Temporal Controls of the Asymmetric Cell Division Cycle in Caulobacter crescentus
[['The molecular network relevant to our model of the stalked cell division cycle of Caulobacter has been described in great detail previously [25] , so here we describe only those new components of the model involved in the swarmed-to-stalked cell transition , and some details related to improvements of our core model .'], ['The temporal sequence of physiological events during both the stalked cell and the swarmer cell cycle is correctly reproduced by the model .', '( In our simulations , we track either the swarmer , SW , or the stalked , ST , cell cycle by setting a parameter called H to 1 for ST or to 0 for SW . )', 'After the initiation of DNA synthesis ( Figure 3 , at t\u200a=\u200a0 in both stalked and swarmer cell cycles ) , the DNA molecule is progressively replicated and then methylated over a period of ∼90 minutes .', 'The molecular components necessary for cell division ( CtrA∼P , PodJL/PleC , DivJ , DivK∼P ) are expressed in a timely fashion during S phase ( Figure 3 ) .', 'At the end of S phase , the Z-ring starts to constrict ( as described by the variable [Z] in Eq . 28 of Table S1 ) , and it takes about 15 min to finish this process ( Figure 3A&D ) .', 'After that , the predivisional cell enters into G2/M phase during which cell division ( cytokinesis ) begins , and the swarmer and stalked cell compartments embark on different developmental programs .', 'During 30 min of G2/M phase , PodJL/PleC and DivJ are completely separated into the swarmer and stalked cell compartments respectively ( Figure 3B&E ) due to the constriction of the Z-ring ( i . e . , as [Z] falls from 1 to 0 ) .', 'During G2/M phase , the regulatory proteins PodJL/PleC , DivJ , and DivK∼P take on different values in our simulated swarmer and stalked cell compartments ( Figure 3A , B , D &E ) .', 'These differences lead to different developmental tracks of the two progeny cells .', 'After 30 min of G2/M phase , the progeny stalked cell is ready ( because of its low level of CtrA∼P , see Figure 3E ) to enter another cell cycle .', 'The progeny swarmer cell , however , enters into a G1-like phase which lasts about 30 min , as experimentally observed .', 'During G1 phase , our simulation shows how the proteins ( PodJL/PleC , DivJ , DivK/DivK∼P and CtrA/CtrA∼P in Figure 3 ) change with time to convert the swarmer cell back to a stalked cell , ready to enter another cell cycle .', 'In a summary , the timing of such major events of the cell cycle as DNA replication , Z-ring assembly and constriction , cytokinesis , and cell differentiation agrees well with experimental observations [26] , [27] , [29] , [31] , [72] .', 'Figure 4 provides more details about variations of proteins included in the model during the division cycle of a swarmer cell .', 'The swarmer cell cycle is identical to the stalked cell cycle from the initiation of DNA synthesis ( at t\u200a=\u200a0 , Figure 4A&B ) until the Z-ring constriction ( at t\u200a=\u200a90 min , see Figure 4C ) .', 'At this period of time , DivJ is located at the stalked cell pole and PodJL/PleC at the swarmer cell pole ( Figure 4F ) .', 'Because DivK has access to both PodJL/PleC and DivJ in the pre-divisional cell , the level of DivK∼P is very low at the onset of Z-ring constriction ( Figure 4G ) .', 'During G2/M phase ( 90∼120 min in Figure 4 ) , the Z-ring assembles and constricts ( Figure 4C&D ) in about 15 min , and total DNA divides ( Figure 4A ) evenly between the two progeny cells .', 'PodJL/PleC is separated into the swarmer cell compartment ( Figure 4F ) while DivJ remains behind in the stalked cell compartment .', 'Therefore , DivK∼P drops sharply in the incipient swarmer cell ( 70–100 min in Figure 4G ) .', 'With DivK∼P level low and CckA∼P level high ( Figure 4H ) in the incipient swarmer cell , CtrA∼P is maintained at a high level of activity ( 90∼120 min in Figure 4E ) .', 'During the swarmer-to-stalked cell transition ( 120∼150 min in Figure 4 ) , PodJL/PleC plummets and DivJ becomes active again ( Figure 4F ) ; hence , DivK becomes phosphorylated and CtrA∼P is rapidly degraded ( Figure 4E ) .', 'GcrA and DnaA levels climb ( Figure 4E ) , and the new stalked cell is ready for a new round of DNA replication .', 'In some panels in Figure 4 ( see also Figure S2 ) , we compare our simulation with experimental data , collected from many different publications .', 'The protein variations are given in relative units .', 'In most cases , experimental uncertainties were not reported , but it is reasonable to assume that the error bounds should be quite generous .', 'The data sets provide us with qualitative benchmarks for our simulations , but a quantitative assessment of goodness-of-fit would be inappropriate .', 'Based on visual comparison , we conclude that our simulated protein variations agree reasonably well with the experimentally observed patterns .', 'Mutant cells provide valuable information about how individual components of the cell cycle control system affect phenotypes of cells .', 'We simulate mutants using exactly the same differential equations , parameter values , and initial conditions as for wild type ( wt ) cells ( Tables , S1 , S2 , and S3 ) , except for those modifications to parameters dictated by the mutation ( Table S4 ) .', 'For instance , a mutant with a particular gene deleted is modeled by zeroing the production rate of the corresponding protein .', 'This change propagates through the network , modifying the time courses of other proteins , and from these profiles we infer the phenotype of the mutant .', 'Here we present our simulations for ctrAD51E , ctrAΔ3Ω , ctrAD51EΔ3Ω , ctrA constitutive expression , ctrAop , ΔdivJ , and ΔpleC/ΔpodJ mutants .', 'The first five mutants were not correctly simulated in our earlier model because we made no distinction between phosphorylated ( active ) and unphosphorylated ( inactive ) CtrA .', 'The present model now accounts for the observed phenotypes of these ctrA mutants .', 'The other two mutants , ΔdivJ and ΔpleC/ΔpodJ , were outside the scope of our earlier model .', 'All other mutants that we have simulated are presented in the website http://mpf . biol . vt . edu/research/caulobacter/SWST/pp/ .', 'Predictions of the model provide for directions for designing new experiments , including direct experimental tests of the model .', 'In each simulation of a known mutant genotype , described above , some of the results were compared against experimental observations , and other parts may be considered as predictions , because the experimental studies did not report relevant information ( e . g . variations of some proteins ) .', 'These quantitative predictions are useful for future experimental exploration of these mutants that have already been studied to some extent .', 'In addition , we present in this section simulations of some novel mutants that have not been described in the literature , to our knowledge .', 'Some other novel mutants are also described at our website http://mpf . biol . vt . edu/research/caulobacter/SWST/pp/ .', 'To organize all simulations ( for wild-type cells and for mutants ) and present them in a systematic way , we have developed a website ( http://mpf . biol . vt . edu/research/caulobacter/SWST/pp/ ) that includes an introduction , a description of the mathematical model , wild-type simulation results , simulations of all relevant mutants , model files , modeling tools and an online simulator ( http://mpf . biol . vt . edu/research/caulobacter/SWST/pp/onlinesimulator . php ) to run the mathematical model .', 'The web site is designed to help molecular biologists design new experiments and mathematical modeler to explore the model in greater detail .', 'The online simulator has a friendly interface for running the model without getting unnecessarily involved in the underlying differential equations and parameter settings .'], ['Molecular cell biologists have collected a large amount of experimental information about genes , proteins and biochemical reactions involved in regulating the cell division cycle of Caulobacter crescentus .', 'These molecular details are spread over many specific publications and have not been drawn together into a coherent quantitative model until recently [24] , [25] .', 'Within the framework of nonlinear ordinary differential equations , we have developed a realistic , quantitative mathematical model of the molecular machinery governing the asymmetric division cycle of Caulobacter .', 'Our model provides an opportunity to study and analyze the system-level dynamics of the Caulobacter cell cycle ( beyond the kinetics of individual biochemical reactions ) , in order to test hypotheses about molecular mechanisms in silico , and to suggest new experimental designs .', 'The process of building a computational model is itself a scientifically challenging problem because it involves integrating data from diverse sources , reconciling observations made by different researchers , identifying gaps in our knowledge , hypothesizing mechanisms to fill these gaps , and converting the comprehensive descriptive scheme into a quantitative model capable of generating accurate temporal dynamics of protein fluctuations and physiological events .', 'Our success in building such a model indicates that there is already a “critical mass” of experimental data and theoretical ideas available to hypothesize a reasonable mechanism controlling cell division in Caulobacter .', 'Since our knowledge is incomplete , since any model inevitably contains many assumptions , and since there are alternative ways to express reaction kinetics in mathematical form , the proposed molecular mechanism and mathematical implementation of the model must be considered as an evolving hypothesis to be continually examined , revised , and improved as new observations tell us more about the molecular regulatory system .', 'Confidence in the model and respect for its predictions depend on how realistic is the underlying molecular mechanism , how accurate are the mathematical representations of the reaction network , and how well are the kinetic parameters of the model constrained by experimental data .', 'Our model , consisting of 28 differential equations ( Table S1 ) with 96 parameters ( Table S2 ) , was fitted to available experimental data , including phenotypes of wild-type and mutant cells , evidences for specific regulatory interactions , and quantitative measurements of protein expression .', "From the parameter list , the degradation rate constants of proteins ( 18 of 55 k's ) were determined from experimental data in the literature .", "Four P's , which are relative gene positions on the chromosome , were estimated from the Caulobacter genome sequence .", "The production rate constants of components ( 37 of 55 k's ) , together with 31 J's and 6 θ's ( binding constants and thresholds ) , were estimated by fitting the model to data points of 28 components in wild-type cells and by further tuning the parameter values to account for the phenotypes of 33 known mutants .", 'By carefully fitting parameter values to experimental data wherever possible , we have constructed a model that captures the dynamics of cell cycle control in wild type ( stalked and swarmer ) cells as well as the phenotypic characteristics of numerous mutant strains .', 'The model predicts a large amount of phenotypic properties not previously reported in known mutants , as well as phenotypes of 7 totally novel mutants .', 'Cell cycle regulation in Caulobacter is known to utilize spatial as well as temporal controls [47] , [81] , [82] .', 'Spatial aspects of the control system are left for future versions of the model .', 'As to the time domain , our model has limitations of temporal resolution and duration of a simulation .', 'Details of simulations at the scale of 10 min or less do not necessarily have biological significance .', 'On the other end , we can be reasonably confident of simulations of non-cycling cells up to about 400 min of run-time; for later times the model may exhibit artifacts or completely break down .', 'Caulobacter crescentus has recently been detected as a human pathogen , which makes the study of Caulobacter reproduction directly related to human health .', 'Since many genes and mechanisms discovered in Caulobacter are evolutionarily conserved among other α-proteobacteria , our computational model of cell replication in Caulobacter may be extendable to other family members , in particular to the causative agents of brucellosis in cattle and Rocky Mountain spotted fever in humans .', 'Insights gained into the temporal and spatial control of gene expression and protein interactions in Caulobacter could provide new clues for rational design of antibacterial agents and bacterial-based drug delivery technologies .'], ['The model presented in this publication describes temporal regulation of the asymmetric cell division cycle in Caulobacter crescentus .', 'It accounts for cell cycle regulation in both swarmer and stalked cells .', 'In the former case , the model includes G1 ( swarmer-to-stalked cell transition ) , S , and G2/M phases , while only S and G2/M phases are present for the stalked cell cycle .', 'The regulatory mechanism is described at the protein level with addition of a few phenomenological variables to describe DNA replication and cytokinesis .', 'Justification of our approach may be found in [23] , [25] .', 'At the core of the model are three master regulators ( DnaA , GcrA , and CtrA ) , as in our previous publication [25] .', 'Fluctuations of CtrA activity have been refined here to include explicitly protein activation via CckA-mediated phosphorylation of CtrA , and regulated degradation of CtrA by CpdR , RcdA , and ClpXP .', 'Z-ring formation is described now by a separate variable , and its formation and closing are regulated by FtsZ and FtsQ proteins , which are described here as distinct variables , and by DNA replication .', 'Finally , to capture regulation of the swarmer-to-stalked cell transition ( differentiation ) , we have extended the model to include DivJ , PleC , PodJ , and PerP proteins .', 'A complete list of the genes and proteins considered in this manuscript is provided in Table S5 .', 'Based on our model assumptions ( Text S1 ) , the interaction network for cell cycle controls in Caulobacter ( Figure S1 ) summarizes the current stage of knowledge compiled from the literature .', 'The wiring diagram in Figure 2 projects the interactions of Figure S1 into ‘protein space’ [83] and focuses on their relationships with physiological events [4] .', 'The molecular mechanism is converted into a set of differential equations ( Supplemental Table S1 ) describing the production , degradation , activation , inhibition , binding , release , phosphorylation , dephosphorylation , localization and delocalization of these proteins and physiological variables .', "The current model consists of 28 equations presented in Table S1 , including 55 kinetic constants ( k's ) , 31 binding constants ( J's ) , and 6 thresholds ( θ's ) .", 'The choice of parameter values and initial conditions are given in Supplemental Tables S2 and S3 .', 'Equations of the model were solved numerically with Matlab 2007b ( The MathWorks ) .', 'An online simulator and machine-readable files for reproducing our simulations are made available in Text S2 and on our website ( http://mpf . biol . vt . edu/research/caulobacter/SWST/pp/ ) .', 'Parameter values for our model ( Table S2 ) were determined directly from experimental data , where possible , or chosen as in [25] to provide a good fit to available observations of wild type cells ( see Supplemental Figure S2 ) and of mutant cells .', 'We do not assert that this set of parameter values is optimal in any sense .', 'Initial conditions in Table S3 were taken to represent the beginning of DNA replication whether it is for simulating a stalked cell cycle or swarmer cell cycle , in wild-type cells or mutants .', 'The phenotypes of relevant mutants were collected from the literature .', 'These mutants were simulated , as described in [25] , using exactly the same equations ( Table S1 ) and parameter values ( Table S2 ) except for values of those parameters directly affected by the mutation ( Table S4 ) .', 'In most cases , mutations are introduced in our model at the beginning of the swarmer cell , after 120 min of simulation .']]
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['The asymmetric cell division cycle of Caulobacter crescentus is orchestrated by an elaborate gene-protein regulatory network , centered on three major control proteins , DnaA , GcrA and CtrA .', 'The regulatory network is cast into a quantitative computational model to investigate in a systematic fashion how these three proteins control the relevant genetic , biochemical and physiological properties of proliferating bacteria .', 'Different controls for both swarmer and stalked cell cycles are represented in the mathematical scheme .', 'The model is validated against observed phenotypes of wild-type cells and relevant mutants , and it predicts the phenotypes of novel mutants and of known mutants under novel experimental conditions .', 'Because the cell cycle control proteins of Caulobacter are conserved across many species of alpha-proteobacteria , the model we are proposing here may be applicable to other genera of importance to agriculture and medicine ( e . g . , Rhizobium , Brucella ) .']
['Because of its small genome size and the ease by which it can be manipulated genetically and biochemically , Caulobacter crescentus provides unique opportunities to study the molecular circuitry controlling the asymmetric cell division cycle of bacteria .', 'A large amount of experimental data accumulated on this model organism in recent years needs to be quantitatively reconciled and analyzed in order to generate a full description of the process .', 'Here , from these experimental clues , we suggest a mechanism for the principal molecular interactions that control DNA synthesis and asymmetric cell division in Caulobacter and construct a quantitative ( mathematical ) model of the mechanism in order to analyze the temporal dynamics of the control system .', 'The model is centered around three “master regulator” proteins , whose timing of expression is tightly controlled by the progression of DNA replication .', 'The model has been validated against observed phenotypes of wild-type cells and relevant mutants , and predicts phenotypes of novel mutants and of known mutants under novel experimental conditions .', 'It provides a rigorous account of current intuitive ideas of bacterial cell cycle control and advances our understanding of bacterial cell division .']
['computational biology/systems biology', 'computational biology/signaling networks']