%0 Journal Article
%T A Reduced Drosophila Model Whose Characteristic Behavior Scales Up
%A Andrew David Irving
%J ISRN Computational Biology
%D 2013
%R 10.1155/2013/756829
%X Computational biology seeks to integrate experimental data with predictive mathematical models¡ªtesting hypotheses which result from the former through simulations of the latter. Such models should ideally be approachable and accessible to the widest possible community, motivating independent studies. One of the most commonly modeled biological systems involves a gene family critical to segmentation in Drosophila embryogenesis¡ªthe segment polarity network (SPN). In this paper, we reduce a celebrated mathematical model of the SPN to improve its accessibility; unlike its predecessor our reduction can be tested swiftly on a widely used platform. By reducing the original model we identify components which are unnecessary; that is, we begin to detect the core of the SPN¡ªthose mechanisms that are essentially responsible for its characteristic behavior. Hence characteristic behavior can scale up; we find that any solution of our model (defined as a set of conditions for which characteristic behavior is seen) can be converted into a solution of the original model. The original model is thus made more accessible for independent study through a more approachable reduction which maintains the robustness of its predecessor. 1. Introduction It is widely acknowledged that mathematical models can provide valuable biological predictions [1, 2]. As levels of biological data increase, the scale of representative mathematical models must increase accordingly. This increase in scale will add computational complexity, posing a significant challenge to in silico testing. Hence, there is an ever increasing need for approaches which can facilitate the efficient study of large-scale models. A suitable approach is to reduce the dimension of large-scale models [3]. Predictions of a reduced model will ideally translate to the original model [4]. In this paper, we demonstrate such an approach for a model system in developmental biology. Over the course of Drosophila embryogenesis (when the formation of embryonic cells and organs occurs [5]), a cascade of maternal and zygotic segmentation genes establishes the bodily layout [6]. Normal development of segmental structures in the Drosophila embryo relies on a selective expression of the segment polarity (SP) genes [7¨C10] (which are initiated by the previously expressed pair-rule genes [11] at the beginning of gastrulation [12]) along the anterior-posterior axis. Products of SP genes (e.g., mRNAs and proteins) form a complex network of interaction which gives cells their distinctive identities [13] and functions [14, 15], refines
%U http://www.hindawi.com/journals/isrn.computational.biology/2013/756829/