caramirezal/SQUADBookChapter

Dynamic network models has been used in biological contexts to represent complex regulatory interactions between molecules. Discrete Boolean methods are often used as a first modeling approximation. However in some biological contexts they are not sufficient to represent some behaviors as that which depends on threshold activation or molecular gradients. In these cases, ordinary differential equations are preferred but their application need the knowledge of kinetic parameters. Here we describe a continuous ODE system called Standardized Qualitative Analysis of Dynamics (SQUAD) as a first approximation to simulate continuous models without the need of kinetic parameters.

#SQUAD Book chapter

This project exemplifies the implementation of the Standardized Qualitative Analysis of Dynamics (SQUAD) method as defined in Di Cara et al, 2007 and later modified in Martínez-Sosa et al, 2013. Regulatory network modeling approaches has been shown to be a valuable tool to study the way cells integrate signals that control biological processes. One of these approaches is the SQUAD method, which approximates a Boolean network with the use of a set of ordinary differential equations. The main benefit of the SQUAD method over purely Boolean approaches is the possibility of evaluating the effect of continuous external signals, which are pervasive in biological phenomena.

CartoonNetwork.R file defines the regulatory network comprising three nodes A,B and C shown in Figure 1 from the book Chapter in BoolNet format.

SQUADTransformation.ipynb file exemplifies the simulation of the regulatory network model defined in the CartoonNetwork.R file, first as a boolean regulatory network model, and then as a continuous regulatory network using the SQUAD method.

SQUAD_implementation.ipynb contains a tutorial for implementing node perturbations with the SQUAD methodology. It presents the code used to make the examples in Figure 4 (simulating external perturbations) and Figure 5 (simulating B lymphocyte differentiation), respectively.

animation.gif shows an animation of the Figure 3 that allows to see the direction of the flow of the states of the network at different rotation angles.

References

Di Cara, A., Garg, A., De Micheli, G., Xenarios, I., & Mendoza, L. (2007). Dynamic simulation of regulatory networks using SQUAD. BMC Bioinformatics, 8(1), 462. http://doi.org/10.1186/1471-2105-8-462

Martínez-Sosa, P., & Mendoza, L. (2013). The regulatory network that controls the differentiation of T lymphocytes. BioSystems, 113(2), 96–103. http://doi.org/10.1016/j.biosystems.2013.05.007