Threshold Boolean Formalism

This repository contains an interactive Python framework designed to simulate and analyze Gene Regulatory Networks (GRNs) using a discrete Threshold Boolean Formalism (Ising-like model). It maps out the global attractor landscape of networks under different updating rules to identify fixed-point steady states and periodic limit cycles.

Core Formalism and Features

In this threshold logic model, every biological node (gene/protein) exists in a binary state:

• +1 (ON / Active)
• -1 (OFF / Inactive)

The regulatory state of a node $S_i$ evolves based on the net weighted sum of its inputs: $$S_i(t+1) = \begin{cases} +1 & \text{if } \sum_{j} W_{ji} S_j(t) > 0 \ -1 & \text{if } \sum_{j} W_{ji} S_j(t) \le 0 \end{cases}$$

Updating Schemes

• Synchronous Update: All network nodes update simultaneously in a deterministic fashion. Trajectories from a given initial state follow a single fixed path.
• Asynchronous Update: A single node is selected at random to update at each time increment. This stochastic branching permits a single initial condition near a basin boundary to reach multiple alternative attractors (bistability/multistability).

Outputs Generated

All analysis assets are neatly organized and exported per network topology into ./IsingResults/[Topology_Name]/:

• *_sync.csv / *_async.csv: Raw state value trajectories across time steps.
• *_STG_*.csv: Edge lists and transition probabilities for building structural STGs.
• *_Report.png: Summary plot.

Getting Started

Place your structural network topology target files inside a ./TOPOS/ folder using the standard space-separated format (Source Target Type).

Execute the main pipeline script or import it directly inside a Jupyter/Google Colab workspace:

python ising_sim.py