Date of Completion

5-15-2026

Degree Type

Honors Thesis

Discipline

Biology (BIOL)

First Advisor

Dr. Kam Dahlquist

Second Advisor

Dr. Ben Fitzpatrick

Abstract

A gene regulatory network (GRN) is a set of transcription factors that regulate the expression of genes encoding other transcription factors. The dynamics of a GRN explain how gene expression changes over time. GRNmap is a MATLAB software package that uses ordinary differential equations to model dynamics of small-scale GRNs. We used the program to estimate production rates, expression thresholds, and regulatory weights for each transcription factor in three related literature-derived GRNs based on yeast cold shock microarray data previously collected in the Dahlquist Lab. We noticed large differences in estimated weight values when 1-2% of the expression values were missing from the input data versus when the missing values were replaced with the average value for that gene, strain, and timepoint for the 15-gene, 28-edge GRN. When the alpha value that constrains the penalty term for the least squares error function being minimized for the estimation was changed from 0.002 to 0.02 it lessened the discrepancy between parameters estimated from input with missing and no missing expression data for that GRN. However, changing the alpha value from 0.002 to 0.02 introduced more differences between estimated parameters for the two other networks (14-genes, 25-edges; 16-genes, 35 edges) that each contained a subset of the first network’s genes. Due to these results, we designed a sensitivity assay that could be performed on smaller GRNs. All 21 possible “toy” networks of 3 nodes and 4 edges were generated, which fall into 11 families of network motifs. Parameters were estimated from simulated expression data created when the model underwent a forward simulation with known arbitrary weight parameters (1, 2, -1, -2), production rates, and threshold b values. Comparison of the known to estimated parameters showed that estimating production rates in addition to weights and thresholds reduced the accuracy of the results. To better understand the influence of the weight parameters, we generated all twenty-four possible weight permutations for three network motifs, bi-mutual, mutual cascade, and fan-in with two autoregulatory loops. Through analysis of these permuted networks, we saw that the model was sensitive to the direction and magnitude of the arbitrary weight parameters assigned to networks with the same connectivity. While we would have to run more permutations to completely justify our results, through beginning to assess the biology of our networks, we can begin to understand why some weights caused more accurate results than others and also understand how network motifs may appear in larger networks and influence modeling at that level.

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