Team:Waterloo/Math Book

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Math Book

This page gathers the detailed process information for the mathematical models created by the team this year. Code related to the models can be accessed from this github page.

CRISPR

We decided to create a model of the CRISPR system for two main reasons:

  • Identifying the parts of the network that could be targeted by our lab team to improve repression efficiency
  • To approximate time-series mecA repression data for use in modelling the overall vulnerability of a S. aureus population

Model Formation

After a literature review we were able to construct the CRISPR interference system network. The targeted single guide RNA (sgRNA) associates with nuclease-deficient Cas9 protein (dCas9) to form a complex that binds with the DNA complementary to the sgRNA target . The bound complex prevents transcription elongation by RNA polymerase, repressing YFP mRNA expression . The chemical network is shown below:

CRISPR Network Diagram

Using standard mass-action kinetics, the network simplifies into the following set of differential equations:

Modelling Incomplete Repression

Parameters

Production of dCas9 from dCas9 mRNA

Degradation rate of dCas9

mRNA production from the sarA promoter

Initial Model Results

Updating mRNA Production Rates

Sensitivity Analysis

sRNA

Relevant Biology

Model Formation

Conjugation