Mathematical analysis of enzymic reaction systems using optimization principles

  • Reinhart Heinrich
  • Stefan Schuster
  • Hermann-Georg Holzhütter
Part of the EJB Reviews 1991 book series (EJB REVIEWS, volume 1991)

Abstract

Mathematical modelling of metabolic networks is nowadays an important subject of theoretical biology. Most studies in this field concern (a) the development of models for the simulation of stationary and time dependent states of metabolic pathways; (b) the analysis of complex dynamic phenomena such as transitions between multiple stationary states, oscillations and even chaotic behaviour; and (c) the quantitative characterization of control properties of metabolic pathways.

Keywords

Glutathione Oligomer Photosynthesis Cytosol Rosen 

Glossary of principal symbols

Ai

affinity of a reaction

Az

amplification factor as to signal Z

CiJ

flux control coefficient

E

enzyme

Ei

enzyme concentrations

E0

total concentration of a particular enzyme

ΔG

Gibbs free energy

G

growth rate constant

gi

osmotic coefficients

Ht

measure of time hierarchy

J

steady-state flux

ki, k-i, k+, k-

elementary rate constants

kcat

catalytic constant (turnover number)

Km

Michaelis constant

Kint

equilibrium constant of EP vs ES

Lij

Onsager coefficients

M

Jacobian matrix of a reaction system

Mi

molecular mass of proteins

N

stoichiometric matrix

n

number of metabolites, or kinetic order of cooperative enzymes

ntj

stoichiometric coefficients

nH

Hill coefficient

pi

kinetic parameters of enzymes

qi

equilibrium constants

R

unsealed sensitivity, or universal gas constant

scaled sensitivity

r

coupling constant, or number of reactions

S, P

substrate and product of a reaction or reaction pathway

Si, Pi

metabolite and product concentrations

S0.5

half-saturation constant

T

absolute temperature

V

catalytic activity

vi

reaction rates

V+, V-, Vm

maximal activities

V

cellular volume

Xi

thermodynamic forces

Y

state variable of a metabolic system

Z

external signal

β

Brønsted coefficient

η

thermodynamic efficiency

ϰ

rate constant normalized by enzyme concentration

λ

eigenvalue of the Jacobian

μ

Lagrange multiplier

σ

entropy production

σi

deviation of concentration S i from the steady-state value

τ

transient time

Φ

performance function

χ

cost function

Ω

total osmolarity

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Reinhart Heinrich
    • 1
  • Stefan Schuster
    • 1
  • Hermann-Georg Holzhütter
    • 2
  1. 1.Fachbereich Biologie, Institut für BiophysikHumboldt-Universität zu BerlinFederal Republic of Germany
  2. 2.Fachbereich Medizin, Institut für BiochemieHumboldt-Universität zu BerlinFederal Republic of Germany

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