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

Rajamanickam Murugan,Christof Markus Aegerter

doi:10.1371/journal.pone.0041027

Abstract

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 (wh = γpc/γph where h = a, b, c corresponding to genes A, B and C) between the lifetimes of mRNAs (1/γmh) of genes A, B and C and the protein of C (1/γpc). 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 wh. Group I that includes C1 and I1 type FFLs seem to be less sensitive to the changes in wh. 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.

Highlights

Transcription factors (TFs) regulate the quantitative levels of many proteins inside a cell [1,2,3,4]
The fraction occupancy of promoter of TF gene ‘h’ by the respective regulatory TF protein ‘g’ is denoted as Xhg [ (0, 1) which is the ratio xhg/dhz where xhg is the cellular concentration of the promoter of gene ‘h’ that is bound with the protein of TF gene ‘g’ and dhz is the total concentration of the promoter of gene ‘h’ inside the cellular volume
The free energy barrier associated with the fluctuating dynamics of TF proteins within this electrostatic field is comparable with that of the thermal free energy that in turn helps the TF proteins to freely slide along the DNA within this electrostatic capturing domain without physical dissociation [23]

Summary

Introduction

Transcription factors (TFs) regulate the quantitative levels of many proteins inside a cell [1,2,3,4]. A FFL motif is said to be a coherent type if the direct effect of the general transcription factor (A) on the effector operons (C) has the same sign (negative or positive) as its net indirect effect through the specific transcription factor (B). PPP, NPN, PNN and NNP (termed as C1, C2, C3 and C4) are coherent types and PNP, NNN, PPN and NPP (termed as I1, I2, I3 and I4) are incoherent types [10,11]. A is the general transcription factor that directly regulates the effector operon of gene C and indirectly regulates gene C through B. In PNN coherent type, gene A positively regulates B which in turn negatively regulates C and the net effect of regulation of C by TF gene A indirectly through B is negative. Since A directly regulates C via negative mode, PNN is called as a coherent type

Methods

Results

Conclusion