Boolean models

Boolean network models are a type of logical model. The “logic” in the name refers to rules based on conditions that must be fulfilled for a statement to be true—much like everyday reasoning:

You need eggs AND flour to bake a cake, but you can use butter OR margarine.  

In a Boolean network, each model component is represented by a node, and each node has a binary value — typically 0 or 1—representing something abstract like off/on, inactive/active, or absent/present (Fig 7). These nodes can represent many biological entities: from the presence of a gene product, to the activity of a promoter, all the way to the phenotype of a cell or organism. 

The nodes are connected by directed edges, which represent regulatory interactions—either positive (e.g., activation, synthesis) or negative (e.g., inhibition, degradation). Nodes connected to a given node by incoming edges are its regulatory inputs.

The values of the nodes are updated in a stepwise fashion. At each step, the value of a node is updated based on Boolean logic rules and the current values of its regulators. Steps often represent qualitative progressions, like moving from one step to the next in a regulatory sequence without a defined duration. The updates are synchronous in the most basic version: all nodes update their values simultaneously, based on their inputs at the previous step.

The basic logic rules are NOT, OR and AND. In a NOT logic the regulated node takes the opposite value of its regulating node in the next time step. If a node has multiple inputs, their combined effect needs to be evaluated. This can be achieved with an AND or an OR logic. An AND logic means that all regulators of a node must be active for the node to become active after the next time step (Fig 8). An OR logic means that in case of multiple regulators regulating a node, at least one of them has to be active for the regulated node to become active after the next time step (butter OR margarine!).

Boolean network models have the advantage that they don’t contain any unknown parameters that would need to be calibrated. The Boolean formalism is limited when it comes to feedback loops in a process and in scenarios like weak background activation, where one would need something halfway between 0 and 1. The latter can be cured by using multi valued formalisms where each node can take on more than 2 values (multi-value logic).

Explore a guided example for a Boolean model in the following page.