# SBMLSimulator: A Java Tool for Model Simulation and Parameter Estimation in Systems Biology

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

^{TM}framework EvA2 [12] has been shown to be promising for the optimization of biological systems [11,13,14,15,16].

## 2. Implementation

## 3. Results and Discussion

#### 3.1. Graphical User Interface

**Figure 1.**The graphical user interface (GUI) of The Systems Biology Markup Language (SBML)simulator. The figure shows the main window of SBMLsimulator after importing the model by Bucher et al. [28]. SBMLsimulator enables the user to modify initial quantities (middle left part of window) and to choose the quantities for plotting (upper left). Furthermore, at the bottom of the window the user can specify settings for simulation, such as the integration routine, the simulation start and end time, the simulation step size, and the quality function for comparing the simulated data to experimental data. The simulation can be started by clicking on the simulation button. The right part shows an intermediate solution, whereby the original values are depicted by shapes and the simulated values dependent on the current set of parameters are shown as curves. In the given state, the parameter optimization already found a set of parameters that fit the predefined values with a small error.

#### 3.2. Parameter Estimation Study

**Figure 2.**Distribution of parameters estimated with SBMLsimulator. One hundred parameter estimations with SBMLsimulator for the model by Bucher et al. [28] were run on a computer cluster. The distribution of the 50 estimations with the best fitness values is shown here. For each parameter the estimated values were divided by the original parameter value prior to plotting. It is obvious from the plot that all parameters were estimated closely around their original values. The figure has been created with R software package [40].

**Table 1.**Estimated parameters with units, their initial intervals and their intervals throughout parameter estimation for the model by Bucher et al. [28].

Parameter | Unit | Minimum Initial Value | Maximum Initial Value | Minimum Value | Maximum Value |
---|---|---|---|---|---|

Import_ASLpOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Import_ASLoOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Import_ASpOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Export_ASLpOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Export_ASLoOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Export_ASoOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Export_AS_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Export_ASL_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Import_AS_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Import_ASoOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Export_ASpOH_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

k_PON_OH_c | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

k_PON_ASL_c | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 0.1 | ${10}^{-6}$ | 0.1 |

Import_ASL_k | $\text{mL}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 1 | ${10}^{-6}$ | 1 |

fu_AS | dimensionless | ${10}^{-6}$ | 1 | ${10}^{-6}$ | 1 |

fu_ASL | dimensionless | ${10}^{-6}$ | 1 | ${10}^{-6}$ | 1 |

CYP3A4_ASoOH_Vmax | $\text{pmol}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 100 | ${10}^{-6}$ | 100 |

CYP3A4_ASLpOH_Vmax | $\text{pmol}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 100 | ${10}^{-6}$ | 100 |

CYP3A4_ASLoOH_Vmax | $\text{pmol}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 100 | ${10}^{-6}$ | 100 |

CYP3A4_ASpOH_Vmax | $\text{pmol}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 100 | ${10}^{-6}$ | 100 |

UGT1A3_AS_Vmax | $\text{pmol}\xb7{\text{min}}^{-1}$ | ${10}^{-6}$ | 100 | ${10}^{-6}$ | 100 |

## 4. Conclusions

## 5. Availability and Requirements

^{TM}archive file (JAR) together with a documentation of the program.

**Project name:**SBMLsimulator

**Project homepage:**http://www.cogsys.cs.uni-tuebingen.de/software/SBMLsimulator/

**Contact:**[email protected]

**Operating systems:**Platform independent, i.e., for all systems for which a Java

^{TM}Virtual Machine (JVM) is available.

**Programming language:**Java

^{TM}

**Other requirements:**Java

^{TM}Runtime Environment (JRE) 1.6 or above

**License:**GNU Lesser General Public License (LGPL) version 3

## Acknowledgments

## Author Contributions

## Abbreviations/Nomenclature

AMIGO | Advanced Model Identification in systems biology using Global Optimization |

COPASI | COmplex PAthway SImulator |

CellML | Cell Markup Language |

GUI | graphical user interface |

JAR | Java ^{TM} archive file |

JRE | Java ^{TM} Runtime Environment |

JSBML | Java ^{TM} SBML |

JVM | Java ^{TM} Virtual Machine |

LGPL | GNU Lesser General Public License |

ODE | ordinary differential equation |

SBML | Systems Biology Markup Language |

SBML-PET | SBML Parameter Estimation Tool |

SBSCL | Systems Biology Simulation Core Library |

XML | Extensible Markup Language |

## Conflicts of Interest

## References

- Jamshidi, N.; Wiback, S.J.; Palsson, B.Ø. In Silico Model-Driven Assessment of the Effects of Single Nucleotide Polymorphisms (SNPs) on Human Red Blood Cell Metabolism. Genome Res.
**2002**, 12, 1687–1692. [Google Scholar] [CrossRef] [PubMed] - Dräger, A.; Palsson, B.Ø. Improving collaboration by standardization efforts in systems biology. Front. Bioeng.
**2014**, 2. [Google Scholar] [CrossRef] - Hucka, M.; Finney, A.; Bornstein, B.J.; Keating, S.M.; Shapiro, B.E.; Matthews, J.; Kovitz, B.L.; Schilstra, M.J.; Funahashi, A.; Doyle, J.C.; et al. Evolving a lingua franca and associated software infrastructure for computational systems biology: The Systems Biology Markup Language (SBML) project. Syst. Biol. IEE
**2004**, 1, 41–53. [Google Scholar] [CrossRef] - Dräger, A.; Planatscher, H. Encyclopedia of Systems Biology; Springer-Verlag: New York, NY, USA, 2013; pp. 1249–1251. [Google Scholar]
- Keller, R.; Dörr, A.; Tabira, A.; Funahashi, A.; Ziller, M.J.; Adams, R.; Rodriguez, N.; Le Novère, N.; Hiroi, N.; Planatscher, H.; et al. The systems biology simulation core algorithm. BMC Syst. Biol.
**2013**, 7, 55. [Google Scholar] [CrossRef] [PubMed] - Costa, R.; Machado, D.; Rocha, I.; Ferreira, E. Critical perspective on the consequences of the limited availability of kinetic data in metabolic dynamic modelling. IET Syst. Biol.
**2011**, 5, 157–163. [Google Scholar] [CrossRef] [PubMed][Green Version] - Chen, N.; Del, V.I.; Kyriakopoulos, S.; Polizzi, K.; Kontoravdi, C. Metabolic network reconstruction: Advances in in silico interpretation of analytical information. Curr. Opin. Biotechnol.
**2012**, 23, 77–82. [Google Scholar] [CrossRef] [PubMed] - Dräger, A.; Planatscher, H. Encyclopedia of Systems Biology; Springer-Verlag: New York, NY, USA, 2013; pp. 1627–1631. [Google Scholar]
- Barrett, T.; Wilhite, S.E.; Ledoux, P.; Evangelista, C.; Kim, I.F.; Tomashevsky, M.; Marshall, K.A.; Phillippy, K.H.; Sherman, P.M.; Holko, M.; et al. NCBI GEO: Archive for functional genomics data sets-update. Nucl. Acids Res.
**2013**, 41, 991–995. [Google Scholar] [CrossRef] - Costa, R.S.; Veríssimo, A.; Vinga, S. KiMoSys: A web-based repository of experimental data for KInetic MOdels of biological SYStems. BMC Syst. Biol.
**2014**, 8, 85. [Google Scholar] [CrossRef] [PubMed] - Dräger, A.; Kronfeld, M.; Ziller, M.J.; Supper, J.; Planatscher, H.; Magnus, J.B.; Oldiges, M.; Kohlbacher, O.; Zell, A. Modeling metabolic networks in C. glutamicum: A comparison of rate laws in combination with various parameter optimization strategies. BMC Syst. Biol.
**2009**, 3, 5. [Google Scholar] [CrossRef] [PubMed] - Kronfeld, M.; Planatscher, H.; Zell, A. The EvA2 Optimization Framework. In Learning and Intelligent Optimization; Blum, C., Battiti, R., Eds.; Springer Verlag: Venice, Italy, 2010; pp. 247–250. [Google Scholar]
- Dräger, A.; Supper, J.; Planatscher, H.; Magnus, J.B.; Oldiges, M.; Zell, A. Comparing Various Evolutionary Algorithms on the Parameter Optimization of the Valine and Leucine Biosynthesis in Corynebacterium glutamicum. In Proceedings of the 2007 IEEE Congress on Evolutionary Computation, Singapore, 25–28 September 2007; pp. 620–627.
- Dräger, A.; Kronfeld, M.; Supper, J.; Planatscher, H.; Magnus, J.B.; Oldiges, M.; Zell, A. Benchmarking Evolutionary Algorithms on Convenience Kinetics Models of the Valine and Leucine Biosynthesis in C. glutamicum. In Proceedings of the 2007 IEEE Congress on Evolutionary Computation, Singapore, 25–28 September 2007; pp. 896–903.
- Kronfeld, M.; Dräger, A.; Aschoff, M.; Zell, A. On the Benefits of Multimodal Optimization for Metablic Network Modeling. In Proceedings of the German Conference on Bioinformatics, Halle, Germany, 30 September 2009; pp. 191–200.
- Raue, A.; Schilling, M.; Bachmann, J.; Matteson, A.; Schelke, M.; Kaschek, D.; Hug, S.; Kreutz, C.; Harms, B.D.; Theis, F.J.; Klingmüller, U.; Timmer, J. Lessons Learned from Quantitative Dynamical Modeling in Systems Biology. PLoS ONE
**2013**, 8, e74335. [Google Scholar] [CrossRef] [PubMed] - Balsa-Canto, E.; Banga, J.R. AMIGO, a toolbox for advanced model identification in systems biology using global optimization. Bioinformatics
**2011**, 27, 2311–2313. [Google Scholar] [CrossRef] [PubMed] - Schmidt, H.; Jirstrand, M. Systems Biology Toolbox for MATLAB: A computational platform for research in systems biology. Bioinformatics
**2006**, 22, 514–515. [Google Scholar] [CrossRef] [PubMed] - Zi, Z.; Klipp, E. SBML-PET: A Systems Biology Markup Language-based parameter estimation tool. Bioinformatics
**2006**, 22, 2704–2705. [Google Scholar] [CrossRef] [PubMed] - Hoops, S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. COPASI—A COmplex PAthway SImulator. Bioinformatics
**2006**, 22, 3067–3074. [Google Scholar] [CrossRef] [PubMed] - Maiwald, T.; Timmer, J. Dynamical modeling and multi-experiment fitting with PottersWheel. Bioinformatics
**2008**, 24, 2037–2043. [Google Scholar] [CrossRef] [PubMed] - Bergmann, F.T.; Hucka, M.; Smith, L.; Keating, S.M. SBML Test Suite Database. Available online: http://sbml.org/Facilities/Database/ (accessed on 17 December 2014).
- Rechenberg, I. Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution; Frommann-Holzboog: Stuttgart, Germany, 1973. (In German) [Google Scholar]
- Holland, J. Adaptation in Natural and Artificial Systems; University of Michigan Press: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Storn, R.; Price, K. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Opt.
**1997**, 11, 341–359. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995; Volume 4, pp. 1942–1948.
- Dräger, A.; Rodriguez, N.; Dumousseau, M.; Dörr, A.; Wrzodek, C.; le Novère, N.; Zell, A.; Hucka, M. JSBML: A flexible Java library for working with SBML. Bioinformatics
**2011**, 27, 2167–2168. [Google Scholar] [CrossRef] [PubMed] - Bucher, J.; Riedmaier, S.; Schnabel, A.; Marcus, K.; Vacun, G.; Weiss, T.S.; Thasler, W.E.; Nüssler, A.K.; Zanger, U.M.; Reuss, M. A systems biology approach to dynamic modeling and inter-subject variability of statin pharmacokinetics in human hepatocytes. BMC Syst. Biol.
**2011**, 5, 66. [Google Scholar] [CrossRef] [PubMed][Green Version] - Tovey, C.A. Hill climbing with multiple local optima. SIAM J. Algebr. Discret. Methods
**1985**, 6, 384–393. [Google Scholar] [CrossRef] - Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P. Optimization by Simulated Annealing. Science
**1983**, 220, 671–680. [Google Scholar] [CrossRef] [PubMed] - Schwefel, H.P. Evolutionsstrategie und Numerische Optimierung. Ph.D. Thesis, Department of Process Engineering, Technical University of Berlin, Berlin, Germany, 1975. [Google Scholar]
- Hansen, N.; Ostermeier, A. Completely Derandomized Self-Adaptation in Evolution Strategies. Evolut. Comput.
**2001**, 9, 159–195. [Google Scholar] [CrossRef] [PubMed] - Storn, R. On the Usage of Differential Evolution for Function Optimization. In Proceedings of the 1996 Biennial Conference of the North American Fuzzy Information Processing Society, Berkeley, CA, USA, June 1996; pp. 519–523.
- Clerc, M.; Kennedy, J. The Particle Swarm—Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Trans. Evolut. Comput.
**2002**, 6, 58–73. [Google Scholar] [CrossRef] - Clerc, M. Particle Swarm Optimization; ISTE Ltd.: London, UK, 2005; pp. 139–149. [Google Scholar]
- Chelliah, V.; Laibe, C.; le Novère, N. BioModels Database: A Repository of Mathematical Models of Biological Processes. In In Silico Systems Biology; Schneider, M.V., Ed.; Springer: New York, NY, USA, 2013; Volume 1021, pp. 189–199. [Google Scholar]
- Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. Numerical Recipes in FORTRAN; The Art of Scientific Computing; Cambridge University Press: New York, NY, USA, 1993. [Google Scholar]
- Dräger, A. Computational Modeling of Biochemical Networks. Ph.D. Thesis, University of Tuebingen, Tübingen, Germany, 31 March 2011. [Google Scholar]
- Schilling, M.; Maiwald, T.; Hengl, S.; Winter, D.; Kreutz, C.; Kolch, W.; Lehmann, W.D.; Timmer, J.; Klingmüller, U. Theoretical and experimental analysis links isoform-specific ERK signalling to cell fate decisions. Mol. Syst. Biol.
**2009**, 5. [Google Scholar] [CrossRef] [PubMed] - R Development Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2008. [Google Scholar]
- Cooling, M.T. A Primer on Modular Mass-Action Modelling with CellML. In Systems Biology for Signaling Networks; Choi, S., Ed.; Springer: New York, NY, USA, 2010; Volume 1, pp. 721–750. [Google Scholar]
- Nickerson, D.P.; Corrias, A.; Buist, M.L. Reference descriptions of cellular electrophysiology models. Bioinformatics
**2008**, 24, 1112–1114. [Google Scholar] [CrossRef] [PubMed]

© 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dörr, A.; Keller, R.; Zell, A.; Dräger, A. SBMLSimulator: A Java Tool for Model Simulation and Parameter Estimation in Systems Biology. *Computation* **2014**, *2*, 246-257.
https://doi.org/10.3390/computation2040246

**AMA Style**

Dörr A, Keller R, Zell A, Dräger A. SBMLSimulator: A Java Tool for Model Simulation and Parameter Estimation in Systems Biology. *Computation*. 2014; 2(4):246-257.
https://doi.org/10.3390/computation2040246

**Chicago/Turabian Style**

Dörr, Alexander, Roland Keller, Andreas Zell, and Andreas Dräger. 2014. "SBMLSimulator: A Java Tool for Model Simulation and Parameter Estimation in Systems Biology" *Computation* 2, no. 4: 246-257.
https://doi.org/10.3390/computation2040246