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1.  Single-gene tuning of Caulobacter cell cycle period and noise, swarming motility, and surface adhesion 
We established that the sensor histidine kinase DivJ has an important role in the regulation of C. crescentus cell cycle period and noise. This was accomplished by designing and conducting single-cell experiments to probe the dependence of cell cycle noise on divJ expression and constructing a simplified cell cycle model that captures the dependence of cell cycle noise on DivJ with molecular details.In addition to its role in regulating the cell cycle, DivJ also affects polar cell development in C. crescentus, regulating swarming motility and surface adhesion. We propose that pleiotropic control of polar cell development by the DivJ–DivK–PleC signaling pathway underlies divJ-dependent tuning of cell swarming and adhesion behaviors.We have integrated the study of single-cell fluorescence dynamics with a kinetic model simulation to provide direct quantitative evidence that the DivJ histidine kinase is localized to the cell pole through a dynamic diffusion-and-capture mechanism during the C. crescentus cell cycle.
Temporally-coordinated localization of various structural and signaling proteins is critical for proper cell cycle regulation and polar cell development in the bacterium, Caulobacter crescentus. Included among these dynamically-localized regulatory proteins is the sensor histidine kinase, DivJ (Wheeler and Shapiro, 1999). Co-localized with DivJ in the early stalked phase is the phosphorylated response regulator DivK∼P (Jacobs et al, 2001), and the protease ClpXP (McGrath et al, 2006), which degrades the master cell cycle regulator, CtrA (Jenal and Fuchs, 1998). Recent single-cell measurements of surface attached C. crescentus cells have revealed an intriguing role for DivJ in the control of noise in cell division period (Siegal-Gaskins and Crosson, 2008). The noise of the cell cycle increases significantly upon disruption of the divJ gene, with a relatively small accompanying increase in the mean cell cycle time. The deterministic nature of the existing cell cycle models (Li et al, 2008, 2009; Shen et al, 2008) cannot explain the measured increase in cell cycle period and noise in a divJ null strain. Moreover, mechanistic descriptions of how DivJ and its signaling partners are localized and how these proteins underlie the control of polar cell development and cell adhesion in C. crescentus remain immature.
The single-cell experiments and analysis presented herein reveal that C. crescentus cell cycle period and noise can be tuned by DivJ (Figure 2). Specifically, in the case of low (or no) divJ expression the cell cycle is perturbed, and this is quantified by way of the (measured) noise in the cell cycle period. The level of noise is readily controlled through regulated expression of the divJ gene (Figure 2B). A simplified protein interaction network of stalked C. crescentus cell cycle regulation involving minimal components (CtrA, CtrA∼P, DivK, DivK∼P, and DivJ) was constructed to explore such tunability at the molecular level. The agreement of our model with our (and other) experiments suggests this simplified protein regulatory network is sufficient to explain the major features of the C. crescentus cell cycle. Indeed, stochastic simulations of this model using the Gillespie method (Gillespie, 1976) establish the importance of robust DivJ-mediated phosphorylation of its cognate receiver protein, DivK, in regulating the variance of cell cycle oscillations. Increased variability in the concentration of DivK∼P at the single cell level under divJ depletion subsequently leads to increased noise in the regulation of CtrA phosphorylation and degradation. Our experiments and simulations provide evidence that the steady state level of DivK∼P at the single-cell level (as maintained by DivJ) is essential in maintaining regular timing of the cell division period in C. crescentus.
In addition to its role in regulating cell cycle, divJ expression also affects polar cell development in C. crescentus. Specifically, the capacity of swarmer cells to adhere to a glass surface is suppressed at high levels of divJ expression. The effect of elevated divJ expression on the adhesive capacity of the cell is reflected in a reduced rate of two-dimensional biofilm formation. This effect is quantitatively captured by our mathematical model that relates single-cell surface adhesion physiology and biofilm formation dynamics. This result, and our observation that divJ expression tunes swarming motility in semi-solid growth medium, suggests a model in which increased DivJ concentration in the swarmer compartment (due to constitutive overexpression) ultimately results in improper development of polar organelles that are required for adhesion of swarming motility.
Despite the appreciated significance of protein localization for bacterial physiological functions, the molecular mechanism of how polar protein localization is achieved has only been tested in a few cases (Shapiro et al, 2002; Thanbichler and Shapiro, 2008). Mechanisms such as the polar insertion model and diffusion-and-capture have been proposed but the community's knowledge is limited to very few examples (Charles et al, 2001; Rudner et al, 2002). We provide direct evidence from experiments and simulations that the DivJ histidine kinase becomes localized to the cell pole through a dynamic diffusion-and-capture mechanism during the C. crescentus cell cycle (Figure 7). We show that a kinetic model based on a Langmuir adsorption/desorption relationship (Figure 7D) is sufficient to explain the time evolution of the single cell fluorescence time traces (Figure 7C and E) and allows establishing quantitative correspondences between the simulated dynamics and experimentally determined DivJ–EGFP dynamics. This localization mechanism is consistent with a diffusion-and-capture model. In short, the model posits that proteins are randomly distributed and are freely diffusing until they are captured at the site where they ultimately reside (Rudner et al, 2002; Shapiro et al, 2002; Bardy and Maddock, 2007). With a diffusion-and-capture pathway, it has been argued that proteins can be adsorbed either dynamically or statically (Shapiro et al, 2009). Our analysis of DivJ–EGFP in single cells supports a dynamic diffuse-and-capture mechanism for DivJ localization.
Sensor histidine kinases underlie the regulation of a range of physiological processes in bacterial cells, from chemotaxis to cell division. In the gram-negative bacterium Caulobacter crescentus, the membrane-bound histidine kinase, DivJ, is a polar-localized regulator of cell cycle progression and development. We show that DivJ localizes to the cell pole through a dynamic diffusion and capture mechanism rather than by active localization. Analysis of single C. crescentus cells in microfluidic culture demonstrates that controlled expression of divJ permits facile tuning of both the mean and noise of the cell division period. Simulations of the cell cycle that use a simplified protein interaction network capture previously measured oscillatory protein profiles, and recapitulate the experimental observation that deletion of divJ increases the cell cycle period and noise. We further demonstrate that surface adhesion and swarming motility of C. crescentus in semi-solid media can also be tuned by divJ expression. We propose a model in which pleiotropic control of polar cell development by the DivJ–DivK–PleC signaling pathway underlies divJ-dependent tuning of cell swarming and adhesion behaviors.
PMCID: PMC3018171  PMID: 21179017
cell cycle; histidine kinase; protein interaction network; protein localization; single cell
2.  Phase Resetting Reveals Network Dynamics Underlying a Bacterial Cell Cycle 
PLoS Computational Biology  2012;8(11):e1002778.
Genomic and proteomic methods yield networks of biological regulatory interactions but do not provide direct insight into how those interactions are organized into functional modules, or how information flows from one module to another. In this work we introduce an approach that provides this complementary information and apply it to the bacterium Caulobacter crescentus, a paradigm for cell-cycle control. Operationally, we use an inducible promoter to express the essential transcriptional regulatory gene ctrA in a periodic, pulsed fashion. This chemical perturbation causes the population of cells to divide synchronously, and we use the resulting advance or delay of the division times of single cells to construct a phase resetting curve. We find that delay is strongly favored over advance. This finding is surprising since it does not follow from the temporal expression profile of CtrA and, in turn, simulations of existing network models. We propose a phenomenological model that suggests that the cell-cycle network comprises two distinct functional modules that oscillate autonomously and couple in a highly asymmetric fashion. These features collectively provide a new mechanism for tight temporal control of the cell cycle in C. crescentus. We discuss how the procedure can serve as the basis for a general approach for probing network dynamics, which we term chemical perturbation spectroscopy (CPS).
Author Summary
During the cell cycle, the cell progresses through a series of stages that are associated with various cell cycle events such as replication of genetic materials. Genetic and molecular dissections have revealed that the cell cycle is regulated by a network of interacting molecules that produces oscillatory dynamics. The major cell cycle regulators have been identified previously in different species and the activity of these regulators oscillates. However, the question of how cell cycle regulators coordinate different cell cycle events during the cell cycle remains controversial. Here, we investigate this question in a model bacterial system for cell cycle, Caulobacter crescentus. We perturb the expression of the master cell cycle regulator ctrA in a pulsatile fashion and quantify the response of the cell cycle to such perturbations. The measured response is contradictory to the existing mechanism of Caulobacter cell cycle control, which views the cell cycle progression as a sequential activation/inhibition process. We propose a new model that involves coupling of multiple oscillators and show the quantitative agreement between this new model and our measurements. We expect this procedure to be generalized and applied to a broad range of systems to obtain information that complements that obtained from other methods.
PMCID: PMC3510036  PMID: 23209388
3.  Fundamental Limits to Position Determination by Concentration Gradients 
PLoS Computational Biology  2007;3(4):e78.
Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially varying distribution allows the measurement of position within the system. For these systems to work effectively, position determination must be robust to noise. Here, we calculate fundamental limits to the precision of position determination by concentration gradients due to unavoidable biochemical noise perturbing the gradients. We focus on gradient proteins with first-order reaction kinetics. Systems of this type have been experimentally characterised in both developmental and cell biology settings. For a single gradient we show that, through time-averaging, great precision potentially can be achieved even with very low protein copy numbers. As a second example, we investigate the ability of a system with oppositely directed gradients to find its centre. With this mechanism, positional precision close to the centre improves more slowly with increasing averaging time, and so longer averaging times or higher copy numbers are required for high precision. For both single and double gradients, we demonstrate the existence of optimal length scales for the gradients for which precision is maximized, as well as analyze how precision depends on the size of the concentration-measuring apparatus. These results provide fundamental constraints on the positional precision supplied by concentration gradients in various contexts, including both in developmental biology and also within a single cell.
Author Summary
Many biological systems require precise positional information to function correctly. Examples include positioning of the site of cell division and determination of cell fate during embryonic development. This positional information often is encoded in concentration gradients. A specific protein is produced only within a small region, and subsequently spreads into the surrounding space. This leads to a spatial concentration gradient, with the highest protein concentration near the source. By switching on a signal only where the local concentration is above a certain threshold, this gradient can provide positional information. However, intrinsic randomness in biochemical reactions will lead to unavoidable fluctuations in the concentration profile, which in turn will lead to fluctuations in the identified position. We therefore investigated how precisely a noisy concentration gradient can specify positional information. We found that time-averaging of concentration measurements potentially allows for great precision to be achieved even with remarkably low protein copy numbers. We applied our results to a number of examples in both cell and developmental biology, including positioning of the site of cell division in bacteria and yeast, as well as gene expression in the developing Drosophila embryo.
PMCID: PMC1857820  PMID: 17465676
4.  Temporal Controls of the Asymmetric Cell Division Cycle in Caulobacter crescentus 
PLoS Computational Biology  2009;5(8):e1000463.
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).
Author Summary
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.
PMCID: PMC2714070  PMID: 19680425
5.  The CtrA phosphorelay integrates differentiation and communication in the marine alphaproteobacterium Dinoroseobacter shibae 
BMC Genomics  2014;15(1):130.
Dinoroseobacter shibae, a member of the Roseobacter clade abundant in marine environments, maintains morphological heterogeneity throughout growth, with small cells dividing by binary fission and large cells dividing by budding from one or both cell poles. This morphological heterogeneity is lost if the quorum sensing (QS) system is silenced, concurrent with a decreased expression of the CtrA phosphorelay, a regulatory system conserved in Alphaproteobacteria and the master regulator of the Caulobacter crescentus cell cycle. It consists of the sensor histidine kinase CckA, the phosphotransferase ChpT and the transcriptional regulator CtrA. Here we tested if the QS induced differentiation of D. shibae is mediated by the CtrA phosphorelay.
Mutants for ctrA, chpT and cckA showed almost homogeneous cell morphology and divided by binary fission. For ctrA and chpT, expression in trans on a plasmid caused the fraction of cells containing more than two chromosome equivalents to increase above wild-type level, indicating that gene copy number directly controls chromosome number. Transcriptome analysis revealed that CtrA is a master regulator for flagellar biosynthesis and has a great influence on the transition to stationary phase. Interestingly, the expression of the autoinducer synthase genes luxI2 and luxI3 was strongly reduced in all three mutants, resulting in loss of biosynthesis of acylated homoserine-lactones with C14 side-chain, but could be restored by expressing these genes in trans. Several phylogenetic clusters of Alphaproteobacteria revealed a CtrA binding site in the promoters of QS genes, including Roseobacters and Rhizobia.
The CtrA phosphorelay induces differentiation of a marine Roseobacter strain that is strikingly different from that of C. crescentus. Instead of a tightly regulated cell cycle and a switch between two morphotypes, the morphology and cell division of Dinoroseobacter shibae are highly heterogeneous. We discovered for the first time that the CtrA phosphorelay controls the biosynthesis of signaling molecules. Thus cell-cell communication and differentiation are interlinked in this organism. This may be a common strategy, since we found a similar genetic set-up in other species in the ecologically relevant group of Alphaproteobacteria. D. shibae will be a valuable model organism to study bacterial differentiation into pleomorphic cells.
Electronic supplementary material
The online version of this article (doi:10.1186/1471-2164-15-130) contains supplementary material, which is available to authorized users.
PMCID: PMC4046655  PMID: 24524855
6.  Predicting Chemical Environments of Bacteria from Receptor Signaling 
PLoS Computational Biology  2014;10(10):e1003870.
Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.
Author Summary
Outside the laboratory, bacteria live in complex microenvironments characterized by competition for space and available nutrients. Although often inaccessible by experiments, understanding the spatio-temporal dynamics of bacterial microenvironments is biomedically important. For instance, the chemical environment that symbiotic Escherichia coli encounter in the human gut relates to health of the gastrointestinal tract, gut metabolism, immune response, and tissue homeostasis. Other complex microenvironments include soil and biofilms. Assuming that bacterial sensory systems have evolved to optimally sense typical gradients, we treat signaling data, the signaling pathway with its architecture and reaction rates, and computer simulations of swimming bacteria in different gradients as “prior knowledge” to “reverse engineer” E. coli's habitat. Our identified gradients are exponentially shaped with wide-ranging rate values. These microenvironments most likely stem from local fluctuating nutrient sources and degradation by competing species, in which bacteria have evolved to swim with optimal performance.
PMCID: PMC4207464  PMID: 25340783
7.  Coordination of Division and Development Influences Complex Multicellular Behavior in Agrobacterium tumefaciens 
PLoS ONE  2013;8(2):e56682.
The α-Proteobacterium Agrobacterium tumefaciens has proteins homologous to known regulators that govern cell division and development in Caulobacter crescentus, many of which are also conserved among diverse α-Proteobacteria. In light of recent work demonstrating similarity between the division cycle of C. crescentus and that of A. tumefaciens, the functional conservation for this presumptive control pathway was examined. In C. crescentus the CtrA response regulator serves as the master regulator of cell cycle progression and cell division. CtrA activity is controlled by an integrated pair of multi-component phosphorelays: PleC/DivJ-DivK and CckA-ChpT-CtrA. Although several of the conserved orthologues appear to be essential in A. tumefaciens, deletions in pleC or divK were isolated and resulted in cell division defects, diminished swimming motility, and a decrease in biofilm formation. A. tumefaciens also has two additional pleC/divJ homologue sensor kinases called pdhS1 and pdhS2, absent in C. crescentus. Deletion of pdhS1 phenocopied the ΔpleC and ΔdivK mutants. Cells lacking pdhS2 morphologically resembled wild-type bacteria, but were decreased in swimming motility and elevated for biofilm formation, suggesting that pdhS2 may serve to regulate the motile to non-motile switch in A. tumefaciens. Genetic analysis suggests that the PleC/DivJ-DivK and CckA-ChpT-CtrA phosphorelays in A. tumefaciens are vertically-integrated, as in C. crescentus. A gain-of-function mutation in CckA (Y674D) was identified as a spontaneous suppressor of the ΔpleC motility phenotype. Thus, although the core architecture of the A. tumefaciens pathway resembles that of C. crescentus there are specific differences including additional regulators, divergent pathway architecture, and distinct target functions.
PMCID: PMC3577659  PMID: 23437210
8.  The CckA-ChpT-CtrA Phosphorelay System Is Regulated by Quorum Sensing and Controls Flagellar Motility in the Marine Sponge Symbiont Ruegeria sp. KLH11 
PLoS ONE  2013;8(6):e66346.
Bacteria respond to their environment via signal transduction pathways, often two-component type systems that function through phosphotransfer to control expression of specific genes. Phosphorelays are derived from two-component systems but are comprised of additional components. The essential cckA-chpT-ctrA phosphorelay in Caulobacter crescentus has been well studied and is important in orchestrating the cell cycle, polar development and flagellar biogenesis. Although cckA, chpT and ctrA homologues are widespread among the Alphaproteobacteria, relatively few is known about their function in the large and ecologically significant Roseobacter clade of the Rhodobacterales. In this study the cckA-chpT-ctrA system of the marine sponge symbiont Ruegeria sp. KLH11 was investigated. Our results reveal that the cckA, chpT and ctrA genes positively control flagellar biosynthesis. In contrast to C. crescentus, the cckA, chpT and ctrA genes in Ruegeria sp. KLH11 are non-essential and do not affect bacterial growth. Gene fusion and transcript analyses provide evidence for ctrA autoregulation and the control of motility-related genes. In KLH11, flagellar motility is controlled by the SsaRI system and acylhomoserine lactone (AHL) quorum sensing. SsaR and long chain AHLs are required for cckA, chpT and ctrA gene expression, providing a regulatory link between flagellar locomotion and population density in KLH11.
PMCID: PMC3692519  PMID: 23825536
9.  Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution 
PLoS Computational Biology  2009;5(8):e1000460.
In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell.
Author Summary
Time-series analyses of cellular regulatory processes have successfully drawn attention to the importance of temporal regulation in biological systems. A number of model systems can be synchronized such that data collected on cell populations better reflect the dynamic properties of the individual cell. However, experimental synchronization is never perfect, and the degree of synchrony that does exist at the outset of an experiment is quickly lost over time as cells grow at different rates and enter different developmental or physiological states on cell division. Thus, data collected from a population of synchronized cells can lead to incorrect models of temporal regulation. Here we demonstrate that the problem of relating population data to the individual cell can be resolved with a computational method that effectively removes the effects of both imperfect synchrony and time-dependent loss of synchrony. Application of this deconvolution algorithm to a cell cycle time-series data set from the model bacterium Caulobacter crescentus uncovers critical temporal details in the expression of essential genes that are not evident in the raw population-based data. The deconvolution routine presented here is a robust and general tool for extracting biochemical parameters of the average single cell from population time-series data.
PMCID: PMC2718844  PMID: 19680537
10.  Regulated proteolysis of a transcription factor complex is critical to cell cycle progression in Caulobacter crescentus 
Molecular microbiology  2013;87(6):1277-1289.
Cell cycle transitions are often triggered by the proteolysis of key regulatory proteins. In Caulobacter crescentus, the G1-S transition involves the degradation of an essential DNA-binding response regulator, CtrA, by the ClpXP protease. Here, we show that another critical cell cycle regulator, SciP, is also degraded during the G1-S transition, but by the Lon protease. SciP is a small protein that binds directly to CtrA and prevents it from activating target genes during G1. We demonstrate that SciP must be degraded during the G1-S transition so that cells can properly activate CtrA-dependent genes following DNA replication initiation and the reaccumulation of CtrA. These results indicate that like CtrA, SciP levels are tightly regulated during the Caulobacter cell cycle. In addition, we show that formation of a complex between CtrA and SciP at target promoters protects both proteins from their respective proteases. Degradation of either protein thus helps trigger the destruction of the other, facilitating a cooperative disassembly of the complex. Collectively, our results indicate that ClpXP and Lon each degrade a critical cell cycle regulator, helping to trigger the onset of S phase and prepare cells for the subsequent programs of gene expression critical to polar morphogenesis and cell division.
PMCID: PMC3596498  PMID: 23368090
11.  A Quantitative Study of the Division Cycle of Caulobacter crescentus Stalked Cells 
Progression of a cell through the division cycle is tightly controlled at different steps to ensure the integrity of genome replication and partitioning to daughter cells. From published experimental evidence, we propose a molecular mechanism for control of the cell division cycle in Caulobacter crescentus. The mechanism, which is based on the synthesis and degradation of three “master regulator” proteins (CtrA, GcrA, and DnaA), is converted into a quantitative model, in order to study the temporal dynamics of these and other cell cycle proteins. The model accounts for important details of the physiology, biochemistry, and genetics of cell cycle control in stalked C. crescentus cell. It reproduces protein time courses in wild-type cells, mimics correctly the phenotypes of many mutant strains, and predicts the phenotypes of currently uncharacterized mutants. Since many of the proteins involved in regulating the cell cycle of C. crescentus are conserved among many genera of α-proteobacteria, the proposed mechanism may be applicable to other species of importance in agriculture and medicine.
Author Summary
The cell cycle is the sequence of events by which a growing cell replicates all its components and divides them more or less evenly between two daughter cells. The timing and spatial organization of these events are controlled by gene–protein interaction networks of great complexity. A challenge for computational biology is to build realistic, accurate, predictive mathematical models of these control systems in a variety of organisms, both eukaryotes and prokaryotes. To this end, we present a model of a portion of the molecular network controlling DNA synthesis, cell cycle–related gene expression, DNA methylation, and cell division in stalked cells of the α-proteobacterium Caulobacter crescentus. The model is formulated in terms of nonlinear ordinary differential equations for the major cell cycle regulatory proteins in Caulobacter: CtrA, GcrA, DnaA, CcrM, and DivK. Kinetic rate constants are estimated, and the model is tested against available experimental observations on wild-type and mutant cells. The model is viewed as a starting point for more comprehensive models of the future that will account, in addition, for the spatial asymmetry of Caulobacter reproduction (swarmer cells as well as stalked cells), the correlation of cell growth and division, and cell cycle checkpoints.
PMCID: PMC2217572  PMID: 18225942
12.  Chemotaxis: A Feedback-Based Computational Model Robustly Predicts Multiple Aspects of Real Cell Behaviour 
PLoS Biology  2011;9(5):e1000618.
A simple feedback model of chemotaxis explains how new pseudopods are made and how eukaryotic cells steer toward chemical gradients.
The mechanism of eukaryotic chemotaxis remains unclear despite intensive study. The most frequently described mechanism acts through attractants causing actin polymerization, in turn leading to pseudopod formation and cell movement. We recently proposed an alternative mechanism, supported by several lines of data, in which pseudopods are made by a self-generated cycle. If chemoattractants are present, they modulate the cycle rather than directly causing actin polymerization. The aim of this work is to test the explanatory and predictive powers of such pseudopod-based models to predict the complex behaviour of cells in chemotaxis. We have now tested the effectiveness of this mechanism using a computational model of cell movement and chemotaxis based on pseudopod autocatalysis. The model reproduces a surprisingly wide range of existing data about cell movement and chemotaxis. It simulates cell polarization and persistence without stimuli and selection of accurate pseudopods when chemoattractant gradients are present. It predicts both bias of pseudopod position in low chemoattractant gradients and—unexpectedly—lateral pseudopod initiation in high gradients. To test the predictive ability of the model, we looked for untested and novel predictions. One prediction from the model is that the angle between successive pseudopods at the front of the cell will increase in proportion to the difference between the cell's direction and the direction of the gradient. We measured the angles between pseudopods in chemotaxing Dictyostelium cells under different conditions and found the results agreed with the model extremely well. Our model and data together suggest that in rapidly moving cells like Dictyostelium and neutrophils an intrinsic pseudopod cycle lies at the heart of cell motility. This implies that the mechanism behind chemotaxis relies on modification of intrinsic pseudopod behaviour, more than generation of new pseudopods or actin polymerization by chemoattractants.
Author Summary
The efficiency, sensitivity, and huge dynamic range of eukaryotic cell chemotaxis have proven very hard to explain. Cells respond to shallow gradients of chemotactic molecules with directed movement, but the mechanisms remain elusive. Most current models predict that cells have an internal “compass” produced by processing the extracellular signal into an intracellular mechanism that points the cell towards the gradient and steers it in that direction. In this article, we present evidence that this internal compass does not exist; instead, the cell orients itself simply by making use of its pseudopods—the dynamic finger-like projections on the surface of the cell. We approached the question by making a computational model of the movement of a cell without a compass. In this model, the cell moves in a convincingly natural way simply by using its pseudopods, which respond to positive- and negative-feedback loops. The concentration of the chemoattractant molecule modulates the amount of positive feedback. Apart from this, no signal processing is necessary. This simple model reproduces many observations about normal chemotaxis. It also accurately predicts the angle at which new pseudopods split off from old ones, which had not been previously measured. The computational model thus demonstrates that pseudopod-based mechanisms are powerful enough to explain chemotaxis.
PMCID: PMC3096608  PMID: 21610858
13.  The diversity and evolution of cell cycle regulation in alpha-proteobacteria: a comparative genomic analysis 
BMC Systems Biology  2010;4:52.
In the bacterium Caulobacter crescentus, CtrA coordinates DNA replication, cell division, and polar morphogenesis and is considered the cell cycle master regulator. CtrA activity varies during cell cycle progression and is modulated by phosphorylation, proteolysis and transcriptional control. In a phosphorylated state, CtrA binds specific DNA sequences, regulates the expression of genes involved in cell cycle progression and silences the origin of replication. Although the circuitry regulating CtrA is known in molecular detail in Caulobacter, its conservation and functionality in the other alpha-proteobacteria are still poorly understood.
Orthologs of Caulobacter factors involved in the regulation of CtrA were systematically scanned in genomes of alpha-proteobacteria. In particular, orthologous genes of the divL-cckA-chpT-ctrA phosphorelay, the divJ-pleC-divK two-component system, the cpdR-rcdA-clpPX proteolysis system, the methyltransferase ccrM and transcriptional regulators dnaA and gcrA were identified in representative genomes of alpha-proteobacteria. CtrA, DnaA and GcrA binding sites and CcrM putative methylation sites were predicted in promoter regions of all these factors and functions controlled by CtrA in all alphas were predicted.
The regulatory cell cycle architecture was identified in all representative alpha-proteobacteria, revealing a high diversification of circuits but also a conservation of logical features. An evolutionary model was proposed where ancient alphas already possessed all modules found in Caulobacter arranged in a variety of connections. Two schemes appeared to evolve: a complex circuit in Caulobacterales and Rhizobiales and a simpler one found in Rhodobacterales.
PMCID: PMC2877005  PMID: 20426835
14.  Cell Fate Regulation Governed by a Repurposed Bacterial Histidine Kinase 
PLoS Biology  2014;12(10):e1001979.
The pathway that regulates asymmetric cell division in Caulobacter involves a signaling kinase whose catalytic output domain has been repurposed as an input sensor of the phosphorylation state of the response regulator – a reversal of the conventional direction of information flow; this allows wiring of simple linear signaling pathways into complex eukaryote-like networks.
One of the simplest organisms to divide asymmetrically is the bacterium Caulobacter crescentus. The DivL pseudo-histidine kinase, positioned at one cell pole, regulates cell-fate by controlling the activation of the global transcription factor CtrA via an interaction with the response regulator (RR) DivK. DivL uniquely contains a tyrosine at the histidine phosphorylation site, and can achieve these regulatory functions in vivo without kinase activity. Determination of the DivL crystal structure and biochemical analysis of wild-type and site-specific DivL mutants revealed that the DivL PAS domains regulate binding specificity for DivK∼P over DivK, which is modulated by an allosteric intramolecular interaction between adjacent domains. We discovered that DivL's catalytic domains have been repurposed as a phosphospecific RR input sensor, thereby reversing the flow of information observed in conventional histidine kinase (HK)-RR systems and coupling a complex network of signaling proteins for cell-fate regulation.
Author Summary
Across all kingdoms of life the generation of cell-type diversity is the consequence of asymmetry at the point of cell division. The bacterium Caulobacter crescentus divides asymmetrically to produce daughter cells that have distinct morphology and behavior. As in eukaryotes, an unequal distribution of signaling proteins in daughter Caulobacter cells triggers the differential read-out of identical genomes. A critical interaction between two protein molecules – a protein kinase (DivL) and a response regulator (DivK) – is known to occur exclusively in one daughter cell and to thereby regulate differentiation. However, mapping the observed signaling interconnections that drive asymmetric division has been difficult to reconcile with traditional models of bacterial signaling. Here we determine how DivL detects and processes this DivK signal. Although DivL has an architecture that is typical of histidine kinases, which normally act by regulating the phosphorylation state of the appropriate response regulator, DivL's essential functions do not require kinase activity and DivL does not add or remove phosphate from DivK. Instead we find that DivL has converted its output kinase domain into an input sensor domain that specifically detects phosphorylated DivK, and we identify key features of DivL that underlie this specificity. This novel reassignment of sensory functions reverses the conventional kinase-to-response-regulator signaling flow and logically couples linear signaling pathways into complex eukaryote-like networks to regulate cell development.
PMCID: PMC4211667  PMID: 25349992
15.  Optimal Noise Filtering in the Chemotactic Response of Escherichia coli 
PLoS Computational Biology  2006;2(11):e154.
Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.
Bacterial motility involves successive periods of relatively straight runs, interspersed by tumbles—periods in which the bacteria are reoriented randomly. To move in the direction of chemical gradients—a process known as chemotaxis—cells modulate the duration of the runs. To ascertain whether the direction of the current run is desirable, cells continuously monitor temporal changes in the chemoattractant concentration. However, the decisions can only be based on imperfect information about the environment because binding noise implies that receptor occupancy is a limited measure of the chemoattractant concentration. Bacteria cope by filtering the sensed signal to reduce the effect of this binding noise. Through simulations, Andrews, Yi, and Iglesias demonstrate that there is a particular filter cutoff frequency that achieves optimal chemotaxis. Moreover, using a model of the sensing mechanism, the authors also compute the theoretically optimal system for estimating the chemoattractant concentration from the noisy receptor-occupancy signal. Andrews and colleagues show that these two filtering systems are closely matched, and that their frequency-dependent behavior corresponds to published experimental data. Their results highlight the constraints that noise places on cellular performance as well as demonstrating how cells have evolved to deal with this uncertainty in an optimal fashion.
PMCID: PMC1636674  PMID: 17112312
16.  Dynamics of Two Phosphorelays Controlling Cell Cycle Progression in Caulobacter crescentus▿ †  
Journal of Bacteriology  2009;191(24):7417-7429.
In Caulobacter crescentus, progression through the cell cycle is governed by the periodic activation and inactivation of the master regulator CtrA. Two phosphorelays, each initiating with the histidine kinase CckA, promote CtrA activation by driving its phosphorylation and by inactivating its proteolysis. Here, we examined whether the CckA phosphorelays also influence the downregulation of CtrA. We demonstrate that CckA is bifunctional, capable of acting as either a kinase or phosphatase to drive the activation or inactivation, respectively, of CtrA. By identifying mutations that uncouple these two activities, we show that CckA's phosphatase activity is important for downregulating CtrA prior to DNA replication initiation in vivo but that other phosphatases may exist. Our results demonstrate that cell cycle transitions in Caulobacter require and are likely driven by the toggling of CckA between its kinase and phosphatase states. More generally, our results emphasize how the bifunctional nature of histidine kinases can help switch cells between mutually exclusive states.
PMCID: PMC2786585  PMID: 19783630
17.  A Homolog of the CtrA Cell Cycle Regulator Is Present and Essential in Sinorhizobium meliloti 
Journal of Bacteriology  2001;183(10):3204-3210.
During development of the symbiotic soil bacterium Sinorhizobium meliloti into nitrogen-fixing bacteroids, DNA replication and cell division cease and the cells undergo profound metabolic and morphological changes. Regulatory genes controlling the early stages of this process have not been identified. As a first step in the search for regulators of these events, we report the isolation and characterization of a ctrA gene from S. meliloti. We show that the S. meliloti CtrA belongs to the CtrA-like family of response regulators found in several α-proteobacteria. In Caulobacter crescentus, CtrA is essential and is a global regulator of multiple cell cycle functions. ctrA is also an essential gene in S. meliloti, and it is expressed similarly to the autoregulated C. crescentus ctrA in that both genes have complex promoter regions which bind phosphorylated CtrA.
PMCID: PMC95222  PMID: 11325950
18.  Polarity and cell fate asymmetry in Caulobacter crescentus 
Current opinion in microbiology  2012;15(6):744-750.
The production of asymmetric daughter cells is a hallmark of metazoan development and critical to the life cycle of many microbes, including the α-proteobacterium Caulobacter crescentus. For Caulobacter, every cell division is asymmetric, yielding daughter cells with different morphologies and replicative potentials. This asymmetry in daughter cell fate is governed by the response regulator CtrA, a transcription factor that can also bind and silence the origin of replication. CtrA activity is controlled by a complex regulatory circuit that includes several polarly localized histidine kinases. This circuit ensures differential activation of CtrA in daughter cells, leading to their asymmetric replicative potentials. Here, we review progress in elucidating the molecular mechanisms regulating CtrA and the role of cellular polarity in this process.
PMCID: PMC3587792  PMID: 23146566
19.  Reconstitution of self-organizing protein gradients as spatial cues in cell-free systems 
eLife  2014;3:e03949.
Intracellular protein gradients are significant determinants of spatial organization. However, little is known about how protein patterns are established, and how their positional information directs downstream processes. We have accomplished the reconstitution of a protein concentration gradient that directs the assembly of the cell division machinery in E.coli from the bottom-up. Reconstituting self-organized oscillations of MinCDE proteins in membrane-clad soft-polymer compartments, we demonstrate that distinct time-averaged protein concentration gradients are established. Our minimal system allows to study complex organizational principles, such as spatial control of division site placement by intracellular protein gradients, under simplified conditions. In particular, we demonstrate that FtsZ, which marks the cell division site in many bacteria, can be targeted to the middle of a cell-like compartment. Moreover, we show that compartment geometry plays a major role in Min gradient establishment, and provide evidence for a geometry-mediated mechanism to partition Min proteins during bacterial development.
eLife digest
When a cell divides, it is important that its contents are separated in the right place to make sure that both daughter cells have everything that they need to survive. To do this, the molecular ‘machinery’ that physically divides the cell needs to know where to assemble.
In the bacterium E. coli, the location of cell division depends on a group of proteins called the Min proteins. These proteins are not evenly distributed over the cell. Instead, they oscillate back and forth to set up concentration gradients, with the concentration of Min proteins being lowest in the middle of the cell and highest at the ends. The machinery that divides the cell assembles at the point where the concentration of Min proteins is lowest. However, it is not clear exactly how the protein gradients are set up in the cell, and whether these gradients are indeed sufficient to position the cell division machinery.
To explore this process, Zieske et al. engineered artificial cells that mimicked some of the basic properties of living cells. In these artificial cells, the Min proteins organized themselves into gradients that were similar to those found in living cells. This gradient then caused another protein called FtsZ—which is involved in cell division—to accumulate in the middle of the artificial cell. Zieske et al. also showed that the shape of the artificial cell influenced the shape of the protein gradient.
This research shows that the interplay between the shape of a bacterial cell and a defined set of proteins could control the position of cell division. The simplified system that Zieske et al. have developed could also be used to study other aspects of cell organization and cell division.
PMCID: PMC4215534  PMID: 25271375
protein gradient; FtsZ; cytoskeleton; cell division; cell-free reconstitution; min proteins; E. coli
20.  An Information-Theoretic Characterization of the Optimal Gradient Sensing Response of Cells 
PLoS Computational Biology  2007;3(8):e153.
Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient—for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.
Author Summary
For many cell types, the direction of migration is determined in response to spatial differences in the concentration of chemoattractant, a process known as chemotaxis. Precise chemotaxis—that is, motility with low directional distortion—requires that cells make accurate decisions based on the stochastic fluctuations inherent in cell-surface receptor occupancy. Here, we use rate distortion theory, a branch of information theory, to determine chemotaxis strategies for cells based on this imperfect information about their environment. In engineering, rate distortion theory provides the information processing capabilities required to achieve a desired accuracy. We demonstrate that more accurate chemotaxis requires greater information. We also show that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes to existing experimental measurements and models of eukaryotic gradient sensing and demonstrate that different observed types of cellular responses (polarized and unpolarized) are optimal under varying information assumptions. Our results also highlight the constraints that noise places on the performance of cellular systems.
PMCID: PMC1937015  PMID: 17676949
21.  Sinorhizobium meliloti CpdR1 is critical for coordinating cell-cycle progression and the symbiotic chronic infection 
Molecular microbiology  2009;73(4):586-600.
ATP-driven proteolysis plays a major role in regulating the bacterial cell cycle, development and stress responses. In the nitrogen-fixing symbiosis with host plants, Sinorhizobium meliloti undergoes a profound cellular differentiation including endoreduplication of the genome. The regulatory mechanisms governing the alterations of the S. meliloti cell cycle in planta are largely unknown. Here, we report the characterization of two cpdR homologs, cpdR1 and cpdR2, of S. meliloti that encode single-domain response regulators. In Caulobacter crescentus, CpdR controls the polar localization of the ClpXP protease, thereby mediating the regulated proteolysis of key protein(s), such as CtrA, involved in cell-cycle progression. The S. meliloti cpdR1-null mutant can invade the host cytoplasm, however, the intracellular bacteria are unable to differentiate into bacteroids. We show that S. meliloti CpdR1 has a polar localization pattern and a role in ClpX positioning similar to C. crescentus CpdR, suggesting a conserved function of CpdR proteins among f¿-proteobacteria. However, in S. meliloti, free-living cells of the cpdR1-null mutant show a striking morphology of irregular coccoids and aberrant DNA replication. Thus, we demonstrate that CpdR1 mediates the coordination of cell-cycle events, which are critical for both the free-living cell division and the differentiation required for the chronic intracellular infection.
PMCID: PMC2756024  PMID: 19602145
22.  A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli 
Combining in vivo FRET with time-varying stimuli, such as steps, ramps, and sinusoids allowed deduction of the molecular mechanisms underlying cellular signal processing.The bacterial chemotaxis pathway can be described as a two-module feedback circuit, the transfer functions of which we have characterized quantitatively by experiment. Model-driven experimental design allowed the use of a single FRET pair for measurements of both transfer functions of the pathway.The adaptation module's transfer function revealed that feedback near steady state is weak, consistent with high sensitivity to shallow gradients, but also strong steady-state fluctuations in pathway output.The measured response to oscillatory stimuli defines the frequency band over which the chemotaxis system can compute time derivatives.
In searching for better environments, bacteria sample their surroundings by random motility, and make temporal comparisons of experienced sensory cues to bias their movement toward favorable directions (Berg and Brown, 1972). Thus, the problem of sensing spatial gradients is reduced to time-derivative computations, carried out by a signaling pathway that is well characterized at the molecular level in Escherichia coli. Here, we study the physiology of this signal processing system in vivo by fluorescence resonance energy transfer (FRET) experiments in which live cells are stimulated by time-varying chemoeffector signals. By measuring FRET between the active response regulator of the pathway CheY-P and its phosphatase CheZ, each labeled with GFP variants, we obtain a readout that is directly proportional to pathway activity (Sourjik et al, 2007). We analyze the measured response functions in terms of mechanistic models of signaling, and discuss functional consequences of the observed quantitative characteristics.
Experiments are guided by a coarse-grained modular model (Tu et al, 2008) of the sensory network (Figure 1), in which we identify two important ‘transfer functions': one corresponding to the receptor–kinase complex, which responds to changes in input ligand concentration on a fast time scale, and another corresponding to the adaptation system, which provides negative feedback, opposing the effect of ligand on a slower time scale. For the receptor module, we calibrate an allosteric MWC-type model of the receptor–kinase complex by FRET measurements of the ‘open-loop' transfer function G([L],m) using step stimuli. This calibration provides a basis for using the same FRET readout (between CheY-P and CheZ) to further study properties of the adaptation module.
It is well known that adaptation in E. coli's chemotaxis system uses integral feedback, which guarantees exact restoration of the baseline activity after transient responses to step stimuli (Barkai and Leibler, 1997; Yi et al, 2000). However, the output of time-derivative computations during smoothly varying stimuli depends not only on the presence of integral feedback, but also on what is being integrated. As this integrand can in general be any function of the output, we represent it by a black-box function F(a) in our model, and set out to determine its shape by experiments with time-varying stimuli.
We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, ac that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of ac versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.
To obtain the feedback transfer function, F(a), we apply a simple coordinate transformation, identified using our model, to the same ramp-response data (Figure 5B). This function reveals how the temporal rate of change of the feedback signal m depends on the current output signal a. The shape of this function is analyzed using a biochemical reaction scheme, from which in vivo kinetic parameters of the feedback enzymes, CheR and CheB, are extracted. The fitted Michaelis constants for these enzymatic reactions are small compared with the steady-state abundance of their substrates, thus indicating that these enzymes operate close to saturation in vivo. The slope of the function near steady state can be used to assess the strength of feedback, and to compute the relaxation time of the system, τm. Relaxation is found to be slow (i.e. large τm), consistent with large fluctuations about the steady-state activity caused by the near-saturation kinetics of the feedback enzymes (Emonet and Cluzel, 2008).
Finally, exponential sine-wave stimuli are used to map out the system's frequency response (Figure 5C). The measured data points for both the amplitude and phase of the response are found to be in excellent agreement with model predictions based on parameters from the independently measured step and ramp responses. No curve fitting was required to obtain this agreement. Although the amplitude response as a function of frequency resembles a first-order high-pass filter with a well-defined cutoff frequency, νm, we point out that the chemotaxis pathway is actually a low-pass filter if the time derivative of the input is viewed as the input signal. In this latter perspective, νm defines an upper bound for the frequency band over which time-derivative computations can be carried out.
The two types of measurements yield complementary information regarding time-derivative computations by E. coli. The ramp-responses characterize the asymptotically constant output when a temporal gradient is held fixed over extended periods. Interestingly, the ramp responses do not depend on receptor cooperativity, but only on properties of the adaptation system, and thus can be used to reveal the in vivo adaptation kinetics, even outside the linear regime of the kinase response. The frequency response is highly relevant in considering spatial searches in the real world, in which experienced gradients are not held fixed in time. The characteristic cutoff frequency νm is found by working within the linear regime of the kinase response, and depends on parameters from both modules (it increases with both cooperativity in the receptor module, and the strength of feedback in the adaptation module).
Both ramp responses and sine-wave responses were measured at two different temperatures (22 and 32°C), and found to differ significantly. Both the slope of F(a) near steady state, from ramp experiments, and the characteristic cutoff frequency, from sine-wave experiments, were higher by a factor of ∼3 at 32°C. Fits of the enzymatic model to F(a) suggest that temperature affects the maximal velocity (Vmax) more strongly than the Michaelis constants (Km) for CheR and CheB.
Successful application of inter-molecular FRET in live cells using GFP variants always requires some degree of serendipity. Genetic fusions to these bulky fluorophores can impair the function of the original proteins, and even when fusions are functional, efficient FRET still requires the fused fluorophores to come within the small (<10 nm) Förster radius on interactions between the labeled proteins. Thus, when a successful FRET pair is identified, it is desirable to make the most of it. We have shown here that combined with careful temporal control of input stimuli, and appropriately calibrated models, a single FRET pair can be used to study the structure of multiple transfer functions within a signaling network.
The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22°C and below 0.018 Hz at 32°C. Our results show how dynamic input–output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.
PMCID: PMC2913400  PMID: 20571531
adaptation; feedback; fluorescence resonance energy transfer (FRET); frequency response; Monod–Wyman–Changeux (MWC) model
23.  Computational Model of Vascular Endothelial Growth Factor Spatial Distribution in Muscle and Pro-Angiogenic Cell Therapy 
PLoS Computational Biology  2006;2(9):e127.
Members of the vascular endothelial growth factor (VEGF) family of proteins are critical regulators of angiogenesis. VEGF concentration gradients are important for activation and chemotactic guidance of capillary sprouting, but measurement of these gradients in vivo is not currently possible. We have constructed a biophysically and molecularly detailed computational model to study microenvironmental transport of two isoforms of VEGF in rat extensor digitorum longus skeletal muscle under in vivo conditions. Using parameters based on experimental measurements, the model includes: VEGF secretion from muscle fibers; binding to the extracellular matrix; binding to and activation of endothelial cell surface VEGF receptors; and internalization. For 2-D cross sections of tissue, we analyzed predicted VEGF distributions, gradients, and receptor binding. Significant VEGF gradients (up to 12% change in VEGF concentration over 10 μm) were predicted in resting skeletal muscle with uniform VEGF secretion, due to non-uniform capillary distribution. These relative VEGF gradients were not sensitive to extracellular matrix composition, or to the overall VEGF expression level, but were dependent on VEGF receptor density and affinity, and internalization rate parameters. VEGF upregulation in a subset of fibers increased VEGF gradients, simulating transplantation of pro-angiogenic myoblasts, a possible therapy for ischemic diseases. The number and relative position of overexpressing fibers determined the VEGF gradients and distribution of VEGF receptor activation. With total VEGF expression level in the tissue unchanged, concentrating overexpression into a small number of adjacent fibers can increase the number of capillaries activated. The VEGF concentration gradients predicted for resting muscle (average 3% VEGF/10 μm) is sufficient for cellular sensing; the tip cell of a vessel sprout is approximately 50 μm long. The VEGF gradients also result in heterogeneity in the activation of blood vessel VEGF receptors. This first model of VEGF tissue transport and heterogeneity provides a platform for the design and evaluation of therapeutic approaches.
It is not currently possible to experimentally quantify the gradients of protein concentration in the extracellular space in vivo. However, the concentration gradients of vascular endothelial growth factor (VEGF) are essential for both initiation and directed guidance of new blood vessels. The authors develop a computational model of VEGF transport in tissue in vivo (skeletal muscle, though the method is applicable to other tissues and other proteins) with realistic geometry and including biophysical interactions of VEGF, its receptors, and the extracellular matrix. Using this model, the authors predict for the first time the distribution of VEGF concentration and VEGF receptor activation throughout the tissue. VEGF concentration gradients are significant, up to 12% change in VEGF concentration over 10 μm in resting muscle. Transplanting VEGF-overexpressing myocytes (for therapeutic induction of blood vessel growth) increases the gradients significantly. Endothelial cells in sprouting vessels are approximately 50 μm long, and therefore the predicted gradients across the cell are high and sufficient for chemotactic guidance of the new vessels. The VEGF concentration gradients also result in significant heterogeneity in the activation of VEGF receptors on blood vessels throughout the tissue, a possible reason for the sporadic nature of sprout initiation.
PMCID: PMC1570371  PMID: 17002494
24.  Protein Sequences and Cellular Factors Required for Polar Localization of a Histidine Kinase in Caulobacter crescentus 
Journal of Bacteriology  2002;184(21):6037-6049.
The Caulobacter crescentus sensor kinase DivJ is required for an early cell division step and localizes at the base of the newly formed stalk during the G1-to-S-phase transition when the protein is synthesized. To identify sequences within DivJ that are required for polar localization, we examined the ability of mutagenized DivJ sequences to direct localization of the green fluorescent protein. The effects of overlapping C-terminal deletions of DivJ established that the N-terminal 326 residues, which do not contain the kinase catalytic domain, are sufficient for polar localization of the fusion protein. Internal deletions mapped a shorter sequence between residues 251 and 312 of the cytoplasmic linker that are required for efficient localization of this sensor kinase. PleC kinase mutants, which are blocked in the swarmer-to-stalked-cell transition and form flagellated, nonmotile cells, also fail to localize DivJ. To dissect the cellular factors involved in establishing subcellular polarity, we have examined DivJ localization in a pleC mutant suppressed by the sokA301 allele of ctrA and in a pleD mutant, both of which display a supermotile, stalkless phenotype. The observation that these Mot+ strains localize DivJ to a single cell pole indicate that localization may be closely coupled to the gain of motility and that normal stalk formation is not required. We have also observed, however, that filamentous parC mutant cells, which are defective in DNA segregation and the completion of cell separation, are motile and still fail to localize DivJ to the new cell pole. These results suggest that formation of new sites for DivJ localization depends on events associated with the completion of cell separation as well as the gain of motility. Analysis of PleC and PleD mutants also provides insights into the function of the His-Asp proteins in cell cycle regulation. Thus, the ability of the sokA301 allele of ctrA to bypass the nonmotile phenotype of the pleC null mutation provides evidence that the PleC kinase controls cell motility by initiating a signal transduction pathway regulating activity of the global response regulator CtrA. Analysis of the pleD mutant cell cycle demonstrates that disruption of the swarmer-to-stalked-cell developmental sequence does not affect the asymmetric organization of the Caulobacter cell cycle.
PMCID: PMC135399  PMID: 12374838
25.  Mutations in DivL and CckA Rescue a divJ Null Mutant of Caulobacter crescentus by Reducing the Activity of CtrA 
Journal of Bacteriology  2006;188(7):2473-2482.
Polar development and cell division in Caulobacter crescentus are controlled and coordinated by multiple signal transduction proteins. divJ encodes a histidine kinase. A null mutation in divJ results in a reduced growth rate, cell filamentation, and mislocalized stalks. Suppressor analysis of divJ identified mutations in genes encoding the tyrosine kinase (divL) and the histidine kinase (cckA). The divL and cckA suppressor alleles all have single amino acid substitutions, some of which confer a temperature-sensitive phenotype, particularly in a wild-type background. Analysis of transcription levels from several positively regulated CtrA-dependent promoters reveals high expression in the divJ mutant, suggesting that DivJ normally serves to reduce CtrA activity. The divL and cckA suppressors reduce the amount of transcription from promoters positively regulated by CtrA, indicating that the mutations in divL and cckA are suppressing the defects of the divJ mutant by reducing the abnormally high level of CtrA activity. Immunoblotting showed no major perturbations in the CtrA protein level in any of these strains, suggesting that the high amount of CtrA activity seen in the divJ mutant and the reduced amount of activity in the suppressors are regulated at the level of activation and not transcription, translation, or degradation. In vivo phosphorylation assays confirmed that divJ mutants have elevated levels of CtrA phosphorylation and that this level is reduced in the suppressors with mutations in divL.
PMCID: PMC1428409  PMID: 16547034

Results 1-25 (1061351)