, Leibniz Institute for Natural Product Research and Infection Biology  HansKnöllInstitute, Beutenbergstr. 11a, D07745 Jena, Germany
Institute for Biochemistry, Faculty of Medicine, University of Leipzig, Johannesallee 30, D04103 Leipzig, Germany
Department of Scientific Computing, Florida State University, Florida 323104120, Tallahassee, USA
, GermanFederal Institute for Risk Assessment, MaxDohrn Str. 810, D10589 Berlin, Germany
Abstract
Background
Network inference is an important tool to reveal the underlying interactions of biological systems. In the liver, a complex system of transcription factors is active to distribute signals and induce the cellular response following extracellular stimuli. Plenty of information is available about single transcription factors important for the different functions of the liver, but little is known about their causal relations to each other.
Results
Given a DNA microarray time series dataset of collagen monolayers cultured murine hepatocytes, we identified 22 differentially expressed genes for which the corresponding protein is known to exhibit transcription factor activity. We developed the Extended TILAR (ExTILAR) network inference algorithm based on the modeling concept of the previously published TILAR algorithm. Using ExTILAR, we inferred a transcription factor network based on gene expression data which puts these important genes into a functional context. This way, we identified a previously unknown relationship between Tgif1 and Atf3 which we validated experimentally. Beside its known role in metabolic processes, this extends the knowledge about Tgif1 in hepatocytes towards a possible influence of processes such as proliferation and cell cycle. Moreover, two positive (i.e. double negative) regulatory loops were predicted that could give rise to bistable behavior. We further evaluated the performance of ExTILAR by systematic inference of an
Conclusions
We present the ExTILAR algorithm, which combines the advantages of the regression based inference algorithm TILAR, like large network sizes processable and low computational costs, with the advantages of dynamic network models based on ordinary differential equation (i.e.
Background
One of the aims in systems biology is to reveal functions and uncover causalities in the behavior of biological systems. As these systems are usually a composition of multiple processes, mathematical modeling is often applied to investigate processes of interest. The understanding of the parts contributes to the understanding of the system as a whole. One biological process of interest is the regulation of gene expression which is mostly influenced by transcription factors (TFs). These regulating proteins can have an activating or repressing effect on the expression of a gene. The extend of regulation largely depends on the activity of the TF which is determined on multiple levels, mostly the posttranslational level
To reconstruct GRNs, gene expression databased network inference is a widely accepted approach. Although highthroughput technologies such as microarrays and RNAseq have become more accessible (in terms of quality of the measurements, decreasing costs and advancing standard operating procedures) there are still central problems that hamper their inference. A major difficulty is that the number of available measurements is usually lower than required. Often, more genes than the number of available measurements are included in the model. This leads to an underdetermined system with a large amount of possible solutions. When dealing with time series data, a low temporal resolution of measurements contributes to this problem making it more difficult to obtain a reliable solution. Additionally, the usually low number of replicates does not account for the variability introduced by the methods of measurement and the natural biological variation. Hecker
Depending on whether or not the utilized model is based on linear or nonlinear differential equations the number of free parameters and therefore the detail of the model, but also the complexity of the inference problem is increasing drastically
In the second group of algorithms, there is a tradeoff between the flexibility and possibility for quantitative, dynamic modeling and the advantage of processing larger network sizes. There are regressionbased algorithms such as LASSO
In the following, we present an algorithm which combines the advantages of both of these classes, fast inference of medium size networks that can quantitatively model the dynamic behavior of the inferred network. We extend the existing TILAR algorithm that uses a linear network model based on the LARS algorithm. Networks inferred with TILAR consist of two types of nodes, the genes with measured expression profile to model and the regulating TFs, that connect these genes. Due to this concept of modeling, the algorithm makes use of various biological knowledge sources such as transcription factor binding site (TFBS) information and gene interaction knowledge. This information decreases the number of possible network structures and therefore, allows fast inference of reliable, biologically meaningful networks. While the TFBS knowledge is represented by the network edges that go from a regulating TF to a target gene (TFtogene relations), the gene interaction knowledge is represented by the edges that connect the target genes with the regulating TFs (genetoTF relations).
Extended TILAR (ExTILAR) adapts this modeling concept to produce network models that are based on linear ordinary differential equations. This allows the inference of networks from time series data, which can be used to uncover the most important unknown relations between genes and to identify potential key regulators. Linear models represent approximations close to a steady state (operating point) of nonlinear models that are adequate for living systems in principle. Nonlinear terms can and should be included in the proposed modeling algorithm if prior knowledge about the type of nonlinearity is available and if the number of experimental data is sufficient to identify the increased number of model parameters. However, the automatic identification of additional nonlinear model terms in general requires more independent experimental data in order to ensure a stable convergence of the algorithm to a unique model structure (see in
ExTILAR was applied to data from Zellmer
Results and discussion
Inference from biological data
Data of primary murine hepatocytes from Zellmer
Workflow used to analyze the response of murine primary hepatocytes to the change of culture medium after a period of starvation.
Workflow used to analyze the response of murine primary hepatocytes to the change of culture medium after a period of starvation. The workflow of the ExTILAR inference study presented here can be roughly divided into 7 single steps. After preprocessing of the the raw data (step 1), the gene expression profiles were clustered and DETFs were extracted (step 2). Overrepresented TFBSs for the clusters were determined. Regulating TFs for the selected DETFs were extracted from literature knowledge (step 3). In step 4, the information of the two previous steps were pooled to extract priorknowledge and validation knowledge. Using the expression profiles of the DETFs, the mean cluster expression profiles, the information about the regulating TFs and the priorknowledge, ExTILAR was applied to infer a TFN (step 5). The resulting network was checked for present validation knowledge, analyzed and interpreted to extract testable hypothesis (step 6). The extracted hypotheses were validated experimentally (step 7).
Preprocessing and gene filtering
The latest custom chip definition file from Brainarray
Detailed table of differentially expressed genes. Table of the differentially expressed genes containing the corresponding BrainarrayID, EntrezID, GenSymbol, assigned cluster number and the mean expression values at each time point.
Click here for file
Enrichment analysis results of the DEGs. Details of the gene enrichment analysis using all differentially expressed genes.
Click here for file
Clustering
To identify groups of similarly regulated genes, the DEGs were clustered according to their expression profile using the selforganizing tree algorithm (SOTA)
Enriched GOterms and KEGGpathways of the single clusters. Significant GO biological process (GOBP) terms and KEGGpathway (KEGG) terms for each cluster returned by GOstats.
Click here for file
Results of the SOTA clustering.
Results of the SOTA clustering. Clustering of the 950 differentially expressed genes resulted in 6 clusters denoted as slow down (cluster 1), fast up (cluster 2), up (cluster 3), down (cluster 4), fast down (cluster 5) and middle peak down (cluster 6). Shown are the median scaled log2FC expression profiles (’Expr.Level’). The results of the enrichment analysis for each cluster are outlined in the Additional file
Extraction of DETFs
A total of 22 DETFs were extracted by filtering all DEGs associated with the GOcategory “sequencespecific DNA binding transcription factor activity” (GO:0003700). According to the Gene Ontology (GO) terms obtained from the MGI database
DETF
Cluster
Associated biological processes
DETF cluster membership and associated biological functions based on the information of GeneOntology. For all but Gatad1 and Klf16 it was found that the TFs can either be associated with metabolic processes and/or cell faith.
Atf3
5
gluconeogenesis; regulation of cell proliferation
Cebpa
4
liver development; fat cell differentiation; regulation of cell proliferation; urea cycle
Cebpb
6
cell differentiation; antiapoptotic
Cebpd
4
fat cell differentiation
Csrnp1
5
apoptotic process; plateletderived growth factor receptor signaling pathway
Dbp
6
rhythmic processes
E2f6
2
regulation of transcription involved in G1/S phase of mitotic cell cycles;
Egr1
6
BMP signaling; Il1 mediated signaling pathway; regulation of Wnt signaling pathway; regulation of celldeath; response to glucose stimulus; response to insulin stimulus
Fos
6
cellular response to extracellular stimuli; response to stress
Foxa1
2
glucose homeostasis; chromatin remodeling
Gatad1
2

Id3
3
regulation of cell cycle; regulation of apoptosis
Irf1
3
cellular response to Il1; regulation of celldeath
Klf16
6

Maff
5
epidermal celldifferentiation
Nr1h4
2
bile acid metabolic process; regulation of carbohydrate and urea metabolic process;
Ppara
4
Glucose metabolic process; lipid metabolic process; response to insulin stimulus
Srebf1
4
Steroid metabolic process; response to glucose stimulus; lipid metabolic process;
Srf
4
actin filament organization; cellcell adhesion; developmental growth;
Tgif1
3
regulation of cell proliferation; regulation of retinoic acid receptor signaling pathway
Tsc22d1
2
regulation of apoptotic process; regulation of cell proliferation
Zbtb16
4
positive regulation of apoptosis; negative regulation of proliferation
Extraction of priorknowledge
oPOSSUM was used to identify possible regulators for each cluster
Transfac
Extraction of validation knowledge
PathwayStudio 8.0 was used to extract known, direct relations between the DETFs included in the model. As these 36 relations are not used for the network inference process, they can be used to validate the final network.
TFBS integrating LARS (TILAR)
TILAR uses a linear network model to construct GRNs based on LARS
Concept of modeling of TILAR (AD) compared to ExTILAR (EG).
Concept of modeling of TILAR (AD) compared to ExTILAR (EG). AD) The modeling concept of the TILAR algorithm. The genes are labeled with their expression values. A) In TILAR, a gene can only be regulated by another gene via a TF
The predicted expression level
To use regression for the estimation of the parameters
The predicted expression value
The regression matrix
Variable selection and estimation of the regression coefficients can be performed by using the least shrinkage and selection operator (LASSO) algorithm, a constraint ordinary least square (OLS) approach
with the residual sum of squares (RSS)
LASSO chooses the vector of regression coefficients
with the additional constrain
that the sum of the absolute regression coefficients is lower than a certain threshold
Extended TILAR (ExTILAR)
TILAR was extended to enable the inference of gene regulatory networks from time resolved data by a system of differential equations approximated by a set of difference equations with the time interval
According to this equation, the quotient of difference of expression
Here, the regression matrix
Experiments often have biological replicates for the measurements at each time point. This leads to the same time series being measured
LARS can now be used to efficiently perform automatic variable selection and simultaneous regression coefficient estimation (equations 47). However, for the adaptive LARS it is important to notice that the
Although the introduction of these input parameters offers greater possibilities for finetuning of the algorithm, parameter identification is a crucial step for the inference of networks from biological data. A major problem is that the true underlying structures and processes are often unknown and the mathematical model that the inference algorithm is based on can always only be an abstraction of the truth. Therefore, a good set of parameters needs to be found which leads to inferred networks that maximize the amount of integrated biological priorknowledge and adequately reproduce the observed dynamics. Regarding the integration of priorknowledge a requirement is that the knowledge used to infer the network must be different from the knowledge that is used for its validation. An advantage of the TILARfamily algorithms is that genetoTF knowledge is used during the inference, which can be obtained by literature textmining. The genetoTF relations together with the TFtogene relations implicitly define genetogene interaction information which can also be derived from literature. Therefore, this concept of modeling makes use of two distinct priorknowledge sets, one that is used during the network inference and one that is used for validation purposes only. The advantage of using these multiple priorknowledge sources was shown by Hecker
Network inference using ExTILAR
For the network inference, the measured expression profiles for the 22 DETFs as well as the mean gene expression profile for each cluster were scaled to an absolute maximum value of 1. Linearly interpolated data was added to provide equidistant measurements (
In an initial parameter study the autoregulation weight and the input weight were tuned by testing 25 combinations of these two parameters. The best results in terms of quality of the fit (deviation from the measured data, RSS), number of included priorknowledge edges and number of the total edges was found when using an input weight of 0.5 and an autoregulation weight of 0.75 (Figure
Transcription factor network. Cytoscape session of the transcription factor network shown in Figure 5.
Click here for file
Results of the parameter study optimizing the parameter values for the input weight and the autoregulation weight.
Results of the parameter study optimizing the parameter values for the input weight and the autoregulation weight. Outlined is the ratio of the number of included priorknowledge relations to the total number of inferred relations excluding the inputtogene relations (precision). Based on this result and whether or not numerical simulation of the inferred network led to dynamics comparable to the observed ones, the autoregulation weight was set to 0.75 while the input weight was set to 0.5.
Transcription factor network describing the cellular response of murine primary hepatocytes to the addition of fresh medium.
Transcription factor network describing the cellular response of murine primary hepatocytes to the addition of fresh medium. The ExTILARinferred transcription factor network consists of 3 types of nodes differentiated by their shape, the target DETFs (circle), the regulating transcription factors (diamond) and clusters (octagon). The color of the nodes denote for the corresponding cluster membership, while the rim color reflects the general tendency of the expression profile (increasing: red; decreasing: green). The size of the nodes corresponds to the number of outgoing edges (higher numbers equal more outgoing edges) and highlights DETFs with a hublike role. TFtogene interactions are outlined using blue edges. Inferred genetoTF edges are either green or gray, depending on whether they are supported by priorknowledge (green) or not (gray). The regulating function of these edges is reflected by the target arrow. A red bar denotes for repression while a green arrow represents activation. Waved edges represent inferred direct genetogene relations which were found in literature. As this information was not used during the inference, the presence of these relations within the inferred network supports the validity of the constructed TFN
Measured and simulated expression profiles.
Measured and simulated expression profiles. The dots represent the measured mean log2FC of the three replicates and the errorbars denotes for the standard deviation of the log2FCs. The simulation results (solid lines) show the fit of the model to the measured data. The simulated dynamics are always close to the mean log2FC and mostly within the bounds of the standard deviation.
Delta
# of
# priorknowledge
Precision
RSS
edges
edges
Results of the knowledge analysis using 7 different delta values (Delta) showing the total number of inferred relations (# of edges) excluding the inputtogene edges, the number of integrated priorknowledge genetoTF relations (# priorknowledge edges), their ratio (Precision) and the deviation of the simulated data to the measured ones (the RSS as defined in equation 5).
1
56
5
0.0893
29.07801
0.75
54
12
0.2223
23.07626
0.5
47
27
0.5744
23.62479
0.25
49
25
0.5102
25.50705
0.1
64
47
0.7344
23.79333
0.05
81
60
0.7407
69.28333
0.01
119
77
0.6471
14233.39749
Network nodes
Inputtogene weight
Inferred inputtogene edges which were removed from Figure
Egr1
0.294
Fos
0.257
Cl6
0.242
Cl5
0.241
E2f6
0.223
Dbp
0.184
Cl2
0.184
Gatad1
0.184
Atf3
0.181
Maff
0.179
Ppara
0.178
Foxa1
0.178
Cebpd
0.174
Srebf1
0.171
Csrnp1
0.168
Zbtb16
0.167
Cebpb
0.159
Cebpa
0.156
Cl4
0.148
Nr1h4
0.136
Klf16
0.132
Srf
0.098
Irf1
0.088
Cl3
0.067
Id3
0.051
Tsc22d1
0.034
Cl1
0.025
Tgif1
0
Network interpretation
The inferred TFN (Figure
In Figure
Regulation of metabolic processes
Regulation of metabolic processes is mainly exerted by Cebpa, Foxa1, Nr1h4, Ppara, Srf, Srebf1 and Tgif1. Of these DETFs, Cebpa plays a distributing role within this group. This is consistent with literature as the TF was described to be an important regulator of the energy metabolism
The second loop, which is supported by priorknowledge regarding the genetoTF interactions is formed by Foxa1 and Nr1h4. Foxa1 is also associated with metabolic processes and plays a central role in the glucose homeostasis
Loops, where both edges are negatively regulating can exert a switch like function. This can lead to interesting biological features such as bistability of the system.
Tgif1 is one of the DETFs of which less is known so far. This TF was found to repress transcription of RXR and LXR target genes
Proliferation and regulation of the cell cycle
Hepatocytes remain in the quiescent G0 phase in the liver under normal conditions. Events that lead to the loss of liver mass result in the release of cytokines and the subsequent activation of TFs that prime the hepatocytes for proliferation. Zellmer
Among the DETFs modeled in the inferred network, regulation of proliferation and the cell cycle is mainly exerted by Atf3, Cebpb, Cebpd, Dbp, E2f6, Fos, Irf1 and Tsc22d1. Within this group, Fos is highly connected and regulated by seven other DETFs including Egr1. Moreover, Fos was found to have the second largest inputtogene weight. This central function is supported by the finding that Fos expression is a prerequisite for the reentry of quiescent cells into the cell cycle
Id3, Atf3 and Tsc22d1 are rather terminal nodes within the inferred network and are (beside Tsc22d1) not regulating any other DETFs. This could be due to the missing available priorknowledge regarding these DETFs. Atf3 is a transcriptional repressor that was found to delay cell cycle progression by slowing down the transition of the cell from G1 to S phase. It was shown that the TF also mediates positive and negative effects on proliferation
Experimental validation
For experimental validation, we were interested whether or not a relation between Tgif1 and Atf3 expression exists. It is known that the two TFs are related as Atf3 has a promoter binding site for Smad3
To investigate the effect that a Tgif1 knockdown might have on the system, we performed an
Click here for file
For validation, a real siRNAmediated knockdown of Tgif1 in cultured hepatocytes was carried out. At 6, 12 and 24 hours after transfection of the Tgif1 siRNA, expression levels of Atf3 and Dbp were measured using quantitative real time PCR (qRTPCR).An unambiguous upregulation of Atf3 and a downregulation of Dbp were detected (Figure
Expression profiles of Atf3 and Dbp in response to the siRNAmediated knockdown of Tgif1.
Expression profiles of Atf3 and Dbp in response to the siRNAmediated knockdown of Tgif1. epatocytes were cultured for 24 hours and then transfected with siRNA against Tgif1 (referred to as zero time point) as described in Methods. After further incubation for 24 hours, RNA was extracted and expression levels of Atf3 (black squares) and Dbp (open circles) were determined by qRTPCR.
Conclusions
In this work, the linear model of the recently published network inference algorithm TILAR was extended to infer ODE based network models. With this approach, the ExTILAR algorithm combines the benefits of the regression based TILAR (low computational costs, large network size processable, incorporation of various knowledge sources, partial separation of network structure identification and parameter estimation) with the possibilities that ODE based models offer (
Performance analysis of ExTILAR. A performance analysis of ExTILAR using
Click here for file
Applying the algorithm to biological data, we were able to present a TFN that models the main biological processes induced in hepatocytes upon culture medium exchange. We highlighted two possible regulatory loops between Srebf1, Nr1h4 and Foxa1. The function of these interesting network motifs will be motivation for further studies. Using a knockdown experiment read out by qRTPCR, the biological relevance of the inferred network was shown by the validation of two hypothesized relations between Tgif1 and Atf3, and between Tgif1 and Dbp. Thereby, we detected new, potential functions of Tgif1 and further highlight the TF’s importance in the hepatic transcription factor network. Although the exact mechanism of regulation remains to be clarified, this example highlights how ExTILAR can be successfully used combining various priorknowledge sources to infer biologically relevant, data supported regulatory networks.
Methods
All analysis were performed using the biological data analysis package Bioconductor
Microarray preprocessing and gene filtering
Analysis of Affymetrix microarrays involves the initial annotation of the probe sets of the chips. A custom chip definition file is used to map the probes on the microarray to a genomic sequence and thus, to the transcript of a certain gene. However, it is well known that a large number of probe sets includes probes which match multiple transcripts and also probes which do not match any transcript
Detection calls of the raw data were obtained and used as an additional filter to remove uncertain probe sets. The method is used to remove transcripts for which the expression level is below the threshold of detection. This is described in detail in the Affymetrix Statistical Algorithms Description Document
The mas5calls function of the affy package
RMA
The preprocessed dataset was analyzed for DEGs using the twofold criterion. A gene was called differentially expressed if its mean expression profile exhibited an absolute log2FC of 1 or greater with respect to the 0 hour sample.
Clustering and identification of overrepresented TFBSs
The data was prepared for clustering by scaling each mean expression profile to the absolute maximum foldchange value of 1. The clustering algorithm and the number of clusters was determined by using the clValid package for R
oPOSSUM was used to search for overrepresented TFBS among the genes of each cluster
ExTILAR GRN inference
The log2FC profiles for the genes as well as the mean cluster log2FC profiles were standardized to a maximum absolute log2FC of 1. To obtain equidistant measurements for the regression based on difference equations, missing measurements were added using linear interpolation. An exponential decreasing input function was defined. This choice is based on the assumption that the change of culture medium is an initially strong stimulus that the cells adapt to. Over time, the stimulus becomes less severe as the effects induced in response to the stimulus become the dominating stimulus. Also, the supplied nutrients are consumed by all cells in the culture and thus, are decreased. However, together with the extracted TFtogene relations, the regression matrix was constructed according to equation 9. LARS was used to select and estimate the variables and calculate the
Model selection
Regardless of the implementation of LASSO used, the result is always a set of models with a differing number of variables (regression coefficients) and their estimates. The user has to apply a criterion to find a model with good quality. The quality of the network selection is always a tradeoff between the datafit and the number of parameters used in the network. One way to define the quality of a model is how well a model fits to the measured data, disregarding the number of parameters used. This is described by minimization of the
Another model selection criterion is the Mallows Coefficient
where
The
The model which minimizes the
Experimental procedure Tgif1knockdown
Hepatocyte isolation, cultivation and transfection
Primary hepatocytes from C57BL/6N mice were isolated by collagenase perfusion of the liver according to Gebhardt et al., 2003
After 24 hours total cultivation time, the serumfree medium was renewed and chemically synthesized siRNA for Tgif1 (20 nmol) was transfected with INTERFERin^{TM} purchased from Peqlab (Erlangen, Germany) according to the manufacturer’s instructions. Tgif1specific siRNA (Gene Solution siRNA; target sequence CACCTACAGTCTAATGAGTAA) and the respective scrambled control siRNA was purchased from Qiagen (Hilden, Germany). The cells were incubated with the siRNA for additional 6, 12 and 24 hours. Total RNA from hepatocytes was isolated with RNeasy plus Mini Kit (Qiagen, Hilden, Germany) from three wells and pooled.
Quantitative qRTPCR
RNA was reverse transcribed using oligo(dt) primers and IM Promm II reverse transcriptase (Promega, Mannheim, Germany). The levels of the mRNA transcripts for Atf3, Dbp and
Gene
Primer forward 5’ → 3’
Primer reverse 5’ → 3’
Tgif1
GAAACCCCAGCTTCACCTCT
GCCAGATGCTGCAACAAG
Atf3
GCTGGAGTCAGTTACCGTCAA
CGCCTCCTTTTCCTCTCAT
Dbp
CTTTTGACCCTCGGAGACAC
TGGCTGCTTCATTGTTCTTG
CATCCGTAAAGACCTCTATGCCAAC
ATGGAGCCACCGATCCACA
Abbreviations
DETF: Differentially expressed genes for which the corresponding protein is known to exhibit transcription factor activity; GRN: Gene regulatory network; TFN: Transcription factor network; LARS: Least angle regression; TILAR: TFBSintegrating LARS; ARACNE: Reverse engineering of accurate cellular networks; CLR: Context likelyhood of relatedness; TFBS: Transcription factor binding site; ExTILAR: Extended TILAR; TF: Transcription factor; RMA: Robust multiarray average; log2FC: Log2 foldchange; SOTA: Selforganizing tree algorithm; DEG: Differentially expressed gene; OLS: Ordinary least squares; ODE: Ordinary differential equation; Cp: Mallows Cp coefficient; RSS: Residual sums of squares; Pm: Proposal measure; qRTPCR: Quantitative real time polymerase chain reaction; Egr1: Early growth response 1; Srf: Serum response factor; Tsc22d1: Transforming growth factorbeta stimulated clone22; Atf3: Activating transcription factor 3; E2f6: E2F transcription factor 6; Irf1: Interferon regulatory factor 1; Cebpa: CCAAT/enhancer binding protein alpha; Foxa1: Forkhead box A1; Tgif1: TGFBinduced factor homeobox 1; Dbp: D site albumin promoter binding protein; Fos: FBJ osteosarcoma oncogen; Id3: Inhibitor of DNA binding 3; Maff: Vmaf musculoaponeurotic fibrosarcoma oncogene family, protein F (avian); Nr1h4: Nuclear receptor subfamily 1, group H, member 4; Klf16: Kruppellike factor 16; Zbtb16: Zinc finger and BTB domain containing 16; Srebf1: Sterol regulatory element binding transcription factor 1; Cebpb: CCAAT/enhancer binding protein beta; Ppara: Peroxisome proliferator activated receptor alpha, Sp1: Transacting transcription factor 1; E2f1: E2F Transcription factor 1.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
RGu and RGe directed the study. RGe, SZ, MMS and EM performed the experiments and collected the data. SV carried out the analyses and wrote the paper. Part of the source code is from the TILAR publication of Hecker et al.
Acknowledgements
This work was supported by grants from the German Federal Ministry of Education and Research (BMBF FKZ 0315736, FKZ 0315735, Virtual Liver Network). We would like to thank Kerstin Heise and Doris Mahn (Institute for Biochemistry, Leipzig) for excellent technical assistance and Dr. Ekaterina Shelest (HansKnöllInstitute, Jena) for discussions and suggestions on the manuscript.