Fig. 1

Boolean model, asynchronous simulation and the framework underlying BTR. a A Boolean model can be expressed graphically in terms of nodes and edges, as well as in tabular form in terms of update functions. Note that the small black node refers to AND interaction. b The asynchronous update scheme is best explained with the use of a graph representation of state space, in which each connected state differs in only one node. Starting from the initial state s ₁ = {0, 0, 1, 1} and evaluated using the update functions in (a), asynchronous simulation produces a model state space with 15 states. The initial state is shown in red node, while the final steady state is shown in pink node. c The framework underlying BTR. A Boolean model can be simulated to give a model state space, while a single-cell expression data can be preprocessed to give a data state space. Boolean state space scoring function can then calculate the distance score between the model and data state spaces. Lastly, BTR uses the computed distance score to guide the improvement of the Boolean model through an optimisation process that minimises the distance between model and data state spaces