  In this report a systematic approach is used to determine the approximate
genetic network and robust dependencies underlying differentiation. The data
considered is in the form of a binary matrix and represent the expression of
the nine genes across the ninety-nine colonies. The report is divided into two
parts: the first part identifies significant pair-wise dependencies from the
given binary matrix using linear correlation and mutual information. A new
method is proposed to determine statistically significant dependencies
estimated using the mutual information measure. In the second, a Bayesian
approach is used to obtain an approximate description (equivalence class) of
network structures. The robustness of linear correlation, mutual information
and the equivalence class of networks is investigated with perturbation and
decreasing colony number. Perturbation of the data was achieved by generating
bootstrap realizations. The results are refined with biological knowledge. It
was found that certain dependencies in the network are immune to perturbation
and decreasing colony number and may represent robust features, inherent in the
differentiation program of osteoblast progenitor cells. The methods to be
discussed are generic in nature and not restricted to the experimental paradigm
addressed in this study.
