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- What is a mathematical model?
- Introduction to networks and graphs
- How to get from biology to mathematics
- Case study – Infectious diseases (SIR Models)
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Exploring model behaviour
Now, let’s play out distinct scenarios of sugar availability to see whether creating our model based on what we know about the interactions between the different biological entities in the process leads to an overall behaviour of the model that is consistent with the experimentally observed responses.
Let’s consider two different scenarios:
1. Simulating different environmental conditions
This model can now be used to simulate responses to environmental conditions (values 1 and 0 represented by green and black boxes, respectively) (Fig 11):
Allolactose present, glucose absent → Lactose metabolism = 1
Lactose absent, glucose present → Lactose metabolism = 0
Allolactose and glucose present → Lactose metabolism = 0
Neither sugar present → Lactose metabolism = 0
Figure 11 Simulating responses to environmental conditions.
2. Simulating dynamic behaviour
The overall logic of the regulatory network therefore follows an AND logic with one of the inputs being negated: presence of lactose AND absence of glucose lead to activation of lactose metabolism.
To answer our initial question, about what happens when allolactose is removed after being present for some time we can look at the model dynamics (Fig 12).
t = 0, allolactose present, no glucose
t = 1, allolactose removal
t = 2, allolactose absent
Figure 12 Simulating dynamic behaviour.
We can also simulate perturbations, like permanently inactivating CAP, and check whether the system’s behaviour aligns with experimental observations.