Category Cross-Omics>Pathway Analysis/Gene Regulatory Networks/Tools and Cross-Omics>Agent-Based Modeling/Simulation/Tools

Abstract SQUAD (Standardized Qualitative Dynamical Modeling Suite) is a software product for the ‘dynamic modeling’ of regulatory networks using the Standardized Qualitative Approach [A method for the generation of Standardized Qualitative Dynamical Systems (see below...) of regulatory networks].

SQUAD converts the network into a discrete dynamical system, and it uses a ‘binary decision diagram’ algorithm to identify all the steady states of the system. Then, the software creates a continuous dynamical system and localizes its steady states which are located near the steady states of the discrete system.

The software permits you to make simulations on the continuous system, allowing for the modification of several parameters.

Importantly, SQUAD includes a framework for ‘perturbing networks’ in a manner similar to what is performed in experimental laboratory protocols, for example by activating receptors or knocking out molecular components.

Using this software the manufacturer has been able to successfully reproduce the behavior of the regulatory network implicated in T-helper cell differentiation.

The simulation of ‘regulatory networks’ aims at predicting the behavior of a whole system when subject to stimuli, such as drugs, or determine the role of specific components within the network. The predictions can then be used to interpret and/or drive laboratory experiments.

SQUAD provides a user-friendly graphical interface, accessible to both computational and experimental biologists for the fast qualitative simulation of large regulatory networks for which kinetic data is Not necessarily available.

Standardized Qualitative Dynamical Systems --

Standardized Qualitative Dynamical Systems is a ‘hybrid modeling’ method combining Boolean (discrete) and continuous modeling methodologies. This approach enables the dynamic simulation of regulatory networks in the absence of kinetic data.

Boolean networks have been used as a convenient modeling tool due to their computational simplicity, giving rise to a large body of literature regarding their suitability for modeling diverse biological processes. In Boolean models, nodes are represented as variables that can attain only two (2) values: 0 or 1, which represent the minimal and maximal state of activation, respectively.

These nodes are connected through directed relationships, which can be either positive (i.e. activatory) or negative (i.e. inhibitory).

In most cases, the specification of the network connectivity is Not sufficient to determine the response of a given node to all its possible inputs. Because of this, modelers have to specify a Boolean function for every node, incorporating as much information related to the biological system as possible.

While Boolean models give appropriate qualitative descriptions of the real biological systems, models can be refined by incorporating nodes with more than two levels of activation. This is usually possible when enough experimental evidence is available, allowing you to distinguish among different levels of activation.

In other cases, however, defining multiple activation levels helps to incorporate distinct functional levels into the nodes. Also, Boolean models have been extended by introducing stochasticity in the updating order of the nodes.

The Standardized Qualitative Dynamical Systems modeling approach can also be seen as an extension of the Boolean methodology, because it creates a system of Ordinary Differential Equations (ODEs) that have a similar overall form to the step functions of Boolean models.

In this way, the nodes in the network can attain a continuous range of values while at the same time allowing a direct comparison with Boolean nodes, since both implementations have their lowest value at 0, and their highest value at 1.

This approach permits the ‘qualitative modeling’ of networks, but allows for the possibility of incorporating ‘quantitative information’ into the model via the fitting of parameters.

In order to facilitate the use of Standardized Qualitative Dynamical Systems, the manufacturers developed the SQUAD modeling suite, which provides a graphical interface accessible to modelers and biologists to perform simulations of regulatory or signaling networks.

This tool can speed up the process of ‘modeling signaling networks’, because it provides a rapid way to obtain the set of all stable steady states of a network as implied by its topology. Also, it provides a convenient graphical user interface (GUI) to make dynamical simulations and evaluate the effect of altering parameters.

Simulations using SQUAD --

Simulations using SQUAD are divided in three (3) main parts.

First, the manufacturer supplies the program with a ‘directed graph’ representing the topology of a network, which can be done in the form of simple text or Systems Biology Markup Language (SBML) file formats (see below...). The program converts the network into a ‘discrete dynamical system’, and uses Boolean algorithms to identify all its stable steady states.

Second, the program converts the network into a continuous dynamical system, in the form of a set of ODEs, and uses the ‘steady states’ found in the discrete model as a guide to localize the stable steady states in the continuous model.

And third, SQUAD allows the user to perform ‘dynamic simulations’, which may include perturbations, to assess the behavior of the network and identify the roles of specific nodes within the network.

SQUAD input file formats --

SQUAD accepts three (3) types of input formats: NET, MML and SBML files. The NET format is a simple text file, and the MML format is a XML file; both were developed specifically for SQUAD.

Since defining a network topology for large networks in text format can be difficult and error-prone, the manufacturer has included the possibility of using CellDesigner generated files as input.

CellDesigner is a free, widely used graphical tool that allows the easy construction and edition of diagrams of metabolic and regulatory networks.

CellDesigner provides an implementation of the SBML format, used by a large number of modeling tools. Whenever CellDesigner files are used as input, SQUAD retains the spatial layout of the nodes providing a more intuitive interpretation of the simulation results.

The distribution of SQUAD includes a folder containing the T-helper network sample files in the three (3) aforementioned formats.

SQUAD Implementation --

SQUAD is written in Java. The network topology is loaded using any of three possible formats (stated above…). SBML files are parsed using the JigCell SBML parser.

In order to represent the graphs both in memory and graphically, the manufacturers use an extension to the JUNG library built purposely to integrate parameters required for the dynamic simulations.

The steady states of the loaded graphs are computed using a ‘Reduced Order Binary Decision Diagram’ algorithm. This algorithm is written in C++ and is integrated to the package through the Java Native Interface (JNI).

The ordinary differential equations used for the dynamic simulations are implemented using the Open Source Physics framework (OSP), using an adapted version of the Runge-Kutta4 solver to do the numerical computation.

Furthermore, the OSP library is also used to display the activity using dynamic plots. The results of the simulations are stored in matrices using the Dcolt package, which allows mapping of the matrices to a file system in order to reduce the memory expenditure.

Finally, the user interface is built using Java Swing components, and the Synthetica library is used to provide a consistent aspect on multiple platforms.

System Requirements

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Manufacturer Web Site SQUAD

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G6G Abstract Number 20563

G6G Manufacturer Number 104170