Noise characteristics of the Escherichia coli rotary motor

BackgroundThe chemotaxis pathway in the bacterium Escherichia coli allows cells to detect changes in external ligand concentration (e.g. nutrients). The pathway regulates the flagellated rotary motors and hence the cells' swimming behaviour, steering them towards more favourable environments. While the molecular components are well characterised, the motor behaviour measured by tethered cell experiments has been difficult to interpret.ResultsWe study the effects of sensing and signalling noise on the motor behaviour. Specifically, we consider fluctuations stemming from ligand concentration, receptor switching between their signalling states, adaptation, modification of proteins by phosphorylation, and motor switching between its two rotational states. We develop a model which includes all signalling steps in the pathway, and discuss a simplified version, which captures the essential features of the full model. We find that the noise characteristics of the motor contain signatures from all these processes, albeit with varying magnitudes.ConclusionsOur analysis allows us to address how cell-to-cell variation affects motor behaviour and the question of optimal pathway design. A similar comprehensive analysis can be applied to other two-component signalling pathways.

[1]  Jeffrey W. Smith,et al.  Stochastic Gene Expression in a Single Cell , .

[2]  H. Berg,et al.  Physics of chemoreception. , 1977, Biophysical journal.

[3]  Dan V. Nicolau,et al.  Conformational Spread as a Mechanism for Cooperativity in the Bacterial Flagellar Switch , 2010, Science.

[4]  Bonnie L. Bassler,et al.  Three Parallel Quorum-Sensing Systems Regulate Gene Expression in Vibrio harveyi , 2004, Journal of bacteriology.

[5]  M. Elowitz,et al.  Functional roles for noise in genetic circuits , 2010, Nature.

[6]  A S Stern,et al.  Temperature dependence of switching of the bacterial flagellar motor by the protein CheY(13DK106YW). , 1999, Biophysical journal.

[7]  D. DeRosier,et al.  Self-assembly of receptor/signaling complexes in bacterial chemotaxis , 2006, Proceedings of the National Academy of Sciences.

[8]  H. Berg.  Random Walks in Biology , 2018 .

[9]  T. Mora,et al.  Limits of sensing temporal concentration changes by single cells. , 2010, Physical review letters.

[10]  Ned S Wingreen,et al.  Accuracy of direct gradient sensing by cell-surface receptors. , 2009, Progress in biophysics and molecular biology.

[11]  G. Goodhill,et al.  Axon guidance by growth-rate modulation , 2010, Proceedings of the National Academy of Sciences.

[12]  G. L. Hazelbauer,et al.  Cellular Stoichiometry of the Components of the Chemotaxis Signaling Complex , 2004, Journal of bacteriology.

[13]  Ned S. Wingreen,et al.  Chemotaxis in Escherichia coli: A Molecular Model for Robust Precise Adaptation , 2007, PLoS Comput. Biol..

[14]  I. Shmulevich,et al.  Dynamic analysis of MAPK signaling using a high-throughput microfluidic single-cell imaging platform , 2009, Proceedings of the National Academy of Sciences.

[15]  Judith P Armitage,et al.  Spatial organization in bacterial chemotaxis , 2010, The EMBO journal.

[16]  R. G. Medhurst,et al.  Topics in the Theory of Random Noise , 1969 .

[17]  H. Berg,et al.  Temporal comparisons in bacterial chemotaxis. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Karen A. Fahrner,et al.  Control of direction of flagellar rotation in bacterial chemotaxis. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[19]  M. Buttner,et al.  The vancomycin resistance VanRS two‐component signal transduction system of Streptomyces coelicolor , 2006, Molecular microbiology.

[20]  Fan Bai,et al.  Torque–speed relationship of the bacterial flagellar motor , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Naama Barkai,et al.  Noise Propagation and Signaling Sensitivity in Biological Networks: A Role for Positive Feedback , 2007, PLoS Comput. Biol..

[22]  M. Eisenbach,et al.  Oligomerization of the Phosphatase CheZ Upon Interaction with the Phosphorylated Form of CheY , 1996, The Journal of Biological Chemistry.

[23]  G. Wadhams,et al.  Making sense of it all: bacterial chemotaxis , 2004, Nature Reviews Molecular Cell Biology.

[24]  J. Stock,et al.  Bacterial chemotaxis , 2003, Current Biology.

[25]  P. Cluzel,et al.  Relationship between cellular response and behavioral variability in bacterial chemotaxis , 2007, Proceedings of the National Academy of Sciences.

[26]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[27]  H. Berg,et al.  Adaptation kinetics in bacterial chemotaxis , 1983, Journal of bacteriology.

[28]  R. L. Stratonovich,et al.  Topics in the theory of random noise , 1967 .

[29]  X. Xie,et al.  Probing Gene Expression in Live Cells, One Protein Molecule at a Time , 2006, Science.

[30]  H. Berg,et al.  Functional interactions between receptors in bacterial chemotaxis , 2004, Nature.

[31]  M. Ueda,et al.  Stochastic signal processing and transduction in chemotactic response of eukaryotic cells. , 2007, Biophysical journal.

[32]  Robert G. Endres,et al.  Chemotactic Response and Adaptation Dynamics in Escherichia coli , 2010, PLoS Comput. Biol..

[33]  M. Eisenbach,et al.  Mutants with Defective Phosphatase Activity Show No Phosphorylation-dependent Oligomerization of CheZ , 1996, The Journal of Biological Chemistry.

[34]  R. Kubo.  Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[35]  G. Vinnicombe,et al.  Fundamental limits on the suppression of molecular fluctuations , 2010, Nature.

[36]  Ned S Wingreen,et al.  Variable sizes of Escherichia coli chemoreceptor signaling teams , 2008, Molecular systems biology.

[37]  R C Stewart,et al.  Rapid phosphotransfer to CheY from a CheA protein lacking the CheY-binding domain. , 2000, Biochemistry.

[38]  Ned S. Wingreen,et al.  Precise adaptation in bacterial chemotaxis through “assistance neighborhoods” , 2006, Proceedings of the National Academy of Sciences.

[39]  S. Leibler,et al.  An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells. , 2000, Science.

[40]  F. Tostevin,et al.  Mutual information between input and output trajectories of biochemical networks. , 2009, Physical review letters.

[41]  Yuhai Tu,et al.  Modeling the chemotactic response of Escherichia coli to time-varying stimuli , 2008, Proceedings of the National Academy of Sciences.

[42]  J. Hoch,et al.  Multiple histidine kinases regulate entry into stationary phase and sporulation in Bacillus subtilis , 2000, Molecular microbiology.

[43]  H. Berg,et al.  Receptor sensitivity in bacterial chemotaxis , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[44]  D. Bray,et al.  Computer analysis of the binding reactions leading to a transmembrane receptor-linked multiprotein complex involved in bacterial chemotaxis. , 1995, Molecular biology of the cell.

[45]  G L Hazelbauer,et al.  Transmembrane signaling in bacterial chemoreceptors. , 2001, Trends in biochemical sciences.

[46]  H. Berg,et al.  Impulse responses in bacterial chemotaxis , 1982, Cell.

[47]  S. L. Porter,et al.  Rhodobacter sphaeroides: complexity in chemotactic signalling. , 2008, Trends in microbiology.

[48]  J. Stock,et al.  Systems biology of bacterial chemotaxis. , 2006, Current opinion in microbiology.

[49]  H. Berg.  Motile Behavior of Bacteria , 2000 .

[50]  M. Thattai,et al.  Attenuation of noise in ultrasensitive signaling cascades. , 2002, Biophysical journal.

[51]  F. Dahlquist,et al.  Regulation of phosphatase activity in bacterial chemotaxis. , 1998, Journal of molecular biology.

[52]  H. Berg,et al.  Binding of the Escherichia coli response regulator CheY to its target measured in vivo by fluorescence resonance energy transfer , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[53]  Monica L. Skoge,et al.  Chemosensing in Escherichia coli: two regimes of two-state receptors. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[54]  N. Wingreen,et al.  A quantitative comparison of sRNA-based and protein-based gene regulation , 2008, Molecular systems biology.

[55]  Christopher V. Rao,et al.  Site-specific methylation in Bacillus subtilis chemotaxis: effect of covalent modifications to the chemotaxis receptor McpB , 2011, Microbiology.

[56]  W. Bialek,et al.  Physical limits to biochemical signaling. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[57]  Yuhai Tu,et al.  Dynamics of the bacterial flagellar motor with multiple stators , 2009, Proceedings of the National Academy of Sciences.

[58]  Ellen S. Vitetta,et al.  An allosteric model for heterogeneous receptor complexes : Understanding bacterial chemotaxis responses to multiple stimuli , 2006 .

[59]  Henry A. Lester,et al.  Gating Transitions in Bacterial Ion Channels Measured at 3 μs Resolution , 2004, The Journal of general physiology.

[60]  M. Laub,et al.  Specificity in two-component signal transduction pathways. , 2007, Annual review of genetics.

[61]  Thierry Mora,et al.  Steps in the Bacterial Flagellar Motor , 2009, PLoS Comput. Biol..

[62]  Kingshuk Ghosh,et al.  Maximum Caliber: a variational approach applied to two-state dynamics. , 2008, The Journal of chemical physics.

[63]  Alexander van Oudenaarden,et al.  Material for A General Mechanism for Network-Dosage Compensation in Gene Circuits , 1656 .

[64]  Yuhai Tu,et al.  How white noise generates power-law switching in bacterial flagellar motors. , 2005, Physical review letters.

[65]  Johan Paulsson,et al.  Models of stochastic gene expression , 2005 .

[66]  A. van Oudenaarden,et al.  Noise Propagation in Gene Networks , 2005, Science.

[67]  C. Pesce,et al.  Regulated cell-to-cell variation in a cell-fate decision system , 2005, Nature.

[68]  P. Cluzel,et al.  Interdependence of behavioural variability and response to small stimuli in bacteria , 2010, Nature.

[69]  R C Stewart,et al.  Activating and inhibitory mutations in the regulatory domain of CheB, the methylesterase in bacterial chemotaxis. , 1993, The Journal of biological chemistry.

[70]  Thierry Mora,et al.  Modeling torque versus speed, shot noise, and rotational diffusion of the bacterial flagellar motor. , 2009, Physical review letters.

[71]  Pieter Rein ten Wolde,et al.  The switching dynamics of the bacterial flagellar motor , 2008, Molecular systems biology.

[72]  H. Haus.  Topics in the theory of random noise, vol. I , 1964 .

[73]  Thierry Emonet,et al.  Hidden stochastic nature of a single bacterial motor. , 2006, Physical review letters.

[74]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[75]  Victor Sourjik,et al.  Receptor clustering and signal processing in E. coli chemotaxis. , 2004, Trends in microbiology.

[76]  D. Bray,et al.  Predicting temporal fluctuations in an intracellular signalling pathway. , 1998, Journal of theoretical biology.

[77]  Anirvan M. Sengupta,et al.  Engineering aspects of enzymatic signal transduction: photoreceptors in the retina. , 2000, Biophysical journal.

[78]  References , 1971 .

[79]  C. J.,et al.  Predicting Temporal Fluctuations in an Intracellular Signalling Pathway , 1998 .

[80]  K. Fujimoto,et al.  Noisy signal amplification in ultrasensitive signal transduction. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[81]  H. Berg,et al.  A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli , 2010, Molecular systems biology.

[82]  Sebastian Thiem,et al.  Protein exchange dynamics at chemoreceptor clusters in Escherichia coli , 2008, Proceedings of the National Academy of Sciences.

[83]  H. Eisen,et al.  Evidence that a single peptide-MHC complex on a target cell can elicit a cytolytic T cell response. , 1996, Immunity.

[84]  J. Vilar,et al.  From molecular noise to behavioural variability in a single bacterium , 2004, Nature.

[85]  J. Kirkwood.  The statistical mechanical theory of irreversible processes , 1949 .

[86]  Gerardo Aquino,et al.  Optimal receptor-cluster size determined by intrinsic and extrinsic noise. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.