A semi-classical approach of the relationship between simple cells' size and their living temperature limits based on number fluctuations of water coherence domains

Starting from the concepts of the quantum electrodynamics (QED) theory of coherence domains (CD) in water we propose a model aimed to evaluate the relationship between the size and the living temperature limits for simple, small cells. Cells are described as spherical potential wells with impenetrable walls, with CDs moving inside. The radius of the spherical potential well was estimated for physiological temperatures and the results match to bacteria and yeasts cells' size. As a CD in the spherical cell exerts a force upon the membrane, a 'gas' formed by CDs bears a pressure on the walls. A classical statistical stability condition relates this pressure to cell volume and to the relative fluctuations of the CD number, allowing the evaluation of an upper temperature limit as a function of cellular volume. Assuming further that the CDs in the living cell form together a coherent state, the number-phase incertitude relationship (Heisenberg limit) applies. The maximum coherence between CDs is found in the ground state, a picture consistent also to Frohlich's postulate. For a given phase dispersion, a lower temperature limit as a function of the cell volume is found. Although we neglected the rod-like shape of certain bacteria and the presence of nucleus in yeasts, the biological data of volume and optimal living temperature intervals fit well to our model's predictions. Moreover the larger the cell volume, the higher are the number of CDs and the coherence of their system. In addition we suggest a new classification criterion for small cells based on model's parameters, which show discontinuities between Gram negative and positive microorganisms as well as between prokaryotes and the smallest eukaryotes.