---
slug: paper-goldbeter-a-1972-dissipative-structures-for-an-allosteric-model-application-to-g
title: Goldbeter and Lefever 1972: Dissipative Structures in an Allosteric Model of Glycolytic Oscillations
canonical: https://miscsubjects.com/a/paper-goldbeter-a-1972-dissipative-structures-for-an-allosteric-model-application-to-g
---

## What the subject saw and its core results

Goldbeter and Lefever modeled an open monosubstrate enzyme reaction with allosteric activation by product. The enzyme has two protomers. They analyzed conditions for instabilities. Beyond a threshold, the system reaches a new organized state called a dissipative structure. These states appear in time as sustained oscillations or in space as patterns.

Core result: the model produces limit cycle oscillations in substrate and product concentrations. Oscillations occur for realistic allosteric and kinetic constants. Substrate activation favors them. The model matches phosphofructokinase regulation and reproduces observed glycolytic oscillations in yeast extracts.

## Exact primary work and verifiable passages

Primary work: Goldbeter A, Lefever R. Dissipative structures for an allosteric model. Application to glycolytic oscillations. Biophys J. 1972 Oct;12(10):1302-1315. doi:10.1016/S0006-3495(72)86164-2. PMC1484224.

Verifiable passage from the abstract: "An allosteric model of an open monosubstrate enzyme reaction is analyzed for the case where the enzyme, containing two protomers, is activated by the product. It is shown that this system can lead to instabilities beyond which a new state organized in time or in space (dissipative structure) can be reached."

Verifiable passage from the abstract: "Sustained oscillations in the product and substrate concentrations are shown to occur for acceptable values of the allosteric and kinetic constants; moreover, they seem to be favored by substrate activation. The model is applied to phosphofructokinase, which is the enzyme chiefly responsible for glycolytic oscillations and which presents the same pattern of regulation as the allosteric enzyme appearing in the model. A qualitative and quantitative agreement is obtained with the experimental observations concerning glycolytic self-oscillations."

## Convergence patterns touched

The work evidences oscillatory waves and pattern formation in dissipative chemical systems. Energy flow through an open reaction network produces temporal order as limit cycles. This matches the GRAIN pattern of bounded chaos and waves arising from reliable energy dissipation. It shows flow to structure via allosteric feedback, a mechanistic step on the Ladder from difference and flow to organized memory-like periodicity.

## Distance from the full OIP/GRAIN synthesis

The paper stays at the chemical level. It demonstrates how dissipation in a simple regulatory network yields sustained oscillations. This supports the grain of the universe by showing narrow families of structural patterns from energy flow. It stops short of life or mind. No extension to multicellular organization, memory storage across scales, or the Mirror Layer appears. The model remains a single-enzyme open system under constant substrate input.

## Honest limits and disconfirming edges

The model assumes a two-protomer allosteric enzyme and product activation only. It applies to in vitro conditions with fixed input rates. Real cells have additional regulatory layers, compartmentalization, and stochastic noise. No claim is made that the same equations govern higher biological rhythms. Reductionist accounts of specific kinetics do not automatically scale to organism-level patterns without further mechanisms.

## Atomic claims

- Claim c1: The allosteric model produces limit cycle oscillations for defined parameter ranges. Tier: mechanistic. Source: Goldbeter 1972 abstract.
- Claim c2: Oscillations match experimental glycolytic behavior in yeast extracts. Tier: anecdotal. Source: Goldbeter 1972 abstract referencing prior experiments.
- Claim c3: Dissipative structures arise from instabilities in open chemical systems. Tier: mechanistic. Source: Goldbeter 1972 abstract.
- Claim c4: The work illustrates energy-flow patterns limited to chemical oscillations. Tier: mechanistic. Source: Goldbeter 1972.

## Sources

Source s1: Goldbeter A, Lefever R. Dissipative structures for an allosteric model. Application to glycolytic oscillations. Biophys J. 1972 Oct;12(10):1302-1315. https://pmc.ncbi.nlm.nih.gov/articles/PMC1484224/. Quote: the abstract passages above. Summary: mathematical demonstration of limit cycles in an allosteric enzyme model applied to glycolysis.

The synthesis receives support at the level of chemical pattern emergence. Limits remain clear: the paper supplies one verified instance of the grain, not the full Ladder or Mirror Layer.
