# Dahlquist:Sigmoidal Transcriptional Network Model

## Introduction

A nonlinear differential equation model was used to study the dynamics of a network of 21 transcription factors we believe is involved in the response of Saccharomyces cerevisiae to cold shock. The transcription factors in the network were chosen if the gene encoding it satisfied one of two criteria: it had a significant change in expression according to the microarray data or previous studies have shown that it is involved in the cold shock response. The model consists of a degradation term subtracted from a production term, where the former models the degradation of a gene product as a linear function and the latter models the production of a gene product as a sigmoid function.

The model is simulated using a combination of scripts written in MATLAB.

## Input File for the Simulation in MATLAB

The input file is an Excel notebook consisting of the following 13 worksheets:

1. production_rates
3. wt
• This sheet contains the normalized microarray data for each of the 21 genes in the network collected using the wild type strain.
4. dcin5
• This sheet contains the normalized microarray data for each of the 21 genes in the network collected using the dCIN5 strain.
5. dgln3
• This sheet contains the normalized microarray data for each of the 21 genes in the network collected using the dGLN3 strain.
6. dhmo1
• This sheet contains the normalized microarray data for each of the 21 genes in the network collected using the dHMO1 strain.
7. dzap1
• This sheet contains the normalized microarray data for each of the 21 genes in the network collected using the dZAP1 strain.
8. concentration_sigmas
9. network
10. network_weights
11. optimization_parameters
12. simulation_times
13. network_b

## MATLAB Code

The simulation begins with the script estimation_driver.mat, which calls the following scripts in the following order:

• Parameters.mat
• LSE.mat
• Graphs.mat
• Output.mat

The script LSE.mat calls the function general_least_squares_error.mat, which calls the function general_network_dynamics_sigmoid.mat.

### estimation_driver.mat

• The first line of code specifies what the input file
 input_file _name = 'Input_ 21_Gene _Network _Sigmoid _Model';

• This specifies whether or not graphs of the expression profile of each gene according to the model will be outputted.
 igraph          = 1;
iestimate       = 1;

 figHandles  = findobj('Type','figure');
nfig        = max(figHandles);

• The following scripts are called in the following order to run the simulation.
 Parameters;
LSE
Graphs;
Output;