Studies on the Quantitative Relation Between the Nuclei and the Cytoplasm in Actinosphaerium eichhorni

PART II. GROWTH, DIVISION AND INCREASE IN NUMBER OF MULTIPLE NUCLEI1) The quantitative relationships between the multiple nuclei and the cytoplasm in the vegetative cells of Actinosphaerium eichhorni are studied from the cytometrical view-point. The term “cytometry” is proposed to denote the biometrical works on the parts of the cell.2) Comparative measurements have been made on cell and nuclear diameters in the living state and on permanent preparations. Thus the reciprocal of the shrinkage index, 1.15±0.013, has been determined for multiple nuclei, and used for obtaining the original size of the nuclei.3) The average diameter of multiple nuclei is nearly constant (7.8μ) in the cells reared under the same condition. Strictly speaking, however, the deviation of the average diameter within 3% is found among the cultures: this seems to be due to the minute inequalities in the culture conditions such as quantity of food and age of strains.4) The fluctuation in size and number of multiple nuclei which is found in a single cell as well as in different cells can be ascribed to the growth and subsequent binary fission of multiple nuclei as represented by the following schemata:-l13→l23= 2l13→2l23 (for one nucleus)nl13→nl23=2nl13→2nl23 (for n nuclei)where l1 and l1 are diameters of nuclei and n the nuclear number in a cell. This means simply that doubling of unit volume of multiple nuclei is invariably followed by nuclear division and increase. The constancy of average diameter of multiple nuclei (3) is expected theoretically from this relation. The data obtained by actual measurements have been found to follow the schemata very well.PART III. CYTOMETRICAL BASIS FOR THE DIFFERENTIATION OF MULTIPLE NUCLEI5) The number of multiple nuclei accords very well with the general allometrical formula y=b Lα, in which y is the value in question and L is the cell diameter left out the dimension μ while b, a are a set of constants. The term “nuclear constant” is proposed for a designating the nuclear number. Four old cultures out of the six examined had the nuclear constant of approximately 2, while the rest, one newly germinated and the other rather over-fed, had the values between 2 and 3. The nuclear constant in the newly germinated culture decreased to nearly 2 about a half month later: this offers an evidence that the nuclear constant changes according to conditions, both internal and external.6) A definite value of nuclear constant is found in all vegetative cells of the same culture with diameters ranging from 45μ to 171μ.7) Six fundamental quantitative relations existing between multiple nuclei and cytoplasm have been considered cytometrically from the viewpoint of the surface law of comparative physiology. The actual data agree well with the theoretically expected values.8) The nuclear volume-cell surface area ratio or nucleo-surface ratio and the nuclear surface area-cell surface area ratio are given by 3 the formulae bl3/6Laand bl2Larespectively. They are constant regardless of the difference in cell size when a=2 (therefore a=0), and increase in exact proportion to the cell diameter when a=3 (therefore a=1).9) The nuclear volume-cell volume ratio are given by the formulae bl3 L-1 a and 6bl2 L-1+a respectively.