RustySpigot

Boolean Network Modeller Tutorial

BNM is a tool to aid the modelling of organic systems through the formalism of boolean networks.

This brief tutorial is intended to introduce the main features of BNM. Example networks can be found under the Example folder where BNM is installed.

• Run BNM

Fig 1 The initial state of BNM

• Create a node by clicking the circular "Add Node" button then clicking on the drawing area.

Fig 2 The creation of a node

• Rename the node by clicking the "Name" box, and add two more nodes to produce the network shown in figure 3.
  

Fig 3 A simple network of three unconnected nodes

• Connect the nodes as shown in figure 4 by selecting the "Add Activator" button (a blue arrow with a plus sign) then clicking first in the source node, then in the destination node.

Activator and inhibitor arcs are used to define the functions of the nodes. By default, when simulated a node will have a value of 1 in the next state if the sum of activator arcs from activated (value 1) nodes is greater than the sum of activated inhibitors.

Fig 4 A network of three nodes, each with one positive input

• You can also add connections from a node back to itself by clicking in the node, then releasing the mouse button.
• A node's function can be manually defined rather than using the default summation formula, by selecting the node then changing the default drop down box from True to False.

Fig 5 The same network with an additional self regulation arc

• Clicking the custom drop down box then allows you to define the formula manually.
• In the example below, if a and b are both 0 then the node will have the value 0. Under any other state it will have the value 1.
• Clicking save stores the formula
  

Fig 6 The definition of a node's custom formula

• You can exhausitvely simulate a network by clicking the Simulate button (indicated by an image of a spreadsheet). This also highlights all Singleton attractors and Cyclic attractors.
• There is the option to use the faster Singleton attractor finder instead, by clicking the lightning bolt button.

Fig 7 The simulation of the network

• You can export the network in Reactive Module modelling language for simulation in a tool such as JMocha
• To do this click File then Export then select the output type as reactive modules.
  

Boolean Networks
Boolean networks were first introduced by Kauffmanas a way of modeling biological systems. They provide a mathematical framework for dynamic systems that allow complex, unpredictable behavior from the deterministic local interactions of many simple components acting in parallel.
Boolean networks were chosen as they are both fairly simple to implement and understand, and have there is a rich history of their use in computational biology literature.

A Boolean network can be built from traditional graphs representing biochemical interactions. In such graphs there are nodes representing biochemical components (such as genes or proteins) and between them there are arcs that can either be weighted positive (for activation) or negative (for inhibition). This graph can be used to define the Boolean functions of each component, which update the components value to true if the amount of activation is greater than the amount of inhibition. They have been used with much success in modeling a genetic regulatory networks, and have been proved useful in analyzing system dynamics and reasoning about stability and robustness of biological systems.
A Boolean network G(V,F) is defined by a set of nodes corresponding to genes V = {x1, . . . , xn} and a list of Boolean functions F = (f1, . . . , fn).
The state of a node (gene) is completely determined by the values of other nodes at time t by means of underlying logical Boolean functions. The model is represented in the form of directed graph.

We are often finding states in which a biological system is stable, as these are the states that we can expect to find real organisms in.
Attractor states are states in which the network is stable; that is either on the next iteration nothing will change (called simple attractor states), or the network is in a continuous loop.

More information on Boolean Networks is available at http://www.calresco.org/boolean.htm