Abstract
BackgroundOver the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary.ResultsHere we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems.To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters.ConclusionsPeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0972-2) contains supplementary material, which is available to authorized users.
Highlights
Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models
Model time series and solution derivatives PeTTSy has been applied to a broad range of examples, but for purposes of illustrating the software we will be applying it to two exemplar systems: the plant circadian clock model of [18] and the model of NF-κB oscillations from [19]
Since it is clear that the first principal components (PCs) indicates the largest change to the model trajectories, and all the current analysis has indicated that GI mRNA as a variable that will be most affected by any parameter changes, we can plot the a composite plots just looking at this specific variable and the first PC
Summary
Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. There is a rapidly increasing number of complex, high dimensional deterministic models in Systems Biology and these play a crucial role in gaining an understanding of important biological systems that would be impossible to achieve using lab-based approaches alone. Sensitivity analysis is an important approach that has been successfully employed to do the above, but it is just one part of dynamical systems perturbation theory [1, 2]. This extensive theory enables one to probe the behaviour of dynamical systems locally in parameter space. These changes can mimic perturbations to some rates, pulse experiments, or can even mimic the creation of specific mutations such as gene knock-outs or knock-downs
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