# ISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks

## Abstract

Stochastic simulation and modeling play an important role to elucidate the fundamental mechanisms in complex biochemical networks. The parametric sensitivity analysis of reaction networks becomes a powerful mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, due to overwhelming computational cost, parametric sensitivity analysis is a extremely challenging problem for stochastic models with a high-dimensional parameter space and for which existing approaches are very slow. Here we present an information-theoretic sensitivity analysis in path-space (ISAP) MATLAB package that simulates stochastic processes with various algorithms and most importantly implements a gradient-free approach to quantify the parameter sensitivities of stochastic chemical reaction network dynamics using the pathwise Fisher information matrix (PFIM; Pantazis, Katsoulakis, and Vlachos 2013). The sparse, block-diagonal structure of the PFIM makes its computational complexity scale linearly with the number of model parameters. As a result of the gradientfree and the sparse nature of the PFIM, it is highly suitable for the sensitivity analysis of stochastic reaction networks with a very large number of model parameters, which are typical in the modeling and simulation of complex biochemical phenomena. Finally, the PFIM provides a fast sensitivity screening method (Arampatzis, Katsoulakis, and Pantazis 2015) whichmore »

- Authors:

- Univ. of Massachusetts, Amherst, MA (United States)

- Publication Date:

- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); Defense Advanced Research Projects Agency (DARPA) (United States)

- OSTI Identifier:
- 1509830

- Grant/Contract Number:
- SC0010723; W911NF1520122

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Statistical Software

- Additional Journal Information:
- Journal Volume: 85; Journal Issue: 3; Journal ID: ISSN 1548-7660

- Publisher:
- Foundation for Open Access Statistics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; stochastic biochemical networks; parametric sensitivity analysis; high-dimensional parameter space; pathwise Fisher information matrix; fast sensitivity screening

### Citation Formats

```
Hu, Weilong, Pantazis, Yannis, and Katsoulakis, Markos A. ISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks. United States: N. p., 2018.
Web. doi:10.18637/jss.v085.i03.
```

```
Hu, Weilong, Pantazis, Yannis, & Katsoulakis, Markos A. ISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks. United States. doi:10.18637/jss.v085.i03.
```

```
Hu, Weilong, Pantazis, Yannis, and Katsoulakis, Markos A. Thu .
"ISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks". United States. doi:10.18637/jss.v085.i03. https://www.osti.gov/servlets/purl/1509830.
```

```
@article{osti_1509830,
```

title = {ISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks},

author = {Hu, Weilong and Pantazis, Yannis and Katsoulakis, Markos A.},

abstractNote = {Stochastic simulation and modeling play an important role to elucidate the fundamental mechanisms in complex biochemical networks. The parametric sensitivity analysis of reaction networks becomes a powerful mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, due to overwhelming computational cost, parametric sensitivity analysis is a extremely challenging problem for stochastic models with a high-dimensional parameter space and for which existing approaches are very slow. Here we present an information-theoretic sensitivity analysis in path-space (ISAP) MATLAB package that simulates stochastic processes with various algorithms and most importantly implements a gradient-free approach to quantify the parameter sensitivities of stochastic chemical reaction network dynamics using the pathwise Fisher information matrix (PFIM; Pantazis, Katsoulakis, and Vlachos 2013). The sparse, block-diagonal structure of the PFIM makes its computational complexity scale linearly with the number of model parameters. As a result of the gradientfree and the sparse nature of the PFIM, it is highly suitable for the sensitivity analysis of stochastic reaction networks with a very large number of model parameters, which are typical in the modeling and simulation of complex biochemical phenomena. Finally, the PFIM provides a fast sensitivity screening method (Arampatzis, Katsoulakis, and Pantazis 2015) which allows it to be combined with any existing sensitivity analysis software.},

doi = {10.18637/jss.v085.i03},

journal = {Journal of Statistical Software},

number = 3,

volume = 85,

place = {United States},

year = {2018},

month = {9}

}