An emerging research area in computational biology and biotechnology is devoted to modelling and prediction of gene-expression patterns. In this article, after a short review of recent achievements we deepen and extend them, especially, by emphasizing and analysing the elegant means of matrix algebra. Based on experimental data, ordinary differential equations with nonlinearities on the right-hand side and a generalized treatment of the absolute shift term, representing the environmental effects, are investigated. Then, the genetic process is studied by a time-discretization, in particular, Runge-Kutta type discretization. By a utilization of the combinatorial algorithm of Brayton and Tong, which is based on the orbits of polyhedra, the possibility of detecting stability and instability regions has been shown. The time-continuous and -discrete systems can be represented by means of matrices allowing biological implications, such as thresholds, and interpretations; which are motivated by our gene-environment networks. A specific contribution of this article consists of a careful but rigorous integration of the environment into modelling and dynamics, and in further new sights. Relations to the parameter estimation within modelling, especially, by using optimization, are indicated, and future research is addressed.