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.
Introduc tionBiological processes such as cell differentiation are mediated by specific networks of genes, which interact with one another. Such systems evolved with time and can be aptly characterized as coupled nonlinear dynamical systems. Dynamical systems can be broadly classified into linear and nonlinear systems. While the former can exhibit interesting behavior only in the presence of noise, the latter can give rise to a wide range of behavior even in the absence of noise. Current techniques used in modeling genetic networks rely on the concepts of biochemical networks (Goldbeter, 1996;Jacob and Monod, 1961;Kauffman, 1969;Tyson et al, 2001;Yagil and Yagil, 1971). The interaction between genes is often modeled as the outcome of a deterministic sequence of events (Gardner et al., 2000;Huang and Ferrell, 1996). However, recent reports have indicated that, in spite of the deterministic phenotypic outcome, the underlying dynamics may be noisy (Hasty et al, 2000;McAdams and Arkin, 1997;McAdams and Arkin, 1999). Noise can be categorized broadly into either dynamical or measurement noise.While the former is coupled to the dynamics, the latter occurs externally (Fig. 1). Various factors that contribute to dynamical noise include: fluctuations in protein concentrations, variation in cell-to-cell switching time and micro-environment. The phenotypic outcome is deterministic in the average sense and has been attributed to population transcriptional cooperation, checkpoints, and redundancies in genes and regulatory p athways, (McAdams and Arkin, 1999). In a recent study, it was demonstrated how noise can be used to control switching and regulation of gene expression (Hasty et al., 2000). On the other hand, a purely nonlinear deterministic approach has been used to model gene interactions (Gardner et al., 2000). The gene expression values are determined with a 4 measurement device, which acts as a black box between the true bio logical activity and the output (Fig. 1). Thus, what is externally observed is the output of the measurement device and not the true biological phenomena. It might not be surprising to note that the input and output of the measurement device m...