Sensitivity Analysis of Oscillatory Circuits

The period of oscillation in natural and designed biomolecular oscillator networks can depend on underlying reaction rate parameters. Although there has been work in investigating the sensitivity of period to parameters, understanding this dependence for other oscillators and relations between these parametric sensitivities is generally unclear. Here, we address these issues by applying tools of sensitivity analysis on models of oscillating networks. We compute the period sensitivities in standard electrical circuit models and find that an increase in one sensitivity can be accompanied by a decrease in another sensitivity. Next, we compute sensitivities for a biomolecular circuit design and notice similar trends. In particular, we find that the constraints are also apparent in how the state sensitivities vary for different parts of the oscillation cycle. This analysis presents foundational work towards understanding parametric dependence of oscillation period with applications to biomolecular circuit design.