A Formal Approach for Tuning Stochastic Oscillators

TL;DR

This paper introduces a framework combining Approximate Bayesian Computation and hybrid automata to analyze and tune stochastic oscillators, effectively identifying parameter regions that produce desired oscillation periods.

Contribution

It presents a novel method for assessing and tuning stochastic oscillator parameters using hybrid automata and ABC, addressing a gap in existing automata-based analysis approaches.

Findings

Successfully applied to biological models like the Repressilator

Identifies parameter regions likely to produce specific oscillation periods

Provides a quantitative measure of how close an oscillator is to desired behavior

Abstract

Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they are little appropriate in the case of systems in which stochastic noise induced by small population numbers is actually responsible for periodicity. Within the stochastic modelling settings automata-based model checking approaches have proven an effective means for the analysis of oscillatory dynamics, the main idea being that of coupling a period detector automaton with a continuous-time Markov chain model of an alleged oscillator. In this paper we address a complementary aspect, i.e. that of assessing the dependency of oscillation related measure (period and amplitude) against the parameters of a stochastic oscillator. To this aim we introduce a framework which, by combining an Approximate Bayesian Computation scheme with a hybrid automata capable of quantifying how distant an instance of a stochastic oscillator is from matching a desired (average) period, leads us to identify regions of the parameter space in which oscillation with given period are highly likely. The method is demonstrated through a couple of case studies, including a model of the popular Repressilator circuit.