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Conservation Laws and Identifiability of Models for Cellular Metabolism
Published on Apr 04, 20075075 Views
New experimental techniques in the biosciences provide us with high-quality data allowing quantitative mathematical modeling. When fitting model parameters to experimental data, it is important to kno
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Conservation laws and identifiability of models for metabolism Milena Anguelova1 Gunnar Cedersund2 Carl Johan Franzén3 Mikael Johansson3 Bernt Wennberg100:01
A model for glycolytic oscillations in yeast00:31
The identification problem given a time series of measured concentrations ( [GAP], [NAD+], [BPG] and [NADH]) determine the 6 parameters the model: a set of ODE’s for the concentrations, together 01:16
Unidentifiability due to the assumption of a conserved moiety - in this model [NAD+] + [NADH] assumed to be constant (=p)02:07
An outline of the talk: Symmetries and unidentifiability: two more examples A general formalism based on linear algebra Demonstration of a Mathematica code to help with calculations03:26
Kinetic models of metabolism03:27
Original rate expression04:10
A symmetry group for the parameters05:29
A linear algebra formalism05:59
The expressions:07:18
Picture08:36
The general formalism10:03
Number of unidentifiable pararameters10:40
Computing symmetry groups11:55
Symbolic calculation: a Mathematica implementation for reasonably complicated expressions, + reparameterisation to identifiable expressions + full description of symmetry groups available 13:29
symmBerData.nb13:44
symmBerData.nb - here one should enter model data, and execute the corresponding cell13:49
symmBerStart.nb - normally one can just execute this notebook14:23
symmBer.nb this notebook should just be evaluated; final results are presented at the end14:43
The matrix A14:53
The results presented are the degree of freedom a list of identifiable parameters - a list of un identifiable parameters - a list of identifiable parameter combinations15:08
This gives a vector field that defines the symmetry transformation15:48
The last part is an example of an identifiable reparameterisation of the rate expression16:15
The notebook is not always useful:16:34
The rate 17:06
Matrix dimension 1975 x 336517:30
symmBerData.nb - here one should enter model data, and execute the corresponding cell18:06