Phase-Locked Signals Elucidate Circuit Architecture of an Oscillatory Pathway

This paper introduces the concept of phase-locking analysis of oscillatory cellular signaling systems to elucidate biochemical circuit architecture. Phase-locking is a physical phenomenon that refers to a response mode in which system output is synchronized to a periodic stimulus; in some instances, the number of responses can be fewer than the number of inputs, indicative of skipped beats. While the observation of phase-locking alone is largely independent of detailed mechanism, we find that the properties of phase-locking are useful for discriminating circuit architectures because they reflect not only the activation but also the recovery characteristics of biochemical circuits. Here, this principle is demonstrated for analysis of a G-protein coupled receptor system, the M3 muscarinic receptor-calcium signaling pathway, using microfluidic-mediated periodic chemical stimulation of the M3 receptor with carbachol and real-time imaging of resulting calcium transients. Using this approach we uncovered the potential importance of basal IP3 production, a finding that has important implications on calcium response fidelity to periodic stimulation. Based upon our analysis, we also negated the notion that the Gq-PLC interaction is switch-like, which has a strong influence upon how extracellular signals are filtered and interpreted downstream. Phase-locking analysis is a new and useful tool for model revision and mechanism elucidation; the method complements conventional genetic and chemical tools for analysis of cellular signaling circuitry and should be broadly applicable to other oscillatory pathways.

[1]  Amy E Palmer,et al.  Measuring calcium signaling using genetically targetable fluorescent indicators , 2006, Nature Protocols.

[2]  T. Chay,et al.  Modelling receptor-controlled intracellular calcium oscillators. , 1991, Cell calcium.

[3]  T. Rink,et al.  Repetitive spikes in cytoplasmic calcium evoked by histamine in human endothelial cells , 1988, Nature.

[4]  Haluk Resat,et al.  Rapid and sustained nuclear–cytoplasmic ERK oscillations induced by epidermal growth factor , 2009, Molecular systems biology.

[5]  Frederick R. Cross,et al.  Periodic Cyclin-Cdk Activity Entrains an Autonomous Cdc14 Release Oscillator , 2010, Cell.

[6]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[7]  P. Cobbold,et al.  Repetitive transient rises in cytoplasmic free calcium in hormone-stimulated hepatocytes , 1986, Nature.

[8]  E Bornberg-Bauer,et al.  Switching from simple to complex oscillations in calcium signaling. , 2000, Biophysical journal.

[9]  M. Berridge,et al.  Calcium signalling: dynamics, homeostasis and remodelling , 2003, Nature reviews. Molecular cell biology.

[10]  D. Kirschner,et al.  A methodology for performing global uncertainty and sensitivity analysis in systems biology. , 2008, Journal of theoretical biology.

[11]  D. Perez,et al.  Synergism of constitutive activity in alpha 1-adrenergic receptor activation. , 1997, Biochemistry.

[12]  G B Willars,et al.  Single-cell imaging of graded Ins(1,4,5)P3 production following G-protein-coupled-receptor activation. , 2001, The Biochemical journal.

[13]  A. Atri,et al.  A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte. , 1993, Biophysical journal.

[14]  Tobias Meyer,et al.  STIM Is a Ca2+ Sensor Essential for Ca2+-Store-Depletion-Triggered Ca2+ Influx , 2005, Current Biology.

[15]  Nicholas T. Ingolia,et al.  Systems biology: Reverse engineering the cell , 2008, Nature.

[16]  S. Swillens,et al.  Computer simulation of a cytosolic calcium oscillator. , 1990, The Biochemical journal.

[17]  Shuichi Takayama,et al.  Rapid Prototyping of Microstructures with Bell‐Shaped Cross‐Sections and Its Application to Deformation‐Based Microfluidic Valves , 2004 .

[18]  Martin Falcke,et al.  Calcium Signals Driven by Single Channel Noise , 2010, PLoS Comput. Biol..

[19]  L. Glass,et al.  Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. , 1981, Science.

[20]  Jonathan W. Song,et al.  Characterization and resolution of evaporation-mediated osmolality shifts that constrain microfluidic cell culture in poly(dimethylsiloxane) devices. , 2007, Analytical chemistry.

[21]  T J Sluckin,et al.  Driven oscillations of a limit-cycle oscillator. , 1980, Journal of theoretical biology.

[22]  K Prank,et al.  Precision of intracellular calcium spike timing in primary rat hepatocytes. , 2005, Systems biology.

[23]  S Ponce Dawson,et al.  Simplified model of cytosolic Ca2+ dynamics in the presence of one or several clusters of Ca2+ -release channels. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Thomas Höfer,et al.  Models of IP3 and Ca2+ oscillations: frequency encoding and identification of underlying feedbacks. , 2006, Biophysical journal.

[25]  Xudong Huang,et al.  A quantitative kinetic model for ATP-induced intracellular Ca2+ oscillations. , 2007, Journal of theoretical biology.

[26]  Mario di Bernardo,et al.  Global Entrainment of Transcriptional Systems to Periodic Inputs , 2009, PLoS Comput. Biol..

[27]  G. Shull,et al.  Functional comparisons between isoforms of the sarcoplasmic or endoplasmic reticulum family of calcium pumps. , 1992, The Journal of biological chemistry.

[28]  J. Dunlap Molecular Bases for Circadian Clocks , 1999, Cell.

[29]  James R. Johnson,et al.  Oscillations in NF-κB Signaling Control the Dynamics of Gene Expression , 2004, Science.

[30]  L. Glass,et al.  A simple model for phase locking of biological oscillators , 1979, Journal of mathematical biology.

[31]  Hadi Dowlatabadi,et al.  Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example , 1994 .

[32]  Y. S. Lee,et al.  Appearance of phase-locked Wenckebach-like rhythms, devil's staircase and universality in intracellular calcium spikes in non-excitable cell models. , 1995, Journal of theoretical biology.

[33]  S. Morris,et al.  Trypanosoma cruzi: infection of cultured human endothelial cells alters inositol phosphate synthesis. , 1989, Experimental parasitology.

[34]  James Sneyd,et al.  Modeling IP3-Dependent Calcium Dynamics in Non-Excitable Cells , 2005 .

[35]  Lin Ji,et al.  Stimulus perturbation induced signal: a case study in mesoscopic intracellular calcium system. , 2009, Biophysical chemistry.

[36]  D B Kell,et al.  Oscillations in NF-kappaB signaling control the dynamics of gene expression. , 2004, Science.

[37]  J. Putney,et al.  Formation and metabolism of [3H]inositol phosphates in AR42J pancreatoma cells. Substance P-induced Ca2+ mobilization in the apparent absence of inositol 1,4,5-trisphosphate 3-kinase activity. , 1988, The Journal of biological chemistry.

[38]  J. Rinzel,et al.  Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. , 1994, Journal of theoretical biology.

[39]  R Wessel In vitro study of phase resetting and phase locking in a time-comparison circuit in the electric fish, Eigenmannia. , 1995, Biophysical journal.

[40]  J. Putney,et al.  The inositol phosphate-calcium signaling system in nonexcitable cells. , 1993, Endocrine reviews.

[41]  J. Putney,et al.  Signaling Pathways Underlying Muscarinic Receptor-induced [Ca2+] i Oscillations in HEK293 Cells* , 2001, The Journal of Biological Chemistry.

[42]  G. Dupont,et al.  Simulations of the effects of inositol 1,4,5-trisphosphate 3-kinase and 5-phosphatase activities on Ca2+ oscillations. , 1997, Cell calcium.

[43]  G. Whitesides,et al.  Soft Lithography. , 1998, Angewandte Chemie.

[44]  Shuichi Takayama,et al.  Computerized microfluidic cell culture using elastomeric channels and Braille displays. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[45]  Ty C. Voss,et al.  Ultradian hormone stimulation induces glucocorticoid receptor-mediated pulses of gene transcription , 2009, Nature Cell Biology.

[46]  Tamara L. Kinzer-Ursem,et al.  Both Ligand- and Cell-Specific Parameters Control Ligand Agonism in a Kinetic Model of G Protein–Coupled Receptor Signaling , 2007, PLoS Comput. Biol..

[47]  Shuichi Takayama,et al.  Handheld recirculation system and customized media for microfluidic cell culture. , 2006, Lab on a chip.

[48]  Curtis W. Sabrosky,et al.  How Many Insects Are There , 1953 .

[49]  O. Orwar,et al.  A chemical waveform synthesizer. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[50]  David Szekely,et al.  Effectors of the frequency of calcium oscillations in HEK-293 cells: wavelet analysis and a computer model , 2009, European Biophysics Journal.

[51]  Christopher C. Goodnow,et al.  Differential activation of transcription factors induced by Ca2+ response amplitude and duration , 1997, Nature.

[52]  A. Miyawaki,et al.  Expanded dynamic range of fluorescent indicators for Ca(2+) by circularly permuted yellow fluorescent proteins. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[53]  G Schreiber,et al.  Rate constants of agonist binding to muscarinic receptors in rat brain medulla. Evaluation by competition kinetics. , 1985, The Journal of biological chemistry.

[54]  P. Camello,et al.  Calcium dependence of calcium extrusion and calcium uptake in mouse pancreatic acinar cells. , 1996, The Journal of physiology.

[55]  Patricia A. Mahama,et al.  Calcium Signaling in Individual BC3H1 Cells: Speed of Calcium Mobilization and Heterogeneity , 1994 .

[56]  Onn Brandman,et al.  STIM2 Is a Feedback Regulator that Stabilizes Basal Cytosolic and Endoplasmic Reticulum Ca2+ Levels , 2007, Cell.

[57]  A. Goldbeter A model for circadian oscillations in the Drosophila period protein (PER) , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[58]  F M Matschinsky,et al.  Cell-specific patterns of oscillating free Ca2+ in carbamylcholine-stimulated insulinoma cells. , 1988, The Journal of biological chemistry.

[59]  Keli Xu,et al.  Calcium oscillations increase the efficiency and specificity of gene expression , 1998, Nature.

[60]  K. Tsaneva-Atanasova,et al.  A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[61]  William C. Messner,et al.  Probing Cellular Dynamics with a Chemical Signal Generator , 2009, PloS one.

[62]  R. Bertram,et al.  Synchronization of pancreatic islet oscillations by intrapancreatic ganglia: a modeling study. , 2009, Biophysical journal.

[63]  Shuichi Takayama,et al.  Lateral propagation of EGF signaling after local stimulation is dependent on receptor density. , 2002, Developmental cell.

[64]  J. Tyson,et al.  A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. , 1999, Biophysical journal.