Possible Physical Determination of the Mass, Size, Doubling Time and Density of the Unicellular Organisms Based on the Fundamental Physical Constants

Abstract

In manuscript the hypothesis 'that the mass, size, doubling time and density of the unicellular organisms (Prokaryotes and Eukaryotes) are determined by the gravitational constant (G, N·m²/kg²), Planck constant (h, J·s) and growth rate v_gr (m/s)' is investigated. By scaling analyses it is indicated that the growth rate of the unicellular organisms ranges in a narrow window of 1.0×10^-11–1.0×10^-10 m/s, in comparison to 10 orders of magnitudes difference between their mass. Dimension analyses demonstrates that the combination between the growth rate of unicellular organisms, gravitational constant and Planck constant provides the equations with dimension of mass M(v_gr) = (h·v_gr/G)^½ in kilogram, length L(v_gr) = (h·G/v_gr³)^½ in meter, time T(v_gr) = (h·G/v_gr⁵)^½ in seconds and density ρ = v_gr^.3.5/hG² in kg per 1 m³. For values of growth rate in numerical diapason of 1.0×10^-11–1.0×10^-9.5 m/s, the calculated numerical values for mass (3.0×10^-18–1.0×10^-16 kg), length (5.0×10⁸–1.0×10^-5 m), time (1.0×10²–1.0×10⁶ s) and density (1.0×10^-1–1.0×10⁴ kg/m³) overlap with diapason of experimentally measured values for cell mass (3.0×10^-18–1.0×10^-15 kg), volume to surface ratio (1.0×10^-7–1.0×10^-4 m), doubling time (1.0×10³–1.0×10⁷ s) and density (1050-1300 kg/m³) in both bacteria and protozoa.