  Temporal order in living matters reflects the self-organizing nature of
dynamical processes driven out of thermodynamic equilibrium. Because of
functional reason, the period of a biochemical oscillation must be tuned to a
specific value with precision; however, according to the thermodynamic
uncertainty relation (TUR), the precision of oscillatory period is constrained
by the thermodynamic cost of generating it. After reviewing the basics of
chemical oscillations using Brusselator as a model system, we study the
glycolytic oscillation generated by octameric phosphofructokinase (PFK), which
is known to display a period of several minutes. By exploring the phase space
of glycolytic oscillations, we find that the glycolytic oscillation under the
cellular condition is realized in a cost effective manner. Specifically, over
the biologically relevant range of parameter values of glycolysis and octameric
PFK, the entropy production from the glycolytic oscillation is minimal when the
oscillation period is (5 - 10) minutes. Further, the glycolytic oscillation is
found at work near the phase boundary of limit cycles, suggesting that a
moderate increase of glucose injection rate leads to the loss of oscillatory
dynamics, which is reminiscent of the loss of pulsatile insulin release
resulting from elevated blood glucose level.
