The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the parameters of the system. Perturbation analysis on LIFE systems results in less overall variability of the system, leading to results that more closely resemble empirical data. These systems can be associated to graphs, and characteristics of the graph give insight into the dynamics of the system.This work addresses two main problems: 1. for fixed metabolite levels, find all fluxes for which the metabolite levels are an equilibrium, and 2. for fixed fluxes, find all metabolite levels which are equilibria for the system. We characterize the set of solutions for both problems, and show general results relating stability of systems to the structure of the associated graph. We show that there is a structure of the graph necessary for stable dynamics. Along with these general results, we show how stability analysis from the fields of network flows, compartmental systems, control theory and Markov chains apply to LIFE systems.
One of the essential characteristics of an authentic circadian clock is that the free-running period sustains an approximately 24-hour cycle. When organisms are exposed to an external stimulus, the endogenous oscillators synchronize to the cycling environment signal in a process known as entrainment. These environmental cues perform an important role in resetting the phase and period of the circadian clock. A "generalized assumption" states that when an organism has a short period, it will experience a phase advance, while an organism with a long period experiences a phase delay. Despite widespread use,
Circadian rhythms are ubiquitous and are observed in all biological kingdoms. In nature, their primary characteristic or phenotype is the phase of entrainment. There are two main hypotheses related to how circadian clocks entrain, parametric and non-parametric models. The parametric model focuses on the gradual changes of the clock parameters in response to the changing ambient condition, whereas the non-parametric model focuses on the instantaneous change of the phase of the clock in response to the zeitgeber. There are ample empirical data supporting both models. However, only recently has a unifying model been proposed, the circadian integrated response characteristic (CiRC). In the current study, we developed a system of ordinary differential equations, dynamic CiRC (dCiRC), that describes parameters of circadian rhythms and predicts the phase of entrainment in zeitgeber cycles. dCiRC mathematically extracts the underlying information of velocity changes of the internal clock that reflects the parametric model and the phase shift trajectory that reflects the non-parametric model from phase data under entraining conditions. As a proof of concept, we measured clock parameters of 26 Neurospora crassa ecotypes in both cycling and constant conditions using dCiRC. Our data showed that the morning light shortens the period of the clock while the afternoon light lengthens it. We also found that individual ecotypes have different strategies of integrating light effects to accomplish the optimal phase of entrainment, a model feature that is consistent with our knowledge of how circadian clocks are organized and encoded. The unified model dCiRC will provide new insights into how circadian clocks function under different zeitgeber conditions. We suggest that this type of model may be useful in the advent of chronotherapies.
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