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In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.
To counteract the antagonistic relationship between milk yield and fertility in dairy cow, a
deeper understanding of the underlying biological mechanisms is required. For this purpose,
we study physiological networks related to reproduction and metabolism in dairy cows. We
interactively develop dynamic, mechanistic models by fitting the models to experimental data
and mechanistic knowledge. We have already developed models for potassium balance and
hormonal regulation of fertility in the dairy cow, which will briefly be reviewed here. The main
focus of this article is a glucose-insulin model currently developed by us. This model links the
bovine hormonal cycle and the potassium balance to glucose and thus to energy metabolism.
The models can be applied in scientific research, education, experimental planning, drug
development and production on farms.