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Experimental design in systems biology |
One
of the great challenges in systems biology is the coupling of mathematical
models and experimental data. To construct a quantitative model one needs many
steps in the iterative cycle "experiment -> data -> model ->
experiment". For each new model, parameters that cannot be measured should
be estimated using available experimental data. In the first few stages the
model will be crude and parameter estimation is in general not critical. These
models have limited predictive value, but can still be used to guide new
experiments. However, systems biology now enters the stage that data becomes
abundant and models complicated and are expected to give realistic quantitative
predictions. To
fit a mathematical model to experimental data and design new experiments e.g.
to discriminate between rivalry models is in itself a series of mathematical
and computational challenges: (i) a priori parameter
identification – prove that the parameters of the model can be identified if
there were continuous and error-free data available for the experimental
observables, (ii) the actual optimization procedure to minimize a chosen
measure or fitness function with global, local or hybrid search methods, (iii)
a posteriori parameter identification - the statistical analysis of the obtained
parameters corresponding to the minimum, (iv) optimal experimental design. The
current methods in systems biology for steps (ii)-(iv)
are based on the Maximum Likelihood Estimation, i.e. the observations have a
joint probability density function, and on the assumptions that the
observations are independent and that the data contain normally distributed
errors. In this case the maximum likelihood solution is the least squares
solution (i.e. the measure in (ii) is the least squares sum). However,
in practice the assumption of independent, normally distributed observations is
often not valid. The data used to fit the models may be gene-expression data (cDNA, SAGE, Affy), proteomics
data (MS based), metabolomics data (NMR or MS based)
or spectroscopic data (UV, NIR, Raman). The
instruments used to generate these data have their characteristics resulting in
heteroscedastic and colored instrumental error. The
sampling process also contributes in a nonhomogenous
way to the error distribution. The
focus of this workshop is to develop a more general strategy for steps
(ii)-(iv) that take into account the influence of the experimental heteroscedastic error structure, where possibly the PDF is
not even available in a closed form, and certain requirements for the models
like robustness. Topics to be discussed during the workshop are: i) (design of) biological experiments, (ii) multivariate
data analysis, (iii) parameter identification, (iv) model
discrimination and experimental design. The
aim of this workshop is to bring together scientists working on the above
subjects but with a different disciplinary background in statistics, biology, mathematics. The workshop will thus provide a forum to
interact and make progress in the integrative approach. [Back] |