Definition of the Subject
Understanding the operation cellular networks is probably one of the most challenging and intellectually exciting scientific fields today. With theavailability of new experimental and theoretical techniques our understanding of the operation of cellular networks has made great strides in the last fewdecades. An important outcome of this work is the development of predictive quantitative models. Such models of cellular function will havea profound impact on our ability of manipulate living systems which will lead to new opportunities for generating energy, mitigating our impact onthe biosphere and last but not least, opening up new approaches and understanding of important disease states such as cancer and aging.
Introduction
Cellular networks are some of the most complex natural systems we know. Even in a “simple” organism such as E. coli, there are at least four thousand genes with many thousands of interactions between molecules of many differentsizes [11]....
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Abbreviations
- Deterministic continuous model:
-
A mathematical model where the variables of the model can take any real value and where the time evolution of the model is set by the initial conditions.
- Stochastic discrete model:
-
A mathematical model where the variables of the model take on discrete values and where the time evolution of the model is described by a set of probability distributions.
Bibliography
Alon U (2006) An Introduction to Systems Biology: Design Principles ofBiological Circuits. Chapman & Hall/Crc Mathematical and Computational Biology Series. Chapman & Hall/CRC, Boca Raton
Alon U (2007) Network motifs: theory and experimental approaches. Nat Rev Genet8(6):450–461
Andrianantoandro E, Basu S, Karig DK, Weiss R (2006) Synthetic biology: newengineering rules for an emerging discipline. Mol Syst Biol 2:2006–2006
Ariew R (1976) Ockham's Razor: A Historical and Philosophical Analysis ofOckham's Principle of Parsimony. Champaign-Urbana, University of Illinois
Aris R (1965) Prolegomena to the Rational Analysis of Systems of ChemicalReactions. Arch Rational Mech Anal 19:81–99
Arkin A, Ross J, McAdams HH (1998) Stochastic kinetic analysis of developmentalpathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149:1633–48
Atkins P (2001) Physical Chemistry, 7thedn. W. H. Freeman
Bayer TS, Smolke CD (2005) Programmable ligand-controlled riboregulators ofeukaryotic gene expression. Nat Biotechnol 23(3):337–343
Becskei A, Serrano L (2000) Engineering stability in gene networks byautoregulation. Nature 405:590–593
Bergmann FT, Vallabhajosyula RR, Sauro HM (2006) Computational Tools forModeling Protein Networks. Current Proteomics 3(3):181–197
Blattner FR, Plunkett G, Bloch CA, Perna NT, Burland V, Riley M, Collado-VidesJ, et al (1997) The complete genome sequence of Escherichia coli K-12. Science 277(5331):1453–1474
Bliss RD, Painter PR, Marr AG (1982) Role of feedback inhibition instabilizing the classical operon. J Theor Biol 97(2):177–193
Burns JA (1971) Studies on Complex Enzyme Systems. Dissertation, University ofEdinburgh. http://www.sys-bio.org/BurnsThesis
Cannon RH (1967) Dynamics of Physical Systems. McGraw-Hill College, NewYork
Chen YD, Westerhoff HV (1986) How do Inhibitors and Modifiers of IndividualEnzymes Affect Steady-state Fluxes and Concentrations in Metabolic Systems? Math Model 7:1173–1180
Chickarmane V, Kholodenko BN, Sauro HM (2007) Oscillatory dynamics arisingfrom competitive inhibition and multisite phosphorylation. J Theor Biol 244(1):68–76
Chickarmane V, Ray A, Sauro HM, Nadim A (2007) A Model for p53Dynamics Triggered by DNA Damage. SIAM J Appl Dynamical Syst 6(1):61–78
Cinquin O, Demongeot J (2002) Roles of positive and negative feedback inbiological systems. C R Biol. 325:1085–1095
Clarke BL (1980) Stability of complex reaction networks. Adv. Chem. Phys,vol. 42. Wiley, New York
Cornish-Bowden A (1995) Fundamentals of Enzyme Kinetics. Portland Press, London
Cornish-Bowden A, Cárdenas ML (2002) Metabolic balance sheets. Nature420(6912):129–130
Dibrov BF, Zhabotinsky AM, Kholodenko BN (1982) Dynamic stability of steadystates and static stabilization in unbranched metabolic pathways. J Math Biol 15:51–63
Elowitz MB, Leibler S (2000) A synthetic oscillatory network oftranscriptional regulators. Nature 403:335–338
Entus R, Aufderheide B, Sauro HM (2007) Design and implementation of threeincoherent feed-forward motif based biological concentration sensors. Systems and SyntheticBiology. doi:10.1007/s11693-007-9008-6
Erdi P, Toth J (1989) Mathematical Models of Chemical Reactions. Theory andApplications of Deterministic and Stochastic Models. Manchester University Press, Manchester, Princeton University Press,Princeton
Fell D (1997) Understanding the Control of Metabolism. Portland Press,London
Fell DA, Sauro HM (1985) Metabolic Control Analysis: Additional relationshipsbetween elasticities and control coefficients. Eur J Biochem 148:555–561
Fell DA, Small JR (1986) Fat synthesis in adipose tissue: an examination ofstoichiometric constraints. Biochem J 238:781–786
Ferrell JE (1996) Tripping the switch fantastic: how a protein kinasecascade can convert graded inputs into switch-like outputs. Trends in Biochemical Sciences 21:460–466
Gardner TS, Cantor CR, Collins JJ (2000) Construction of a genetic toggleswitch in Escherichia coli. Nature 403:339–342
Gillespie DT (2007) Stochastic simulation of chemical kinetics. Annu Rev PhysChem 58:35–55
Goldbeter A (1997) Biochemical Oscillations and Cellular Rhythms: TheMolecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press, Cambridge
Goldbeter A, Koshland DE (1984) Ultrasensitivity in biochemical systemscontrolled by covalent modification. Interplay between zero-order and multistep effects. J Biol Chem 259:14441–7
Heinrich R, Rapoport TA (1974) A Linear Steady-state Treatment ofEnzymatic Chains; General Properties, Control and Effector Strength. Eur J Biochem 42:89–95
Heinrich R, Schuster S (1996) The Regulation of Cellular Systems. Chapman andHall, New York
Heinrich R, Rapoport SM, Rapoport TA (1977) Metabolic regulation andmathematical models. Prog Biophys Molec Biol 32:1–82
Hofmeyr JHS (1986) Steady state modelling of metabolic pathways: a guidefor the prespective simulator. Comp Appl Biosci 2:5–11
Hofmeyr JHS (1986) Studies in steady state modelling and control analysis ofmetabolic systems. Dissertation, University of Stellenbosch
Hofmeyr JHS (2001) Metabolic Control Analysis in a Nutshell. In:Proceedings of the Second International Conference on Systems Biology, Caltech
Hood L, Heath JR, Phelps ME, Lin B (2004) Systems biology and new technologiesenable predictive and preventative medicine. Science 306(5696):640–643
Horn F, Jackson R (1972) General Mass Action Kinetics. Arch Rational Mech Anal47:81–116
Ideker T, Galitski T, Hood L (2001) A new approach to decoding life:systems biology. Annu Rev Genomics Hum Genet 2:343–372
Jones MH (1977) A practical introduction to electroniccircuits. Cambridge University Press, Cambridge
Kacser H, Burns JA (1973) The Control of Flux. In D. D. Davies (eds) RateControl of Biological Processes, Symp Soc Exp Biol, vol 27, Cambridge University Press, Cambridge, pp 65–104
Kholodenko BN (2000) Negative feedback and ultrasensitivity can bring aboutoscillations in the mitogen-activated protein kinase cascades. Eur J Biochem 267:1583–1588
Kholodenko BN (2006) Cell-signalling dynamics in time and space. Nat Rev MolCell Biol 7(3):165–176
Klipp E, Herwig R, Kowald A, Wierling C, Lehrach H (2005) Systems Biology inPractice. Wiley-VCH, Weinheim
Koebmann BJ, Westerhoff HV, Snoep JL, Nilsson D, Jensen PR (2002) TheGlycolytic Flux in Escherichia coli Is Controlled by the Demand for ATP. J Bacteriol 184(14):3909–3916
Lahav G, Rosenfeld N, Sigal A, Geva-Zatorsky N, Levine AJ, Elowitz MB, Alon U(2004) Dynamics of the p53-Mdm2 feedback loop in individual cells. Nature, Genetics 36(2):147–150
Lauffenburger DA (2000) Cell signaling pathways as control modules: complexityfor simplicity? Proc Natl Acad Sci U S A 97:5031–3
Lev Bar-Or R, Maya R, Segel LA, Alon U, Levine AJ, Oren M (2000) Generation ofoscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study. Proc Natl Acad Sci USA97(21):11250–11255
Mangan S, Itzkovitz S, Zaslaver A, Alon U (2006) The incoherent feed-forwardloop accelerates the response-time of the gal system of Escherichia coli. J Mol Biol 356(5):1073–1081
Markevich NI, Hoek JB, Kholodenko BN (2004) Signaling switches and bistabilityarising from multisite phosphorylation in protein kinase cascades. J Cell Biol 164:353–9
Moniz-Barreto P, Fell DA (1993) Simulation of dioxygen free radicalreactions. Biochem Soc Trans 21(3):256–256
Moore WJ (1972) Physical Chemistry. 5th edn. Longman, London, Prentice Hall,NJ
Oda K, Kitano H (2006) A comprehensive map of the toll-like receptorsignaling network. Mol Syst Biol 2:2006–2006
Othmer HH (1976) The quantitative dynamics of a class of biochemicalcontrol circuits. J Math Biol 37:53–78
Ozbudak EM, Thattai M, Lim HN, Shraiman BI, Van Oudenaarden A (2004)Multistability in the lactose utilization network of Escherichia coli. Nature 427(6976):737–740
Papin JA, Stelling J, Price ND, Klamt S, Schuster S, Palsson BO (2004)Comparison of network-based pathway analysis methods. Trends Biotechnol 22(8):400–405
Paulsson J, Berg OG, Ehrenberg M (2000) Stochastic focusing:fluctuation-enhanced sensitivity of intracellular regulation. Proc Natl Acad Sci USA 97(13):7148–7153
Reder C (1988) Metabolic Control Theory: A StructuralApproach. J Theor Biol 135:175–201
Reich JG, Selkov EE (1981) Energy metabolism of the cell. Academic Press,London
Ro DK, Paradise EM, Ouellet M, Fisher KJ, Newman KL, Ndungu JM, Ho KA,et al (2006) Production of the antimalarial drug precursor artemisinic acid in engineered yeast. Nature440(7086):940–943
Rosenfeld N, Elowitz MB, Alon U (2002) Negative autoregulation speeds theresponse times of transcription networks. J Mol Biol 323(5):785–793
Samoilov M, Plyasunov S, Arkin AP (2005) Stochastic amplification andsignaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc Natl Acad Sci USA102(7):2310–2315
Sauro HM, Ingalls B (2004) Conservation analysis in biochemical networks:computational issues for software writers. Biophys Chem 109:1–15
Sauro HM, Kholodenko BN (2004) Quantitative analysis of signalingnetworks. Prog Biophys Mol Biol. 86:5–43
Sauro HM, Small JR, Fell DA (1987) Metabolic Control and its Analysis:Extensions to the theory and matrix method. Eur J Biochem 165:215–221
Savageau MA (1972) The behaviour of intact biochemical control systems. CurrTopics Cell Reg 6:63–130
Savageau MA (1974) Optimal design of feedback control by inhibition:Steady-state considerations. J Mol Evol 4:139–156
Savageau MA (1975) Optimal design of feedback control by inhibition: dynamicconsiderations. J Mol Evol 5(3):199–222
Savageau MA (1976) Biochemical systems analysis: a study of function anddesign in molecular biology. Addison-Wesley, Reading
Schuster S, Dandekar T, Fell DA (1999) Detection of elementary flux modes inbiochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol17(2):53–60
Schuster S, Fell DA, Dandekar T (2000) A general definition of metabolicpathways useful for systematic organization and analysis of complex metabolic networks. Nature Biotechnology 18:326–332
Segel IH (1975) Enzyme Kinetics: Behavior and Analysis of Rapid Equilibriumand Steady-State Enzyme Systems. Wiley-Interscience, New York
Stephanopoulos GN, Aristidou AA, Nielsen J (1998) Metabolic Engineering: Principlesand Methodologies. Academic Press, San Diego
Strogatz S (2001) Nonlinear Dynamics and Chaos: With Applications to Physics,Biology, Chemistry, and Engineering. Perseus Books Group, Reading
Tyson J, Othmer HG (1978) The dynamics of feedback control circuits inbiochemical pathways. In: Rosen R, Snell FM (eds) Progress in Theoretical Biology, vol 5. Academic press, New York,pp 1–62
Tyson JJ, Chen K, Novak B (2001) Network Dynamics And Cell Physiology. Nat RevMol Cell Biol 2:908–916
Tyson JJ, Chen KC, Novak B (2003) Sniffers, buzzers, toggles and blinkers:dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15:221–231
Umbarger HE (1956) Evidence for a Negative-Feedback Mechanism in theBiosynthesis of Leucine. Science 123:848
Vallabhajosyula RR, Chickarmane V, Sauro HM (2006) Conservation analysis oflarge biochemical networks. Bioinformatics 22(3):346–353
Vass M, Allen N, Shaffer CA, Ramakrishnan N, Watson LT, Tyson JJ (2004) theJigCell model builder and run manager. Bioinformatics 20(18):3680–3681
Voigt CA (2006) Genetic parts to program bacteria. Curr Opin Biotechnol17(5):548–557
Wilkinson DJ (2006) Stochastic Modelling for Systems Biology. Chapman and Hall, New York
Win MN, Smolke CD (2007) A modular and extensible RNA-basedgene-regulatory platform for engineering cellular function. Proc Natl Acad Sci U S A 104(36):14283–14288
Wolf DM, Arkin AP (2003) Motifs, modules and games in bacteria. CurrentOpinion in Microbiology 6:125–34
Wolkenhauer O, Ullah M, Wellstead P, Cho KH (2005) The dynamic systemsapproach to control and regulation of intracellular networks. FEBS Lett 579(8):1846–1853
Yates RA, Pardee AB (1956) Control of Pyrimidine Biosynthesis in Escherichiacoli by a Feed-Back Mechanism. J Biol Chem 221:757–770
Zaslaver A, Mayo AE, Rosenberg R, Bashkin P, Sberro H, Tsalyuk M, Surette MG,et al (2004) Just-in-time transcription program in metabolic pathways. Nat Genet 36(5):486–491
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Sauro, H.M. (2009). Biological Models of Molecular Network Dynamics. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_37
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