  As a model for gene and protein interactions we study a set for molecular
catalytic reactions. The model is based on experimentally motivated interaction
network topologies, and is designed to capture some key statistics of gene
expression statistics. We impose a non-linearity to the system by a boundary
condition which guarantees non-negative concentrations of chemical
concentrations and study the system stability quantified by maximum Lyapunov
exponents. We find that the non-negativity constraint leads to a drastic
inflation of those regions in parameter space where the Lyapunov exponent
exactly vanishes. We explain the finding as a self-organized critical
phenomenon. The robustness of this finding with respect to different network
topologies and the role of intrinsic molecular- and external noise is
discussed. We argue that systems with inflated 'edges of chaos' could be much
more easily favored by natural selection than systems where the Lyapunov
exponent vanishes only on a parameter set of measure zero.
