Abstract
Networks of oscillating processes are a common occurrence in living systems. This is as true as anywhere in the energy metabolism of individual cells. Exchanges of molecules and common regulation operate throughout the metabolic processes of glycolysis and oxidative phosphorylation, making the consideration of each of these as a network a natural step. Oscillations are similarly ubiquitous within these processes, and the frequencies of these oscillations are never truly constant. These features make this system an ideal example with which to discuss an alternative approach to modeling living systems, which focuses on their thermodynamically open, oscillating, non-linear and non-autonomous nature. We implement this approach in developing a model of non-autonomous Kuramoto oscillators in two all-to-all weighted networks coupled to one another, and themselves driven by non-autonomous oscillators. Each component represents a metabolic process, the networks acting as the glycolytic and oxidative phosphorylative processes, and the drivers as glucose and oxygen supply. We analyse the effect of these features on the synchronization dynamics within the model, and present a comparison between this model, experimental data on the glycolysis of HeLa cells, and a comparatively mainstream model of this experiment. In the former, we find that the introduction of oscillator networks significantly increases the proportion of the model's parameter space that features some form of synchronization, indicating a greater ability of the processes to resist external perturbations, a crucial behavior in biological settings. For the latter, we analyse the oscillations of the experiment, finding a characteristic frequency of 0.01–0.02 Hz. We further demonstrate that an output of the model comparable to the measurements of the experiment oscillates in a manner similar to the measured data, achieving this with fewer parameters and greater flexibility than the comparable model.
Highlights
Analyzing the energy metabolism of a cell can be key to understanding more about its functions, states and health
There are six possible modes of synchronization within our cellular metabolism model: glycolysis to glucose, glycolysis network, glycolysis to oxidative phosphorylation (OXPHOS), OXPHOS network, and OXPHOS to oxygen. While it would not be possible for glycolysis to be synchronized to OXPHOS, but OXPHOS to not synchronize to glycolysis in an individual oscillator model, it is possible for a network to become synchronized to a mean field driving, without the network from which that mean field arises becoming synchronized to the network it is driving
The conversion of established metabolic models, such as that of Lancaster et al (2016), to consider networks of processes offers both greater biological realism and a resulting transformation of the dynamics we expect to see from such models
Summary
Analyzing the energy metabolism of a cell can be key to understanding more about its functions, states and health. But there is further evidence to suggest these oscillations may be non-autonomous (O’Rourke et al, 1994; Tu and McKnight, 2006; Kurz et al, 2010b; Battle et al, 2016; Rupprecht and Prost, 2016; Amemiya et al, 2017): that their frequencies vary over time. Modeling this behavior is a challenge for many traditional techniques, which often rely on perturbations of a steady state to give rise to oscillations, and the addition of noise to simulate nonautonomous variation. We present here an alternative approach to modeling non-autonomous oscillations in living systems, and what we can learn from such models
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