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Team:ZJU-China/Modeling/Biobrick
From 2011.igem.org
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Modeling|biobrick |
This model is used for simulating the behavior of three genetic circuits we designed
Overview
Modeling
Results
Introduction
abstract:
We will model our gene regulatory networks using Michaelis-Menten enzymatic kinetics,together with the usual rules of reaction kinetics. The resulting models, when spatial
effects are neglected, are given in terms of ordinary differential equations describing the
rate of change of the concentrations of gene products and proteins. A key component of all
these models is the Hill function, used to describe the transcription phase. The presence of
this highly nonlinear function, whilst accurately modeling the network, inevitably leads to
restrictions on the analytical tools available to understand and predict the
dynamics.
Basic concepts and assumptions
The ODE formalism models the concentrations of RNAs, proteins, and other molecules by time-dependent variables with values contained in the set of nonnegative real numbers. Regulatory interactions take the form of functional and differential relations between the concentration variables. For a typical transcription-translation process, the ODEs modeling approach associates two ODEs with any given gene i; one modeling the rate of change of the concentration of the transcribed mRNA r_i, and the other describing the rate of change of the concentration of its corresponding translated protein p_i. Thus for our network with 3 genes we have:
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