Mathematical model of chaotic oscillations and oscillatory entrainment in glycolysis originated from periodic substrate supply

Abstract

We study the influence of periodic influx on a character of glycolytic oscillations within the forced Selkov system. We demonstrate that such a simple system demonstrates a rich variety of dynamical regimes (domains of entrainment of different order (Arnold tongues), quasiperiodic oscillations, and chaos), which can be qualitatively collated with the known experimental data. We determine detailed dynamical regimes exploring the map of Lyapunov characteristic exponents obtained in numerical simulations of the Selkov system with periodic influx. In addition, a special study of the chaotic regime and the scenario of its origin in this system was evaluated and discussed.

Model-based Identification of Some Conditions Leading to Glycolytic Oscillations in E. coli Cells

“…2). Valuable contributions to explain and model, on an experimental basis, the glycolytic oscillations "engine" and their self-control, have been done on E. coli, 27,28,[30][31][32][33] or on yeast. 34 Glycolytic oscillation occurrence and characteristics (period) are influenced by both external (environmental) and internal (genomic) factors, that is: 35,36 I) From one side it is the glucose (Glc) import driving force through the phosphotransferase (PTS)-system ( Fig.…”

“…Valuable contributions to model the glycolytic oscillations related to the system characteristics and environmental conditions have been reported. 27,28,[30][31][32][33] The advantage of the mTRM model of Maria 4 is its capacity to reproduce glycolytic oscillations using a reduced kinetic model but still preserving the essential glycolytic and environmental parameters with a major influence on the process (see the next chapter on oscillation conditions).…”

Nonlinear dynamics and entrainment in a continuously forced pulse-modulated model of testosterone regulation

“…Periodicity arises due to natural (endogenous) phenomena within the system but is also affected by signals (cues) from the environment. When the exogenous signal is periodic, the so-called entrainment of the endogenous (unforced) dynamics can arise [33]. Entrainment, also known as a frequency (phase) locking, is a kind of synchronization which occurs in dynamical systems under external force (for which reason it is sometimes also referred to as a forced synchronization).…”

“…Entrainment, also known as a frequency (phase) locking, is a kind of synchronization which occurs in dynamical systems under external force (for which reason it is sometimes also referred to as a forced synchronization). Even though, in most cases, entrainment of periodical solutions is considered, there is also a more inclusive interpretation of the phenomenon, when nonperiodic endogenous solutions are entrained to the periodicity of the exogenous signal [33]. For instance, in the present paper, when an external periodic forcing is applied in the regime of periodic oscillations, the self-sustained oscillator displays regions of two-mode quasiperiodic dynamics interrupted by a dense set of resonance zones, where the internally generated periodic oscillations synchronize with the external forcing.…”

Dynamics in a delayed diffusive cell cycle model

“…Mathematical modeling is a powerful tool to investigate the dynamics of biological systems such as epidemiology [3,34], ecology [26,28,37,40] and molecular network [32,35]. A number of mathematical models have been proposed to explore the regulatory mechanism of cell cycle in early embryos [10,18,21,31], yeast [6,7,27] and mammalian cells [1,9,22].…”