Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Ordinary Differential Equation (ODE), Model

  • Rui-Sheng Wang
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_381



An ODE (ordinary differential equation) model is a set of differential equations involving functions of only one independent variable and one or more of their derivatives with respect to that variable. ODEs are the most widespread formalism to model dynamical systems in science and engineering. In systems biology, many biological processes such as gene regulation and signal transduction can be modeled by reaction-rate equations expressing the rate of production of one species (e.g., protein, mRNA, metabolite, or small molecules) as a function of the concentration of other species in the system. ODE models provide a general framework to model such processes as continuous dynamic systems.

Generally, a gene regulatory network can be expressed by a set of first-order nonlinear ordinary differential equations with the expression level of each gene as a variable:
$$ \frac{{d{x_i}}}{{dt}} = {f_i}(x) $$
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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Department of PhysicsPennsylvania State UniversityUniversity ParkUSA