Uncertainty Quantification and Global Sensitivity Analysis

In the field of systems biology, chemical reaction networks are modeled in various ways, two of those are: (i) stochastic simulations (e.g. Gillespie algorithm) and (ii) ordinary differential equations. In this package we use a simple tabular model description of reaction systems and automatically generate C code for either solver type. We use the ordinary differential equation solvers from the GNU Scientific Library and provide an interface that deals with lists of simulation experiments. Each simulation experiment contains both the data, and instructions for the model to replicate the data. We use approximate Bayesian computation methods (combined with Markov chain Monte Carlo and sequential Monte Carlo, particle filters) as well as classic methods such as Random Walk Metropolis (Gaussian transition kernel) and Simplified Manifold Metropolis adjusted Langevin algorithm for a Bayesian investigation of the model´s parameter space. Experiments can be evaluated in a sequence; intermediate probability densities are modeled using the 'VineCopula' package. The package is also intended to be useful in an HPC environment, with some functions that use 'pbdMPI' capabilities.

Uncertainty Quantification (UQ) and Sensitivity Analysis (SA)

This is an R package that performs parameter estimation, uncertainty quantification, and global sensitivity analysis using Bayesian (UQ) and variance decomposition methods (GSA). It is primarily designed for biochemical reaction networks describing intracellular cellular pathways and similar. All information about the model as well as the experimental data used for parameter estimation and uncertainty quantification is stored in the SBtab table format for Systems Biology projects.

• Source code: https://github.com/icpm-kth/uqsa/
• Documentation https://icpm-kth.github.io/uqsa/
• Examples: https://icpm-kth.github.io/uqsa/articles/examples_overview.html
• Cite: https://icpm-kth.github.io/uqsa/articles/cite.html

Acknowledgements

This open source software code was developed with support from the Swedish e-Science Research Centre (SeRC) as well as within the Human Brain Project, funded from the European Union’s Horizon 2020 Framework Programme for Research and Innovation (945539) (Human Brain Project SGA1, SGA2 and SGA3).

Technical summary of the UQSA tool-set

• An easy-to-use, human- and machine-readable format for reaction-based models and calibration data (as tables/data-frames).
• Converting biological models into mathematical models, and code:
  • Deterministic models ODE solvers from the GSL odeiv2 module written in C
  • Stochastic models built in Gillespie algorithm implementation written in C
• We also create R-files for the optional use of ODE solvers from the deSolve package, by writing a custom likelihood function
• It is possible to use the GillespieSSA2 package by writing a custom distance function.
• MCMC algorithms for sampling from the posterior distribution
  • Deterministic models Random Walk Metropolis and SMMALA, both available in a parallel tempering setting.
  • Stochastic models ABC-SMC or ABC-MCMC algorithm.
• By default we use an ABC distance function in the form of weighted Euclidean distance, with weights given by (the reciprocals of) the experimental measurement errors (when available). The ABC distance function can be defined by the user.
• A vine-copula-based approach for sampling from a non-trivial, non-orthogonal prior.
• Functionality for global sensitivity analysis on orthogonal and non-orthogonal input factors.
• Model simulations are specified as lists (a convenient abstraction)
• An event system for scheduled events within an experiment to model sudden activation (and similar interventions) in an experimental protocol.
• Complex experimental (transient) input data, such as neuroscience spike-trains, can be easily fitted to corresponding model functions.
• Both the uq and sa algorithms can be run on compute clusters across several nodes using pbdMPI.