Describing function-based approximations of biomolecular signalling systems

Developing tools to understand biomolecular systems is important both for the analysis of naturally occurring systems as well as for the design of new ones. However, there is a need to develop new tools suited for analysis of such systems and to adapt existing tools used in other similar contexts. Here, we apply the method of sinusoidal-input describing function for the analysis of such systems using a combination of analytic and computational means. Using this technique, we approximate the input-output response of simple representative biomolecular signaling systems exhibiting different saturating as well as hysteretic input-output maps. We investigate the dependence of this approximation on system parameters. Finally, we estimate the error involved in these approximations finding that they are always better than standard linearization. These results provide system approximations that can help to compute system response to other periodic inputs as well as analysis and design of cell behaviour such as limit cycles and frequency entrainment.