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Peletier LA, Gabrielsson J. Impact of enzyme turnover on the dynamics of the Michaelis–Menten model. Math Biosci 2022; 346:108795. [DOI: 10.1016/j.mbs.2022.108795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Revised: 02/14/2022] [Accepted: 02/17/2022] [Indexed: 11/29/2022]
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2
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Eilertsen J, Schnell S. On the Validity of the Stochastic Quasi-Steady-State Approximation in Open Enzyme Catalyzed Reactions: Timescale Separation or Singular Perturbation? Bull Math Biol 2021; 84:7. [PMID: 34825985 PMCID: PMC8768927 DOI: 10.1007/s11538-021-00966-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 10/26/2021] [Indexed: 10/19/2022]
Abstract
The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from singular perturbation theory. For several closed enzymatic reactions, the homologous extension of the quasi-steady-state approximation to the stochastic regime, known as the stochastic quasi-steady-state approximation, has been shown to be accurate under the analogous conditions that permit the quasi-steady-state reduction in the deterministic counterpart. However, it was recently demonstrated that the extension of the stochastic quasi-steady-state approximation to an open Michaelis-Menten reaction mechanism is only valid under a condition that is far more restrictive than the qualifier that ensures the validity of its corresponding deterministic quasi-steady-state approximation. In this paper, we suggest a possible explanation for this discrepancy from the lens of geometric singular perturbation theory. In so doing, we illustrate a misconception in the application of the quasi-steady-state approximation: timescale separation does not imply singular perturbation.
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Affiliation(s)
- Justin Eilertsen
- Department of Molecular & Integrative Physiology, University of Michigan Medical School, Ann Arbor, MI, 48109, USA
- Mathematical Reviews, American Mathematical Society, 416 4th Street, Ann Arbor, MI, 48103, USA
| | - Santiago Schnell
- Department of Molecular & Integrative Physiology, University of Michigan Medical School, Ann Arbor, MI, 48109, USA.
- Department of Computational Medicine & Bioinformatics, University of Michigan Medical School, Ann Arbor, MI, 48109, USA.
- Department of Biological Sciences, and Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA.
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3
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Padoan A, Forni F, Sepulchre R. Balanced truncation for model reduction of biological oscillators. BIOLOGICAL CYBERNETICS 2021; 115:383-395. [PMID: 34382116 PMCID: PMC8382660 DOI: 10.1007/s00422-021-00888-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 07/14/2021] [Indexed: 06/13/2023]
Abstract
Model reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.
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Affiliation(s)
- Alberto Padoan
- Department of Engineering, University of Cambridge, Cambridge, UK
| | - Fulvio Forni
- Department of Engineering, University of Cambridge, Cambridge, UK
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4
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Eilertsen J, Roussel MR, Schnell S, Walcher S. On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism. AIMS MATHEMATICS 2021; 6:6781-6814. [PMID: 34142000 PMCID: PMC8208640 DOI: 10.3934/math.2021398] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis-Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.
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Affiliation(s)
- Justin Eilertsen
- Department of Molecular & Integrative Physiology, University of Michigan Medical School, Ann Arbor, Michigan 49109, USA
| | - Marc R. Roussel
- Alberta RNA Research and Training Institute, Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Alberta, Canada, T1K 3M4
| | - Santiago Schnell
- Department of Molecular & Integrative Physiology, University of Michigan Medical School, Ann Arbor, Michigan 49109, USA
- Department of Computational Medicine & Bioinformatics, University of Michigan Medical School, Ann Arbor, Michigan 49109, USA
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5
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Abstract
The ability of bacterial cells to adjust their gene expression program in response to environmental perturbation is often critical for their survival. Recent experimental advances allowing us to quantitatively record gene expression dynamics in single cells and in populations coupled with mathematical modeling enable mechanistic understanding on how these responses are shaped by the underlying regulatory networks. Here, we review how the combination of local and global factors affect dynamical responses of gene regulatory networks. Our goal is to discuss the general principles that allow extrapolation from a few model bacteria to less understood microbes. We emphasize that, in addition to well-studied effects of network architecture, network dynamics are shaped by global pleiotropic effects and cell physiology.
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Affiliation(s)
- David L Shis
- Department of Biosciences, Rice University, Houston, Texas 77005, USA;
| | - Matthew R Bennett
- Department of Biosciences, Rice University, Houston, Texas 77005, USA; .,Department of Bioengineering, Rice University, Houston, Texas 77005, USA
| | - Oleg A Igoshin
- Department of Biosciences, Rice University, Houston, Texas 77005, USA; .,Department of Bioengineering, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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6
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Martins AR. Representação do efeito de inibição enzimática reversível para o modelo cinético de Michaelis-Menten no estado transiente. BRAZILIAN JOURNAL OF FOOD TECHNOLOGY 2015. [DOI: 10.1590/1981-6723.5714] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
ResumoOs processos enzimáticos que seguem o modelo cinético de Michaelis-Menten foram estudados a partir de diferentes propostas para descrever a etapa de inibição reversível. As propostas de inibição foram comparadas a partir de um processo genérico, onde as constantes cinéticas receberam valores unitários e o valor numérico da concentração de substrato foi dez (10) vezes superior ao valor numérico da concentração de enzima. Para cada proposta de modelo de inibição foram obtidas soluções numéricas a partir de sistema não linear de equações diferenciais ordinárias, gerando gráficos que apresentaram, separadamente, a variação das concentrações da enzima, dos complexos enzimáticos, do substrato e do produto da reação. Foi obtido um modelo, dentre as propostas avaliadas, com desempenho indicando comportamento similar ao verificado no modelo clássico de Michaelis-Menten, onde o complexo de reação é rapidamente formado e, ao longo do processo, decai até tender a zero. Em contrapartida, diferentemente do modelo clássico, na nova proposta de modelo o efeito de inibição começa em zero e, ao longo do processo, tende ao valor nominal da concentração inicial da enzima. Tais respostas mostraram-se válidas para valores distintos de concentração de enzima e de tempo de processo, mostrando robustez e indicando uma tendência do somatório do substrato e do produto atingir o valor nominal da concentração inicial do substrato ao longo do tempo de processamento.
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Affiliation(s)
- André Rosa Martins
- Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul, Brazil
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7
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Armbruster D, Nagy J, Young J. Three level signal transduction cascades lead to reliably timed switches. J Theor Biol 2014; 361:69-80. [PMID: 25036439 DOI: 10.1016/j.jtbi.2014.07.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2014] [Revised: 07/07/2014] [Accepted: 07/08/2014] [Indexed: 11/19/2022]
Abstract
Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades.
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Affiliation(s)
| | - John Nagy
- Arizona State University, United States; Scottsdale Community College, United States
| | - Jon Young
- Arizona State University, United States.
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8
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Hochendoner P, Ogle C, Mather WH. A queueing approach to multi-site enzyme kinetics. Interface Focus 2014; 4:20130077. [PMID: 24904740 DOI: 10.1098/rsfs.2013.0077] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Multi-site enzymes, defined as where multiple substrate molecules can bind simultaneously to the same enzyme molecule, play a key role in a number of biological networks, with the Escherichia coli protease ClpXP a well-studied example. These enzymes can form a low latency 'waiting line' of substrate to the enzyme's catalytic core, such that the enzyme molecule can continue to collect substrate even when the catalytic core is occupied. To understand multi-site enzyme kinetics, we study a discrete stochastic model that includes a single catalytic core fed by a fixed number of substrate binding sites. A natural queueing systems analogy is found to provide substantial insight into the dynamics of the model. From this, we derive exact results for the probability distribution of the enzyme configuration and for the distribution of substrate departure times in the case of identical but distinguishable classes of substrate molecules. Comments are also provided for the case when different classes of substrate molecules are not processed identically.
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Affiliation(s)
- Philip Hochendoner
- Department of Physics , Virginia Polytechnic Institute and State University , Blacksburg, VA 24061 , USA
| | - Curtis Ogle
- Department of Physics , Virginia Polytechnic Institute and State University , Blacksburg, VA 24061 , USA
| | - William H Mather
- Department of Physics , Virginia Polytechnic Institute and State University , Blacksburg, VA 24061 , USA ; Department of Biology , Virginia Polytechnic Institute and State University , Blacksburg, VA 24061 , USA
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9
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Oscillatory enzyme reactions and Michaelis-Menten kinetics. FEBS Lett 2013; 587:2778-84. [PMID: 23892075 DOI: 10.1016/j.febslet.2013.07.031] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2013] [Revised: 07/09/2013] [Accepted: 07/16/2013] [Indexed: 11/24/2022]
Abstract
Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis-Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis-Menten phosphorylation-dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase.
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10
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Thomas P, Straube AV, Grima R. Communication: limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks. J Chem Phys 2012; 135:181103. [PMID: 22088045 DOI: 10.1063/1.3661156] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.
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Affiliation(s)
- Philipp Thomas
- Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489 Berlin, Germany
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11
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O'Brien EL, Itallie EV, Bennett MR. Modeling synthetic gene oscillators. Math Biosci 2012; 236:1-15. [PMID: 22266166 DOI: 10.1016/j.mbs.2012.01.001] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2011] [Revised: 01/05/2012] [Accepted: 01/06/2012] [Indexed: 11/19/2022]
Abstract
Genetic oscillators have long held the fascination of experimental and theoretical synthetic biologists alike. From an experimental standpoint, the creation of synthetic gene oscillators represents a yardstick by which our ability to engineer synthetic gene circuits can be measured. For theorists, synthetic gene oscillators are a playground in which to test mathematical models for the dynamics of gene regulation. Historically, mathematical models of synthetic gene circuits have varied greatly. Often, the differences are determined by the level of biological detail included within each model, or which approximation scheme is used. In this review, we examine, in detail, how mathematical models of synthetic gene oscillators are derived and the biological processes that affect the dynamics of gene regulation.
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Affiliation(s)
- Erin L O'Brien
- Department of Biochemistry & Cell Biology, Rice Univeristy, 6100 Main St., Houston, TX, USA
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12
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Gonze D, Abou-Jaoudé W, Ouattara DA, Halloy J. How molecular should your molecular model be? On the level of molecular detail required to simulate biological networks in systems and synthetic biology. Methods Enzymol 2011; 487:171-215. [PMID: 21187226 DOI: 10.1016/b978-0-12-381270-4.00007-x] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The recent advance of genetic studies and the rapid accumulation of molecular data, together with the increasing performance of computers, led researchers to design more and more detailed mathematical models of biological systems. Many modeling approaches rely on ordinary differential equations (ODE) which are based on standard enzyme kinetics. Michaelis-Menten and Hill functions are indeed commonly used in dynamical models in systems and synthetic biology because they provide the necessary nonlinearity to make the dynamics nontrivial (i.e., limit-cycle oscillations or multistability). For most of the systems modeled, the actual molecular mechanism is unknown, and the enzyme equations should be regarded as phenomenological. In this chapter, we discuss the validity and accuracy of these approximations. In particular, we focus on the validity of the Michaelis-Menten function for open systems and on the use of Hill kinetics to describe transcription rates of regulated genes. Our discussion is illustrated by numerical simulations of prototype systems, including the Repressilator (a genetic oscillator) and the Toggle Switch model (a bistable system). We systematically compare the results obtained with the compact version (based on Michaelis-Menten and Hill functions) with its corresponding developed versions (based on "elementary" reaction steps and mass action laws). We also discuss the use of compact approaches to perform stochastic simulations (Gillespie algorithm). On the basis of these results, we argue that using compact models is suitable to model qualitatively biological systems.
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Affiliation(s)
- Didier Gonze
- Laboratoire de Bioinformatique des Génomes et des Réseaux, Université Libre de Bruxelles, Bruxelles, Belgium
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13
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Gianinetti A. A theoretical framework for β-glucan degradation during barley malting. Theory Biosci 2009; 128:97-108. [DOI: 10.1007/s12064-008-0055-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2008] [Accepted: 12/12/2008] [Indexed: 12/01/2022]
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14
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Abstract
We present an approximation scheme for deriving reaction rate equations of genetic regulatory networks. This scheme predicts the timescales of transient dynamics of such networks more accurately than does standard quasi-steady state analysis by introducing prefactors to the ODEs that govern the dynamics of the protein concentrations. These prefactors render the ODE systems slower than their quasi-steady state approximation counterparts. We introduce the method by examining a positive feedback gene regulatory network, and show how the transient dynamics of this network are more accurately modeled when the prefactor is included. Next, we examine the repressilator, a genetic oscillator, and show that the period, amplitude, and bifurcation diagram defining the onset of the oscillations are better estimated by the prefactor method. Finally, we examine the consequences of the method to the dynamics of reduced models of the phage lambda switch, and show that the switching times between the two states is slowed by the presence of the prefactor that arises from protein multimerization and DNA binding.
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Affiliation(s)
- Matthew R Bennett
- Institute for Nonlinear Science, University of California at San Diego, La Jolla, California, USA
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15
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Abstract
The transient kinetic behaviour of an open single enzyme, single substrate reaction is examined. The reaction follows the Van Slyke-Cullen mechanism, a spacial case of the Michaelis-Menten reaction. The analysis is performed both with and without applying the quasi-steady-state approximation. The analysis of the full system shows conditions for biochemical pathway coupling, which yield sustained oscillatory behaviour in the enzyme reaction. The reduced model does not demonstrate this behaviour. The results have important implications in the analysis of open biochemical reactions and the modelling of metabolic systems.
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Affiliation(s)
- E H Flach
- Indiana University School of Informatics and Biocomplexity Institute, 1900 East Tenth Street, Bloomington, IN 47406, USA
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16
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Liu J. Dissipation and maintenance of stable states in an enzymatic system: analysis and simulation. Biophys Chem 2005; 120:207-14. [PMID: 16378675 DOI: 10.1016/j.bpc.2005.11.011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2005] [Revised: 11/29/2005] [Accepted: 11/29/2005] [Indexed: 10/25/2022]
Abstract
The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. An essential assumption for constraint-based analysis is the formation of a stable steady state. This work investigates dissipation and maintenance of stable states in a simple reversible enzymatic reaction with substrate inhibition. Under mass-action kinetics, the conditions under which the reaction maintains a stable steady state are analytically derived and numerically confirmed. It is shown that, in order to maintain a steady state in the regulated reaction, maximal enzyme activity must be much higher than input rate. Moreover, it is revealed that requirements for large enzyme activity are due to substrate inhibition. It is suggested that high activities of enzymes may play a vital role in protecting a stable state from its catastrophic collapse, giving an additional explanation to an intriguing problem--why the activities of some enzymes greatly exceed the flux capacity of a pathway. In addition, dissipation of the enzymatic reaction is analysed. It is shown that the collapse of stable states is always associated with a point at which dissipation is the highest. Therefore, in order to maintain a stable state, dissipation of the reaction must be less than a critical value. Moreover, although external forcing may not change net mass flow, it may lead to collapse of stable states. Furthermore, when stable states collapse at a critical forcing amplitude and period, dissipation also reaches a highest value. It is concluded that collapse of stable steady state in the enzyme system with substrate inhibition always corresponds to critical points at which dissipation is highest, regardless if the reaction is forced or not. Therefore, for the substrate inhibited reaction, maintenance of stable states is intrinsically related to level of dissipation.
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Affiliation(s)
- Junli Liu
- Computational Biology Programme, Scottish Crop Research Institute, Dundee, DD2 5DA, UK.
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17
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Liu J, Crawford JW, Leontiou KI. Collapse of single stable states via a fractal attraction basin: analysis of a representative metabolic network. Proc Math Phys Eng Sci 2005. [DOI: 10.1098/rspa.2004.1436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The impact of external forcing on an enzymatic reaction system with a single finite stable state is investigated. External forcing impacts on the system in two distinct ways: firstly, the reaction system undergoes a series of discontinuous changes in dynamical state. Secondly, a critical level of forcing exists, beyond which all finite states become unstable. It is shown that the results stem from the conditions for global stability of the system. Competition between the attractor for stable states and the unbounded states leads to a loss of integrity and the fractal fragmentation of the attraction basin for the finite state. The consequences of a fractal basin in this context are profound. Initial states which are infinitesimally close diverge to a finite and an unbounded state where only the finite state is consistent with biological functionality. Furthermore, above a critical forcing amplitude, the system does not converge to a finite state from any initial state, implying that there is no configuration of metabolite concentrations that is consistent with sustained evolution of the system. These results point to opportunities for constraining uncertainty in cell networks where nonlinear saturating kinetics form an important component.
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Affiliation(s)
- Junli Liu
- Computational Biology Programme, Scottish Crop Research InstituteDundee DD2 5DA, UK
| | - John W Crawford
- School of Computing and Advanced Technologies, University of Abertay DundeeDundee DD1 1HG, UK
| | - Konstantinos I Leontiou
- School of Computing and Advanced Technologies, University of Abertay DundeeDundee DD1 1HG, UK
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18
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Abstract
The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. This work introduces the concept of kinetic constraints. It is shown that maximal reaction rates are appropriate constraints only for isolated enzymatic reactions. For biochemical networks, it is revealed that constraints for formation of a steady state require specific relationships between maximal reaction rates of all enzymes. The constraints for a branched network are significantly different from those for a cyclic network. Moreover, the constraints do not require Michaelis-Menten constants for most enzymes, and they only require the constants for the enzymes at the branching or cyclic point. Reversibility of reactions at system boundary or branching point may significantly impact on kinetic constraints. When enzymes are regulated, regulations may impose severe kinetic constraints for the formation of steady states. As the complexity of a network increases, kinetic constraints become more severe. In addition, it is demonstrated that kinetic constraints for networks with co-regulation can be analyzed using the approach. In general, co-regulation enhances the constraints and therefore larger fluctuations in fluxes can be accommodated in the networks with co-regulation. As a first example of the application, we derive the kinetic constraints for an actual network that describes sucrose accumulation in the sugar cane culm, and confirm their validity using numerical simulations.
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Affiliation(s)
- Junli Liu
- Computational Biology Programme, Scottish Crop Research Institute, Dundee, United Kingdom.
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19
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Stoleriu I, Davidson FA, Liu JL. Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions. J Math Biol 2004; 50:115-32. [PMID: 15322823 DOI: 10.1007/s00285-004-0282-6] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2003] [Revised: 04/26/2004] [Indexed: 11/28/2022]
Abstract
In this paper we investigate the validity of a quasi-steady state assumption in approximating Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions that are subject to periodic substrate input.
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Affiliation(s)
- I Stoleriu
- Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK
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