  Coexpression of genes or, more generally, similarity in the expression
profiles poses an unsurmountable obstacle to inferring the gene regulatory
network (GRN) based solely on data from DNA microarray time series. Clustering
of genes with similar expression profiles allows for a course-grained view of
the GRN and a probabilistic determination of the connectivity among the
clusters. We present a model for the temporal evolution of a gene cluster
network which takes into account interactions of gene products with genes and,
through a non-constant degradation rate, with other gene products. The number
of model parameters is reduced by using polynomial functions to interpolate
temporal data points. In this manner, the task of parameter estimation is
reduced to a system of linear algebraic equations, thus making the computation
time shorter by orders of magnitude. To eliminate irrelevant networks, we test
each GRN for stability with respect to parameter variations, and impose
restrictions on its behavior near the steady state. We apply our model and
methods to DNA microarray time series' data collected on Escherichia coli
during glucose-lactose diauxie and infer the most probable cluster network for
different phases of the experiment.
