Guided example: ligand-receptor binding

Let’s consider a simple biological process: receptor activation through ligand binding. In this system, an inactive membrane receptor becomes active when a ligand binds to it.

Model Components

1. Ligand (L)
2. Inactive receptor (R₀)
3. Active receptor (R₁)

Each of these three components can take the value 1, if it is present, or 0, if it is absent.

Interactions

Both the ligand and the inactive receptor have a positive interaction with the active receptor (Fig 8).

Boolean formalism

The receptor becomes active only if both its inputs, the ligand and the inactive receptor are present. This corresponds to a Boolean AND logic:

R₁ = L AND R₀

We can incorporate this in the conceptual model graph for illustration (Fig 9).

This captures the essential logic of the system — receptor activation requires both inputs to be 1. If either the ligand or the inactive receptor is absent, the active receptor remains off. In this very small Boolean network model the input nodes of the active receptor node are at the same time also the input nodes of the model. The input nodes of a model are independent of any logical rules and represent the connection of the model with all the unmodelled processes outside of the model focus. 

Exploring model behaviour

The dynamic behaviour of this model can be summarised in a so-called truth table (Table 1) It indicates  the state of the active receptor R1, after the next update, for all possible combinations of the input nodes L and R0. Whenever either the ligand or the inactive receptor are removed from the system (value = 0), the active receptor becomes 0 after the next update.