Conservation Laws and Identifiability of Models for Cellular Metabolism

author: Bernt Wennberg, Chalmers University of Technology

Description

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 know whether all parameters can be uniquely estimated from available data. In this paper we discuss a class of models for metabolism, where the introduction of conserved moieties may cause an otherwise identifiable model to be unidentifiable. A general method for reparametrization to identifiable rate expressions is presented, and the general results are exemplified by three well-cited models for yeast metabolism.

Joint work with Milena Anguelova, Gunnar Cedersuna, Carl Johan Franzen, Mikael Johansson

Categories

Top: Computer Science: Bioinformatics

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*Slides*
0:01	Conservation laws and identifiability of models for metabolism Milena Anguelova1 Gunnar Cedersund2 Carl Johan Franzén3 Mikael Johansson3 Bernt Wennberg1
0:31	A model for glycolytic oscillations in yeast
1:16	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
2:07	Unidentifiability due to the assumption of a conserved moiety - in this model [NAD+] + [NADH] assumed to be constant (=p)
3:26	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 calculations
3:27	Kinetic models of metabolism
4:10	Original rate expression
5:29	A symmetry group for the parameters
5:59	A linear algebra formalism
7:18	The expressions:
8:36	Picture
10:03	The general formalism
10:40	Number of unidentifiable pararameters
11:55	Computing symmetry groups
13:29	Symbolic calculation: a Mathematica implementation for reasonably complicated expressions, + reparameterisation to identifiable expressions + full description of symmetry groups available
13:44	symmBerData.nb
13:49	symmBerData.nb - here one should enter model data, and execute the corresponding cell
14:23	symmBerStart.nb - normally one can just execute this notebook
14:43	symmBer.nb this notebook should just be evaluated; final results are presented at the end
14:53	The matrix A
15:08	The results presented are the degree of freedom a list of identifiable parameters - a list of un identifiable parameters - a list of identifiable parameter combinations
15:48	This gives a vector field that defines the symmetry transformation
16:15	The last part is an example of an identifiable reparameterisation of the rate expression
16:34	The notebook is not always useful:
17:06	The rate
17:30	Matrix dimension 1975 x 3365
18:06	symmBerData.nb - here one should enter model data, and execute the corresponding cell

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