Reconstruction of the genetic regulatory dynamics of the rat spinal cord development: Local Invariants approach

Recently, many attempts have been made to describe the gene expression temporal dynamics by using systems of differential equations. This is fraught with difficulty, given the current experimental level of understanding. Another way to extract useful information regarding regulation in genetic networks can be provided by our method of Incomplete Modeling using Local Invariants, although at the price of not being able to construct a complete model of the whole system. In this approach we are looking for a set of simple models describing the algebraic or differential relations among just a few variables, genes in this case, which fit the experimental data with the required accuracy. In the present work, we apply this method to gene expression time profiles of 112 genes from rat spinal cord development experiments. We found that many different types of Local Invariants exist in this dataset. Moreover, some isolated self-contained subsystems, whose behavior can be described by closed systems of differential equations, were also found.