TY - JOUR
UR - https://doi.org/10.7287/peerj.preprints.1272v1
DO - 10.7287/peerj.preprints.1272v1
TI - Modeling biological oscillations: integration of short reaction pauses into a stationary model of a negative feedback loop generates sustained long oscillations
AU - Yang,Louis
AU - Yang,Ming
DA - 2015/07/29
PY - 2015
KW - biological rhythmicity
KW - emergent system behavior
KW - diffusion-based reaction pause
KW - mathematical modeling
KW - negative feedback
AB -
Sustained oscillations are frequently observed in biological systems consisting of a negative feedback loop, but a mathematical model with two ordinary differential equations (ODE) that has a negative feedback loop structure fails to produce sustained oscillations. Only when a time delay is introduced into the system by expanding to a three-ODE model, transforming to a two-DDE model, or introducing a bistable trigger do stable oscillations present themselves. In this study, we propose another mechanism for producing sustained oscillations based on periodic reaction pauses of chemical reactions in a negative feedback system. We model the oscillatory system behavior by allowing the coefficients in the two-ODE model to be periodic functions of time – called pulsate functions – to account for reactions with go-stop pulses. We find that replacing coefficients in the two-ODE system with pulsate functions with micro-scale (several seconds) pauses can produce stable system-wide oscillations that have periods of approximately one to several hours long. We also compare our two-ODE and three-ODE models with the two-DDE, three-ODE, and three-DDE models without the pulsate functions. Our numerical experiments suggest that sustained long oscillations in biological systems with a negative feedback loop may be an intrinsic property arising from the slow diffusion-based pulsate behavior of biochemical reactions.
VL - 3
SP - e1272v1
T2 - PeerJ PrePrints
JO - PeerJ PrePrints
J2 - PeerJ PrePrints
SN - 2167-9843
ER -