TI - Original model : The canonical push-pull network . AB - We now address the question whether the canonical model for the chemotaxis pathway of E.coli , as given by Equations 1-3 , can describe the experimental results of Vaknin and Berg [2] . We first study the effect of the spatial distribution of CheZ , thus leaving the other parameters unchanged . As we will show , the spatial distribution of CheZ alone is not sufficient to explain their experimental results . We will then also vary rate constants and concentrations to see whether the canonical model can describe these results . To elucidate the effect of CheZ localization , we have computed the input-output relations for a network in which CheA and CheZ are colocalized at the receptor cluster ( corresponding to wild-type cells ) and for a network in which CheA is localized at the receptor cluster , while CheZ is distributed in the cytoplasm ( corresponding to CheZ mutant cells ) ; for both networks , the chemical reactions are given by Equations 1-3 . The steady-state input-output relations of these networks were obtained numerically by discretizing the system on a 1D grid and propagating the chemical rate equations , which are given in the Methods section , in space and time until steady state was reached . As pointed out in the previous section , the input of the intracellular network is not directly the ligand concentration [L] , but rather ( see Eq 1 ) , which implicitly depends upon [L] . Importantly , we first assume that the functional dependence of on the ligand concentration [L] , as well as the rate constants of all the reactions , is the same for wild-type and CheZ mutant cells : this allows us to elucidate the effect of colocalization of the antagonistic enzymes on the input-output relations . The model and the values of its parameters were taken from Sourjik and Berg [14] . The principal results of our calculations are shown in Figure 2 . This figure shows for wild-type and CheZ mutant cells , the concentration of CheYpCheZ ( a CheYp molecule bound to a CheZ dimer ) and the concentration of CheYp as a function of ( see Equation 1 ) ; the bullets correspond to the non-stimulated state of the network [14] . Figure 2 shows that the model predicts that the spatial distribution of CheZ affects the response to the addition of repellent or the removal of attractant , which corresponds to an increase in . More importantly , the model predicts that the CheZ distribution should not affect the response to the addition of attractant : When is lowered from its value in the non-stimulated state , both the change in and do not depend much on the spatial distribution of CheZ . This result is thus in contrast with the drastic effect of enzyme localization on the response found by Vaknin and Berg [2] . The network given by Equations 1-3 is very similar to a canonical push-pull network , in which two enzymes covalently modify a SUBstrate in an antagonistic manner [15] ( see Text S2 for how these networks can be mapped onto each other ) . We have recently studied in detail the effect of enzyme localization on the response of a push-pull network [3] . Our principal finding is that enzyme localization can have a marked effect on the gain and sensitivity of push-pull networks , seemingly consistent with the experiments of Vaknin and Berg [2] , but contradicting the numerical results shown in Figure 2 . The resolution of this paradox is that both the quantitative and qualitative consequences of enzyme localization depend upon the regime in which the push-pull network operates . In particular , if the activation rate is independent of the SUBstrate concentration and if the deactivation rate is linear in the messenger concentration , then phosphatase localization has no effect on the response curve [3] . This is precisely the case for the chemotaxis network studied here . For , CheZ is unsaturated [14] and the dePHOSphorylation rate of CheYp is thus proportional to . The influx of CheYp is constant , i.e.independent of [Y] . This is not because the PHOSphorylation reaction is in the zero-order regime ; this reaction is , in fact , in the linear regime [14] . The influx of CheYp at the cell pole is constant because a ) in steady state and b ) in the weak activation regime CheA is predominantly unPHOSphorylated ) , which means that is fairly insensitive to the spatial distribution of CheZ . Hence , according to the model of Equations 1-3 , in this regime the concentration of CheYp does not depend upon the spatial distribution of CheZ , which is indeed what Figure 2 shows . However , while the model of Equations 1-3 predicts that in wild-type cells the response of [YpZ] to the addition of attractant does not depend on the location of CheZ , the experiments by Vaknin and Berg clearly demonstrate that it does [2] . What could be the origin of the discrepancy between the model predictions and the experimental results of Vaknin and Berg? As mentioned above , the response of [YpZ] to the ligand concentration [L] depends upon the response of [Yp] to the activity of the receptor cluster , , and upon the response of to the ligand concentration [L] . If we keep with the assumption that the functional dependence of on [L] , betak0 ([L]) , is the same for both wild type and CheZ mutant cells , the discrepancy between the predictions of the canonical model and the experimental observations of Vaknin and Berg must lie in the dependence of [YpZ] on . It is quite likely that the rate constants and/or concentrations that are used in the calculations differ from those in vivo . It is also possible that the topology of the canonical model of the intracellular chemotactic pathway , Eqs. 1-3 , is incorrect . In order to discriminate between these two scenarios , we will , in the rest of this section , first address the question whether it is possible to explain the experimental observations with the canonical model by allowing for different values of parameters such as rate constants and protein concentrations . We will then argue that simply allowing for different parameter values is probably not sufficient to explain the experiments of Vaknin and Berg , and that thus the canonical model should be reconsidered . Irrespective of the model parameters , it is always true that the rate of phosphorylaTION equals the rate of dePHOSphorylation if the system is in steady state . For the canonical model , i.e . Equations 1-3 , this means that for both the spatially uniform network in which CheA and CheZ are colocalized , and the spatially non-uniform network in which CheZ is distributed in the cytoplasm , the following relation holds in steady state : (4) Here , "FRET" denotes the FRET signal , which is proportional to the total , integrated , concentration of CheYp bound to CheZ , [YpZ] . For the regime of interest , , the concentration of unphosphorylaTED CheA , [A] , is essentially constant for the conventional model , because only a small fraction of the total amount of CheA is PHOSphorylated ; below we discuss scenarios in which this relation might not hold . Equation 4 thus shows that if , the FRET signal only depends upon the activity of the receptor cluster , , and upon the phosphatase activity , , but not upon other rate constants in the network , nor upon the expression levels of , for instance , CheY and CheZ . Moreover , if , the FRET signal , in this model , is linear in the activity of the receptor cluster : , where is the proportionality constant . Incidentally , this explains the linear dependence of [YpZ] on for in Figure 2B . The linear relation between [YpZ] and as predicted by the canonical model would mean that the dose-response curves , i.e . FRET ([L]) , solely reflect the response of the receptor cluster to the addition of ligand , betak0 ([L]) . Vaknin and Berg report the renormalized FRET response : they normalize the FRET signal at ligand concentration [L] to the FRET signal at zero ligand concentration , [2] . If the response of [YpZ] to would indeed be linear , then the renormalized FRET signal would be given by . Hence , the proportionality factor would drop out . The renormalized FRET signal would thus be given by the dependence of the activity of the receptor cluster on the ligand concentration , betak0 ([L]) .