Modeling biological systems in hybrid concurrent constraint programming

Constraint programming is a new programming language paradigm that appeared in the late 80’s and became more and more popular during the 90’s [5]. In a constraint program, the user specifies a number of constraints. Each constraint defines a relation between the variables that describe the state of the system under investigation. The constraint programming tool provides constraint solving algorithms which infer new constraints from given ones and which compute solutions, i.e., valuations of the variables satisfying all the constraints. In concurrent constraint programming, different computation processes may run concurrently. Interaction is possible via the constraint store. The store contains all the constraints currently known about the system. A process may tell the store a new constraint, or ask the store whether some constraint is entailed by the information currently available, in which case further action is taken [4]. Hybrid concurrent constraint programming (Hybrid cc) is an extension of concurrent constraint programming which allows one to model and to simulate the temporal evolution of hybrid systems, i.e., systems that exhibit both discrete and continuous state changes [3]. Constraints in Hybrid cc may be both algebraic and differential equations. State changes can be specified using the combinators of concurrent constraint programming and default logic. The following example shows how to model in Hybrid cc an interaction between two genes. x=0; y=0; always { if (y < 0.8) x’ = -0.02*x+0.01; if (y >= 0.8) x’ = -0.02*x; y’ = 0.01*x; } sample(x,y); Gene x activates gene y. Above a certain threshold, gene y inhibits expression of gene x. Executing this simple program yields the following time-dependant behavior: 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 250 300 350 400 time out