Effects of Ribosome Autocatalysis and Negative Feedback in Resource Competition

Resource competition, and primarily competition for ribosomes, can lead to unexpected behavior in synthetic genetic circuits as well as affect the growth of host cells. Current models studying the effects of resource competition assume a constant production of ribosomes and these models describe the experimental results well.  However, ribosomes are autocatalytic since they are partially made of protein which must be translated by ribosomes themselves. Autocatalysis has been shown to have detrimental effects on a system’s stability and robustness. Additionally, there are known feedback regulations on ribosome synthesis such as inhibition of rRNA synthesis via ppGpp. We have developed and compared three two-state models of ribosome and protein synthesis to investigate conditions under which these regulatory actions have a significant effect in situations of increased ribosome demand, defined by the mRNA level of synthetic genes. These models incorporate: 1) constant production of ribosomes, 2) autocatalytic production of ribosomes, and 3) autocatalysis and negative feedback, respectively. Our modeling results indicate that for sufficiently low demand, autocatalysis has little or no effect. However, beyond a certain demand level, the system goes through a transcritical bifurcation at which the only non-negative steady state is at zero ribosome concentration.  The presence of negative feedback, in turn, can shift this bifurcation, thus restoring the qualitative behavior observed in a model with a constant ribosome production at low demand. Additionally, autocatalysis affects the dynamics of the system, leading to a potential overshoot in the time response of the synthetic gene to changes in induction level. Our results show that ribosome autocatalysis has a significant effect on the system robustness both in the steady state concentration of ribosomes and the transient responses of the desired synthetic product, however the existing negative feedback on ribosome production compensates for the effects of the necessary autocatalytic loop and restores the behavior seen in the system with constant ribosome production.