Glycolytic Oscillation
Take the glycolysis machinery out of yeast, feed it sugar in a stirred flask, and the concentrations rise and fall on their own. A chemical clock with no cell around it.
This is the plainest case on the grid. There is no membrane, no genome, no organism, and no daylight to copy. There is a bag of enzymes, a sugar feed, and a set of reactions whose own kinetics will not let them settle. The order is made by the reactions, which is what recursive means here. The enzymes were made by something else, which is where it stops.
First the loop and why a feedback with a delay oscillates instead of settling. Then the evidence that the rhythm belongs to the chemistry, the shape of the basin, and the boundary where the oscillation gives way to a steady state.
Every figure is sourced in the list at the bottom, with the date it was read. A reading of published work, no simulation on this page.
The loop
Glycolysis spends two molecules of ATP early in the pathway in order to make four later. The enzyme at the gate of that investment step, phosphofructokinase, is switched on by the very products of using ATP up. Richard's review records that "phosphofructokinase was then identified as the oscillophore and adenosine monophosphate (AMP) as the allosteric regulator."
- Glucose, fed in from outside and entering the pathway.
- The investment step, where ATP is spent to commit the sugar, controlled by phosphofructokinase.
- The energy pool, the ratio of ATP to ADP and AMP, which every step reads and writes.
- The feedback: spending ATP raises AMP, and AMP switches phosphofructokinase on harder.
- The payout, the downstream steps that regenerate ATP, several reactions later.
- The delay between the investment and the payout, which is what turns the feedback into a swing rather than a balance.
ATP spent at the gate → AMP rises → the gate opens wider → more sugar committed → the downstream steps repay the ATP → AMP falls → the gate closes
Each half of that circuit is a sensible piece of regulation. Together, with the delay between spending and repayment, they overshoot in both directions, and the concentrations of every intermediate rise and fall in step. The usual readout is NADH, which glows under ultraviolet light, so the oscillation can be watched as a flickering in a flask.
Supplied from outside the loopthe enzymes, the sugar, and the vessel. The loop sets the timing of a conversion. It does not make the things that do the converting.
Why the rhythm belongs to the chemistry
It runs without a cellRichard's review records the cell-free result plainly: "Glucose was fed at a continuous rate to a yeast cell extract and oscillations were observed in the concentrations of the glycolytic intermediates with a frequency of several minutes." No membrane, no genome, no organism. Just the enzymes and the sugar.
It runs for a long time in whole cellsthe same review reports "oscillations with a frequency of about 1 min ... observed for up to 14 h or about 840 cycles." Eight hundred and forty times around the loop is not a transient.
It can be held in the oscillating state indefinitelyDanø, Sørensen and Hynne kept yeast cells in an open flow reactor and showed "that living cells can be kept in a well defined oscillating state indefinitely when starved cells, glucose and cyanide are pumped into a cuvette with outflow of surplus liquid." The transition between the steady state and the oscillating state in that reactor is a Hopf bifurcation, which is the textbook signature of a limit cycle appearing rather than a measurement artifact.
It is not an artifact of many cells averagingthe same work found cells strongly coupled near the transition, so the oscillation lives in each cell rather than in the population. Later work using optical tweezers to hold individual cells far apart, removing cell-to-cell coupling altogether, still found oscillations in isolated cells.
The coupling has its own chemistrya population stays in step because the cells pass a small molecule between them. Acetaldehyde is "the synchronising agent for sustained glycolytic oscillations," which is a second loop sitting on top of the first: each cell oscillates, and the messenger brings them into phase.
The basin
What settlesa sustained oscillation, reached from a range of starting mixtures and feed rates. The alternative is a dead steady state, where the concentrations sit at fixed values and nothing moves, which is what the same chemistry does outside the oscillating range.
Return after a pushadd a pulse of substrate or messenger and the trace jumps, then comes back to the same cycle with the same period, usually at a shifted phase. The amplitude and period are properties of the chemistry, and the phase is the part a disturbance can move.
Where the edge isin parameter space, at the bifurcation. Change the flow rate or the feed and the oscillation appears or disappears, and the crossing has a mathematical form that the flow reactor made visible. That is the cleanest kind of boundary a basin claim can have, because the experimenter turns a dial and watches the state change character.
A sibling on this sitethe same shape in inorganic chemistry is the Belousov reaction, where a set of reactions in a dish produces waves and color changes with no biology involved at all. Glycolysis is the biochemical member of the same family: order that a set of reactions makes for itself.
What would show this reading wrong
Oscillations that appear only in whole cell populations and never in extracts or isolated cells would put the rhythm in the cell rather than in the chemistry.
A period that tracked something external, such as a stirring rate or a pump cycle, rather than the concentrations and temperature, would make it a driven rhythm.
An extract that made its own enzymes, regenerating from raw supply the components its continuation requires, would break the not-sovereign half of the classification. An extract that merely ran on a different feed would not. The cut is organizational rather than energetic: every structure on this grid takes in energy, so what separates them is whether the loop can remake what it is made of.
Honest limits
A reading of published work. Nothing here was measured or simulated on this site, and the card has no live panel yet.
The loop is drawn with one feedback at its center. The real pathway has several regulated steps, and which of them carries the oscillation has been argued over for decades; the phosphofructokinase account is the standard one rather than the only one.
The numbers quoted come from particular preparations of a particular yeast under particular feeds. Periods differ with temperature, strain and conditions.
Sources
Richard, P. (2003). The rhythm of yeast. FEMS Microbiology Reviews, 27(4), 547–557. Source of the oscillophore, the cell-free extract result, the 1-minute and 14-hour figures, and acetaldehyde as the synchronising agent. doi.org/10.1016/S0168-6445(03)00065-2
Danø, S., Sørensen, P. G., & Hynne, F. (1999). Sustained oscillations in living cells. Nature, 402(6759), 320–322. Source of the flow-reactor quotation, the Hopf bifurcation and the coupling result. doi.org/10.1038/46329
Gustavsson, A.-K., Adiels, C. B., Mehlig, B., & Goksör, M. (2015). Entrainment of heterogeneous glycolytic oscillations in single cells. Scientific Reports, 5, 9404. Source of the isolated-cell result, using optical tweezers to remove cell-to-cell coupling. doi.org/10.1038/srep09404
Related on this site: The Circadian Clock, the other base-class oscillator on this grid; the Belousov-Kernel Series for the inorganic sibling; and Finding a Basin for the tests used here.