Boolean network attractors Landscape

An intuitive method to visualize Boolean network attractors landscape based on probability distribution from trajectories

In this webpage, we provide the Python implementation of our method to draw Boolean network attractors landscape. Please click Download.

How to plot a 3D view of a Boolean network attractor landscape?

A Boolean Network attractor landscape is a 3D visualization of the attractors in Boolean Network as in Waddington's landscape. Here we propose an intuitive method to visualize Boolean network attractors landscape based on probability distribution from all trajectories in the state transition graph. For details please read our paper [1] or listen to the ScienceCast.

3D view of a model of cell cycle proposed by Fauré et al. (2006) [2]

Here, we provide an example plot of the 3D view of Boolean network attractors landscape from our intuitive method. The 3D landscape plotted is consistent with the idea proposed in Waddington's epigenetic landscape where attractors are located at the bottom of the landscape for representing cell states.

cell cycle 3D attractors landscape with the our method

There are two basins of attraction: attractor 1 is a basin of attraction on the left (1 pink node is a cyclic attractor with a self-loop) and attractor 2 a basin of attraction on the right (a cyclic attractor formed by 7 nodes).

Compared with the state-of-the-art software BoolNet [3] generated Boolean network attractors landscape

Below is an example for the visualization of the basins of attraction of the same cell cycle network using BoolNet.

There are two basins of attraction: attractor 1 labeled with blue and attractor 2 labeled with green.

References

1. Chong, K. H. An intuitive method to visualize Boolean network attractors landscape based on probability distribution from trajectories. bioRxiv 2024–10
(2024).
2. Fauré, A., Naldi, A., Chaouiya, C. & Thieffry, D. Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle. Bioinformatics 22,
e124–e131 (2006).
3. Müssel, C., Hopfensitz, M. & Kestler, H. A. BoolNet an R package for generation, reconstruction and analysis of boolean networks. Bioinformatics 26, 1378–
1380 (2010).