Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Parameter identification in systems biology: solving inverse problems using regularization

Workshop on Systems Biology, Fri, 09 Nov, 2007

Speaker: Stefan Müller


The conventional forward analysis of systems biology models comprehends ODE
solving and bifurcation analysis. This approach can be complemented by usage
of methods from the field of inverse problems. In particular, unknown (or
inaccessible) parameters (or initial conditions) can be estimated from
time-series measurements of chemical species. Due to measurement error,
parameter identification is a (non-linear) ill-posed inverse problem such
that stable estimates can be obtained only by the use of regularization

More technically, parameter identification is formulated as an optimization
problem with penalty term. Additionally, adjoint sensitivity analysis is used
to efficiently compute the gradient of the functional - with the
computational effort (essentially) independent of the numbers of parameters
to be identified.

The software package developed in our group is based on the SBML ODE Solver
library (SOSlib). SOSlib is a C/C++ programming library for the construction,
symbolic and fast numerical analysis of an ODE system derived from a
biochemical reaction network encoded in the Systems Biology Markup Language
(SBML) . The local (gradient based) search is performed using forward and
adjoint capabilities of SOSlib within the interior point optimizer IpOpt; the
global (randomization based) search is using a strategy called Scatter

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