Mathematical modeling is a core part of Waterloo iGEM: we have nearly as many team members typing furiously away in our dry lab as we do wrangling transformations in our wet lab. This year, we created models in Python, MATLAB and NetLogo that examine the feasibility of our design and provide tools for assessing future designs. The code for each model is available on our GitHub and details on the formulation of each model may be found in the pages linked below.

Cas9 Frameshift Dynamics

We modelled the accumulation of mutations in a target genome and eventual deactivation of target genes after cutting by CRISPR/Cas9 and repair by Non-Homologous End Joining (NHEJ). A stochastic and probabilistic model of the effect of CRISPR/Cas9 on a single genome allowed us to investigate the accumulation of indels in a genome with multiple targets over time. Our Python model provides a tool for other teams looking to investigate multiplexed Cas9 targeting for deactivation of target genomes.

CRISPR Plant Defense

To model antiviral application, we looked at the antiviral effects of CRISPR/Cas9 targeting on three scales: CaMV genomes, plant cells and plant leaves. A background primer on Cauliflower Mosaic Virus (CaMV) genetics, replication and spread can be found on the CaMV Biology page.

On the scale of individual genomes, we used our dynamics model of CRISPR/Cas9 to model viral genomes becoming non-functional over time as frameshift mutations were introduced. The results of running 1000 simulations using our sgRNA target design to deactivate the CaMV P6 gene predict the following pattern of P6 functionality over time.

The exponential decay fit shown in the graph above was then passed to a model on the scale of plant cells. We modelled CaMV Replication in a single infected cell using ordinary differential equations. The ODE replication model allowed us to see the effect that the CRISPR/Cas9 decay of P6 would have on virion production. We also examined the interaction bewteen intracellular plant defenses (RNA interference) and the CRISPR/Cas9 defense and conducted a sensitivity analysis on our parameters.

The ODE model was then scaled up to the level of plant leaves. We modeled the spread of infection between plant cells using an agent-based framework, which is described in detail on the Intercellular Viral Spread page. The agent-based model allowed us to explore the effect of intercellular defense signalling (which leads plant cells to resist to infection and become suseptible to apoptosis).