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- What is a mathematical model?
- Introduction to networks and graphs
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- Case study – Infectious diseases (SIR Models)
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Guided example: the lac operon
Let’s go through the individual model building steps using a small but famous example: the lac operon. This well-known gene regulatory network in Escherichia coli (E. coli) controls the metabolism of lactose. It is switched on and off depending on sugar availability. This regulation ensures that the operon is transcribed—and the enzymes needed for lactose metabolism are produced—only when lactose is present and glucose is scarce.
To make this concrete, let’s suppose we want to answer the following question with a model:
What happens to lac operon activity if lactose is suddenly removed?
Modelling projects often begin with a cartoon representation — a simplified diagram capturing the key components and their interactions based on current biological knowledge. Figure 5 shows such a cartoon of the lac operon.
Here is a brief overview of the biological interactions represented in the cartoon (Fig 5):
The lac operon in E. coli contains three main structural genes involved in the uptake and breakdown of lactose:
- lacZ encodes β-galactosidase, which breaks down lactose into glucose and galactose.
- lacY encodes permease, a membrane protein that facilitates lactose uptake into the cell.
- lacA encodes transacetylase, whose role in lactose metabolism is less clearly understood.
These genes are transcribed as a single polycistronic mRNA and are regulated by transcriptional repressors and activators depending on the availability of lactose and glucose:
- In the absence of lactose, the lac repressor binds to the operator region, blocking RNA polymerase and preventing transcription.
- When lactose is present, it is converted to allolactose, which binds the repressor and causes it to detach from the operator, allowing transcription to proceed.
- When glucose is scarce, cAMP levels increase. cAMP binds CAP (catabolite activator protein), and the CAP–cAMP complex enhances transcription by facilitating RNA polymerase binding more efficiently to the promoter.
- When glucose is abundant, cAMP levels are low, most CAP is in its unbound form, reducing expression of the lac operon even if lactose is available.
In the following section you will explore a step by step process of translating this biological knowledge on the lac operon regulation into a graph.