How time delay and network design shape response patterns in biochemical negative feedback systems

Strong delayed negative feedback

In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit.

Temporal control of the integrated stress response by a stochastic molecular switch

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay

The network of self-sustained oscillators plays an important role in exploring complex phenomena in many areas of science and technology. The aging of an oscillator is referred to as turning non-oscillatory due to some local perturbations that might have adverse effects in macroscopic dynamical activities of a network. In this article, we propose an efficient technique to enhance the dynamical activities for a network of coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed negative self-feedback, which can effectively enhance dynamical robustness in a mean-field coupled network of active and inactive oscillators. Even for a small value of delay, robustness gets enhanced to a significant level. In our proposed scheme, the enhancing effect is more pronounced for strong coupling. To our surprise even if all the oscillators perturbed to equilibrium mode were delayed negative self-feedback is able to restore oscillatory activities in the network for strong coupling strength. We demonstrate that our proposed mechanism is independent of coupling topology. For a globally coupled network, we provide numerical and analytical treatment to verify our claim. To show that our scheme is independent of network topology, we also provide numerical results for the local mean-field coupled complex network. Also, for global coupling to establish the generality of our scheme, we validate our results for both Stuart-Landau limit cycle oscillators and chaotic Rössler oscillators.

Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations

Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models.

Rhythmic behavior is omnipresent in biology and has many crucial functions. In cells the activation levels and abundances of signaling molecules such as NF-κB, p53, EGFR or calcium repeatedly increase and decrease in response to stimuli. Such a dynamic behavior can also be observed monitoring the concentrations of mRNAs and proteins in the circadian clock and the cell cycle. Period and amplitude which are the time span between peaks and the peak height, respectively, as well as their variabilities are important features of oscillations. The circadian period is very stable allowing for proper time keeping, whereas in calcium signaling the period is very variable encoding different stimulation strengths. Our goal is to examine the origin of differences in sensitivities of periods and amplitudes using a computational approach. We use prototype oscillators and demonstrate that they can be used to derive general principles that explain the degree of robustness in period and amplitude for a set of commonly used models of cellular oscillators. Our findings imply that the robustness of oscillating systems can be influenced by feedback type and kinetic properties to which special attention should be paid when designing mathematical models of cellular rhythms.