  We consider a biochemical model that consists of a system of partial
differential equations based on reaction terms and subject to non--homogeneous
Dirichlet boundary conditions. The model is discretised using the gradient
discretisation method (GDM) which is a framework covering a large class of
conforming and non conforming schemes. Under classical regularity assumptions
on the exact solutions, the GDM enables us to establish the existence of the
model solutions in a weak sense, and strong convergence for the approximate
solution and its approximate gradient. Numerical test employing a finite volume
method is presented to demonstrate the behaviour of the solutions to the model.
