Boolean mathematical modeling for developmental differentiation in higher order organisms
Written by Ron Piran
Ron Piran,a Einat Halperin,b Noga Guttmann-Raviv,b Rami Reshef b and Ehud Keinana,c
aSchulich Faculty of Chemistry, Technion - Israel Institute of Technology, and bFaculty of Biology Technion City, Haifa 32000, Israel, cDepartment of Molecular Biology and the Skaggs Institute for Chemical Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037, USA.
The Boolean satisfiability (SAT) formalism has been primarily applied for solving decision-making problems. Treatment of biochemical events with this formalism is highly advantageous because it provides simple conceptual tools for describing the relationship between causes and results with the kinetic parameters being irrelevant. Surprisingly, however, although SAT formalism has been used for describing complex genomic systems, it has not been applied to developmental biology, where all pathways can be clearly viewed as decision-making processes. We demonstrate the advantages of applying the Boolean formalism to biochemical pathways in general and developmental biology in particular. As an example, we chose an ectopic diffusible system composed of four groups of proteins: the Wnt family of glycoproteins (Wnts), Sonic hedgehog (Shh), Bone Morphogenetic Protein 4 (BMP4) and antagonists of BMP4 such as noggin, which lead to myogenesis. Data was collected from the vast literature exists in this subject and lack of information was filled in with experiments performed both in vivo and in vitro. We have formulized a three-symbol four-state automaton that solves the myogenesis SAT problem, which has lead not only to a comprehensive overview of these non-trivial phenomena, but also to a hypothesis that the myogenic program is extremely simple and could be formulized by Wnt+(-BMP4)=myogenesis. This hypothesis was subsequently verified experimentally.