Occupation measure methods for modelling and analysis of biological hybrid automata

TL;DR

This paper introduces a novel methodology using occupation measures and semidefinite relaxations to revise hybrid automaton models in biology, enabling better modeling of time-varying parameters based on optimal control theory.

Contribution

It presents a new hybrid optimal control framework with occupation measures for model revision in biological hybrid automata, demonstrated on a haemoglobin production model.

Findings

Successfully applied to a haemoglobin production model

Enables efficient handling of time-varying parameters

Provides a systematic approach for model revision

Abstract

Mechanistic models in biology often involve numerous parameters about which we do not have direct experimental information. The traditional approach is to fit these parameters using extensive numerical simulations (e.g. by the Monte-Carlo method), and eventually revising the model if the predictions do not correspond to the actual measurements. In this work we propose a methodology for hybrid automaton model revision, when new type of functions are needed to capture time varying parameters. To this end, we formulate a hybrid optimal control problem with intermediate points as successive infinite-dimensional linear programs (LP) on occupation measures. Then, these infinite-dimensional LPs are solved using a hierarchy of semidefinite relaxations. The whole procedure is exposed on a recent model for haemoglobin production in erythrocytes.