Eur. Phys. J. E (2005) 17: 307-325
https://doi.org/10.1140/epje/i2004-10143-8

Original Article

Stationary cell size distributions and mean protein chain length distributions of Archaea, Bacteria and Eukaryotes described with an increment model in terms of irreversible thermodynamics

¹ Abteilung Experimentelle Physik, Universität Ulm, Albert-Einstein Allee 11, D-89069, Ulm, Germany
² Abteilung Biophysik, Universität Ulm, Albert-Einstein Allee 11, D-89069, Ulm, Germany
³ Abteilung Strahlentherapie, Universitätsklinik, Robert-Kochstrasse 6, 89081, Ulm, Germany
⁴ Abteilung Humangenetik, Universitätsklinik Ulm, Robert-Kochstrasse 6, 89081, Ulm, Germany

^* e-mail: hanns-georg.kilian@uni-ulm.de

Received: 26 July 2004
Accepted: 18 April 2005
Published online: 29 June 2005

Abstract

In terms of an increment model irreversible thermodynamics allows to formulate general relations of stationary cell size distributions observed in growing colonies. The treatment is based on the following key postulates: i) The growth dynamics covers a broad spectrum of fast and slow processes. ii) Slow processes are considered to install structural patterns that operate in short periods as temporary stationary states of reference in the sense of irreversible thermodynamics. iii) Distortion during growth is balanced out via the many fast processes until an optimized stationary state is achieved. The relation deduced identifies the numerous different stationary patterns as equivalents, predicting that they should fall on one master curve. Stationary cell size distributions of different cell types, like Hyperphilic archaea, E. coli (Prokaryotes) and S. cerevisiae (Eukaryotes), altogether taken from the literature, are in fact consistently described. As demanded by the model they agree together with the same master curve. Considering the “protein factories” as subsystems of cells the mean protein chain length distributions deduced from completely sequenced genomes should be optimized. In fact, the mean course can be described with analogous relations as used above. Moreover, the master curve fits well to the patterns of different species of Archaea, Bacteria and Eukaryotes. General consequences are discussed.