# Multi-scenario modelling of uncertainty in stochastic chemical systems

## Abstract

Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent onmore »

- Authors:

- Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)
- Department of Chemical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)
- (Canada)

- Publication Date:

- OSTI Identifier:
- 22382109

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 273; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; DIFFERENTIAL EQUATIONS; GENE REGULATION; ISOMERIZATION; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; STOCHASTIC PROCESSES; SURFACES

### Citation Formats

```
Evans, R. David, Ricardez-Sandoval, Luis A., E-mail: laricardezsandoval@uwaterloo.ca, and Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1.
```*Multi-scenario modelling of uncertainty in stochastic chemical systems*. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2014.05.028.

```
Evans, R. David, Ricardez-Sandoval, Luis A., E-mail: laricardezsandoval@uwaterloo.ca, & Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1.
```*Multi-scenario modelling of uncertainty in stochastic chemical systems*. United States. doi:10.1016/J.JCP.2014.05.028.

```
Evans, R. David, Ricardez-Sandoval, Luis A., E-mail: laricardezsandoval@uwaterloo.ca, and Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1. Mon .
"Multi-scenario modelling of uncertainty in stochastic chemical systems". United States. doi:10.1016/J.JCP.2014.05.028.
```

```
@article{osti_22382109,
```

title = {Multi-scenario modelling of uncertainty in stochastic chemical systems},

author = {Evans, R. David and Ricardez-Sandoval, Luis A., E-mail: laricardezsandoval@uwaterloo.ca and Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1},

abstractNote = {Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo.},

doi = {10.1016/J.JCP.2014.05.028},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 273,

place = {United States},

year = {2014},

month = {9}

}