Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems.

[1]  G. Briggs,et al.  A Note on the Kinetics of Enzyme Action. , 1925, The Biochemical journal.

[2]  Reinhart Heinrich,et al.  A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. , 1974, European journal of biochemistry.

[3]  D. Gillespie Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[4]  M. Kennedy,et al.  Regulation of brain Type II Ca 2+ calmodulin -dependent protein kinase by autophosphorylation: A Ca2+-triggered molecular switch , 1986, Cell.

[5]  C Reder,et al.  Metabolic control theory: a structural approach. , 1988, Journal of theoretical biology.

[6]  J. Lisman,et al.  Feasibility of long-term storage of graded information by the Ca2+/calmodulin-dependent protein kinase molecules of the postsynaptic density. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[7]  A Goldbeter,et al.  Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[8]  A Goldbeter,et al.  A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[9]  R. Heinrich,et al.  Mathematical analysis of enzymic reaction systems using optimization principles. , 1991, European journal of biochemistry.

[10]  L. Stryer,et al.  Calcium spiking. , 1991, Annual review of biophysics and biophysical chemistry.

[11]  A Goldbeter,et al.  Protein phosphorylation driven by intracellular calcium oscillations: a kinetic analysis. , 1992, Biophysical chemistry.

[12]  B. Palsson,et al.  Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use , 1994, Bio/Technology.

[13]  Lubert Stryer,et al.  Dual role of calmodulin in autophosphorylation of multifunctional cam kinase may underlie decoding of calcium signals , 1994, Neuron.

[14]  S. Schuster,et al.  ON ELEMENTARY FLUX MODES IN BIOCHEMICAL REACTION SYSTEMS AT STEADY STATE , 1994 .

[15]  Seth Michelson,et al.  CAM KINASE : A MODEL FOR ITS ACTIVATION AND DYNAMICS , 1994 .

[16]  H. Kacser,et al.  The control of flux. , 1995, Biochemical Society transactions.

[17]  R. Albers,et al.  A mechanism for synaptic frequency detection through autophosphorylation of CaM kinase II. , 1996, Biophysical journal.

[18]  R. Heinrich,et al.  The Regulation of Cellular Systems , 1996, Springer US.

[19]  D. Fell Understanding the Control of Metabolism , 1996 .

[20]  S. Leibler,et al.  Robustness in simple biochemical networks , 1997, Nature.

[21]  K Nasmyth,et al.  Finishing the cell cycle. , 1999, Journal of theoretical biology.

[22]  M. Schwartz,et al.  Interactions between mitogenic stimuli, or, a thousand and one connections. , 1999, Current opinion in cell biology.

[23]  M Kaufman,et al.  A logical analysis of T cell activation and anergy. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[24]  U. Bhalla,et al.  Emergent properties of networks of biological signaling pathways. , 1999, Science.

[25]  B. Kholodenko,et al.  Quantification of Short Term Signaling by the Epidermal Growth Factor Receptor* , 1999, The Journal of Biological Chemistry.

[26]  W. R. Burack,et al.  Signal transduction: hanging on a scaffold. , 2000, Current opinion in cell biology.

[27]  Katherine C. Chen,et al.  Kinetic analysis of a molecular model of the budding yeast cell cycle. , 2000, Molecular biology of the cell.

[28]  Jehoshua Bruck,et al.  Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[29]  B. Kholodenko,et al.  Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. , 2000, European journal of biochemistry.

[30]  Jens U. Wurthner,et al.  A cellular automaton model of cellular signal transduction , 2000, Comput. Biol. Medicine.

[31]  B. Palsson,et al.  Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems. , 2000, Biotechnology and bioengineering.

[32]  Ravi Iyengar,et al.  Robustness of the bistable behavior of a biological signaling feedback loop. , 2001, Chaos.

[33]  M. Reuss,et al.  Signal transduction dynamics of the protein kinase-A/phosphofructokinase-2 system in Saccharomyces cerevisiae. , 2001, Metabolic engineering.

[34]  B. Palsson,et al.  In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data , 2001, Nature Biotechnology.

[35]  Upinder S Bhalla,et al.  Simulations of inositol phosphate metabolism and its interaction with InsP(3)-mediated calcium release. , 2002, Biophysical journal.

[36]  Marco Siderius,et al.  Selectivity in overlapping MAP kinase cascades. , 2002, Journal of theoretical biology.

[37]  Reinhart Heinrich,et al.  Mathematical models of protein kinase signal transduction. , 2002, Molecular cell.

[38]  Edda Klipp,et al.  Prediction of temporal gene expression. Metabolic opimization by re-distribution of enzyme activities. , 2002, European journal of biochemistry.

[39]  Upinder S Bhalla,et al.  Mechanisms for temporal tuning and filtering by postsynaptic signaling pathways. , 2002, Biophysical journal.

[40]  A. Hall,et al.  Guanine nucleotide exchange factors for Rho GTPases: turning on the switch. , 2002, Genes & development.

[41]  S. Bhattacharya,et al.  Signaling through the JAK/STAT pathway, recent advances and future challenges. , 2002, Gene.

[42]  J. Bromberg JAK-STAT signaling in human disease , 2002 .

[43]  E. Gilles,et al.  Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors , 2002, Nature Biotechnology.

[44]  Hans V Westerhoff,et al.  Control analysis for autonomously oscillating biochemical networks. , 2002, Biophysical journal.

[45]  Edda Klipp,et al.  Metabolic optimization by re-distribution of enzyme activities , 2002 .

[46]  C. Schindler,et al.  Series Introduction: JAK-STAT signaling in human disease , 2002 .

[47]  Andrzej M. Kierzek,et al.  STOCKS: STOChastic Kinetic Simulations of biochemical systems with Gillespie algorithm , 2002, Bioinform..

[48]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[49]  E. O’Shea,et al.  Global analysis of protein expression in yeast , 2003, Nature.

[50]  U. Bhalla Temporal computation by synaptic signaling pathways , 2003, Journal of Chemical Neuroanatomy.

[51]  Reinhart Heinrich,et al.  The Roles of APC and Axin Derived from Experimental and Theoretical Analysis of the Wnt Pathway , 2003, PLoS biology.

[52]  Hans V Westerhoff,et al.  Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law. , 2002, Journal of theoretical biology.

[53]  H. Kitano,et al.  A quantitative characterization of the yeast heterotrimeric G protein cycle , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[54]  J. Snoep,et al.  JWS online cellular systems modelling and microbiology. , 2003, Microbiology.

[55]  Stefan Schuster,et al.  Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations. , 2003, Journal of theoretical biology.

[56]  J. Timmer,et al.  Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[57]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[58]  Herbert M Sauro,et al.  Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories. , 2003, Journal of theoretical biology.

[59]  U. Alon,et al.  Just-in-time transcription program in metabolic pathways , 2004, Nature Genetics.

[60]  Jacky L. Snoep,et al.  Web-based kinetic modelling using JWS Online , 2004, Bioinform..

[61]  Jeremy S Edwards,et al.  MAPK cascade possesses decoupled controllability of signal amplification and duration. , 2004, Biophysical journal.

[62]  H. Holzhütter The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. , 2004, European journal of biochemistry.

[63]  Upinder S. Bhalla,et al.  Biochemical Signaling Networks Decode Temporal Patterns of Synaptic Input , 2002, Journal of Computational Neuroscience.

[64]  Katherine C. Chen,et al.  Integrative analysis of cell cycle control in budding yeast. , 2004, Molecular biology of the cell.

[65]  Jan-Marino Ramirez,et al.  Pacemaker neurons and neuronal networks: an integrative view , 2004, Current Opinion in Neurobiology.

[66]  Edda Klipp,et al.  Modelling the dynamics of the yeast pheromone pathway , 2004, Yeast.

[67]  Jason A. Papin,et al.  The JAK-STAT signaling network in the human B-cell: an extreme signaling pathway analysis. , 2004, Biophysical journal.

[68]  Jason A. Papin,et al.  Topological analysis of mass-balanced signaling networks: a framework to obtain network properties including crosstalk. , 2004, Journal of theoretical biology.

[69]  K. Sachs,et al.  Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data , 2005, Science.

[70]  Mary B. Kennedy,et al.  Integration of biochemical signalling in spines , 2005, Nature Reviews Neuroscience.

[71]  Axel Kowald,et al.  Systems Biology in Practice: Concepts, Implementation and Application , 2005 .

[72]  Takako Takai-Igarashi,et al.  Ontology Based Standardization of Petri Net Modeling for Signaling Pathways , 2005, Silico Biol..

[73]  Bernd Binder,et al.  Structural and dynamical analyses of the kinase network derived from the transpath database. , 2005, Genome informatics. International Conference on Genome Informatics.

[74]  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.

[75]  J. Timmer,et al.  Design principles of a bacterial signalling network , 2005, Nature.

[76]  Linda R Petzold,et al.  The slow-scale stochastic simulation algorithm. , 2005, The Journal of chemical physics.

[77]  Jan Lankelma,et al.  Principles behind the multifarious control of signal transduction , 2004, The FEBS journal.

[78]  L Holm,et al.  Algorithms for protein interaction networks. , 2005, Biochemical Society transactions.

[79]  E. Klipp,et al.  Integrative model of the response of yeast to osmotic shock , 2005, Nature Biotechnology.

[80]  Jason A. Papin,et al.  Reconstruction of cellular signalling networks and analysis of their properties , 2005, Nature Reviews Molecular Cell Biology.

[81]  P. Salinas,et al.  Signalling in neural development: WNTS in the vertebrate nervous system: from patterning to neuronal connectivity , 2005, Nature Reviews Neuroscience.

[82]  Hugh D. Spence,et al.  Minimum information requested in the annotation of biochemical models (MIRIAM) , 2005, Nature Biotechnology.

[83]  Matjaz Perc,et al.  A minimal model for decoding of time-limited Ca2+ oscillations. , 2006, Biophysical chemistry.