Influence of parameter values on the oscillation sensitivities of two p53–Mdm2 models

Abstract

Biomolecular networks that present oscillatory behavior are ubiquitous in nature. While some design principles for robust oscillations have been identified, it is not well understood how these oscillations are affected when the kinetic parameters are constantly changing or are not precisely known, as often occurs in cellular environments. Many models of diverse complexity level, for systems such as circadian rhythms, cell cycle or the p53 network, have been proposed. Here we assess the influence of hundreds of different parameter sets on the sensitivities of two configurations of a well-known oscillatory system, the p53 core network. We show that, for both models and all parameter sets, the parameter related to the p53 positive feedback, i.e. self-promotion, is the only one that presents sizeable sensitivities on extrema, periods and delay. Moreover, varying the parameter set values to change the dynamical characteristics of the response is more restricted in the simple model, whereas the complex model shows greater tunability. These results highlight the importance of the presence of specific network patterns, in addition to the role of parameter values, when we want to characterize oscillatory biochemical systems.

Molecular Titration Promotes Oscillations and Bistability in Minimal Network Models with Monomeric Regulators

“…We integrate the differential eqs – numerically, and we test the capacity of the system to oscillate when certain parameters are varied. First, we randomly varied reaction rates and total concentrations of species , (Section 2.3.1 of the SI), and we used that infomation to identify a nominal set of parameters (Table ) that yields oscillations with a period of roughly 1 h, as shown in Figure B. Equilibrium conditions intersect at a single equilibrium point, as expected based on our analytical derivations (Figure C).…”

“…We identified a set of nominal parameters (Table ) via a preliminary randomized exploration , of the parameter space (SI, Section 3.3.1), where for simplicity we assumed the two subsystems have the same parameters. The trajectories of x T and z T obtained with the nominal parameter set are shown in Figure B, and their behavior in phase space is shown in Figure C.…”

“…A parameter set is classified as "oscillatory" if at least 3 oscillations are detected, their average period is beween 0.5h and 10h, and their average amplitude is larger than 10 nM. Each trajectory was integrated to have a duration of 20 h. Our method follows the approach proposed in [5].…”