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a software tool to model genetic regulatory networks. applications to the modeling of threshold phenomena and of spatial patterning in drosophila一个软件工具,基因调控网络模型。
A Software Tool to Model Genetic Regulatory Networks.
Applications to the Modeling of Threshold Phenomena
and of Spatial Patterning in Drosophila
˜
Rui Dilao*, Daniele Muraro
´
Nonlinear Dynamics Group, Instituto Superior Tecnico, Lisbon, Portugal
Abstract
We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is
based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically
by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the
transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of
a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software.
Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic
properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in
Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the
gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the
zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of
Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap
genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators.
˜
Citation: Dilao R, Muraro D (2010) A Software Tool to Model Genetic Regulat
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