### Abstract

An important aspect of systems biology research is the so-called "reverse engineering" of cellular metabolic dynamics from measured input-output data. This allows researchers to estimate and validate both the pathway's structure as well as the kinetic constants. In this paper, the recently published 'Proximate Parameter Tuning' (PPT) method for the identification of biochemical networks is analysed. In particular, it is shown that the described PPT algorithm is essentially equivalent to a sequential linear programming implementation of a constrained optimization problem. The corresponding objective function consists of two parts, the first emphasises the data fitting where a residual 1-norm is used, and the second emphasises the proximity of the calculated parameters to the specified nominal values, using an ∞-norm. The optimality properties of PPT algorithm solution as well as its geometric interpretation are analyzed. The concept of optimal parameter locus is applied for the exploration of the entire family of optimal solutions. An efficient implementation of the parameter locus is also developed. Parallels are drawn with 1-norm parameter deviation regularization which attempt to fit the data with a minimal number of parameters. Finally, a small example is used to illustrate all of these properties.

Original language | English |
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Pages (from-to) | 697-718 |

Number of pages | 22 |

Journal | Bulletin of Mathematical Biology |

Volume | 72 |

Issue number | 3 |

Early online date | 5 Jan 2010 |

DOIs | |

Publication status | Published - 1 Apr 2010 |

Externally published | Yes |

### Keywords

- Inverse modelling
- Parameter estimation
- Proximate parameter tuning
- Regularization
- Systems biology

### ASJC Scopus subject areas

- Neuroscience(all)
- Immunology
- Mathematics(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Pharmacology
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics

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## Cite this

*Bulletin of Mathematical Biology*,

*72*(3), 697-718. https://doi.org/10.1007/s11538-009-9466-y