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

摘要

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 T_(gt)(s) via growth rate v (m s~(-1)): V×S~(-1) = V_(gt) ~×T~r . 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/m~3), minimum and maximum doubling time T_(dt) (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) = 4.4610~(-11)×T_(dt) was found, where V_(gr) = 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 V_(gr) satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M×V_(gr) ＞ h/2π and T_(dt) ×M×v_(gr)~2 ＞ 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?