Research

A comparative study of qualitative and quantitative dynamic models of biological regulatory networks

¹ Department of Physics, The Pennsylvania State University, University Park, PA, USA
² Department of Biology, The Pennsylvania State University, University Park, PA, USA
³ Present address: Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute and Harvard T. H. Chan School of Public Health, Boston, MA, USA

^* e-mail: rza1@psu.edu

Received: 22 January 2016
Accepted: 2 May 2016
Published online: 4 June 2016

Abstract

Background

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.

Methods

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.

Results

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.

Conclusions

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.