Centromeric locations in karyotypes: a rule derived from the theory of branched polymers

It is believed that chromosomes occupy non-overlapping domains in the interphase nucleus, and that the nuclear volume can be divided into the interchromosomal space and the chromosome domains. Concentrations of various components (e.g., small ions) are different in these compartments. Since nuclear volume is twice as large in G2 as in G1 phase, V2/V1 (the G2/G1 ratio of total chromosomal volumes) must be two in order to keep the interchromosomal concentrations unchanged. The aim of this study is to test the 'V2/V1 = 2' hypothesis. It has been shown that G1-chromosomes behave as real flexible polymers. If a G2-chromosome behaves as a four-arm star-type branched polymer, then, according to polymer theory, its chromosome volume should depend on its centromere position. We calculated V2/V1 values for 40 karyotypes, from yeast to human, and 19 of them have V2/V1 = 2 +/- 10%. There are two types of exceptions from the 'V2/V1 = 2' rule: karyotypes with a large number of telocentric chromosomes (V2/V1 > 2), and karyotypes with a large number of metacentric chromosomes (V2/V1 < 2). It has been observed in the literature that for all-telocentric karyotypes of mouse and Chinese muntjac, their chromosomes form branch-like structures by association of centromeres in clusters in G2 phase. When calculated for these temporary structures, V2/V1 decreases to two if the number of associated chromosomes per cluster is greater than or equal to five. This corresponds to a number of centromere clusters per nucleus less than or equal to 8-9 for mouse and Chinese muntjac, which is consistent with observation. For rye, all-metacentric karyotype, the calculated V2/V1 value increases to nearly two if B-chromosomes are taken into account.