Quantum thermodynamics approach to phosphorylation and heterotrophic growth yields

A model of cell growth is presented which is based on the double postulates of quantized loss of energy during phosphorylation and reversible biosynthesis of cell structure. An immediate consequence of the postulates is the identical value for the energy efficiency of the phosphorylation and for that of the whole growth process. Another consequence is the relationship between the energy level of the biomass and the phosphorylation potential as embodied in the equation: EO = gamma'M X EATP, where EO is the heat of transfer of a pair of electrons to oxygen, EATP, the molar heat of hydrolysis of ATP, and gamma'M, the degree of reduction of the biomass, gamma M being constant and equal to 5. The model predicts five levels of growth yields corresponding to five permissible values for the P/O ratio (r = 0, 1, 2, 3, and 4). Any growth process would be characterized by a set of two integers N and lambda; N is the maximal P/O ratio prescribed by the energy content of the substrate as compared with that of the biomass, and lambda the number of further downward quantum jumps of the P/O ratio resulting from the adversity of the growth condition (N - lambda = r). Under full aerobiosis, one has 0 less than or equal to lambda less than or equal to N less than or equal to 3. When growth is limited only by the energy content of the substrate (lambda = 0), the time-independent dispersion of N, owing to substrate-level phosphorylations and (or) dephosphorylations, leads to effective values which are higher than the nominal ones for the yield per mole of oxygen and the heat of transfer of a pair of electrons. Under adverse conditions (lambda greater than 0), the apparent variations of the yields and the P/O ratio in function of the growth rate are shown to be an effect of the random dispersion of lambda and of the existence of a maximal rate of substrate consumption. Statistical evidence for the macroscopic quantum effect in heterotrophic growth is presented.