### Abstract

A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in that the number of ATP molecules produced in the second half of the pathway exceeds the number consumed in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that it is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting linear flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior.

Original language | English (US) |
---|---|

Pages (from-to) | 794-803 |

Number of pages | 10 |

Journal | Biophysical Journal |

Volume | 60 |

Issue number | 4 |

State | Published - 1991 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Biophysics

### Cite this

*Biophysical Journal*,

*60*(4), 794-803.

**Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system.** / Cortassa, S.; Aon, M. A.; Westerhoff, H. V.

Research output: Contribution to journal › Article

*Biophysical Journal*, vol. 60, no. 4, pp. 794-803.

}

TY - JOUR

T1 - Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system

AU - Cortassa, S.

AU - Aon, M. A.

AU - Westerhoff, H. V.

PY - 1991

Y1 - 1991

N2 - A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in that the number of ATP molecules produced in the second half of the pathway exceeds the number consumed in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that it is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting linear flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior.

AB - A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in that the number of ATP molecules produced in the second half of the pathway exceeds the number consumed in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that it is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting linear flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior.

UR - http://www.scopus.com/inward/record.url?scp=0026054728&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026054728&partnerID=8YFLogxK

M3 - Article

C2 - 1742453

AN - SCOPUS:0026054728

VL - 60

SP - 794

EP - 803

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 4

ER -