Exemplary Term Paper Proposal 2

Claire Plunkett

BIOL 300

3/3/2015

Term Paper Proposal

Hongyu and I are going to recreate the mathematical model created in Transcriptional Dynamics of the Embryonic Stem Cell Switch by Vijay Chickarmane, Carl Troein, Ulrike A. Nuber, Herbert M. Sauro, and Carsten Peterson. This model considers the effect of the three transcription factors OCT4, SOX2, and NANOG and their effects on target genes that help regulate the differentiation of embryonic stem cells. These transcription factors form a self-regulating network that can be switched on and off, therefore either transcribing self-renewal genes or differentiation genes, in response to an external signal. Two possible methods of control, a coherent feedforward network and an incoherent feedforward network with differences based on which transcription factors act as activators or repressors, are explored and both are found to produce the same results. This paper hypothesizes that the concentration of outside signals switches the stem cell from maintaining its state as a stem cell or differentiating, and that this behavior exhibits bistability. Further, the authors propose that it would be possible to modify a stem cell so that it will be self-renewing, by changing the binding strength between NANOG and OCT4 and SOX2 or increasing the transcription rate leads to a system that is permanently turned on.

This model is described with five state variables using differential equations: the concentrations of OCT4, SOX2, NANOG, and the OCT4-SOX2 complex, as well as the transcription of the target genes. These equations are dependent not only on the state variables but also on parameters including the concentrations of two types of signals ([A₊] and [B_-]), kinetic constants (k_1c, k_2c, and k_3c), and binding strengths between different transcription factors, complexes, and operators (a_i, b_i, c_i, d_i, e_i, f_i, g_i, and h_i). While many of these are expected to be constants, the authors explore the effects of changing many of these values, thus considering them as parameters. Constants include basal transcription rates of the different transcription factors (η_i) and degradation constants of the transcription factors (γ_i). This model is based on the OCT4-SOX2 and a complex it forms with NANOG, which act as activators for the transcription factors as well as the target genes. While signals A₊, A_-, B₊, and B_- are theoretically considered in this paper, only A₊ and B_- are addressed in the model, since the first increases the amount of OCT4 and SOX2 present and the second decreases the amount of NANOG. Therefore, A₊ is used to turn the system on and B_- is used to turn the system off. Additionally, it is assumed that the signals A₊ and B_- act on the complexes but do not affect the transcription factors themselves.

In order to recreate this model, it is necessary to recreate the five differential equations governing the system. Initially we will focus on the four state variables of the concentrations of the three transcription factors and the OCT4-SOX2 complex, and only after that portion of the model is recreated will we recreate the final part of the system, the transcription of the target genes. It is necessary to recreate the model for the first four state variables concurrently since the network within the system is tightly intertwined. The success of this portion of the model will be checked against Figures 3 and 4 in the text, which show the steady state behaviors of the concentrations of the OCT4-SOX2 complex and NANOG in response to varying concentrations of signals [A₊] and [B_-]. After recreating the final equation governing the transcription of the target genes, it will be possible to recreate the many figures within the paper, including figures demonstrating the effect of varying concentrations of the signals on the transcription of the differentiation and stem cell state genes. We will recreate figures demonstrating the bistable behavior of this system, such as Figures 10, 11, and 12, as well as explore conditions under which the bistable behavior ceases to exist. Further, we will recreate the bifurcation plots presented in the supplementary information (Figures S1, S2, S3, and S4) and the figures of target gene expression due to changes in parameter value and OCT4-SOX2 concentration (Figure S5). To extend this paper, we will further explore the effects of varying the parameters, particularly the binding strengths as partially shown in Figure S5, as the authors explored some results from parameter variations but further work can be done. Additionally, we will use the Manipulate function within Mathematica to create figures with variable parameter or initial values, allowing the results from varying parameters to be more obvious.