Book of Abstracts: Albany 2003
June 17-21 2003
Polymer Model for the Relationship between Chromosomal Configurations/ Associations and Nuclear Size/Shape
Chromosomes, the largest biopolymers in nature, are a suitable subject for polymer science. Specific parameters of chromosomes - number per nucleus (1-100), DNA content per chromosome (10-1-105Mb), etc. - vary several orders of magnitude among species from yeast to mammals to plants. Huge variability is also characteristic of nuclear size (1-50 μm) and shape (3-D or flat ellipsoid, cone, cylinder, etc.), even for various tissues of the same organism. Chromosome configurations (linear, folded, loop, etc., which are defined through a pattern of centromere and/or telomere anchoring to the nuclear membrane), and chromosome associations (homologous pairing, number of centromere or telomere clusters per nucleus, number of branches per cluster, etc.) are both very variable, often changing in parallel with nuclear size/shape.
This report focuses on the polymer model for diffuse chromatin, which describes the relationship between chromosome configurations and associations, on the one hand, and nuclear size and shape as indicators of geometrical constraints, on the other. The model was applied to various cell types and stages (G1 and G2 phases, meiotic, polytene, etc.) of divergent species: budding yeast S. cerevisiae and fission yeast S. pombe, fruit fly Drosophila, nematode C. elegans, mammals (human, mouse, Indian and Chinese muntjac), and plants (Arabidopsis, maize, Vicia faba, barley, wheat) (see (1) and references therein).
Discrete chromatin domains are formed in the nucleus by random and transient attachments of chromosomal fibers to nuclear structures (the nuclear membrane, nucleolus, etc.). Calculation of the total volume of these domains in the nucleus is based on two statements: i) the coil-like behavior of chromosomal fibers at relatively short range (0.1 - 1Mb); and ii) the tight packing of discrete chromatin domains in the nucleus. Although these statements are supported by experiments, the general applicability of each of them is not fully accepted in the literature.
To describe the relationship between chromosome associations and nuclear shape (relative constraints) the model needs only one parameter ? the number of anchors of the chromosomal fiber per arm. This quantity has been measured in several cases, and use of these values in the model yields correct predictions: i) During the meiotic stage of S. pombe (diffuse chromatin), the nuclear shape changes from pear-like with a cone angle ~60° to cone-like (?horse tail?) with ~30° angle. The model predicts that the angle ~60° is the minimal one to accommodate all six loop chromosomes, even overlapped in a single domain, without additional anchoring, while the 30° cone needs ~2.5 anchors per arm to accommodate loops. This estimate is close to the number of ?rigid? elements per nucleus observed at the late meiosis stage. II) The existence of two chromocenters in the Drosophila midgut polytene ellipsoidal nucleus is consistent with the model prediction that no more than three of the five chromosomal arms can cluster at the apex of such a nucleus with the observed number of anchoring sites per arm; iii) For the oblate ellipsoid nuclei of G1 Indian muntjac cells, the model predicts that the folded polar chromosome configuration for arms is possible if the number of their attachments to the nuclear membrane is ~5 per arm. It is shown in the literature that chromosomes of Indian muntjac have ~7 interstitial sites of satellite DNA (centomere-like) per arm. IV) The model predicts that, on the nuclear surface, there can be a maximum of ~6-9 telomere clusters in S. cerevisiae, and ~8-10 centromere clusters in mouse neurons, very close to the observed numbers in both cases. V) The model predicts ~25 acentric mouse chromosomes attached to a central nucleolus by telomeres or centromeres in the spherical G1 neuron nucleus; the same total number of telomeres and centromeres attached to the nucleolus has been observed in experiment.
To describe the relationship between nuclear size and chromosome configuration (absolute geometrical constraints) the model needs an additional parameter, a coefficient B (μm2/ Mb) in the dependence of the mean square of geometrical distance vs. the genomic distance. The model suggests that in nuclei with relatively lower DNA concentration (<5-10 Mb/μm3, e.g., yeast, Drosophila), the chromosomal fiber does not have higher-order levels above the 30-nm fiber, and has B ~1 μm2/Mb, on average. This value of B is consistent with other parameters observed for a single 30-nm fiber: persistence length ~30 nm, and linear density of nucleosomes ~4-5 nucleosomes per 10 nm of fiber contour length. This value of B is also supported by the agreement between the maximal sizes of corresponding chromosomal domains in S. cerevisiae and Drosophila estimated in the model, and the measured diameters of confinement spheres for chromatin diffusional motion for these nuclei.
In nuclei with higher DNA concentration (>5-10 Mb/μm3, e.g., in mammals or high plants), the chromosomal fiber seems to have a ?higher-order? structure above that of the 30-nm fiber, which yields an apparent B ~0.1 μm2/Mb, observed at the 10-100 Mb scale in these cells. We argue that one such possible ?higher-order? structure is the linear coil of loop clusters of the 30-nm fiber with ~10 loops per cluster, which is consistent with many experimental results including the viscoelastometry data for mammalian chromatin/DNA solutions (2).
SUNY-Downstate Medical Center