# Final Technical Report "Multiscale Simulation Algorithms for Biochemical Systems"

## Abstract

Biochemical systems are inherently multiscale and stochastic. In microscopic systems formed by living cells, the small numbers of reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA, Gillespie, 1976), a numerical simulation procedure that is essentially exact for chemical systems that are spatially homogeneous or well stirred. Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multiscale nature of the underlying problem: (1) stiffness, i.e. the presence of multiple timescales, the fastest of which are stable; and (2) the need to include in the simulation both species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation (or at some scale in between). This project has focused on the development of fast and adaptive algorithms, and the fun- damental theory upon which they must be based, for the multiscale simulation of biochemicalmore »

- Authors:

- Publication Date:

- Research Org.:
- University of California, Santa Barbara

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1148588

- Report Number(s):
- DOE-UCSB-ER25621

- DOE Contract Number:
- FG02-04ER25621

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Multiscale simulation; discrete stochastic simulation; chemically reacting systems

### Citation Formats

```
Petzold, Linda R.
```*Final Technical Report "Multiscale Simulation Algorithms for Biochemical Systems"*. United States: N. p., 2012.
Web. doi:10.2172/1148588.

```
Petzold, Linda R.
```*Final Technical Report "Multiscale Simulation Algorithms for Biochemical Systems"*. United States. doi:10.2172/1148588.

```
Petzold, Linda R. Thu .
"Final Technical Report "Multiscale Simulation Algorithms for Biochemical Systems"". United States. doi:10.2172/1148588. https://www.osti.gov/servlets/purl/1148588.
```

```
@article{osti_1148588,
```

title = {Final Technical Report "Multiscale Simulation Algorithms for Biochemical Systems"},

author = {Petzold, Linda R.},

abstractNote = {Biochemical systems are inherently multiscale and stochastic. In microscopic systems formed by living cells, the small numbers of reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA, Gillespie, 1976), a numerical simulation procedure that is essentially exact for chemical systems that are spatially homogeneous or well stirred. Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multiscale nature of the underlying problem: (1) stiffness, i.e. the presence of multiple timescales, the fastest of which are stable; and (2) the need to include in the simulation both species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation (or at some scale in between). This project has focused on the development of fast and adaptive algorithms, and the fun- damental theory upon which they must be based, for the multiscale simulation of biochemical systems. Areas addressed by this project include: (1) Theoretical and practical foundations for ac- celerated discrete stochastic simulation (tau-leaping); (2) Dealing with stiffness (fast reactions) in an efficient and well-justified manner in discrete stochastic simulation; (3) Development of adaptive multiscale algorithms for spatially homogeneous discrete stochastic simulation; (4) Development of high-performance SSA algorithms.},

doi = {10.2172/1148588},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {10}

}