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

Abstract

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.

A quantitative modular modeling approach reveals the consequences of different A20 feedback implementations for the NF-kB signaling dynamics

“…The non-redundant functions of the two negative feedbacks could be due to their structural properties: the two feedbacks are interlocked, with the IκBα feedback serving as an inner feedback loop and the A20 feedback as an outer feedback loop. Previous studies indicted distinct functions of interlocked feedback loops with respect to the oscillatory behavior of a system (30, 31). Here, a weak or strong outer feedback loop may cause an on or off response, respectively, independent of the strength of the inner feedback loop.…”

An inactivation switch enables rhythms in aNeurosporaclock model

“…To quantify period changes for varying the parameters, we calculate the control coefficients quantifying the sensitivity of the system. In Figure 6 we show a comprehensive control analysis of our model along the lines of [37, 74,75]. All parameters were changed by +/-10 percent and the corresponding period changes were extracted from simulations.…”

Perspective on the dynamics of cancer

“…A key element of this view of cancer dynamics is the role of feedback as a double edge lever of biological regulation. Indeed, on one hand feedback enables robustness of biological processes and the maintenance of cellular and tissue homeostasis [ 23 – 26 ]. However, beyond a certain degree of signaling and metabolic dysregulation, feedback between the signaling pathways, metabolism and the TME may become the mechanistic conduit for exacerbating the drift away from homeostasis and for driving tumor growth.…”