# Comparing Boolean and Piecewise Affine Differential Models for Genetic Networks

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## Abstract

Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in *E. coli*. The asymptotic dynamics of both models are shown to be quite similar. This study suggests new tools for analysis and reduction of biological networks.

## Keywords

Boolean models Piecewise affine models Genetic networks Model reduction## Notes

### Acknowledgments

This work was supported in part by the French National Research Agency through the BioSys project MetaGenoReg.

## Supplementary material

## References

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