The Regulation of Cellular Systems

Introduction Fundamentals of biochemical modeling Balance equations Rate laws Generalized mass-action kinetics Various enzyme kinetic rate laws Thermodynamic flow-force relationships Power-law approximation Steady states of biochemical networks General considerations Stable and unstable steady states Multiple steady states Metabolic oscillations Background Mathematical conditions for oscillations Glycolytic oscillations Models of intracellular calcium oscillations A simple three-variable model with only monomolecular and bimolecular reactions Possible physiological significance of oscillations Stoichiometric analysis Conservation relations Linear dependencies between the rows of the stoichiometry matrix Non-negative flux vectors Elementary flux modes Thermodynamic aspects A generalized Wegscheider condition Strictly detailed balanced subnetworks Onsager's reciprocity reactions for coupled enyme reactions Time hierarchy in metabolism Time constants The quasi-steady-state approximation The Rapid equilibrium approximation Modal analysis Metabolic control analysis Basic definitions A systematic approach Theorems of metabolic control analysis Summation theorems Connectivity theorems Calculation of control coefficients using the theorems Geometrical interpretation Control analysis of various systems General remarks Elasticity coefficients for specific rate laws Control coefficients for simple hypothetical pathways Unbranched chains A branched system Control of erythrocyte energy metabolism The reaction system Basic model Interplay of ATP production and ATP consumption Glycolytic energy metabolism and osmotic states A simple model of oxidative phosphorylation A three-step model of serine biosynthesis Time-dependent control coefficients Are control coefficients always parameter independent? Posing the problem A system without conserved moieties A system with a conserved moiety A system including dynamic channeling Normalized versus non-normalized coefficients Analysis in terms of variables other than steady-state concentrations and fluxes General analysis Concentration ratios and free-energy-differences as state variables Entropy production as response variable Control of transient times Control of oscillations A second-order approach A quantitative approach to metabolic regulations Co-response coefficients Fluctuations of internal variables versus parameter perturbations Internal response coefficients Rephrasing the basic equations of metabolic control analysis in terms of co-response coefficients and internal response coefficients Control within and between subsystems Modular approach Overall elasticities Overall control coefficients Flux control insusceptibility Control exerted by elementary steps in enzyme catalysis Control analysis of metabolic channeling Comparison of metabolic control analysis and power-law formalism Computational aspects Application of optimization methods and the interrelation with evolution Optimization of the catalytic properties of single enzymes Basic assumptions Optimal values of elementary rate constants Optimal Michaelis constants Optimization of multienzyme systems Maximization of steady-state flux Influence of osmotic constraints and minimization of intermediate concentrations Minimization of transient times Optimal stoichiometries.

[1]  Rud. Wegscheider Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reaktionskinetik homogener Systeme , 1902 .

[2]  Alfred J. Lotka Zur Theorie der periodischen Reaktionen , 1910 .

[3]  G N Lewis,et al.  A New Principle of Equilibrium. , 1925, Proceedings of the National Academy of Sciences of the United States of America.

[4]  D. E. Goldman POTENTIAL, IMPEDANCE, AND RECTIFICATION IN MEMBRANES , 1943, The Journal of general physiology.

[5]  J. Field Energy metabolism of the cell. , 1947, Stanford medical bulletin.

[6]  L. Bertalanffy,et al.  Biophysik des Fließgleichgewichts : Einführung in die Physik offener Systeme und ihre Anwendung in der Biologie , 1953 .

[7]  J. Hearon,et al.  The kinetics of linear systems with special reference to periodic reactions , 1953 .

[8]  N. Levinson,et al.  Singular Perturbations of Non-Linear Systems of Differential Equations and an Associated Boundary Layer Equation , 1954 .

[9]  M. Gibbs,et al.  The mechanism of pentose phosphate conversion to hexose monophosphate. I. With a liver enzyme preparation. , 1954, The Journal of biological chemistry.

[10]  B CHANCE,et al.  Respiratory enzymes in oxidative phosphorylation. V. A mechanism for oxidative phosphorylation. , 1955, The Journal of biological chemistry.

[11]  H. E. Umbarger,et al.  Evidence for a negative-feedback mechanism in the biosynthesis of isoleucine. , 1956, Science.

[12]  E. L. King,et al.  A Schematic Method of Deriving the Rate Laws for Enzyme-Catalyzed Reactions , 1956 .

[13]  J. D. Bernal,et al.  “The Origins of Life” , 1957, Nature.

[14]  H. Wood,et al.  The distribution of C14 in the hexose phosphates and the effect of recycling in the pentose cycle. , 1958, The Journal of biological chemistry.

[15]  B. Chance,et al.  Localization of Interaction Sites in Multi-Component Transfer Systems: Theorems Derived from Analogues , 1958, Nature.

[16]  W. Holmes Locating sites of interactions between external chemicals and a sequence of chemical reactions , 1959 .

[17]  E. S. Amis Contributions to the Theory of Chemical Kinetics (Bak, Thor A.) , 1960 .

[18]  J. Wei,et al.  Axiomatic Treatment of Chemical Reaction Systems , 1962 .

[19]  R. Alberty,et al.  Multiple Intermediates in Steady-state Enzyme Kinetics. II. Systems Involving Two Reactants and Two Products , 1962 .

[20]  R. Alberty,et al.  MULTIPLE INTERMEDIATES IN STEADY STATE ENZYME KINETICS. VI. THE MECHANISM INVOLVING A SINGLE SUBSTRATE AND TWO PRODUCTS. , 1959, The Journal of biological chemistry.

[21]  A. Ghosh,et al.  Oscillations of glycolytic intermediates in yeast cells. , 1964, Biochemical and biophysical research communications.

[22]  J. Higgins,et al.  A CHEMICAL MECHANISM FOR OSCILLATION OF GLYCOLYTIC INTERMEDIATES IN YEAST CELLS. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[23]  B. Chance,et al.  CYCLIC AND OSCILLATORY RESPONSES OF METABOLIC PATHWAYS INVOLVING CHEMICAL FEEDBACK AND THEIR COMPUTER REPRESENTATIONS * , 1964, Annals of the New York Academy of Sciences.

[24]  S. Waley,et al.  A note on the kinetics of multi-enzyme systems. , 1964, The Biochemical journal.

[25]  A. Ghosh,et al.  DAMPED SINUSOIDAL OSCILLATIONS OF CYTOPLASMIC REDUCED PYRIDINE NUCLEOTIDE IN YEAST CELLS. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[26]  W. Wasow Asymptotic expansions for ordinary differential equations , 1965 .

[27]  R. Aris Prolegomena to the rational analysis of systems of chemical reactions , 1965 .

[28]  S. Caplan,et al.  Degree of coupling and its relation to efficiency of energy conversion , 1965 .

[29]  A. Katchalsky,et al.  Nonequilibrium Thermodynamics in Biophysics , 1965 .

[30]  D. Koshland,et al.  Comparison of experimental binding data and theoretical models in proteins containing subunits. , 1966, Biochemistry.

[31]  G. Cohen,et al.  The threonine-sensitive homoserine dehydrogenase and aspartokinase activities of Escherichia coli: I. Evidence that the two activities are carried by a single protein , 1966 .

[32]  R. Rosen Optimality Principles in Biology , 1967, Springer US.

[33]  H. M. Tsuchiya,et al.  On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics☆ , 1967 .

[34]  B Hess,et al.  Mechanism of glycolytic oscillation in yeast. I. Aerobic and anaerobic growth conditions for obtaining glycolytic oscillation. , 1968, Hoppe-Seyler's Zeitschrift fur physiologische Chemie.

[35]  E. Sel'kov,et al.  Self-oscillations in glycolysis. 1. A simple kinetic model. , 1968, European journal of biochemistry.

[36]  H. Buc,et al.  Kinetics of the allosteric interactions of phosphofructokinase from , 1968 .

[37]  D. E. Atkinson The energy charge of the adenylate pool as a regulatory parameter. Interaction with feedback modifiers. , 1968, Biochemistry.

[38]  M. Savageau Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[39]  A. Betz,et al.  Control of phosphofructokinase [PFK] activity in conditions simulating those of glycolysing yeast extract , 1969, FEBS letters.

[40]  [Influence of human growth on the glycolysis of human red cells in vitro]. , 1969, Clinica chimica acta; international journal of clinical chemistry.

[41]  M. Endo,et al.  Calcium induced release of calcium from the sarcoplasmic reticulum of skinned skeletal muscle fibres. , 1970, Nature.

[42]  P. Glansdorff,et al.  Thermodynamic theory of structure, stability and fluctuations , 1971 .

[43]  R. Jackson,et al.  General mass action kinetics , 1972 .

[44]  A Goldbeter,et al.  Dissipative structures for an allosteric model. Application to glycolytic oscillations. , 1972, Biophysical journal.

[45]  J. S. Easterby,et al.  Coupled enzyme assays: a general expression for the transient. , 1973, Biochimica et biophysica acta.

[46]  David M. Kovenock,et al.  The theoretical approach , 1973 .

[47]  Reinhart Heinrich,et al.  Linear theory of enzymatic chains; its application for the analysis of the crossover theorem and of the glycolysis of human erythrocytes. , 1973, Acta biologica et medica Germanica.

[48]  A. Fersht,et al.  Catalysis, binding and enzyme-substrate complementarity , 1974, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[49]  M. Yčas,et al.  On earlier states of the biochemical system. , 1974, Journal of theoretical biology.

[50]  D J Park An algorithm for detecting non-steady state moieties in steady state subnetworks. , 1974, Journal of theoretical biology.

[51]  Reinhart Heinrich,et al.  A mathematical model for the influence of fructose 6-phosphate, ATP, potassium, ammonium and magnesium on the phosphofructokinase from rat erythrocytes;. , 1974, European journal of biochemistry.

[52]  Reinhart Heinrich,et al.  A linear steady-state treatment of enzymatic chains. A mathematical model of glycolysis of human erythrocytes. , 1974, European journal of biochemistry.

[53]  B. Hess,et al.  Cyclic-AMP-controlled oscillations in suspended Dictyostelium cells: their relation to morphogenetic cell interactions. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[54]  W. Wonham Linear Multivariable Control: A Geometric Approach , 1974 .

[55]  M. Zeleny Linear Multiobjective Programming , 1974 .

[56]  P. Crowley Natural selection and the Michaelis constant. , 1975, Journal of theoretical biology.

[57]  J. Reich,et al.  Time hierarchy, equilibrium and non-equilibrium in metabolic systems. , 1975, Bio Systems.

[58]  E. Sel'kov,et al.  Stabilization of energy charge, generation of oscillations and multiple steady states in energy metabolism as a result of purely stoichiometric regulation. , 1975, European journal of biochemistry.

[59]  A. Fabiato,et al.  Contractions induced by a calcium‐triggered release of calcium from the sarcoplasmic reticulum of single skinned cardiac cells. , 1975, The Journal of physiology.

[60]  N. Dubin Mathematical Model , 2022 .

[61]  R Heinrich,et al.  The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time-dependent processes. , 1976, The Biochemical journal.

[62]  H. Othmer The qualitative dynamics of a class of biochemical control circuits , 1976, Journal of mathematical biology.

[63]  R. Jensen Enzyme recruitment in evolution of new function. , 1976, Annual review of microbiology.

[64]  J. Pearson,et al.  Structural controllability of multiinput linear systems , 1976 .

[65]  Athel Cornish-Bowden,et al.  Principles of enzyme kinetics , 1976 .

[66]  A. Cornish-Bowden The effect of natural selection on enzymic catalysis. , 1976, Journal of molecular biology.

[67]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

[68]  Paolo Truffa-Bachi,et al.  Homoserine kinase from Escherichia coli K12. , 1976, European journal of biochemistry.

[69]  Reinhart Heinrich,et al.  A mathematical model for the influence of anionic effectors on the phosphofructokinase from rat erythrocytes. , 1977, European journal of biochemistry.

[70]  K. Brocklehurst Evolution of enzyme catalytic power. Characteristics of optimal catalysis evaluated for the simplest plausible kinetic model. , 1977, The Biochemical journal.

[71]  R Heinrich,et al.  Metabolic regulation and mathematical models. , 1977, Progress in biophysics and molecular biology.

[72]  D. G. Herries Biochemical Systems Analysis. A Study of Function and Design in Molecular Biology: By Michael A. Savageau. Pp. 380. Addison-Wesley Publishing Company, Reading Mass. 1976. Paper, $16.50, Cloth £26.50 , 1977 .

[73]  P. Björnbom The relation between the reaction mechanism and the stoichiometric behavior of chemical reactions , 1977 .

[74]  Anthony Hill,et al.  Free Energy Transduction In Biology , 1977 .

[75]  M. Kohn,et al.  Instantaneous flux control analysis for biochemical systems. , 1979, Journal of theoretical biology.

[76]  M. Schauer,et al.  Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction. , 1979, Journal of theoretical biology.

[77]  W. Cleland Optimizing coupled enzyme assays. , 1979, Analytical biochemistry.

[78]  S. Rapoport,et al.  A form of (Ca2+ + Mg2+)‐ATPase of human red cell membranes with low affinity for Mg‐ATP: A hypothesis for its function , 1980, FEBS letters.

[79]  P. B. Chock,et al.  Interconvertible enzyme cascades in cellular regulation. , 1980, Annual review of biochemistry.

[80]  E. Hofmann,et al.  In vitro demonstration of alternate stationary states in an open enzyme system containing phosphofructokinase. , 1980, Archives of biochemistry and biophysics.

[81]  J. Stucki The optimal efficiency and the economic degrees of coupling of oxidative phosphorylation. , 1980, European journal of biochemistry.

[82]  L. Gardini,et al.  Calculation of multicomponent multiphase equilibria , 1980 .

[83]  R Heinrich,et al.  Mathematical modelling of translation of mRNA in eucaryotes; steady state, time-dependent processes and application to reticulocytes. , 1980, Journal of theoretical biology.

[84]  A. Winfree The geometry of biological time , 1991 .

[85]  Stoichiometry of Proton Translocation during Photosynthesis , 1980 .

[86]  F I Ataullakhanov,et al.  Regulation of glycolysis in human erythrocytes. The mechanism of ATP concentration stabilization. , 1981, Acta biologica et medica Germanica.

[87]  S. Caplan Reciprocity or near-reciprocity of highly coupled enzymatic processes at the multidimensional inflection point. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[88]  J. S. Easterby,et al.  A generalized theory of the transition time for sequential enzyme reactions. , 1981, The Biochemical journal.

[89]  C. Sparrow,et al.  Frequency encoded biochemical regulation is more accurate than amplitude dependent control. , 1981, Journal of theoretical biology.

[90]  Enzyme Regulation and Metabolic Diseases , 1981 .

[91]  R. Bohnensack Control of energy transformation of mitochondria. Analysis by a quantitative model. , 1981, Biochimica et biophysica acta.

[92]  Bruce L. Clarke,et al.  Complete set of steady states for the general stoichiometric dynamical system , 1981 .

[93]  J. Ross,et al.  Oscillations and control features in glycolysis: numerical analysis of a comprehensive model. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[94]  M. Kohn,et al.  Metabolic network sensitivity analysis. , 1982, Journal of theoretical biology.

[95]  H. Westerhoff Yes. Kinetics alone are impracticable , 1982 .

[96]  William R. Smith,et al.  Chemical Reaction Equilibrium Analysis: Theory and Algorithms , 1982 .

[97]  B F Dibrov,et al.  Dynamic stability of steady states and static stabilization in unbranched metabolic pathways , 1982, Journal of mathematical biology.

[98]  Self-Organization in Nonequilibrium Systems (G. Nicolis and I. Prigogine) , 1982 .

[99]  R Heinrich,et al.  Dynamics of non-linear biochemical systems and the evolutionary significance of time hierarchy. , 1982, Bio Systems.

[100]  S. Minihan Principles of biochemistry by Albert L Lehninger. pp 1011. Worth Publishers, New York. 1982. £13. ISBN 0‐87901‐136‐X , 1983 .

[101]  L. Petzold Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations , 1983 .

[102]  W. Klonowski Simplifying principles for chemical and enzyme reaction kinetics. , 1983, Biophysical chemistry.

[103]  H. Kacser,et al.  The control of enzyme systems in vivo: elasticity analysis of the steady state. , 1983, Biochemical Society transactions.

[104]  M. Compiani,et al.  Efficiency of energy conversion in model biological pumps. Optimization by linear nonequilibrium thermodynamic relations. , 1983, Biophysical chemistry.

[105]  H. Westerhoff,et al.  The thermodynamic basis for the partial control of oxidative phosphorylation by the adenine-nucleotide translocator , 1983 .

[106]  S. Wakil,et al.  Fatty acid synthesis and its regulation. , 1983, Annual review of biochemistry.

[107]  R. Heinrich,et al.  Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks , 1983 .

[108]  Ionic states and metabolism of erythrocytes. , 1983, Biomedica biochimica acta.

[109]  M. Kohn,et al.  Sensitivity to values of the rate constants in a neurochemical metabolic model. , 1983, Journal of theoretical biology.

[110]  Reinhart Heinrich,et al.  A metabolic osmotic model of human erythrocytes. , 1984, Bio Systems.

[111]  H. Westerhoff,et al.  How do enzyme activities control metabolite concentrations? An additional theorem in the theory of metabolic control. , 1984, European journal of biochemistry.

[112]  Modification Between Zero-Order,et al.  Ultrasensitivity in Biochemical Systems Controlled by Covalent , 1984 .

[113]  Manfred Eigen,et al.  Evolutionary molecular engineering based on RNA replication , 1984 .

[114]  B. Palsson,et al.  Mathematical modelling of dynamics and control in metabolic networks. II. Simple dimeric enzymes. , 1984, Journal of theoretical biology.

[115]  D A Fell,et al.  Metabolic control and its analysis. Additional relationships between elasticities and control coefficients. , 1985, European journal of biochemistry.

[116]  E. Meléndez-Hevia,et al.  The game of the pentose phosphate cycle. , 1985, Journal of theoretical biology.

[117]  R. Heinrich,et al.  Efficiency and design of simple metabolic systems. , 1985, Biomedica biochimica acta.

[118]  D. Fell,et al.  Metabolic control and its analysis , 1985 .

[119]  R Heinrich,et al.  A kinetic model for the interaction of energy metabolism and osmotic states of human erythrocytes. Analysis of the stationary "in vivo" state and of time dependent variations under blood preservation conditions. , 1985, Biomedica biochimica acta.

[120]  M M Domach,et al.  Consideration of the gain, enzymatic capacity utilization, and response time properties of metabolic networks as a function of operating point and structure. , 1985, Bio Systems.

[121]  S. Benner,et al.  Dynamic transduction of energy and internal equilibria in enzymes: a reexamination of pyruvate kinase , 1985 .

[122]  P. Kuchel 7 – Kinetic Analysis of Multienzyme Systems in Homogeneous Solution , 1985 .

[123]  B O Palsson,et al.  Mathematical modelling of dynamics and control in metabolic networks. III. Linear reaction sequences. , 1985, Journal of theoretical biology.

[124]  S. Caplan,et al.  Flow-force relationships for a six-state proton pump model: intrinsic uncoupling, kinetic equivalence of input and output forces, and domain of approximate linearity. , 1985, Biochemistry.

[125]  On optimum properties in the design of metabolic and epigenetic systems. , 1985, Biomedica biochimica acta.

[126]  R. Bohnensack Mathematical modeling of mitochondrial energy transduction. , 1985, Biomedica biochimica acta.

[127]  Compartmental analysis: theoretical aspects and application. , 1985 .

[128]  A. Cornish-Bowden,et al.  Control analysis of metabolic systems , 1985 .

[129]  F. Battelli,et al.  On the pseudo-steady-state approximation and Tikhonov theorem for general enzyme systems , 1985 .

[130]  H. Kacser,et al.  Metabolic control analysis of moiety-conserved cycles. , 1986, European journal of biochemistry.

[131]  F. Battelli,et al.  Singular perturbation theory for open enzyme reaction networks. , 1986, IMA journal of mathematics applied in medicine and biology.

[132]  J. H. Hofmeyr,et al.  METAMOD: software for steady-state modelling and control analysis of metabolic pathways on the BBC microcomputer , 1986, Comput. Appl. Biosci..

[133]  G. Azzone,et al.  Intrinsic uncoupling of mitochondrial proton pumps. 2. Modeling studies. , 1986, Biochemistry.

[134]  M. Peschel,et al.  The Predator-Prey Model: Do We Live in a Volterra World? , 1986 .

[135]  S. Bernhard,et al.  Enzyme-enzyme interactions and the regulation of metabolic reaction pathways. , 1986, Current topics in cellular regulation.

[136]  D J Park The Complete Stoichiometer. , 1986, Computer methods and programs in biomedicine.

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

[138]  W. Holms,et al.  The central metabolic pathways of Escherichia coli: relationship between flux and control at a branch point, efficiency of conversion to biomass, and excretion of acetate. , 1986, Current topics in cellular regulation.

[139]  J. Liao,et al.  Extending the quasi-steady state concept to analysis of metabolic networks. , 1987, Journal of theoretical biology.

[140]  R. Guynn,et al.  Effect of acute ethanol on serine biosynthesis in liver. , 1987, Archives of biochemistry and biophysics.

[141]  Z. X. Wang,et al.  Kinetics of substrate reaction during irreversible modification of enzyme activity for enzymes involving two substrates. , 1987, Journal of theoretical biology.

[142]  H V Westerhoff,et al.  Matrix method for determining steps most rate‐limiting to metabolic fluxes in biotechnological processes , 1987, Biotechnology and bioengineering.

[143]  D. Fell,et al.  Metabolic control and its analysis. Extensions to the theory and matrix method. , 1987, European journal of biochemistry.

[144]  P. Rapp Why are so many biological systems periodic? , 1987, Progress in Neurobiology.

[145]  Eberhard O. Voit,et al.  Biochemical systems theory and metabolic control theory: 1. fundamental similarities and differences , 1987 .

[146]  S. Schuster,et al.  Time hierarchy in enzymatic reaction chains resulting from optimality principles. , 1987, Journal of theoretical biology.

[147]  H. Westerhoff,et al.  Thermodynamics and Control of Biological Free-Energy Transduction , 1987 .

[148]  P. Srere,et al.  Complexes of sequential metabolic enzymes. , 1987, Annual review of biochemistry.

[149]  P. Cobbold,et al.  Agonist-induced oscillations in cytoplasmic free calcium concentration in single rat hepatocytes. , 1987, Cell calcium.

[150]  The general modifier ("allosteric") unireactant enzyme mechanism: redundant conditions for reduction of the steady state velocity equation to one that is first degree in substrate and effector. , 1988, Journal of theoretical biology.

[151]  D A Fell,et al.  Control analysis of mammalian serine biosynthesis. Feedback inhibition on the final step. , 1988, The Biochemical journal.

[152]  G R Welch,et al.  The control of cell metabolism for homogeneous vs. heterogeneous enzyme systems. , 1988, Journal of theoretical biology.

[153]  G. Brown,et al.  Control of respiration in non-phosphorylating mitochondria is shared between the proton leak and the respiratory chain. , 1988, The Biochemical journal.

[154]  Dynamic Structures in the Fructose-6-Phosphate/Fructose' 1,6-Bisphosphatase Cycle , 1988 .

[155]  C. Giersch Control analysis of metabolic networks. 1. Homogeneous functions and the summation theorems for control coefficients. , 1988, European journal of biochemistry.

[156]  H. Holzhütter,et al.  Interrelations between glycolysis and the hexose monophosphate shunt in erythrocytes as studied on the basis of a mathematical model. , 1988, Bio Systems.

[157]  Lee A. Segel,et al.  On the validity of the steady state assumption of enzyme kinetics , 1988 .

[158]  David J. M. Park Positive compositional algorithms in chemical reaction systems , 1988, Comput. Chem..

[159]  E. Meléndez-Hevia,et al.  Economy of design in metabolic pathways: further remarks on the game of the pentose phosphate cycle. , 1988, Journal of theoretical biology.

[160]  J. Liao,et al.  Characteristic reaction paths of biochemical reaction systems with time scale separation , 1988, Biotechnology and bioengineering.

[161]  Ivar Ugi,et al.  Computer-assisted bilateral solution of chemical problems and generation of reaction networks☆ , 1988 .

[162]  D. Fell,et al.  The matrix method of metabolic control analysis: its validity for complex pathway structures. , 1989, Journal of theoretical biology.

[163]  A Sorribas,et al.  A comparison of variant theories of intact biochemical systems. II. Flux-oriented and metabolic control theories. , 1989, Mathematical biosciences.

[164]  S. Schuster,et al.  A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation , 1989 .

[165]  B O Palsson,et al.  Metabolic dynamics in the human red cell. Part II--Interactions with the environment. , 1989, Journal of theoretical biology.

[166]  M. Berridge Cell signalling through cytoplasmic calcium oscillations , 1989 .

[167]  H. Sauro,et al.  Control analysis of time-dependent metabolic systems. , 1989, Journal of theoretical biology.

[168]  Péter Érdi,et al.  Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models , 1989 .

[169]  S. Lengyel On the Relationship between Thermodynamics and Chemical Kinetics , 1989 .

[170]  G. Pettersson Effect of evolution on the kinetic properties of enzymes. , 1989, European journal of biochemistry.

[171]  A Sorribas,et al.  A comparison of variant theories of intact biochemical systems. I. Enzyme-enzyme interactions and biochemical systems theory. , 1989, Mathematical biosciences.

[172]  A. Goldbeter,et al.  Frequency coding in intercellular communication , 1989 .

[173]  L. Raijman,et al.  Channeling of urea cycle intermediates in situ in permeabilized hepatocytes. , 1989, The Journal of biological chemistry.

[174]  K. Cuthbertson Intracellular calcium oscillators , 1989 .

[175]  H. Holzhütter,et al.  Mathematical modelling of metabolic pathways affected by an enzyme deficiency. Energy and redox metabolism of glucose-6-phosphate-dehydrogenase-deficient erythrocytes. , 1989, European journal of biochemistry.

[176]  H. Westerhoff Control, regulation and thermodynamics of free-energy transduction. , 1989, Biochimie.

[177]  H. Kreuzer,et al.  Theory of oscillating reactions , 1990 .

[178]  Athel Corn,et al.  Metabolic Control Theory and Biochemical Systems Theory: Different Objectives, Different Assumptions, Different Results , 1989 .

[179]  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.

[180]  A. Cornish-Bowden,et al.  Control of Metabolic Processes , 1990, NATO ASI Series.

[181]  Metabolic control theory: the geometry of the triangle. , 1990, Biomedica biochimica acta.

[182]  W. Kunz,et al.  Estimation of flux control coefficients from inhibitor titrations by non‐linear regression , 1990, FEBS letters.

[183]  B. Hess,et al.  Control of Metabolic Oscillations: Unpredictability, Critical Slowing Down, Optimal Stability and Hysteresis , 1990 .

[184]  B. Wright,et al.  Cellular concentrations of enzymes and their substrates. , 1990, Journal of theoretical biology.

[185]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[186]  A hysteretic cycle in glucose 6-phosphate metabolism observed in a cell-free yeast extract. , 1990, European journal of biochemistry.

[187]  G. Brown,et al.  A 'top-down' approach to the determination of control coefficients in metabolic control theory. , 1990, European journal of biochemistry.

[188]  E. Meléndez-Hevia,et al.  The game of the pentose phosphate cycle: a mathematical approach to study the optimization in design of metabolic pathways during evolution. , 1990, Biomedica biochimica acta.

[189]  B O Palsson,et al.  Metabolic dynamics in the human red cell. Part IV--Data prediction and some model computations. , 1990, Journal of theoretical biology.

[190]  G. Brown,et al.  Analysis of the control of respiration rate, phosphorylation rate, proton leak rate and protonmotive force in isolated mitochondria using the 'top-down' approach of metabolic control theory. , 1990, European journal of biochemistry.

[191]  S. Bauer Comments on current aspects of chemical kinetics , 1990 .

[192]  H. Sauro,et al.  Enzyme-enzyme interactions and control analysis. 2. The case of non-independence: heterologous associations. , 1990, European journal of biochemistry.

[193]  M. Domach,et al.  Effect of regulatory mechanism on hyperbolic reaction network properties , 1990, Biotechnology and bioengineering.

[194]  S. G. Waley,et al.  Beta-lactamases as fully efficient enzymes. Determination of all the rate constants in the acyl-enzyme mechanism. , 1990, The Biochemical journal.

[195]  Enzyme kinetics and metabolic control. A method to test and quantify the effect of enzymic properties on metabolic variables. , 1990, The Biochemical journal.

[196]  Hans V. Westerhoff,et al.  On the Control of Gene Expression , 1990 .

[197]  C. Topham A generalized theoretical treatment of the kinetics of an enzyme-catalysed reaction in the presence of an unstable irreversible modifier. , 1990, Journal of theoretical biology.

[198]  J. Berden,et al.  Differentiation between leaks and slips in oxidative phosphorylation. , 1990, Biochimica et Biophysica Acta.

[199]  G. Stephanopoulos,et al.  Computer‐aided synthesis of biochemical pathways , 1990, Biotechnology and bioengineering.

[200]  J Ovádi,et al.  Physiological significance of metabolic channelling. , 1991, Journal of theoretical biology.

[201]  T. Letellier,et al.  CONTROL: software for the analysis of the control of metabolic networks , 1991, Comput. Appl. Biosci..

[202]  L. Jaffe The path of calcium in cytosolic calcium oscillations: a unifying hypothesis. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[203]  A. Thomas,et al.  Spatial and temporal organization of calcium signalling in hepatocytes. , 1991, Cell calcium.

[204]  J. Hervagault,et al.  Irreversible transitions in the 6-phosphofructokinase/fructose 1,6-bisphosphatase cycle. , 1991, European journal of biochemistry.

[205]  T. Meyer Cell signalling by second messenger waves , 1991, Cell.

[206]  CONDITIONS FOR REACTION MECHANISMS , 1991 .

[207]  R Somogyi,et al.  Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model. , 1991, The Journal of biological chemistry.

[208]  H. Westerhoff,et al.  Control theory of regulatory cascades. , 1991, Journal of theoretical biology.

[209]  S. Lakatos,et al.  Substrate channeling in glycolysis: a phantom phenomenon. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[210]  J. H. Hofmeyr,et al.  MetaModel: a program for modelling and control analysis of metabolic pathways on the IBM PC and compatibles , 1991, Comput. Appl. Biosci..

[211]  W. Froncisz,et al.  An extended dynamic model of oxidative phosphorylation. , 1991, Biochimica et biophysica acta.

[212]  R. Heinrich,et al.  Metabolic control analysis of relaxation processes , 1991 .

[213]  Why do many Michaelian enzymes exhibit an equilibrium constant close to unity for the interconversion of enzyme-bound substrate and product? , 1991, European journal of biochemistry.

[214]  S. Schuster,et al.  Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks , 1991, Journal of mathematical biology.

[215]  K. Anderson,et al.  Serine modulates substrate channeling in tryptophan synthase. A novel intersubunit triggering mechanism. , 1991, The Journal of biological chemistry.

[216]  A. Cornish-Bowden Failure of channelling to maintain low concentrations of metabolic intermediates. , 1991, European journal of biochemistry.

[217]  A Goldbeter,et al.  Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release. , 1991, Cell calcium.

[218]  G. Betts,et al.  The rationalization of high enzyme concentration in metabolic pathways such as glycolysis. , 1991, Journal of theoretical biology.

[219]  Smita S. Patel,et al.  Pre-steady-state kinetic analysis of processive DNA replication including complete characterization of an exonuclease-deficient mutant. , 1991, Biochemistry.

[220]  S. Schuster,et al.  Determining all extreme semi-positive conservation relations in chemical reaction systems: a test criterion for conservativity , 1991 .

[221]  R Heinrich,et al.  Is metabolic channelling the complicated solution to the easy problem of reducing transient times? , 1991, Journal of theoretical biology.

[222]  H. Gutfreund,et al.  Substrate channeling among glycolytic enzymes: fact or fiction. , 1991, Journal of theoretical biology.

[223]  Stefan Schuster,et al.  Detecting strictly detailed balanced subnetworks in open chemical reaction networks , 1991 .

[224]  B. Wright,et al.  Systems analysis of the tricarboxylic acid cycle in Dictyostelium discoideum. I. The basis for model construction. , 1992, The Journal of biological chemistry.

[225]  D. Fell Metabolic control analysis: a survey of its theoretical and experimental development. , 1992, The Biochemical journal.

[226]  Stefan Schuster,et al.  Simplification of complex kinetic models used for the quantitative analysis of nuclear magnetic resonance or radioactive tracer studies , 1992 .

[227]  H V Westerhoff,et al.  Channelling can decrease pool size. , 1992, European journal of biochemistry.

[228]  C. D. Stoner An investigation of the relationships between rate and driving force in simple uncatalysed and enzyme-catalysed reactions with applications of the findings to chemiosmotic reactions. , 1992, The Biochemical journal.

[229]  A. Goldbeter,et al.  Oscillations and waves of cytosolic calcium: insights from theoretical models. , 1992, BioEssays : news and reviews in molecular, cellular and developmental biology.

[230]  R. Schuster,et al.  Decomposition of biochemical reaction systems according to flux control insusceptibility , 1992 .

[231]  M. Mavrovouniotis Synthesis of reaction mechanisms consisting of reversible and irreversible steps. 2. Formalization and analysis of the synthesis algorithm , 1992 .

[232]  B. Kholodenko,et al.  Control of the metabolic flux in a system with high enzyme concentrations and moiety-conserved cycles. The sum of the flux control coefficients can drop significantly below unity. , 1992, European journal of biochemistry.

[233]  S. Schuster,et al.  The definitions of metabolic control analysis revisited. , 1992, Bio Systems.

[234]  G Pettersson,et al.  Evolutionary optimization of the catalytic efficiency of enzymes. , 1992, European journal of biochemistry.

[235]  B. Kholodenko,et al.  Metabolic channelling and control of the flux , 1993, FEBS letters.

[236]  A Model Study on the Interrelation between the Transmembrane Potential and pH Difference Across the Mitochondrial Inner Membrane , 1993 .

[237]  John J. Tyson,et al.  Modeling the Cell Division Cycle: M-phase Trigger, Oscillations, and Size Control , 1993 .

[238]  A Goldbeter,et al.  One-pool model for Ca2+ oscillations involving Ca2+ and inositol 1,4,5-trisphosphate as co-agonists for Ca2+ release. , 1993, Cell calcium.

[239]  G. Lebon,et al.  Extended irreversible thermodynamics , 1993 .

[240]  J. Mazat,et al.  Control of oxidative phosphorylation in rat muscle mitochondria: implications for mitochondrial myopathies. , 1993, Biochimica et biophysica acta.

[241]  Guido Zacchi,et al.  Derivation of a General Matrix Method for the Calculation of Control Coefficients , 1993 .

[242]  J. Liao,et al.  Advances in Metabolic Control Analysis , 1993 .

[243]  Quality Assessment of a Metabolic Model and Systems Analysis of Citric Acid Production by Aspergillus Niger , 1993 .

[244]  H M Sauro,et al.  SCAMP: a general-purpose simulator and metabolic control analysis program , 1993, Comput. Appl. Biosci..

[245]  R Heinrich,et al.  A second-order approach to metabolic control analysis. , 1993, Journal of theoretical biology.

[246]  Jacques Demongeot,et al.  AN ATTEMPT TO GENERALIZE THE CONTROL COEFFICIENT CONCEPT , 1993 .

[247]  A. Cornish-Bowden,et al.  Taking enzyme kinetics out of control; putting control into regulation. , 1993, European journal of biochemistry.

[248]  Stefan Schuster,et al.  Refined algorithm and computer program for calculating all non-negative fluxes admissible in steady states of biochemical reaction systems with or without some flux rates fixed , 1993, Comput. Appl. Biosci..

[249]  H. Westerhoff,et al.  Modular analysis of the control of complex metabolic pathways. , 1993, Biophysical chemistry.

[250]  Regulation and Homeostasis in Metabolic Control Theory: Interplay between Fluctuations of Variables and Parameter Changes , 1993 .

[251]  G C Brown,et al.  Control analysis applied to single enzymes: can an isolated enzyme have a unique rate-limiting step? , 1993, The Biochemical journal.

[252]  A Cornish-Bowden,et al.  Channelling can affect concentrations of metabolic intermediates at constant net flux: artefact or reality? , 1993, European journal of biochemistry.

[253]  Graphic rule for non-steady-state enzyme kinetics and protein folding kinetics , 1993 .

[254]  D. Fell The Analysis of Flux in Substrate Cycles , 1993 .

[255]  D A Fell,et al.  A computer program for the algebraic determination of control coefficients in Metabolic Control Analysis. , 1993, The Biochemical journal.

[256]  B. Kholodenko,et al.  ‘Channelled’ pathways can be more sensitive to specific regulatory signals , 1993, FEBS letters.

[257]  H. Kacser,et al.  Responses of metabolic systems to large changes in enzyme activities and effectors. 1. The linear treatment of unbranched chains. , 1993, European journal of biochemistry.

[258]  Dramatic changes in control properties that accompany channelling and metabolite sequestration , 1993, FEBS letters.

[259]  H. Westerhoff,et al.  The regulatory strength: How to be precise about regulation and homeostasis , 1993, Acta biotheoretica.

[260]  Metabolic Control Analysis: Sensitivity of Control Coefficients to Experimentally Determined Variables , 1994 .

[261]  J. Engel,et al.  Anisotropic propagation of Ca2+ waves in isolated cardiomyocytes. , 1994, Biophysical journal.

[262]  B. Kholodenko,et al.  Control theory of one enzyme. , 1994, Biochimica et biophysica acta.

[263]  N. Torres,et al.  Modeling approach to control of carbohydrate metabolism during citric acid accumulation by Aspergillus niger: I. Model definition and stability of the steady state , 1994, Biotechnology and bioengineering.

[264]  What is Controlling Life? 50 Years After Erwin Schrödinger's What is Life? , 1994 .

[265]  H. Holzhütter,et al.  Multiphase saturation curves of the oxoglutarate carrier: A mathematical model , 1994 .

[266]  Thomas Wilhelm,et al.  An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms , 1994 .

[267]  M. Brownlee,et al.  Nonenzymatic glycosylation in vitro and in bovine endothelial cells alters basic fibroblast growth factor activity. A model for intracellular glycosylation in diabetes. , 1994, The Journal of clinical investigation.

[268]  F. Montero,et al.  Optimization of Metabolism: The Evolution of Metabolic Pathways Toward Simplicity Through the Game of the Pentose Phosphate Cycle , 1994 .

[269]  Constraints in biochemical reactions , 1994 .

[270]  Generalized theory of the kinetics of tracers in biological systems. , 1994, Bulletin of mathematical biology.

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

[272]  Reinhart Heinrich,et al.  The kinetic basis of threshold effects observed in mitochondrial diseases: a systemic approach. , 1994, The Biochemical journal.

[273]  H. Rabitz,et al.  IDENTIFIABILITY AND DISTINGUISHABILITY OF GENERAL REACTION SYSTEMS , 1994 .

[274]  W A Weigand,et al.  A metabolic model of cellular energetics and carbon flux during aerobic Escherichia coli fermentation , 1994, Biotechnology and bioengineering.

[275]  deduction of pulmonary microvascular hematocrit from indicator dilution curves , 1994 .

[276]  P. Gräber,et al.  The pHin and pHout dependence of the rate of ATP synthesis catalyzed by the chloroplast H(+)-ATPase, CF0F1, in proteoliposomes. , 1994, The Journal of biological chemistry.

[277]  A. Cornish-Bowden,et al.  Determination of control coefficients in intact metabolic systems. , 1994, The Biochemical journal.

[278]  B. Kholodenko,et al.  Rate limitation within a single enzyme is directly related to enzyme intermediate levels , 1994, FEBS letters.

[279]  M Rigoulet,et al.  Mechanistic stoichiometry of yeast mitochondrial oxidative phosphorylation. , 1994, Biochemistry.

[280]  Product inhibition in mechanisms in which the free enzyme isomerizes. , 1994, The Biochemical journal.

[281]  P. Schuster,et al.  How to search for RNA structures. Theoretical concepts in evolutionary biotechnology. , 1995, Journal of biotechnology.

[282]  S. Schuster,et al.  What Information about the Conserved-Moiety Structure of Chemical Reaction Systems Can be Derived from Their Stoichiometry? , 1995 .

[283]  A. Cornish-Bowden Metabolic Control Analysis in Theory and Practice , 1995 .

[284]  H. Holzhütter,et al.  Use of mathematical models for predicting the metabolic effect of large-scale enzyme activity alterations. Application to enzyme deficiencies of red blood cells. , 1995, European journal of biochemistry.

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

[286]  V. Lakshmikantham,et al.  Nonlinear control and self-organization , 1995 .

[287]  Thomas Wilhelm,et al.  Smallest chemical reaction system with Hopf bifurcation , 1995 .