SOME ASPECTS CONCERNING HYBRID AUTOMATA MODELS OF BIOCHEMICAL INTERACTIONS – HYSTEREZIS AND ZENO BEHAVIOUR
Recently, hybrid automata have emerged as a natural modelling abstraction for biochemical interactions. Within discrete states, the local dynamics is usually described by linear differential equations, and generically, the continuous variables are protein concentrations. Transitions between discrete states occur, with possible reset variables, when specific threshold values are reached, thus producing abrupt changes in the right hand side of the differential system. This paper firstly analyses a simple hybrid automaton modelling a repressor mechanism in molecular biology, which presents a hystersis behaviour. Alternate modelling frameworks, limitations of the model and simulation challenges are discussed. Secondly, a second-order piecewise-linear model of a generic biochemical interaction process is abstracted to a Zeno hybrid automaton. A solution for implementation, in MATLAB, of a Zeno path avoidance scheme, based on fixed-step time discretization is proposed and further research directions are emphasized.