Assessment of chromatin activity in mouse and human tissues

Pancreatic deoxyribonuclease preferentially digests active genes during all phases of the cell cycle including mitosis. Recently, a DNAse I-directed in ~ nick translation technique has been used to demonstrate differences in the DNAse I sensitivity of euchromatic and heterochromatic regions of mitotic chromosomes. This ill ~ technique has been used in this study to ask whether facultative heterochromatin of the inactive X chromosome can be distinguished from the active X chromosome in mouse and human tissues. In addition to this, in ~ nick translation has been used to distinguish constitutive heterochromatin in mouse and human mitotic chromosomes. Based on relative levels of DNAse I sensitivity, the inactive X chromosome could not be distinguished from the active X chromosome in either mouse or human tissues but regions of constitutive heterochromatin could be distinguished by their relative DNAse I insensitivity. The use of !D situ nick translation was also applied to tissue sections of 7.5 day mouse embryos to ask whether differing levels of DNAse I sensitivity could be detected between different tissue types. Differences in DNAse I sensitivities were detected in three tissues examined; embryonic ectoderm, an embryo-derived tissue, and two extraembryonic tissues, extraembryonic ectoderm and ectoplacental cone. Embryonic ectoderm and extraembryonic ectoderm nuclei possessed comparable levels of DNAse I sensitivity while ectoplacental cone was significantly less DNAse I sensitive. This suggests that tissue-specific mechanisms such as chromatin structure may be involved in the regulation of gene activity in certain tissue types. This may also shed some light on possible tissue specific mechanisms regulating X chromosome activity in the developing mouse embryo.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.