Nonlinear protein degradation and the function of genetic circuits

Abstract

The functions of most genetic circuits require a sufficient degree of cooperativity in the circuit components. Although 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 work, 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. We discuss molecular mechanisms of cooperative stability and their occurrence in natural or engineered systems. Our results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits.amplification ͉ dimerization ͉ bistability ͉ oscillation I t is widely recognized that controlled proteolysis, where the degradation of one protein depends on the presence of another protein in the cell, can play an important regulatory role in genetic circuits (1). Here, we examine another effect of proteolysis that does not involve such regulatory control, but can nevertheless impact the function of genetic circuits in important ways. It is a kinetic, cooperative effect predicated on the following two essential ingredients: (i) the fact that many proteins perform their physiological functions as dimers or higher-order oligomers, and (ii) the tendency for the oligomers to be more stable (to proteolysis) than their monomeric components. This effect, referred to below as ''cooperative stability,'' has been discussed previously in qualitative terms in the context of many well-studied examples in prokaryotes and eukaryotes (1, 2). For example, in the SOS response of Escherichia coli, UmuC degradation is rescued by oligomerization with UmuDЈ 2 (3). Additionally, in Saccharomyces cerevisiae, the dimerization of a1 and ␣2 reduced the degradation rate by as much as 15-fold (4). Possible molecular mechanisms that give rise to cooperative stability include enhanced thermal stability of proteins upon mutual association [because thermal instability correlates with the rate of degradation (5, 6)] and the burial of proteolytic recogni...

Structural instability in an autophosphorylating kinase switch

“…which is of course consistent with our simple asymptotics and again can be compared with Figure 4(a) of (Buchler et al, 2005). As before, the lower curve is of saddle-node bifurcations and the upper one is of transcritical ones.…”

“…We will see that, as also pointed out in (Buchler et al, 2005) the ratio d * /d has an important influence on bistability.…”

“…There, the authors also suggest a mechanism for enlarging the region of parameter space where bistability persists on addition of protein turnover; in the present paper we show analytically that indeed this mechanism (cooperative stability) have the function suggested for it in (Buchler et al, 2005). We also comment on the lack of cooperative stability in ATM.…”

“…Another paper that deals with this structural instability phenomenon is (Buchler et al, 2005). There, the authors also suggest a mechanism for enlarging the region of parameter space where bistability persists on addition of protein turnover; in the present paper we show analytically that indeed this mechanism (cooperative stability) have the function suggested for it in (Buchler et al, 2005).…”

“…In other words, there is a wedge in the (d, α)-plane where bistability occurs. Compare this with Figure 4(a) of (Buchler et al, 2005). Also note that one of the main points of that paper is reflected in (13).…”