Use and abuse of the quasi-steady-state approximation

Flach, E. H.; Schnell, Santiago

doi:10.1049/ip-syb:20050104

Cited by 76 publications

(55 citation statements)

References 24 publications

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“…We want to illustrate by a simple example that this procedure is problematic and may have to be replaced by more careful reasoning. (Such observations have been made earlier; see Flach and Schnell [6].) The following reaction system describes a situation where the enzyme is formed by degradation of another substance (a proenzyme) and itself is subject to degradation.…”

Section: Reduction and Michaelis-menten Termsmentioning

confidence: 66%

Quasi-Steady State and Nearly Invariant Sets

Noethen¹,

Walcher

2009

SIAM J. Appl. Math.

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We propose the notion of nearly invariant set for an ordinary differential equation to give a clear mathematical meaning to the notion of quasi-steady state (QSS) in equations describing chemically reacting systems. We show that this approach is sensible in view of the intended applications. Moreover, the approach leads to a heuristic for finding "small parameters" to satisfy a QSS assumption. The results are illustrated by several examples.

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Section: Reduction and Michaelis-menten Termsmentioning

confidence: 66%

Quasi-Steady State and Nearly Invariant Sets

Noethen¹,

Walcher

2009

SIAM J. Appl. Math.

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“…Nevertheless, the fact that differences can be identified illustrates an advantage of automating the design procedure. It is also possible that automation could obfuscate poorly justified assumptions, such as in the application of the QSSAs [34]; so it would be important to incorporate rigorous checks for their validity.…”

Section: Resultsmentioning

confidence: 99%

Towards the rational design of synthetic cells with prescribed population dynamics

Dalchau

Smith

Martín

et al. 2012

J. R. Soc. Interface.

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The rational design of synthetic cell populations with prescribed behaviours is a long-standing goal of synthetic biology, with the potential to greatly accelerate the development of biotechnological applications in areas ranging from medical research to energy production. Achieving this goal requires well-characterized components, modular implementation strategies, simulation across temporal and spatial scales and automatic compilation of high-level designs to low-level genetic parts that function reliably inside cells. Many of these steps are incomplete or only partially understood, and methods for integrating them within a common design framework have yet to be developed. Here, we address these challenges by developing a prototype framework for designing synthetic cells with prescribed population dynamics. We extend the genetic engineering of cells (GEC) language, originally developed for programming intracellular dynamics, with cell population factors such as cell growth, division and dormancy, together with spatio-temporal simulation methods. As a case study, we use our framework to design synthetic cells with predator–prey interactions that, when simulated, produce complex spatio-temporal behaviours such as travelling waves and spatio-temporal chaos. An analysis of our design reveals that environmental factors such as density-dependent dormancy and reduced extracellular space destabilize the population dynamics and increase the range of genetic variants for which complex spatio-temporal behaviours are possible. Our findings highlight the importance of considering such factors during the design process. We then use our analysis of population dynamics to inform the selection of genetic parts, which could be used to obtain the desired spatio-temporal behaviours. By identifying, integrating and automating key stages of the design process, we provide a computational framework for designing synthetic systems, which could be tested in future laboratory studies.

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“…The simplifications, for example, of quasi-steady state approximations have been used in a qualitative manner. We have stressed on physical significance at every step rather than following mathematical rigour and accuracy (Flach & Schnell, 2006;Pedersen, Bersani, & Bersani, 2008).…”

Section: Simulation Of Mitochondrial Translation 1639mentioning

confidence: 99%

Kinetic modelling of mitochondrial translation

Korla

Mitra

2013

Journal of Biomolecular Structure and Dynamics

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Mitochondrial genome contains 13 protein coding genes, all being part of the oxidative phosphorylation complexes. The process of translation of these protein coding mRNAs in mitochondrial matrix is a good miniature model of translation in cytoplasm. In this work, we have simulated three phases of mitochondrial translation viz. initiation, elongation and termination (including ribosome recycling). The kinetic equations for these phases have been deduced based on the information available in literature. Various factors involved in the process have been included explicitly. Kinetic simulation was done using Octave, open source software. Scripts were written individually for each phase. Initiation begins with mitoribosome, mRNA, fMet-tRNA and initiation factors. The final product of the initiation script, the initiation complex, was introduced as the start point in the successive step, i.e. elongation. Elongation is a particular extensive process where the various aminoacyl-tRNAs already present in the matrix check for matching with the triplet codon in A-site of mitoribosome. This script consists of two parts: one with the time behaviour of the factors involved in the molecular process (using ordinary differential equation solver) and the other including the reading of triplet codon on the mRNA and incorporating the corresponding aminoacyl-tRNA, and then at each step elongating the peptide chain (using loops and conditions). The peptide chain thus formed in the elongation step (in the loops and conditions segment) was released in the termination step. This was followed by mitoribosome recycling where the mitoribosome reached the native state and was ready for the next cycle of translation.

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Use and abuse of the quasi-steady-state approximation

Cited by 76 publications

References 24 publications

Quasi-Steady State and Nearly Invariant Sets

Quasi-Steady State and Nearly Invariant Sets

Towards the rational design of synthetic cells with prescribed population dynamics

Kinetic modelling of mitochondrial translation

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