receptors, to increase. Thus, the number of active receptors is eventually restored to its pre-stimulus equilibrium level. In turn, the phosphotransfer network then restores the amount of CheY6-P, and hence the flagellar switching frequency, back to its original level. According to the model of the forward signalling pathway, the proteins CheB1-P and CheB2-P therefore act as feedback signals that restore the chemotaxis pathway to its original state. However, the exact connectivity between CheB1-P/CheB2-P and the two receptor clusters is unknown.

To determine the most likely interconnection structure and to provide a rationale of how such a structure may be advantageous in terms of chemotactic performance, we created four variants of the generic ODE model with the forward pathway, each having a different interconnection structure between the proteins CheB1-P/CheB2-P and the two receptor clusters (Figure 2(B)). All models were able to produce wild type response data and behaved as expected for the response data generated with gene deletions available at the time. The unknown parameters in the models () were fitted to wild type data for each model. The significance of these parameters is as follows:

For notational convenience, it is useful to group the CheB1-P/CheB2-P feedback gains into a feedback matrix . The four CheB1-P and CheB2-P feedback connectivities (and their associated ) for which models were constructed are as follows:

  1. CheB1-P regulates the methylation state of the polar receptor cluster and CheB2-P of the cytoplasmic cluster only (shown in solid de-methylation reactions in Figure 2 (B)): .
  2. CheB1-P regulates the methylation state of both the polar cluster and the cytoplasmic cluster while CheB2-P de-methylates only cytoplasmic cluster receptors (solid de-methylation reactions and the dotted de-methylation reaction in Figure 2 (B)): .
  3. CheB1-P and CheB2-P both regulate the methylation state of the polar receptor cluster and CheB2-P of the cytoplasmic receptor cluster only (solid de-methylation reactions and the dashed de-methylation reaction in Figure 2 (B)): .
  4. CheB1-P and CheB2-P both regulate the methylation state of both receptor clusters (solid de-methylation reactions, the dashed de-methylation reaction and the dotted de-methylation reaction in Figure 2 (B)): .

After constructing these four models, we carried out experiments to differentiate between them, by finding the optimal initial conditions of the cells in the assay so as to maximize the difference between the outputs of the different models [20], [24]. The conditions searched were limited to what could be implemented experimentally and included deletions, over-expression of proteins and combinations of these. To confirm these conditions allow for invalidation, simulations were run of the four models I–IV testing the possible initial conditions and inputs. The simulations showed that the initial conditions that allow for the best model invalidation were the deletion of CheR3 and, in a separate experiment, the deletion of CheB1 (Figure 4).

Figure 4. Model invalidation.

Top left: Simulations of the wild type Models I–IV and with CheR3 deleted in response to 100 µM of ligand added at 100 seconds and removed at 220 seconds. Top right: Average responses of wild type cells and CheR3 deletion cells in a tethered cell assay with 100 µM of propionate added at 100 seconds and removed at 220 seconds. Bottom left: Simulations of the wild type Models I–IV (dashed line) and with CheB1 deleted in response to 100 µM of ligand added at 100 seconds and removed at 220 seconds. Bottom right: Average responses of wild type cells and CheB1 deletion cells in a tethered cell assay with 100 µM of propionate added at 100 seconds and removed at 220 seconds. Cells rotate counter clockwise hence negative Hz values are observed. Ligand addition is marked by grey shading.

https://doi.org/10.1371/journal.pcbi.1001130.g004

The experiments were then implemented in R. sphaeroides, subjecting a population of cells to a step increase in ligand concentration (propionate) and then measuring the resulting flagellar activity through a tethered cell assay (Figure 4). Experimentally the deletion of either CheB1 or CheR3 resulted in cells with a rotation frequency of −8 Hz that showed no noticeable response to the addition or removal of ligand. In the simulations, only Models I and III displayed this behaviour upon deletion of CheR3 (Figure 4, top row) and only Model III displayed this behaviour upon deletion of CheB1 (Figure 4, bottom row). Models I, II and IV were thus invalidated and only Model III was able to replicate the experimental data. As a test of this model invalidation, a further experiment wherein CheB2 was deleted was performed. The result of this experiment and the outputs of the four models under the CheB2 deletion (overlaid) are shown in Figure 5. Models I and III were once again able to replicate the deletion data whilst Models II and IV produced outputs that differed from the experimental outcome.

Figure 5. Deletion of CheB2.

Average responses of CheB2 deletion cells in a tethered cell assay with 100 µM of propionate added at 200 seconds and removed at 512 seconds. Solid lines: simulations of the Models I–IV with CheB2 deleted in response to 100 µM of ligand added at 200 seconds and removed at 512 seconds. Cells rotate counter clockwise hence negative Hz values are observed. Ligand addition is marked by grey shading.

https://doi.org/10.1371/journal.pcbi.1001130.g005

Dynamic properties of chemotaxis models

The experiments described above demonstrated that the proposed Models I, II and IV are invalid, being unable to explain experimental data. To compare the four models further, in silico experiments were performed on the data-fitted Models I–IV that compared how the different feedback configurations affect chemotactic performance in terms of the sensitivity of the flagellar stopping frequency in response to variations in the values of the models' biochemical parameters and in response to noise. Following these results, we use linear models with structures that represent the different connectivities of Models I–IV to analyze these structures' relative sensitivities to parametric variations and noise.

Chemotactic performance

The performance of the different chemotaxis models was compared by simulating the efficiency of each model in ascending an attractant gradient, as illustrated in Figure 6 (left). For each chemotaxis model, Figure 6 shows the average distance travelled up the attractant gradient by ten bacteria during a simulation lasting 80 seconds. As shown in Figure 6 (right), the chemotactic performances of the different models according to this measure were nearly identical (see Materials and Methods for more details).

Figure 6. Comparison of chemotactic performance.

The four chemotaxis models are simulated in a two-dimensional environment, wherein the chemoattractant concentration L has a ramp profile that varies along the x-direction only, such that L = 100x for x>0 and L = 0 otherwise (left). The simulation output (right) shows the relative average distance travelled up the attractant gradient by ten cells for each of the chemotaxis models.

https://doi.org/10.1371/journal.pcbi.1001130.g006

Response to noisy ligand variations

The bacterium's environment is typically composed of regions of high and low chemoattractant or chemorepellant concentrations. Additionally, the bacterium will sense small, fast fluctuations in the detected level of ligand due to molecular noise. To test how sensitive the chemotaxis Models I–IV are to such ligand fluctuations, an in silico experiment was performed on each model in which the ligand concentration sensed by the polar cluster, L, was modelled as the noisy signal L = max(0,1+η), where η is a white noise signal with a zero-mean, unit variance Gaussian distribution. The resulting rotation frequencies were then recorded and are shown in Figure 7. As can be seen in Figure 7, ligand level fluctuations sensed at the polar cluster of receptors resulted in larger variance of the rotation frequency in Models I, II and IV than in Model III.

Figure 7. Response to external ligand variations.

Standard deviations of the flagellar rotation frequencies for each of the four chemotaxis models in response to a noisy ligand input sensed at the polar cluster given by L = max(0,1+η) (where η is a white noise signal with a zero-mean, unity variance Gaussian distribution).

https://doi.org/10.1371/journal.pcbi.1001130.g007

The sensitivity of the chemotaxis Models I–IV to ligand inputs was then tested in two in silico experiments which were performed on each model and in which the flagellar rotation frequency was recorded in response to sinusoidal variations in the ligand signals (the latter of which corresponds to ligand inputs acting on the cytoplasmic cluster). As can be seen in Figure 8, ligand level fluctuations sensed at the polar cluster of receptors resulted in larger changes in the rotation frequency in Models II and IV than in I and III. When the ligand concentration variations were sensed at the cytoplasmic cluster the result was a greater variation in the rotation frequency in Models I and III than in the other two models. Once more, these simulations suggest that CheB1-P de-methylating the cytoplasmic cluster differentiates the performance of Models II and IV from Models I and III.

Figure 8. Input-output gains of the two sensing clusters.

Frequency response magnitude plots showing the response of the different models to sinusoidally-varying ligand concentrations modelling noisy ligand input signals. Top: Constant ligand to cytoplasmic cluster and variable ligand to polar cluster (, where ). Bottom: Constant ligand to polar cluster, sinusoidal to cytoplasmic cluster (, where ).

https://doi.org/10.1371/journal.pcbi.1001130.g008

Parametric sensitivity analysis of the chemotaxis models

To investigate the sensitivity of the models to parameter variations, we performed an in silico experiment in which, for each of the different chemotaxis models, the variation of the steady-state of the chemotaxis system was measured under randomly chosen values of the copy numbers of chemotaxis proteins (see Materials and Methods). For each chemotaxis protein, the resulting coefficient of variation of the steady-state is shown in Figure 9. Once more, there was a similarity in the sensitivity of each model to these parametric variations between Models I and III and between Models II and IV, with the latter pair showing slightly higher sensitivity to copy numbers of the chemotaxis protein CheY6 among others. In addition, Model III showed considerably lower sensitivity with respect to CheB1 copy numbers than the other models.

Linear model analysis

Further insight to the differences in performance between the models can be obtained by analyzing the interconnection structure of these models using control theory. In particular, the way in which such feedback arrangements can affect the performance of control systems like the R. sphaeroides chemotaxis pathway can be studied by comparing the behaviour of different linear systems that are structurally similar to Models I–IV. The block diagram in Figure 10 depicts a system composed of two modules representing the polar and cytoplasmic clusters. The CheB1-P/CheB2-P outputs of the two modules exhibit exact adaptation through integral control in response to step changes in the input ligand concentration level, as in E. coli[8]. Depending on the values of feedback gains and (which correspond to respectively in the chemotaxis models described above), the system can represent one of the four chemotaxis models:

  1. Model I:
  2. Model II:
  3. Model III:
  4. Model IV: .

The gains in Figure 10 are such that , representing the fact that the cytoplasmic receptor cluster can, as a result of the measured reaction rates, relay a sensed ligand input signal to the flagellar motor faster than the polar receptors cluster (see Figure 3). For the examples we shall consider we set and . Gains and correspond to and in the chemotaxis model respectively. The frequency domain transfer function of the system in Figure 10 from the ligand inputs and to the output is then(1)where . This function is a frequency-domain map from signals and to the output Y, which corresponds to the flagellar rotation frequency. In the following, we shall use this frequency domain representation of the chemotaxis system to demonstrate how the feedback of linear systems with structures similar to the chemotaxis Models I–IV affects system performance.

The Bode magnitude diagrams (Materials and Methods) in Figure 11(A) illustrate the effect of increasing in reducing the sensitivity function of the system (1) over most excitation frequencies (see the Discussion and Text S1 for a brief introduction to sensitivity functions). At the same time, Figure 11(B) shows that strengthening the feedback , which corresponds to increasing the de-methylation of the cytoplasmic cluster by CheB2-P, decreases the sensitivity of the polar cluster over low frequencies.

Figure 11. Variation of linear system sensitivity under different feedback strengths as a function of frequency.

(A) Bode magnitude plots of the sensitivity function of system (1) with and different values of gain , which corresponds to the feedback strength of CheB2-P de-methylating active polar cluster receptors. With these gains the system is structurally similar to Model III. (B) Sensitivity function of the block corresponding to the cytoplasmic cluster in the linear model (1), for different values of feedback gain , which corresponds to the feedback strength of CheB2-P de-methylating active cytoplasmic cluster receptors. The frequency domain sensitivity function is (see Text S1).

https://doi.org/10.1371/journal.pcbi.1001130.g011

Figure 12 presents a Bode magnitude plot showing the gain of the linear system (1) to inputs and which represent sensed ligand at the polar and cytoplasmic receptor clusters respectively. The figures show that, similar to the simulations of Models I and III, the linear model with a gain (similar in structure to Model I) and (similar in structure to Model III) also shows a relatively low sensitivity to high frequency (noisy) inputs at the polar receptor cluster and a relatively high sensitivity to noise detected at the cytoplasmic receptor cluster.

Figure 12. Variation of linear system gain magnitude under different feedback strengths as a function of frequency.

Bode magnitude plots of transfer functions from ligand inputs to Y in the linear system (1) corresponding to Models I () and III (). (A) Bode magnitude plots from L to Y. (B) Bode magnitude plots from to Y.

https://doi.org/10.1371/journal.pcbi.1001130.g012

Discussion

From the designed experiments performed, it was possible to invalidate all models but Model III. This suggests that the feedback in the chemotaxis system could occur in an asymmetric fashion. That is, CheB1-P may only interact with the membrane signalling cluster whilst CheB2-P interacts with both clusters. It is likely that the two chemotaxis pathways initially evolved independently and then became part of the same organism by horizontal gene transfer. Thus one would possibly expect either full connectivity or complete isolation of the two pathways until a further mutation occurs.

Understanding the outputs of the designed experiments

R. sphaeroides has a more complex chemotaxis network than E. coli and the multiple receptor clusters and multiple feedback pathways mean that mutants will not always have an intuitive phenotype. For example the ΔcheB1 mutant does not have the loss of response phenotype one would expect from a direct comparison with the E. coli system. We can try to understand why ΔcheB1 has a steady state at −8 Hz by looking at the structure of the model we have been unable to invalidate, and the reason is as follows: CheB1, CheB2 and CheY6 (along with CheY3 and CheY4) each compete for phosphoryl groups from CheA2-P. CheB1 is present in relatively large copy numbers and CheB1-P has negligible degradation rate (see Table 1). When present, CheB1 ‘stores’ a large proportion of phosphoryl groups. When absent, the competition for phosphoryl groups from CheA2-P remains between CheB2, CheY6, CheY3 and CheY4. The rate of phosphorylation of CheY6 by CheA2-P is relatively small, CheY6-P receiving most of its phosphorylation from the CheA3A4-P complex. Therefore deleting cheB1 shifts the equilibrium of the system so that a higher proportion of the phosphoryl groups from CheA2-P go to CheY3, CheY4 or CheB2. The increase in CheY3-P and CheY4-P results in a stronger negative feedback to the cytoplasmic cluster, and the steady-state amount of active receptors at the cytoplasmic cluster is therefore less in the case of ΔcheB1. The consequence of this is that the main source of phosphorylation for CheY6-P, which is CheA3A4-P, is reduced, and hence the level of CheY6-P is reduced. The stopping frequency is consequently reduced. Therefore, rather than ΔcheB1 leading to a loss of response to stimulus, the result of this deletion is a shift in the steady state to a high rotation frequency.

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