2005 , Volume 10, № 4, p.3-20

Computational biology is among the most popular research areas. There is the problem of evaluating time-series expression data. In cite{GLPWW0}, we mathematically modelled gene-expression patterns. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, getting the right-hand side with its parametric matrices by a discrete approximation, i.e., least squares optimization. In cite{GPSWW} and cite{GLPWW}, a qualitative observation and anticipation of gene expression patterns is presented. There, an algorithmical and combinatorial stability investigation of the time-discretized ordinary differential equations is worked out, referring to expression-metabolic parameters.
The present work briefly surveys the mathematical modelling and improves it. This is done by incorporating aspects of (in)stability at the stage of the time-discretized system, especially, by taking into account the mixed continuous-discrete nature of state transitions. Here, we approach to transitions (jumps) in the gene expression levels and to discontinuities of the system's right hand side by confidence interval statistics and gene networks. The algorithmical aspect is also taken into consideration.