Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.Comment: 23 pages, 5 figures; The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1007/s00285-011-0495-

Delayed Onset of Positive Feedback Activation of Rab5 by Rabex-5 and Rabaptin-5 in Endocytosis

BACKGROUND: Rabex-5 is a guanine nucleotide exchange factor (GEF) that specifically activates Rab5, i.e., converting Rab5-GDP to Rab5-GTP, through two distinct pathways to promote endosome fusion and endocytosis. The direct pathway involves a pool of membrane-associated Rabex-5 that targets to the membrane via an early endosomal targeting (EET) domain. The indirect pathway, on the other hand, involves a cytosolic pool of Rabex-5/Rabaptin-5 complex. The complex is recruited to the membrane via Rabaptin-5 binding to Rab5-GTP, suggesting a positive feedback mechanism. The relationship of these two pathways for Rab5 activation in the cell is unclear. METHODOLOGY/PRINCIPAL FINDINGS: We dissect the relative contribution of each pathway to Rab5 activation via mathematical modeling and kinetic analysis in the cell. These studies show that the indirect pathway constitutes a positive feedback loop for converting Rab5-GDP to Rab5-GTP on the endosomal membrane and allows sensitive regulation of endosome fusion activity by the levels of Rab5 and Rabex-5 in the cell. The onset of this positive feedback effect, however, contains a threshold, which requires above endogenous levels of Rab5 or Rabex-5 in the cell. We term this novel phenomenon "delayed response". The presence of the direct pathway reduces the delay by increasing the basal level of Rab5-GTP, thus facilitates the function of the Rabex-5/Rabaptin-5-mediated positive feedback loop. CONCLUSION: Our data support the mathematical model. With the model's guidance, the data reveal the affinity of Rabex-5/Rabaptin-5/Rab5-GTP interaction in the cell, which is quantitatively related to the Rabex-5 concentration for the onset of the indirect positive feedback pathway. The presence of the direct pathway and increased Rab5 concentration can reduce the Rabex-5 concentration required for the onset of the positive feedback loop. Thus the direct and indirect pathways cooperate in the regulation of early endosome fusion

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

A Cell-Based Model for Quorum Sensing in Heterogeneous Bacterial Colonies

Although bacteria are unicellular organisms, they have the ability to act in concert by synthesizing and detecting small diffusing autoinducer molecules. The phenomenon, known as quorum sensing, has mainly been proposed to serve as a means for cell-density measurement. Here, we use a cell-based model of growing bacterial microcolonies to investigate a quorum-sensing mechanism at a single cell level. We show that the model indeed predicts a density-dependent behavior, highly dependent on local cell-clustering and the geometry of the space where the colony is evolving. We analyze the molecular network with two positive feedback loops to find the multistability regions and show how the quorum-sensing mechanism depends on different model parameters. Specifically, we show that the switching capability of the network leads to more constraints on parameters in a natural environment where the bacteria themselves produce autoinducer than compared to situations where autoinducer is introduced externally. The cell-based model also allows us to investigate mixed populations, where non-producing cheater cells are shown to have a fitness advantage, but still cannot completely outcompete producer cells. Simulations, therefore, are able to predict the relative fitness of cheater cells from experiments and can also display and account for the paradoxical phenomenon seen in experiments; even though the cheater cells have a fitness advantage in each of the investigated groups, the overall effect is an increase in the fraction of producer cells. The cell-based type of model presented here together with high-resolution experiments will play an integral role in a more explicit and precise comparison of models and experiments, addressing quorum sensing at a cellular resolution

Heterogeneous Response to a Quorum-Sensing Signal in the Luminescence of Individual Vibrio fischeri

The marine bacterium Vibrio fischeri regulates its bioluminescence through a quorum sensing mechanism: the bacterium releases diffusible small molecules (autoinducers) that accumulate in the environment as the population density increases. This accumulation of autoinducer (AI) eventually activates transcriptional regulators for bioluminescence as well as host colonization behaviors. Although V.fischeri quorum sensing has been extensively characterized in bulk populations, far less is known about how it performs at the level of the individual cell, where biochemical noise is likely to limit the precision of luminescence regulation. We have measured the time-dependence and AI-dependence of light production by individual V.fischeri cells that are immobilized in a perfusion chamber and supplied with a defined concentration of exogenous AI. We use low-light level microscopy to record and quantify the photon emission from the cells over periods of several hours as they respond to the introduction of AI. We observe an extremely heterogeneous response to the AI signal. Individual cells differ widely in the onset time for their luminescence and in their resulting brightness, even in the presence of high AI concentrations that saturate the light output from a bulk population. The observed heterogeneity shows that although a given concentration of quorum signal may determine the average light output from a population of cells, it provides far weaker control over the luminescence output of each individual cell

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Noise Reduction by Diffusional Dissipation in a Minimal Quorum Sensing Motif

Cellular interactions are subject to random fluctuations (noise) in quantities of interacting molecules. Noise presents a major challenge for the robust function of natural and engineered cellular networks. Past studies have analyzed how noise is regulated at the intracellular level. Cell–cell communication, however, may provide a complementary strategy to achieve robust gene expression by enabling the coupling of a cell with its environment and other cells. To gain insight into this issue, we have examined noise regulation by quorum sensing (QS), a mechanism by which many bacteria communicate through production and sensing of small diffusible signals. Using a stochastic model, we analyze a minimal QS motif in Gram-negative bacteria. Our analysis shows that diffusion of the QS signal, together with fast turnover of its transcriptional regulator, attenuates low-frequency components of extrinsic noise. We term this unique mechanism “diffusional dissipation” to emphasize the importance of fast signal turnover (or dissipation) by diffusion. We further show that this noise attenuation is a property of a more generic regulatory motif, of which QS is an implementation. Our results suggest that, in a QS system, an unstable transcriptional regulator may be favored for regulating expression of costly proteins that generate public goods

Bacteria clustering by polymers induces the expression of quorum sense controlled phenotypes

Bacteria deploy a range of chemistries to regulate their behaviour and respond to their environment. Quorum sensing is one mean by which bacteria use chemical reactions to modulate pre-infection behaviour such as surface attachment. Polymers that can interfere with bacterial adhesion or the chemical reactions used for quorum sensing are thus a potential means to control bacterial population responses. Here we report how polymeric "bacteria sequestrants", designed to bind to bacteria through electrostatic interactions and thus inhibit bacterial adhesion to surfaces, induce the expression of quorum sensing controlled phenotypes as a consequence of cell clustering. A combination of polymer and analytical chemistry, biological assays and computational modelling has been used to characterise the feedback between bacteria clustering and quorum sensing signaling. We have also derived design principles and chemical strategies for controlling bacterial behaviour at the population leve

A Mechanism for the Polarity Formation of Chemoreceptors at the Growth Cone Membrane for Gradient Amplification during Directional Sensing

Accurate response to external directional signals is essential for many physiological functions such as chemotaxis or axonal guidance. It relies on the detection and amplification of gradients of chemical cues, which, in eukaryotic cells, involves the asymmetric relocalization of signaling molecules. How molecular events coordinate to induce a polarity at the cell level remains however poorly understood, particularly for nerve chemotaxis. Here, we propose a model, inspired by single-molecule experiments, for the membrane dynamics of GABA chemoreceptors in nerve growth cones (GCs) during directional sensing. In our model, transient interactions between the receptors and the microtubules, coupled to GABA-induced signaling, provide a positive-feedback loop that leads to redistribution of the receptors towards the gradient source. Using numerical simulations with parameters derived from experiments, we find that the kinetics of polarization and the steady-state polarized distribution of GABA receptors are in remarkable agreement with experimental observations. Furthermore, we make predictions on the properties of the GC seen as a sensing, amplification and filtering module. In particular, the growth cone acts as a low-pass filter with a time constant ∼10 minutes determined by the Brownian diffusion of chemoreceptors in the membrane. This filtering makes the gradient amplification resistent to rapid fluctuations of the external signals, a beneficial feature to enhance the accuracy of neuronal wiring. Since the model is based on minimal assumptions on the receptor/cytoskeleton interactions, its validity extends to polarity formation beyond the case of GABA gradient sensing. Altogether, it constitutes an original positive-feedback mechanism by which cells can dynamically adapt their internal organization to external signals