Abstract
Mathematical modeling of biological regulatory networks provides valuable insights into the structural and dynamical properties of the underlying systems. While dynamic models based on differential equations provide quantitative information on the biological systems, qualitative models that rely on the logical interactions among the components provide coarse-grained descriptions useful for systems whose mechanistic underpinnings remain incompletely understood. The middle ground class of piecewise affine differential equation models was proven informative for systems with partial knowledge of kinetic parameters. In this work we provide a comparison of the dynamic characteristics of these three approaches applied on several biological regulatory network motifs. Specifically, we compare the attractors and state transitions in asynchronous Boolean, piecewise affine and Hill-type continuous models. Our study shows that while the fixed points of asynchronous Boolean models are observed in continuous Hill-type and piecewise affine models, these models may exhibit different attractors under certain conditions. Overall, qualitative models are suitable for systems with limited knowledge of quantitative information. On the other hand, when practical, using quantitative models can provide detailed information about additional real-valued attractors not present in the qualitative models.
Highlights
Mathematical modeling of biological regulatory networks provides valuable insights into the structural and dynamical properties of the underlying systems
We provide a comparison of the dynamic characteristics of Hill-type models, hybrid models, and asynchronous Boolean models through several illustrative examples
We considered a simplified sub-network of the T cell large granular lymphocyte leukemia (T-LGL) signaling network obtained from [23]
Summary
Mathematical modeling of biological regulatory networks provides valuable insights into the structural and dynamical properties of the underlying systems. The concentration of components in biological systems changes continuously over time, the input-output sigmoid curves of the regulatory interactions can be well approximated by step functions [9] This approximation leads to hybrid models, wherein the production rates are described by logical functions and the degradation rates are considered to be linear. The dynamics of a regulatory network can be described by a set of differential equations in which the rate of change of the concentration of each node at any time instant is given by a continuous function of the concentration of its regulators This function, which can be linear or non-linear, depends on certain kinetic parameters as well.
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