Scaling of Volume to Surface Ratio and Doubling Time in Growing Unicellular Organisms: Do Cells Appear Quantum-Mechanical Systems?

The scaling of physical and biological characteristics of the living organisms is a basic method for searching of new biophysical laws. In series of previous studies the author showed that in Poikilotherms, Mammals and Aves, the volume to surface ratio V×S-1 (m) of organisms is proportional to their generation time Tgt(s) via growth rate v (m s-1 ): V×S-1 = vgr ×T¹ . The power and the correlation coefficients are near to 1.0. Aim of this study is: i) to prove with experimental data the validity of the above equation for Unicellular organisms and ii) to show that perhaps, the cells are quantum-mechanical systems. The data for body mass M (kg), density p (kg/m³), minimum and maximum doubling time Tdt (s) for 50 unicellular organisms are assembled from scientific sources, and the computer program 'Statistics' is used for calculations. In result i) the analytical relationship from type: V×S-1 = 4.46-10-11×Tdt was found, where vgr = 4.46×10-11 m/s and ii) it is shown that the products between cell mass M, cell length expressed by V/S ratio and growth rate vgr satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M#215;vgr > h/2π and Tdt ×M×vgr² > h/2π are valid, where h= 6.626×10-34 J-s is the Planck constant. This rise the question: do cells appear quantum-mechanical systems? [ABSTRACT FROM AUTHOR]