Scaling Laws for Mitotic Chromosomes

During mitosis in higher eukaryotes, each chromosome condenses into a pair of rod-shaped chromatids. This process is co-regulated by the activity of several gene families, and the underlying biophysics remains poorly understood. To better understand the factors regulating chromosome condensation, we compiled a database of mitotic chromosome size and DNA content from the tables and figures of >200 published papers. A comparison across vertebrate species shows that chromosome width, length and volume scale with DNA content to the powers similar to 1/4, similar to 1/2, and similar to 1, respectively. Angiosperms (flowering plants) show a similar length scaling, so this result is not specific to vertebrates. Chromosome shape and size thus satisfy two conditions: (1) DNA content per unit volume is approximately constant and (2) the cross-sectional area increases proportionately with chromosome length. Since viscous drag forces during chromosome movement are expected to scale with length, we hypothesize that the cross-section increase is necessary to limit the occurrence of large chromosome elongations that could slow or stall mitosis. Lastly, we note that individual vertebrate karyotypes typically exhibit a wider range of chromosome lengths as compared with angiosperms.

Automated summary

During mitosis in higher eukaryotes, chromosome condensation is co-regulated by several gene families, with chromosome size and DNA content scaling with powers close to 1/4, 1/2, and 1 across vertebrate species. The increase in chromosome cross-sectional area with length is hypothesized to be necessary to prevent large chromosome elongations that could slow or stall mitosis. Unlike angiosperms, individual vertebrate karyotypes typically exhibit a wider range of chromosome lengths.