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The Regulation of Cellular Systems

31 Aug 1996-
TL;DR: The basic equations of metabolic control analysis are rewritten in terms of co-response coefficients and internal response coefficients to describe the interaction of optimization methods and the interrelation with evolution.
Abstract: 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.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

3,424 citations

Journal ArticleDOI
TL;DR: This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equation, stochastic equations, and so on.
Abstract: The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.

2,739 citations


Cites methods from "The Regulation of Cellular Systems"

  • ...Powerful mathematical methods for modeling biochemical reaction systems by means of rate equations have been developed in the past century, especially in the context of metabolic processes (see CornishBowden [1995], Heinrich and Schuster [1996], and Voit [2000] for introductions)....

    [...]

Journal ArticleDOI
TL;DR: COPASI is presented, a platform-independent and user-friendly biochemical simulator that offers several unique features, and numerical issues with these features are discussed; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic-stochastic methods, and the importance of random number generator numerical resolution in Stochastic simulation.
Abstract: Motivation: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present COPASI, a platform-independent and user-friendly biochemical simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic--stochastic methods, and the importance of random number generator numerical resolution in stochastic simulation. Availability: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel) and Sun Solaris (SPARC), as well as the full source code under an open source license from http://www.copasi.org. Contact: mendes@vbi.vt.edu

2,351 citations

Journal ArticleDOI
24 Dec 2015-Nature
TL;DR: The discovery and cultivation of a completely nitrifying bacterium from the genus Nitrospira, a globally distributed group of nitrite oxidizers, and the genome of this chemolithoautotrophic organism encodes the pathways both for ammonia and nitrite oxidation.
Abstract: Nitrification, the oxidation of ammonia via nitrite to nitrate, has always been considered to be a two-step process catalysed by chemolithoautotrophic microorganisms oxidizing either ammonia or nitrite. No known nitrifier carries out both steps, although complete nitrification should be energetically advantageous. This functional separation has puzzled microbiologists for a century. Here we report on the discovery and cultivation of a completely nitrifying bacterium from the genus Nitrospira, a globally distributed group of nitrite oxidizers. The genome of this chemolithoautotrophic organism encodes the pathways both for ammonia and nitrite oxidation, which are concomitantly activated during growth by ammonia oxidation to nitrate. Genes affiliated with the phylogenetically distinct ammonia monooxygenase and hydroxylamine dehydrogenase genes of Nitrospira are present in many environments and were retrieved on Nitrospira-contigs in new metagenomes from engineered systems. These findings fundamentally change our picture of nitrification and point to completely nitrifying Nitrospira as key components of nitrogen-cycling microbial communities.

1,648 citations

Journal ArticleDOI
TL;DR: The method of minimization of metabolic adjustment (MOMA), whereby the hypothesis that knockout metabolic fluxes undergo a minimal redistribution with respect to the flux configuration of the wild type is tested, is tested and found to be useful in understanding the evolutionary optimization of metabolism.
Abstract: An important goal of whole-cell computational modeling is to integrate detailed biochemical information with biological intuition to produce testable predictions. Based on the premise that prokaryotes such as Escherichia coli have maximized their growth performance along evolution, flux balance analysis (FBA) predicts metabolic flux distributions at steady state by using linear programming. Corroborating earlier results, we show that recent intracellular flux data for wild-type E. coli JM101 display excellent agreement with FBA predictions. Although the assumption of optimality for a wild-type bacterium is justifiable, the same argument may not be valid for genetically engineered knockouts or other bacterial strains that were not exposed to long-term evolutionary pressure. We address this point by introducing the method of minimization of metabolic adjustment (MOMA), whereby we test the hypothesis that knockout metabolic fluxes undergo a minimal redistribution with respect to the flux configuration of the wild type. MOMA employs quadratic programming to identify a point in flux space, which is closest to the wild-type point, compatibly with the gene deletion constraint. Comparing MOMA and FBA predictions to experimental flux data for E. coli pyruvate kinase mutant PB25, we find that MOMA displays a significantly higher correlation than FBA. Our method is further supported by experimental data for E. coli knockout growth rates. It can therefore be used for predicting the behavior of perturbed metabolic networks, whose growth performance is in general suboptimal. MOMA and its possible future extensions may be useful in understanding the evolutionary optimization of metabolism.

1,346 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

5,180 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

3,424 citations

Journal ArticleDOI
TL;DR: A theoretical picture has been presented based on the use of the general kinetic equations for ion motion under the influence of diffusion and electrical forces and on a consideration of possible membrane structures that shows qualitative agreement with the rectification properties and very good agreementwith the membrane potential data.
Abstract: Impedance and potential measurements have been made on a number of artificial membranes. Impedance changes were determined as functions of current and of the composition of the environmental solutions. It was shown that rectification is present in asymmetrical systems and that it increases with the membrane potential. The behavior in pairs of solutions of the same salt at different concentrations has formed the basis for the studies although a few experiments with different salts at the same concentrations gave results consistent with the conclusions drawn. A theoretical picture has been presented based on the use of the general kinetic equations for ion motion under the influence of diffusion and electrical forces and on a consideration of possible membrane structures. The equations have been solved for two very simple cases; one based on the assumption of microscopic electroneutrality, and the other on the assumption of a constant electric field. The latter was found to give better results than the former in interpreting the data on potentials and rectification, showing agreement, however, of the right order of magnitude only. Although the indications are that a careful treatment of boundary conditions may result in better agreement with experiment, no attempt has been made to carry this through since the data now available are not sufficiently complete or reproducible. Applications of the second theoretical case to the squid giant axon have been made showing qualitative agreement with the rectification properties and very good agreement with the membrane potential data.

2,685 citations


Additional excerpts

  • ...The passive transport of sodium and potassium is described by the well-known Goldman equation (Goldman, 1943)....

    [...]

Book
03 Dec 1974
TL;DR: In this article, the authors present an approach to controlability, feedback assignment, and pole shifting in a single linear functional model, where the observer is assumed to be a dynamic observer.
Abstract: 0 Mathematical Preliminaries.- 0.1 Notation.- 0.2 Linear Spaces.- 0.3 Subspaces.- 0.4 Maps and Matrices.- 0.5 Factor Spaces.- 0.6 Commutative Diagrams.- 0.7 Invariant Subspaces. Induced Maps.- 0.8 Characteristic Polynomial. Spectrum.- 0.9 Polynomial Rings.- 0.10 Rational Canonical Structure.- 0.11 Jordan Decomposition.- 0.12 Dual Spaces.- 0.13 Tensor Product. The Sylvester Map.- 0.14 Inner Product Spaces.- 0.15 Hermitian and Symmetric Maps.- 0.16 Well-Posedness and Genericity.- 0.17 Linear Systems.- 0.18 Transfer Matrices. Signal Flow Graphs.- 0.19 Rouche's Theorem.- 0.20 Exercises.- 0.21 Notes and References.- 1 Introduction to Controllability.- 1.1 Reachability.- 1.2 Controllability.- 1.3 Single-Input Systems.- 1.4 Multi-Input Systems.- 1.5 Controllability is Generic.- 1.6 Exercises.- 1.7 Notes and References.- 2 Controllability, Feedback and Pole Assignment.- 2.1 Controllability and Feedback.- 2.2 Pole Assignment.- 2.3 Incomplete Controllability and Pole Shifting.- 2.4 Stabilizability.- 2.5 Exercises.- 2.6 Notes and References.- 3 Observability and Dynamic Observers.- 3.1 Observability.- 3.2 Unobservable Subspace.- 3.3 Full Order Dynamic Observer.- 3.4 Minimal Order Dynamic Observer.- 3.5 Observers and Pole Shifting.- 3.6 Detectability.- 3.7 Detectors and Pole Shifting.- 3.8 Pole Shifting by Dynamic Compensation.- 3.9 Observer for a Single Linear Functional.- 3.10 Preservation of Observability and Detectability.- 3.11 Exercises.- 3.12 Notes and References.- 4 Disturbance Decoupling and Output Stabilization.- 4.1 Disturbance Decoupling Problem (DDP).- 4.2 (A, B)-Invariant Subspaces.- 4.3 Solution of DDP.- 4.4 Output Stabilization Problem (OSP).- 4.5 Exercises.- 4.6 Notes and References.- 5 Controllability Subspaces.- 5.1 Controllability Subspaces.- 5.2 Spectral Assignability.- 5.3 Controllability Subspace Algorithm.- 5.4 Supremal Controllability Subspace.- 5.5 Transmission Zeros.- 5.6 Disturbance Decoupling with Stability.- 5.7 Controllability Indices.- 5.8 Exercises.- 5.9 Notes and References.- 6 Tracking and Regulation I: Output Regulation.- 6.1 Restricted Regulator Problem (RRP).- 6.2 Solvability of RRP.- 6.3 Example 1 : Solution of RRP.- 6.4 Extended Regulator Problem (ERP).- 6.5 Example 2: Solution of ERP.- 6.6 Concluding Remarks.- 6.7 Exercises.- 6.8 Notes and References.- 7 Tracking and Regulation II: Output Regulation with Internal Stability.- 7.1 Solvability of RPIS: General Considerations.- 7.2 Constructive Solution of RPIS: N= 0.- 7.3 Constructive Solution of RPIS: N Arbitrary.- 7.4 Application: Regulation Against Step Disturbances.- 7.5 Application: Static Decoupling.- 7.6 Example 1 : RPIS Unsolvable.- 7.7 Example 2: Servo-Regulator.- 7.8 Exercises.- 7.9 Notes and References.- 8 Tracking and Regulation III: Structurally Stable Synthesis.- 8.1 Preliminaries.- 8.2 Example 1: Structural Stability.- 8.3 Well-Posedness and Genericity.- 8.4 Well-Posedness and Transmission Zeros.- 8.5 Example 2: RPIS Solvable but Ill-Posed.- 8.6 Structurally Stable Synthesis.- 8.7 Example 3: Well-Posed RPIS: Strong Synthesis.- 8.8 The Internal Model Principle.- 8.9 Exercises.- 8.10 Notes and References.- 9 Noninteraeting Control I: Basic Principles.- 9.1 Decoupling: Systems Formulation.- 9.2 Restricted Decoupling Problem (RDP).- 9.3 Solution of RDP: Outputs Complete.- 9.4 Extended Decoupling Problem (EDP).- 9.5 Solution of EDP.- 9.6 Naive Extension.- 9.7 Example.- 9.8 Partial Decoupling.- 9.9 Exercises.- 9.10 Notes and References.- 10 Noninteraeting Control II: Efficient Compensation.- 10.1 The Radical.- 10.2 Efficient Extension.- 10.3 Efficient Decoupling.- 10.4 Minimal Order Compensation: d(?) = 2.- 10.5 Minimal Order Compensation: d(?) = k.- 10.6 Exercises.- 10.7 Notes and References.- 11 Noninteraeting Control III: Generic Solvability.- 11.1 Generic Solvability of EDP.- 11.2 State Space Extension Bounds.- 11.3 Significance of Generic Solvability.- 11.4 Exercises.- 11.5 Notes and References.- 12 Quadratic Optimization I: Existence and Uniqueness.- 12.1 Quadratic Optimization.- 12.2 Dynamic Programming: Heuristics.- 12.3 Dynamic Programming: Formal Treatment.- 12.4 Matrix Quadratic Equation.- 12.5 Exercises.- 12.6 Notes and References.- 13 Quadratic Optimization II: Dynamic Response.- 13.1 Dynamic Response: Generalities.- 13.2 Example 1 : First-Order System.- 13.3 Example 2: Second-Order System.- 13.4 Hamiltoman Matrix.- 13.5 Asymptotic Root Locus: Single Input System.- 13.6 Asymptotic Root Locus: Multivariable System.- 13.7 Upper and Lower Bounds on P0.- 13.8 Stability Margin. Gain Margin.- 13.9 Return Difference Relations.- 13.10 Applicability of Quadratic Optimization.- 13.11 Exercises.- 13.12 Notes and References.- References.- Relational and Operational Symbols.- Letter Symbols.- Synthesis Problems.

2,571 citations