  The functions of most genetic circuits require sufficient degrees of
cooperativity in the circuit components. While mechanisms of cooperativity have
been studied most extensively in the context of transcriptional initiation
control, cooperativity from other processes involved in the operation of the
circuits can also play important roles. In this study, we examine a simple
kinetic source of cooperativity stemming from the nonlinear degradation of
multimeric proteins. Ample experimental evidence suggests that protein subunits
can degrade less rapidly when associated in multimeric complexes, an effect we
refer to as cooperative stability. For dimeric transcription factors, this
effect leads to a concentration-dependence in the degradation rate because
monomers, which are predominant at low concentrations, will be more rapidly
degraded. Thus cooperative stability can effectively widen the accessible range
of protein levels in vivo. Through theoretical analysis of two exemplary
genetic circuits in bacteria, we show that such an increased range is important
for the robust operation of genetic circuits as well as their evolvability. Our
calculations demonstrate that a few-fold difference between the degradation
rate of monomers and dimers can already enhance the function of these circuits
substantially. These results suggest that cooperative stability needs to be
considered explicitly and characterized quantitatively in any systematic
experimental or theoretical study of gene circuits.
