### Abstract

Language | English |
---|---|

Title of host publication | Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) |

Pages | 437-442 |

Number of pages | 6 |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

- cross gramians
- sensitivity analysis
- systems biology

### Cite this

*Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006)*(pp. 437-442)

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*Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006).*pp. 437-442.

**Relating cross gramians and sensitivity analysis in systems biology.** / Streif, S.; Findeisen, R.; Bullinger, Eric.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Relating cross gramians and sensitivity analysis in systems biology

AU - Streif, S.

AU - Findeisen, R.

AU - Bullinger, Eric

PY - 2006

Y1 - 2006

N2 - One of the key challenges in systems biology is the analysis of often complex biochemical reacation networks which contain many uncertain parameters. Typically, the dynamics of these systems strongly depends on a significant amount of parameters, hampering the analysis significantly as even the small changes in the value of the parameters can have significant influences on the overall behaviour of the entire network. Thus one of the key problems in systems biology is to analyse the influence of parameters on the steady state and transient behaviour. In the first part of this work we derive links between first order sensitivity analysis as typically employed in systems biology and the concepts of controllability and observability of systems theory. Specifically we establish a close connection between cross Gramians and the so called response coefficients as used in Metabolic Control Analysis. In a second part we outline an expansion of this approach using empirical cross Gramians, allowing to overcome some of the limitations of first order sensitivity methods such as local validity.

AB - One of the key challenges in systems biology is the analysis of often complex biochemical reacation networks which contain many uncertain parameters. Typically, the dynamics of these systems strongly depends on a significant amount of parameters, hampering the analysis significantly as even the small changes in the value of the parameters can have significant influences on the overall behaviour of the entire network. Thus one of the key problems in systems biology is to analyse the influence of parameters on the steady state and transient behaviour. In the first part of this work we derive links between first order sensitivity analysis as typically employed in systems biology and the concepts of controllability and observability of systems theory. Specifically we establish a close connection between cross Gramians and the so called response coefficients as used in Metabolic Control Analysis. In a second part we outline an expansion of this approach using empirical cross Gramians, allowing to overcome some of the limitations of first order sensitivity methods such as local validity.

KW - cross gramians

KW - sensitivity analysis

KW - systems biology

UR - http://www-ics.acs.i.kyoto-u.ac.jp/mtns06/

M3 - Conference contribution book

SP - 437

EP - 442

BT - Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006)

ER -