Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Role of Noise in Multistable Dynamics of a non-adiabatic Repressilator
Evgeny Volkov, Ilya Potapov, Boris Zhurov

Last modified: 2014-06-09


Living cells are multi-stable and multi-rhythmic dynamical systems. Coexisting multiple stable dynamic behaviors underlie biological diversity and cell differentiation. However, our knowledge of how cells sustain their diverse dynamic behaviors in the presence of molecular noise is still limited. Here, we use a genetic oscillator, known as Repressilator, with a circular design of negative feedback loops. Previously, in the quasi-steady state approximation of protein multimerization and regulatory reactions on the promoter sites, this oscillator was shown to exhibit sustained oscillations emerging via the supercritical Hopf bifurcation. However, recent experimental evidence suggests that the time scales of these processes are comparable with those of the other model reactions (e.g. protein and mRNA degradations). In the light of this suggestion and with allowance for molecular noise, we have to examine the detailed scheme of the chemical reactions constituting the system, i.e. without use of the quasi-steady state approximation (frequently referred to as a non-adiabatic approximation). Therefore, we consider a system with explicit interactions between the transcription factors and their operator sites, as well as dimerization of the proteins. Parametric analysis reveals the subcritical Hopf bifurcation in a broad interval of control parameters. This bifurcation results in hysteretic properties of the model, that is, two stable dynamic regimes, a stable steady state and a limit cycle, co-exist in the parameter space opening the possibility for noise-induced switching. We study the effect of dimerization on the noise levels in the oscillatory signal of this genetic circuit. We show that degradation of the proteins in the dimer form can lead to a significant reduction in the noise levels as judged by the shape of the return time (period) distribution. Finally, we conclude that in the non-adiabatic Repressilator network, exhibiting multi-stable dynamics, degradation of the dimers can be vital for the stability of both attractors.