Theory on the Dynamics of Feedforward Loops in the Transcription Factor Networks

Feedforward loops (FFLs) consist of three genes which code for three different transcription factors A, B and C where B regulates C and A regulates both B and C. We develop a detailed model to describe the dynamical behavior of various types of coherent and incoherent FFLs in the transcription factor networks. We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs. Detailed analysis shows that the response times of FFLs strongly dependent on the ratios (w(h) = γ(pc)/γ(ph) where h = a, b, c corresponding to genes A, B and C) between the lifetimes of mRNAs (1/γ(mh)) of genes A, B and C and the protein of C (1/γ(pc)). Under strong binding conditions we can categorize all the possible types of FFLs into groups I, II and III based on the dependence of the response times of FFLs on w(h). Group I that includes C1 and I1 type FFLs seem to be less sensitive to the changes in w(h). The coherent C1 type seems to be more robust against changes in other system parameters. We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs.