Open AccessOn the existence of a steady state in a biological system.
Author(s) -
Gaetano Fichera,
Maria Adelaide Sneider,
Jeffries Wyman
Publication year - 1977
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.74.10.4182
Subject(s) - uniqueness , nonlinear system , critical point (mathematics) , stability (learning theory) , mathematics , point (geometry) , steady state (chemistry) , relaxation (psychology) , statistical physics , state (computer science) , mathematical economics , mathematical analysis , physics , computer science , chemistry , biology , algorithm , geometry , quantum mechanics , machine learning , neuroscience
This paper deals with the existence, uniqueness, and stability of a critical point (steady state) in the case of a macromolecular system, such as an allosteric or polysteric protein, for which the first-order kinetic equations are nonlinear. It presents a brief outline of a rigorous proof (to be given in full elsewhere) that, in a restricted but not unrepresentative system of this kind, there always exists one and only one positive critical point and that this point is asymptotically stable in the large: no matter what its starting point, the system will always approach this point by some kind of relaxation process, however complex.