Original Paper

Cell Biochemistry and Biophysics

, Volume 57, Issue 2, pp 87-100

First online:

On the Structure-Bounded Growth Processes in Plant Populations

  • H. G. KilianAffiliated withAbteilung Experimentelle Physik, Universität Ulm Email author 
  • , M. KazdaAffiliated withInstitut für Systematische Botanik und Ökologie, Universität Ulm
  • , F. KirályAffiliated withInstitut für Reine Mathematik, Universität Ulm
  • , D. KaufmannAffiliated withInstitut für Humangenetik, Universitätsklinik
  • , R. KemkemerAffiliated withMax-Planck-Institut für Metallforschung
  • , D. BartkowiakAffiliated withKlinik für Strahlentherapie und Radioonkologie, Universitätsklinikum

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


If growing cells in plants are considered to be composed of increments (ICs) an extended version of the law of mass action can be formulated. It evidences that growth of plants runs optimal if the reaction–entropy term (entropy times the absolute temperature) matches the contact energy of ICs. Since these energies are small, thermal molecular movements facilitate via relaxation the removal of structure disturbances. Stem diameter distributions exhibit extra fluctuations likely to be caused by permanent constraints. Since the signal–response system enables in principle perfect optimization only within finite-sized cell ensembles, plants comprising relatively large cell numbers form a network of size-limited subsystems. The maximal number of these constituents depends both on genetic and environmental factors. Accounting for logistical structure–dynamics interrelations, equations can be formulated to describe the bimodal growth curves of very different plants. The reproduction of the S-bended growth curves verifies that the relaxation modes with a broad structure-controlled distribution freeze successively until finally growth is fully blocked thus bringing about “continuous solidification”.


Plants Population Increment model Optimized ensemble structure Growth process Relaxation-frequency dispersion Growth logistics Communities