Analysis of lactose metabolism in E.coli using reachability analysis of hybrid systems

Abstract

We propose an abstraction method for medium-scale biomolecular networks, based on hybrid dynamical systems with continuous multi-affine dynamics. This abstraction method follows naturally from the notion of approximating nonlinear rate laws with continuous piecewise linear functions and can be easily automated. An efficient reachability algorithm is possible for the resulting class of hybrid systems. An efficient reachability algorithm is possible for the resulting class of hybrid systems. An approximation for an ordinary differential equation model of the lac operon is constructed, and it is shown that the abstraction passes the same experimental tests as were used to validate the original model. The well studied biological system exhibits bistability and switching behaviour, arising from positive feedback in the expression mechanism of the lac operon. The switching property of the lac system is an example of the major qualitative features that are the building blocks of higher level, more coarse-grained descriptions. The present approach is useful in helping to correctly identify such properties and in connecting them to the underlying molecular dynamical details. Reachability analysis together with the knowledge of the steady-state structure are used to identify ranges of parameter values for which the system maintains the bistable switching property.