Is there anything left to say on enzyme kinetic constants and quasi-steady state approximation?

Bersani, Alberto Maria; Dell’Acqua, Guido

doi:10.1007/s10910-010-9770-7

Cited by 33 publications

(43 citation statements)

References 33 publications

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“…when the condition e 0 s 0 holds. Let us also remind that under the validity of QSSA the complex concentration c = [ES] is expressed in terms of the MM-substrate concentration via equation (3).…”

Section: Michaelis-menten Equationmentioning

confidence: 99%

“…Equation (4) produces a good approximation s m for s under certain conditions (sometimes called validity criteria) [3], [5], [11], [12], [18], [28], [24], [25]. Thus, the condition e 0 s 0 assures good approximation and is ubiquitous for many fermentation and biotechnological processes, but may not be present, as in living cells [1], [26].…”

Section: Michaelis-menten Equationmentioning

confidence: 99%

“…The HMM reaction scheme induces (via the mass action law) a system of ordinary differential equations (denoted HMM-system) while the approximate MM-model is derived from the HMM-system using well known assumptions ( [3], [4], [5], [6], [16], [18], [21], [22], [28]). The criteria for the validity of the MM-model is briefly commented on.…”

Section: Introductionmentioning

confidence: 99%

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A modeling approach for cell growth based on enzyme kinetics

Dimitrov¹

2017

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The enzyme kinetics reaction scheme of single enzyme-substrate dynamics, originally proposed by V. Henri, is considered. The system of ODEs induced by the reaction scheme is compared to two approximate models, namely the MichaelisMenten model and the model of exponential decay. Validity conditions for the Michaelis-Menten model are briefly reviewed. A case specific for "superefficient enzymes" is used as a setting for a comparison between the three models via computational experiments. The case study proves the importance of validating the applicability of the approximate model.A novel cell growth model is proposed and analyzed. The approach of model development is to make use of the original Henri enzyme kinetics law in the context of metabolic processes in living cells, namely cell growth. Two approximations corresponding to different cell growth phases are introduced in order to study the model analytically.The presented work is a University of Sofia student Master Thesis.Citation: Stanko Dimitrov, A modeling approach for cell growth based on enzyme kinetics, http://dx

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Section: Michaelis-menten Equationmentioning

confidence: 99%

Section: Michaelis-menten Equationmentioning

confidence: 99%

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A modeling approach for cell growth based on enzyme kinetics

Dimitrov¹

2017

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“…From (25) we have f + c = k c c. Assuming that the monomer m is abundant in a time interval ∆ we can apply the QSSA principle and assume that c is approximately equal to 0 in ∆, and accordingly, in ∆ we have approximately f = k c c [1], [4], [5], [13], [32], [35], [36], [37]. Hence, for some t * ∈ ∆ we have f (t * ) = k c c (t * ) = 0, hence function f has inflection and has a sigmoidal form.…”

Section: Denoting the Concentrationsmentioning

confidence: 99%

Building reaction kinetic models for amiloid fibril growth

Markov

2016

BIOMATH

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Abstract-In this work we discuss some methodological aspects of the creation and formulation of mathematical models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We propose several reaction network models for the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using the computer algebra system Mathematica.

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“…We have been able to study the dynamics and stability of the model system using the free software Octave. The roles of new constants and parameters are being explored (Bersani & Dell'Acqua, 2012).…”

mentioning

confidence: 99%