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\title{Statistical Modeling of Transcription Factor Binding Affinities Predicts Regulatory Interactions}
\author{Thomas Manke, Helge G. Roider and Martin Vingron\\
\sc Max Planck Institute for Molecular Genetics, Ihnestr. 73, 14195 Berlin}
\maketitle
\section{Supplementary Material}
\label{sec:supp}
\subsection*{Parametrization for 762 TRANSFAC Matrices}
To simplify the application of our method to mammalian
promoter regions of arbitrary length we provide as supplementary
material the parameters for every TRANSFAC matrix which was used
in this study. The determination of the parameters of the
Generalized Extreme Value Distribution is described in the main text.
Basically, we have three parameters (shape, scale and location),
which all depend on the length of the sequence in question.
This later dependence can be determined by regression against
the logarithm of the sequence length; for example: $c=c_0 + c_1 * \log L$.
Therefore we provide six ($2\times3$) parameters for every matrix.
The list is publically available at\\
http://www.molgen.mpg.de/\~{}manke/papers/STRAP/
\subsection*{Robustness of the TRAP-model against Parameter Changes}
First we like to reiterate, that the two TRAP parameters, $\lambda$ and $R_0$,
are not otpimized for any particular transcription factor or any
specific cellular condition. Our aim is rather, to provide an efficient
model for all factor, for which a motif matrix is known.
In our previous work \cite{Roider2007} we had already investigated to what
extent the affinity-based ranking of sequences for a given
transcription factor is robust against changes of the two parameters.
There we found very high correlation coefficient ($\ge 0.98$),
which illustrated that the ranking of sequences for a given factor
is largely independent of the precise values of $R_0$ and $\lambda$,
at least within the accuracy to which we had determined those parameters.
In the context of the current work, it is equally interesting to study the
effect of parameter changes on our results. Here we show the
analogue of Fig. 5 from the main text, but with perturbed parameters.
Specifically, we increased $R_0$ by 20\% and also changed $\lambda$ from
$0.7$ to $1.0$. The affected rank histograms are almost indistinguishable
from the original result, which is shown as reference in red.
This indicates that the ranking provided by TRAP in combination the
statistical analysis is rather robust against changes in the fundamental
parameters.
\begin{figure}
\begin{center}
\includegraphics[width=16cm]{figures/figS1}
\caption{
TRAP ranks are robust against parameter changes.
In this figure the central result from the main
text is reproduced, which shows a large fraction of promoters, for which
the known regulator is ranked highly by our method (red histogram).
This should be compared to the two other histograms
which have been obtained using the same analysis described
in the main text, but with shifted TRAP-parameters,
as indicated in the legend. The histogram were slightly shifted
for clarity.
}
\label{fig:robustness}
\end{center}
\end{figure}
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\bibitem{Roider2007}
Roider HG, Kanhere A, Manke T, Vingron M (2007) Predicting transcription factor
affinities to {DNA} from a biophysical model.
\newblock Bioinformatics 23:134--41.
\newblock \doi{10.1093/bioinformatics/btl565}.
\newblock \urlprefix\url{http://dx.doi.org/10.1093/bioinformatics/btl565}.
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