Before revision:  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 .
After revision:  Using this technique, we approximate the input-output responses of biomolecular signaling systems. We approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearization. Further, we develop analytical upper bounds for the computational error estimates. Finally, we use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can provide more insight into the local behaviour of these systems, compute responses to other periodic inputs, and to analyze limit cycles .