TI - Results Decomposing the response . AB - Vaknin and Berg performed experiments on four bacterial strains : wild-type cells , cheRcheB cells lacking the methylation and demethylation enzymes CheR and CheB , CheZ mutant cells and CheZ mutant cells lacking CheR and CheB [2] . Analysis of their dose-response curves ( the concentration of CheYpCheZ--a CheYp molecule bound to a CheZ dimer--as a function of the ligand concentration L ) is complicated by the fact that they are determined by both the response of the receptor cluster , , to the change in the ligand concentration , [L] , and by the response of the intra-cellular signaling pathway , , to changes in the activity of the receptor cluster , . However , these two networks can be viewed as two independent modules connected in series , which can be analyzed separately , as we discuss below . Moreover , this modularity means that the dose-response curves , , of the four strains can be obtained by multiplying the response curves of the two modules . The first module is the receptor cluster . Its activity , , depends upon the concentration of ligand , [L] , and upon the methylation states of the receptors , which is controlled by the methylation and demethylation enzymes CheR and CheB , respectively . However , the dynamics of receptor methylation and demethylation by CheR and CheB are much slower than that of receptor -ligand ( un ) binding and phosphorylaTION and dePHOSphorylation of CheY ; in fact , this separation of time scales allows E.coli to both respond and adapt to a changing ligand concentration . This separation of time scales also makes it possible to model the response to ligand at short time scales without explicitly taking into account the ( de ) methylation dynamics ; the absence of CheR and CheB in cells , will lead to different methylation states of the receptors , yet can be modeled implicitly by taking different functional forms for . For wild-type cells , the response of the cluster is thus characterized by the response function , while for cheRcheB cells , the response is described by . The second module of the chemotaxis network , the intracellular signal transduction pathway , is described by the set of reactions in Equations 1-3 . The input of this network is , while the output is the concentration of CheYp , , or , as in the experiments of Vaknin and Berg , the total concentration of CheYp bound to CheZ , [2] . The response curve of this network , , depends upon the nature of CheZ , and will thus be different for wild-type cells and CheZ mutant cells . Importantly , is independent of the methylation states of the receptors . We assume that also does not depend upon the presence of CheB , although phosphorylaTED CheA can PHOSphorylate not only CheY but also CheB , leading to another form of adaptation on a time scale longer than that of the response ; we will come back to this in the Discussion section . Thus , we assume that of cells is the same as that of wild-type cells ; the absence of CheR and CheB in cheRcheB cells only affects . Hence , the response of the intra-cellular signaling pathway in wild-type cells is characterized by the response function , while the response of CheZ mutant cells is characterized by . If the receptor cluster and the intracellular chemotaxis pathway indeed behave as two independent modules connected in series , then the response function should be given by the composite function . Hence , the response function of the four strains in Ref . [2] should be of the form : . . . . . . . As we show in Figure 1 of Text S1 , the experiments of Vaknin and Berg on the four different strains provide strong evidence for the hypothesis that the receptor cluster and the intracellular network are indeed two independent modules connected in series . Yet , these experiments do not uniquely prescribe how the overall response is decomposed . This is illustrated in Figure 1 , which show the response curves of three different models , indicated by different colors , that all can explain the dose-response curves of Figure 1A . Each model consists of the functions and ( Figure 1B ) , corresponding to wild-type and CheZ mutant cells respectively , and the functions and ( Figure 1C ) , corresponding to cells containing CheR and CheB and cheRcheB cells lacking CheR and CheB , respectively . For each model , the four composite functions exactly reproduce the four dose-response curves of Figure 1A . Model I ( red lines and points ) relies on the assumption that is a straight line over the concentration range of interest ( see Figure 1B ) . This means that and are proportional to of CheZ mutant cells lacking CheR and CheB and CheZ mutant cells containing CheR and CheB , respectively ; this can be verified by comparing Figure 1A to Figure 1C . The experiments of Vaknin and Berg [2] now fully determine the function , which can be constructed from and of the wild-type cells , and and of the cheRcheB cells ( see Figure 1B ) ; this function has a strongly convex shape . Model II ( blue lines and points ) relies on the assumption that is a linear function ( see Figure 1B ) . In this case and are proportional to of wild-type and cheRcheB cells , respectively ( see Figure 1A and Figure 1C ) . The functional form of of CheZ mutant cells now has a concave shape ( see Figure 1B ) . These two models are two extreme scenarios that both can explain the data shown in Figure 1A . In the following sections we will also consider models that have less extreme functional forms for ; these models lie in between model I and model II . We construct such models , starting from models I and II , by defining functions as linear combinations , where is a parameter between zero and one ; for the model reduces to model I , while for the model reduces to model II . Model III ( black lines and points ) was constructed by putting equal to 0.5 . For this model , of CheZ mutant cells is slightly concave , whereas of wild-type cells is slightly convex . The model that can describe the response of to changes in ligand concentration should not only be able to reproduce the dose-response curves of Figure 1 , it should also satisfy other important conditions . Most importantly , wild-type cells can chemotax , which means that in their non-stimulated state they can respond to the addition as well as to the removal of attractant . Bacteria lacking are able to chemotax towards attractants as well , although less efficiently than wild-type bacteria [12] . These mutants are probably similar to CheZ mutants in that the binding of CheZ to the receptor cluster is hampered in both strains . The requirement that both strains can chemotax means that the concentration of CheYp in the non-stimulated state should be within the working range of the motor , i.e.between 1 and 5 uM [13] , [14] .