Sinusoidal-Input Describing Function of a Simple Biomolecular Signaling System

Understanding biomolecular systems is important both for the analysis of naturally occurring systems as well as for the design of new ones. However, mathematical tools for analysis of such complex systems are generally lacking. Here, we present an application of the method of sinusoidal-input describing function for the analysis of such a system. Using this technique, we approximate the input-output response of a simple biomolecular signaling system both computationally and analytically. We systematically investigate the dependence of this approximation on system parameters. Finally, we estimate the error involved in this approximation. These results can help in establishing a framework for analysis of biomolecular systems through the use of simplified models.