Studies on the Quantitative Relation between the Nuclei and the Cytoplasm in Actinosphaerium eichhorni. Part IV: On the so-called Nucleo-plasmic Ratio and Nucleo-surface Ratio in Some Protozoa and Other Organisms

Based on the results published in my former paper (1941), the results obtained by several previous investigators on the nucleo-plasmic relation in some protozoan and metazoan cells are discussed, and a general rule governing all the data examined is presented, which may be summarized as follows:- 1) Between the nuclei and the cytoplasm in Actinosphaerium eichhorni, there is the relation n=b L^a, α=2+a, where n is the nuclear number, L the cell diameter, and b and α a set of constants characteristic of the given culture; α may be called nuclear constant and a is the deviation of the observed nuclear constant from 2. The nucleo-plasmic ratio can be expressed by the equation y=bl^3 L^<-1+a>, and the nucleo-surface ratio by y=bl^3/6L^a. 2) The nuclear constant is nearly 2 (accordingly a≒0) for the most of the cultures. It is theoretically expected that the nucleo-plasmic ratio is not constant but decreases in inverse proportion to the cell size, while the nucleo-surface ratio remains constant regardless of the difference in cell size (Table 1 and Figs. 1 and 2). 3) The rate of decrease of the nucleo-plasmic ratio with the growth of cell found in Flagellata (Ceratium), Rhizopoda (Actinosphaerium) and Ciliata (Frontonia, Actinobolus, Paramecium, Stylonychia) accords with thiis rule. The same regular relation obtains in Kentrosphaera, a protophyte. 4) For Metazoa also, the decrease of the nucleo-plasmic ration with the development of cell may be recognized in striated muscle fibers and ganglionic and epidermal cells in some invertebrates (Cladocera, Cambarus) and vertebrates (Necturus, mouse). 5) The nucleo-plasmic ratio tends to increase gradually in the early stages of the egg cleavage (Echinus, Strongylocentrotus, Crepidula and Fulgur). The increase of the ratio is due to the decrease, instead of increase, of cell size, and accords well with the general formula of the nucleo-plasmic ratio established in the case of Actinosphaerium. This indicates that the increase of the ratio in the blastomeres obeys the same rule, as does the decrease of the ratio in the other cells. 6) The controversy found among the works of previous investigators as to whether the nucleoplasmic ratio is "constant" or not seems to be reconcilable by the analysis of the implications of the term "constant". In many of the data presented in favor of either view, evidence for regular decrease of the nucleo-plasnic ratio can be found, if the general tendency between the cell size and the ratio is taken into account. Two examples from Actinobolus and Kentrosphaera are given. 7) The regular decrease of the nucleo-plasmic ratio due to growth is recovered by division of the cell. The "division growth" of the nucleus proposed by HERTWIG's schcol may be condidered as a part of the nuclear division itself, because:-(1) No evidence for the "division growth" can be found in Actinosphaerium, Actinobolus, Kentrosphaera or in other cells; (2) Judging from the time relation, it is not impossible that the "division growth" is nothing but the swelling of the nucleus in the prophase, since this takes place about two hours prior to the next division; such a swelling is recognized in the nucleus of any kind of cell including that of ciliates; (3) If the "division growth" and the division itself were independent phenomena as considered by HERTWIG's school, the objection is possible that the cell, already having the normal nucleo-plasmic ratio, should require no more division, after the normal ratio has been recovered by "division growth". 8) From the results presented above, it may be concluded that the nucleo-plasmic ratio is by no means constant, but decreases in inverse proportion to the cell size, and that, under the same circumstances, the cell retains a constant nucleo-surface ration regardless of the difference in cell size.