BACKGROUND
glioblastoma are highly invasive brain tumors.
the prognosis for patients with glioblastoma depends on many factors, including age, performance status, and histology grade of the glial neoplasm.
the medial survival is approximately  <dig> months with maximal therapy.
glioblastoma are difficult to treat due to the resistance to conventional therapies as well as the ability to diffuse throughout the brain.
therefore, analytical description of tumor growth and response to therapeutic modalities, such as radiation and chemotherapy, has been a central research topic.
modeling of the tumor responding to chemotherapy is mostly of pharmacokinetic nature  <cit> .
other mathematical models are based on a conservation equation describing a modality of how to measure the growth of an infiltrating glioma  <cit> : the rate of change of tumor cell population equals the diffusion  of tumor cells plus the net proliferation of those.
cell death is introduced as a loss term in  <cit> .
a model combining patient's imaging, histopathologic and pharmacodynamic/genetic data when treated with temozolomide is presented in  <cit> .
interesting aspects of glial cell biology have recently been uncovered in laboratories evaluating the tumor suppressor protein wild type  <dig>   <cit> .
it is well established that transfecting glioma cells with wild-type tumor protein p <dig> will trigger brisk apoptosis if the cell line harbors mutant p <dig>  while the same transfection to cell lines which harbor the wt p <dig> will result in a reduction or elimination of invasion and motility  <cit> .
a glioma cell line that harbors the wild-type form of the tumor suppressor protein p <dig> can be sensitized to undergo apoptosis by the addition of wt p <dig> along with chemotherapy   <cit> .
recently, new insights into the pathobiology of glioblastoma cells have been obtained at the m.d.
anderson cancer center in houston, texas: transfer of the p <dig> gene by use of an adenovirus vector  may be clinically applicable in human gliomas.
furthermore, it has been demonstrated that combined adenovirus transfection of wild-type p <dig>  into glioma cells followed with chemotherapy treatment sn- <dig> may act to convert gliomas to an "apoptosis-sensitive" phenotype  <cit> .
moreover, wt p <dig> containing tumor cells, such as u <dig> mg will show reduced mobility and decreased invasion in matrigel motility assays after wt p <dig> gene therapy.
a proteomic approach identified proteins that were involved in a phenotypic change in the high-grade glioma cell line u <dig> mg under the influence of transfection with wild-type p <dig> and additional cytotoxic chemotherapy with sn- <dig>  <cit> .
this study showed that the expression of the protein galectin- <dig> is associated with malignancy and poor prognosis.
the results suggest that galectin- <dig> is a relevant therapeutic target to downregulate in a clinical pharmacological setting to improve overall survival of high-grade glioma patients.
our current understanding of proteins such as galectin- <dig>  interactions and pathways is detailed, yet it is still incomplete.
galectin  <dig> binds free beta-galactose residues on both glycoproteins and gangliosides   <cit> .
gangliosides were first discovered by the german scientist ernst klenk in  <dig>  they are cell-type specific antigens that provide cell membrane structure, and play key roles in control growth, cell differentiation and cell/cell interactions.
gangliosides are implemented in different cancer types  since some typical gangliosides are present in tumors, but are absent in normal healthy tissue  <cit> .
although connections between cancer and glycobiology have been described, the detailed chemical analysis of polar lipids has been problematic due to structural complexity as well as limitation of analytical techniques.
recently, he et al.
<cit>  pioneered new analytical methodology with nano-liquid chromatography  separation followed by high mass accuracy and high mass-resolving power fourier transform ion cyclotron resonance  mass spectrometry  analysis at  <dig> t  <cit> .
ms is useful in dealing with complex mixtures since the high mass resolution  allows the signals of two ions of similar mass-to-charge ratio  to be detected as distinct ions.
this new methodology has opened a new field of polar lipid profiling.
a typical biological analysis from  <dig> million cells results in the identification of 600- <dig> different polar lipids of various polar heads and variable size and modified  nonpolar tails.
relative quantification of each polar lipid between treated and untreated cells results in highly complex, information rich data sets.
the ultimate goal of this research is to link the changes in the polar lipids to the enzymes that control their synthesis/modifications/degradation , which will provide a systems biology approach to the study of glioblastoma.
the data generated will be used to drive logical, hypothesis driven experiments in the search for new therapeutic targets in glioblastoma research.
since the lipid profiling methodology generates comparative semi-quantitative data on hundreds of different polar lipids with each experiment, the data analysis has become a daunting task.
novel approaches  <cit>  are now needed to compile the existing biological lipid profiling experimental data and to maximize the information extraction from these databases.
once correlations in the lipid database have been identified, the reduced data will be correlated to the gene array data and proteomic data sets.
this manuscript describes a novel algorithm for identification of correlations in the complex lipid data sets derived from gene treated and empty vector treated u <dig> glioblastoma cell lines.
we research, implement and test graph clustering techniques as an equivalent to standard correlation networks.
this novel approach combines analysis and visualization with the correlation structure of the lipid profiling data.
this novel technique enables a better understanding and a mathematical analysis of the observed experimental results.
RESULTS
in this paper we develop a novel paradigm to replace correlation networks standardly employed for displaying the topological properties of networks  <cit> .
traditional correlation networks are based on building a graph and determining the correlation scores between the nodes of the graph and then compare those values with a given threshold.
for those exceeding the threshold an undirected edge is linked between the nodes.
as a novel concept in this paper, we research, implement and test graph clustering techniques as an equivalent to standard correlation networks for the analysis of therapeutic outcomes for u <dig> mg glioblastoma cells.
global multivariate approaches such as the proposed novel graph clustering correlation network are needed in order to understand the potential disregulation of normal cellular responses in disease and their response to various therapeutic interventions.
moreover, because nano-lc/ms can find and assign hundred of lipids from glioma cells, it is possible to identify causal influence relationships involving multiple lipids.
building upon lipid measurements such as those illustrated in figure  <dig> for the group of gangliosides for two treatments , figure  <dig> shows the schematic of the graph clustering network based on multidimensional lipidomic data.
the correlation structure is explored by varying the threshold between different lipids and the important changes between treatments by clusters of nodes of different sizes and fan-out degrees.
a graph model based on correlation networks
the notion of networks has recently started to permeate diverse fields of science as well as numerous concepts in our everyday lives.
this development roots particularly strong in social network analysis, an area which spawned many concepts and methods that today experience a renaissance empowered by the ubiquity and availability of social networks, especially in the internet .
the driving force behind the rise of this concept is the fact that a network is a very apt and well-perceivable representation of the interrelation of things.
for this reason, we advocate the use of network analysis  <cit>  in the field of lipidomics.
generally speaking, any set of interrelated entities constitutes a network, and can thus be modeled as a graph, which is the mathematical formalization of the term network.
the evidence that lipids are related in their reaction to treatments leads to the fact that exploration and visualization of co-regulations in glioblastoma data can be done based on correlation network analysis.
such networks describe all dependencies between the domain variables.
more precisely we define the simple , undirected  and weighted graph g =  as follows.
the set v of nodes is the set of all measured lipids while the set e of edges  describes the dependencies between these lipids by a weight function ω : e →  <cit>  which expresses the strength of the dependencies.
in our case ω is based on a matrix of correlation coefficients which is computed based on the pair-wise correlation between the concentrations of lipids in a given sample.
thus, for an edge e = {u, v}, the weight ω  is a measure of correlation, i.e., similarity between lipids u and v, with a value of  <dig> indicating identical measurements x and y, and values close to  <dig> indicating very different measurements.
we base our correlation matrix on measured values x normalized with the standard normalization function f = log.
however, since this proved to be too non-discriminative for network analysis techniques, we actually used f′ = ) <dig>  the correlation of two measurements x and y is then computed as cor = min{f′, f′}/max{f′, f′}, with the special case of cor =  <dig> if x = y =  <dig>
since in this work we divide our studies up into different groups of lipids, i.e., gangliosides, phosphatidylinositol and phosphatidylglycerol, we construct three different base-networks for our exploratory clusterings, one for each group.
actual lipid correlation graphs are then obtained by choosing a treatment and a threshold value for the correlation coefficient values, i.e., edges with insignificant weights are pruned.
two nodes u and v that are connected by an edge are called adjacent, and an edge e and an end node v of e are called incident, abbreviated by u ~ v and e ~ v, respectively.
figure  <dig> is the network of phosphatidylglycerols.
for the sake of readability we do not state full names of lipids in our graphs, but instead denote the index of the lipid in the corresponding chart .
the layout  is determined with so called force-directed graph-drawing techniques.
roughly speaking, strong ties draw nodes together and weak ties let them drift apart.
heavier edges are darker than lighter edges and larger nodes share many heavy edges with other nodes.
we can now identify groups of lipids that exhibit a similar behavior.
graph clustering on correlation networks
we propose and tested a novel concept for analyzing correlation networks based on graph clustering.
in figure  <dig> we can easily perceive three rather densely knit groups of lipids, which share mostly weak links  to the other groups.
such a dense subset indicates that these lipids correlate strongly with each other wrt.
to their reaction to the applied treatment, i.e., it is a cluster of similarly behaving lipids.
while in a single small example this might be done by hand, this task is usually realized with graph clustering  <cit>  algorithms, which automatically identify a clustering.
clustering methods discover natural concentration and large-scale inhomogeneities in relational data.
a clustering c of a graph g =  is a partition c={c <dig> ...,ck} of the set v of nodes into clusters ci .
clusterings always follow the paradigm of intra-cluster density vs. inter-cluster sparsity.
in other words, the edge-connectivity inside clusters is to be strong, while between clusters there should only be few, or light-weighted edges.
in our context this means that the pairwise correlations of nodes inside one cluster are all rather high, and those of nodes in different clusters are comparably low.
it is important to note that the number of clusters to be found is not preset by a parameter, instead it is determined by the algorithm and the instance.
since edge weights represent the strength of ties, our graph clustering algorithm takes these edge weights into account, which yields a higher precision than pruning light edges and then employing an un weighted algorithm.
for the sake of readability, we still use the pruning only for our drawings.
for actual clustering tasks, the informal notion of intra-cluster density vs. inter-cluster sparsity requires amathematical formalization.
a very simple such formula is coverage, which measures the fraction of thetotal edge weight which is covered by  clusters .
while, for a given clustering, coverage is a simple, yet decent measure for clustering goodness, trying to maximize it is unreasonable, as an optimal coverage value of  <dig> is attained by setting c={c1} with c = v, i.e., using only one cluster.
among the established graph clustering algorithms that have successfully been applied to networks with similar structure in the past are algorithms that maximize the quality index modularity  <cit> , which builds upon coverage.
roughly speaking, this index measures the goodness of a clustering  by comparing the coverage of a clustering to the expectation of this value if edges were rewired randomly.
equations  and  give the formulas for coverage and modularity, respectively:
cov:=∑intra–cluster edges eω∑e∈eω
mod:=cov−14)2∑c∈c)2︸exp
for the purpose of this article it is unnecessary to delve into the details of modularity, we refer the reader to  <cit>  and further references therein.
the rationale behind modularity is as follows.
given some clustering, a very low modularity tells us that even a purely random network would t the clustering better than the given graph, while a high modularity score means that the identified clustering captures very well how edges differ from randomness and constitute dense groups.
the modularity of given clustering can be computed in linear time , however, identifying a clustering with a high modularity is harder.
in fact it is np-hard to actually optimize modularity  <cit> , thus heuristics are used, of which a localized agglomerative approach  <cit>  is the current state of the art, which we also use in this work.
we repeated our experiments with other graph clustering algorithms such as orca <cit> , which is strong on very large graphs, minimum-cut tree clustering  <cit> , which is able to guarantee certain bottleneck properties of clusters, and iterative conductance clustering  <cit> , which features a parameterized clustering coarseness.
however, the constructed graphs are not large and we do not impose any specific requirements on the clustering, instead we intend to learn from the clustering and get an impression of the network.
for these reasons, a self-contained modularity-based algorithm worked best for our purpose.
the algorithm we use  <cit>  initializes each node as a singleton cluster, i.e., containing only this one node.
then, iteratively, each node explores its local graph neighborhood, leaves its current cluster and joins the best neighbor cluster, if such a swap yields an increase in modularity.
this process usually merges many clusters.
the iteration is repeated until annealed, which means that modularity can no further be improved by moving any single node to a different cluster.
resulting clusters are then abstracted to super-nodes, which means that a new graph is constructed, where each node represents a cluster in the original graph, and edges between original nodes are summarized into super-edges in the abstracted graph.
in this resulting graph, the above process is repeated.
eventually, at some abstraction stage, modularity will attain its peak and no node will join any other's cluster, then the abstraction hierarchy is unfurled and the final super-nodes induce the clustering of the original graph.
figure  <dig> is an example clustering of treatment  <dig> of the phosphatidylglycerols.
difference graphs and visualization of lipidomic changes
for each treatment  and for each group of lipids we now design a correlation network as described in the previous section, and identify a graph clustering.
each clustering reveals subsets  of lipids which exhibit a very similar reaction to this treatment.
thus, roughly speaking, lipids within the same cluster can be grouped in terms of their behavior and, on the other hand, are more or less well separated from lipids in other clusters in this respect.
generally speaking, comparing a treatment to others, e.g., a control, is of particular interest.
thus, in order to compare a first treatment a to a second treatment b of the same group of lipids, we combine two graphs and their clusterings in one new graph layout, the difference graph, as follows.
a's clustering is represented by boxes, such that each box constitutes a cluster, and b's clustering by node colors, i.e., subsets of nodes with the same color constitute clusters.
comparing these clusterings yields many insights, which are immediately observable in a readable layout.
it shows us how differently the two treatments "correlated the lipids".
a cluster of lipids that react almost identically wrt.
a might be split into different clusters in b's clustering, which strongly indicates that the split apart nodes  share a property that makes them sensitive to treatment b. this selectively leads us back to specific places in the raw data, where we now know what to look for.
in particular, this might even point to some biochemical feature of these lipids, the relevance of which has not yet been known.
we will demonstrate this in the illustration below.
as a side note, there is some literature on quantitatively comparing clusterings of graphs or partitions of data points.
a good overview of this field, with an emphasis on the peculiarities of graph clusterings, is given in  <cit> .
a multitude of difference measures for clusterings exists, with perhaps the most prominent one being the rand measure  <cit> , which is the fraction of node pairs, which are co-classified in the same way by both clusterings, i.e., twice together or twice separated.
technically speaking, for two clusterings c <dig> and c <dig> of graph g =  set ntog.
= |{{u, v}∈|∃c1∈c <dig>  c2∈c <dig> such that u, v ∈ c <dig> and u, v ∈ c2}|, and set nsep.
analogously for u, v separated, then rand  =/|}|.. using such a measure of comparison in our application would give a vague impression about how much treatments differ in terms of correlation of lipid reaction without looking at the graphs or knowing how the difference manifests.
using any such measure requires care and experience as they are prone to biases introduced by the size of a network and the coarseness of the clusterings.
since, additionally, we clearly focus on qualitative differences, which, for small graphs such as those in our application, our figures give a good impression about, we do not use difference measures.
since the edge structure of the two compared graphs are already transferred into clusterings, we have the edges of the new difference graph represent more pressing information.
the weight of edge {u, v} in a difference graph is its weight wrt.
a minus its weight wrt.
b. the crucial observation is as follows.
this weight shows how treatments a and b differ in terms of the behavior of u and v; if this weight is close to zero, then switching from a to b does not discriminate u and v, if it is positive , then u and v correlate stronger  wrt.
treatment a than wrt.
b. we color edges on a linear hsv-scale  by the absolute value of this new edge weight.
thus, edge colors indicate whether switching between treatment a and b discriminates nodes.
however, in order not to overburden the drawing, colors encode only the absolute difference between the a and b's correlations; this hints at where to look for interesting behavior, and detailed quantities can then be read o edge annotations or the raw data.
furthermore, we size nodes proportionally to sum of their incident absolute edge weights.
thus, in a difference-graph for a and b, a node is large if it differs strongly in its correlations to other nodes wrt.
the two treatments, there should thus be several heavy  incident edges on such a node.
small nodes roughly preserve their correlation behavior in both treatments.
illustration of the approach
our approach is illustrated by computing the graph-correlation networks resulting from gene therapy for gangliosides, phosphatidylinositol and phosphatidylglycerol.
in the following we illustrate what can be concluded from the networks constructed from these different groups of lipids, as shown in their respective figures.
please note that we do not predetermine the numbers of clusters, thus different treatments can very well yield different numbers of clusters, this simply reflects that the numbers and sizes of lipids with similar behavior depend on which treatment is used.
we exemplarily show the resulting correlation networks for the group of gangliosides from figure  <dig> for the strong difference of the first two treatments from table  <dig> and figure  <dig>  in figure  <dig>  the result of the control treatment one is summarized by the box-clustering, and the treatment two , is depicted by node colors.
a first observation is that the control yields only two clusters of lipids , and adding p <dig> yields three , thus, treatment two discriminates the reaction of lipids more finely.
the red cluster is striking as it contains many large nodes, i.e., lipids, which differ strongly in their correlations wrt.
the two treatments.
the fan-out degree of every single lipid component in these graphs shows us the modulation degree with a given treatment.
the hot  edges incident to the largest nodes show where these differences manifest most strongly, i.e., which other nodes are discriminated by such a node  by moving from treatment one to treatment two.
looking up the respective lipids in figure  <dig>  the graphical clustering thus confirms the experimental results by showing that the long chain gangliosides go down after p <dig> treatment.
in a similar manner we can use our graphs of other groups of lipids and treatments for pointers to behavioral phenomena.
for the ratio of the third and fourth treatment combinations and the fifth and sixth, respectively, from table  <dig>  we do not observe any relevant changes as shown in figure  <dig> and  <dig>
for the phosphatidylinositol , we see in figure  <dig> the experimental outcome for the first two treatments showing an abundance increase of hydroxilated pis.
we can also see that the hydroxylated pi go up after p <dig> treatment as depicted from the difference network between the first two treatments in figure  <dig>  the highest increase from zero to one hundred for +o as shown in the experimental results is represented in the network as a distinct separate cluster.
there are no significant changes between the treatments u87+sn38/24hr+di312/24hr versus u87+sn38/24hr+p53/24hr and u87+di312/24hr versus u87+p53/24hr.
the biochemical observations are again confirmed by our analysis for the phosphatidylglycerol  profiles.
the results for the first two treatments only are visualized in figure  <dig> showing an abundance increase of hydroxylated pgs.
the correlation network confirming these results is shown in figure  <dig>  cluster  <dig> includes only the two pgs +o and +o showing an increase in signal magnitude from  <dig> for the first treatment to  <dig> for the second one.
there are again as with the pis, no significant changes between the treatments u87+sn38/24hr+di312/24hr versus u87+sn38/24hr+p53/24hr and u87+di312/24hr versus u87+p53/24hr.
we want to emphasize - based on the achieved results - that graph clustering networks compared to traditional correlation networks represent a unique "fingerprint" in lipidomics by revealing analytic properties while displaying the graph structure.
this term from the field of analytic visualizations signifies a superficial drawing on the one hand, as it masks or even ignores some aspects of the raw data, however, on the other hand, it implies that prominent and potentially unknown features of the data become visible in an easily recognizable way.
the above investigations show how observations made with the help of our clusterings coincide with and corroborate findings and interpretations based on expert knowledge.
graph clustering and visualizations certainly cannot replace traditional analysis, but they can be a powerful supporting tool.
CONCLUSIONS
in this paper, we analyzed and interpreted lipidomic data sets acquired by high-throughput measurements such as nano liquid chromatography  separation followed by detection with high mass accuracy and high mass-resolving power  <dig>  ft-icr ms. the samples were taken from u <dig> cell line treated under seven different treatments.
we hypothesize that the observed correlations between the gangliosides concentrations are a result of the underlying lipidomic reaction network.
thus, lipidomic networks in glioblastoma represent highly dynamical processes continuously changing under the influence of fluctuations.
these induce a specific pattern of correlations and are measured in the experiment as a result of network propagation.
as seen in plant metabolism  <cit> , the determined pair-wise correlations represent a snapshot or "finger print" of the biochemical state of the glioblastoma cell at a given point in time.
we introduced a novel concept in correlation network, the so-called graph clustering approach, which results in finding not only the correlations but also the clusters in these networks providing thus based on the concept of modularity a better visualization and analysis in lipidomic data exploration.
the simulations based on the novel theoretical concept have confirmed the experimental findings: a down-regulation for gangliosides and an up-regulation for sulfatides and phosphatidylinositol.
furthermore, we could quantize the regulations across the whole lipidom showing additionally that hydroxylated phosphatidylglycerol is also up-regulated.
among the seven possible treatments, we showed that most visible changes leading to apoptosis can be found in combination with adenovirus therapy.
in summary, this paper revealed in an unique way the "fingerprints" in lipidomics showing us how gene therapy  with wild type p <dig> followed by chemotherapy with the topoisomerase inhibitor sn <dig> induces 95% apoptosis .

 glioblastoma are highly invasive brain tumors. the prognosis for patients with glioblastoma depends on many factors, including age, performance status, and histology grade of the glial neoplasm. the medial survival is approximately months with maximal therapy. glioblastoma are difficult to treat due to the resistance to conventional therapies as well as the ability to diffuse throughout the brain. therefore, analytical description of tumor growth and response to therapeutic modalities, such as radiation and chemotherapy, has been a central research topic. modeling of the tumor responding to chemotherapy is mostly of pharmacokinetic nature. other mathematical models are based on a conservation equation describing a modality of how to measure the growth of an infiltrating glioma: the rate of change of tumor cell population equals the diffusion of tumor cells plus the net proliferation of those. cell death is introduced as a loss term in. a model combining patient's imaging, histopathologic and pharmacodynamic/genetic data when treated with temozolomide is presented in. interesting aspects of glial cell biology have recently been uncovered in laboratories evaluating the tumor suppressor protein wild type. it is well established that transfecting glioma cells with wild-type tumor protein p will trigger brisk apoptosis if the cell line harbors mutant p while the same transfection to cell lines which harbor the wt p will result in a reduction or elimination of invasion and motility. a glioma cell line that harbors the wild-type form of the tumor suppressor protein p can be sensitized to undergo apoptosis by the addition of wt p along with chemotherapy. recently, new insights into the pathobiology of glioblastoma cells have been obtained at the m.d. anderson cancer center in houston, texas: transfer of the p gene by use of an adenovirus vector may be clinically applicable in human gliomas. furthermore, it has been demonstrated that combined adenovirus transfection of wild-type p into glioma cells followed with chemotherapy treatment sn- may act to convert gliomas to an "apoptosis-sensitive" phenotype. moreover, wt p containing tumor cells, such as u mg will show reduced mobility and decreased invasion in matrigel motility assays after wt p gene therapy. a proteomic approach identified proteins that were involved in a phenotypic change in the high-grade glioma cell line u mg under the influence of transfection with wild-type p and additional cytotoxic chemotherapy with sn-. this study showed that the expression of the protein galectin- is associated with malignancy and poor prognosis. the results suggest that galectin- is a relevant therapeutic target to downregulate in a clinical pharmacological setting to improve overall survival of high-grade glioma patients. our current understanding of proteins such as galectin- interactions and pathways is detailed, yet it is still incomplete. galectin binds free beta-galactose residues on both glycoproteins and gangliosides. gangliosides were first discovered by the german scientist ernst klenk in they are cell-type specific antigens that provide cell membrane structure, and play key roles in control growth, cell differentiation and cell/cell interactions. gangliosides are implemented in different cancer types since some typical gangliosides are present in tumors, but are absent in normal healthy tissue. although connections between cancer and glycobiology have been described, the detailed chemical analysis of polar lipids has been problematic due to structural complexity as well as limitation of analytical techniques. recently, he et al. pioneered new analytical methodology with nano-liquid chromatography separation followed by high mass accuracy and high mass-resolving power fourier transform ion cyclotron resonance mass spectrometry analysis at t. ms is useful in dealing with complex mixtures since the high mass resolution allows the signals of two ions of similar mass-to-charge ratio to be detected as distinct ions. this new methodology has opened a new field of polar lipid profiling. a typical biological analysis from million cells results in the identification of 600- different polar lipids of various polar heads and variable size and modified nonpolar tails. relative quantification of each polar lipid between treated and untreated cells results in highly complex, information rich data sets. the ultimate goal of this research is to link the changes in the polar lipids to the enzymes that control their synthesis/modifications/degradation, which will provide a systems biology approach to the study of glioblastoma. the data generated will be used to drive logical, hypothesis driven experiments in the search for new therapeutic targets in glioblastoma research. since the lipid profiling methodology generates comparative semi-quantitative data on hundreds of different polar lipids with each experiment, the data analysis has become a daunting task. novel approaches are now needed to compile the existing biological lipid profiling experimental data and to maximize the information extraction from these databases. once correlations in the lipid database have been identified, the reduced data will be correlated to the gene array data and proteomic data sets. this manuscript describes a novel algorithm for identification of correlations in the complex lipid data sets derived from gene treated and empty vector treated u glioblastoma cell lines. we research, implement and test graph clustering techniques as an equivalent to standard correlation networks. this novel approach combines analysis and visualization with the correlation structure of the lipid profiling data. this novel technique enables a better understanding and a mathematical analysis of the observed experimental results.  in this paper we develop a novel paradigm to replace correlation networks standardly employed for displaying the topological properties of networks. traditional correlation networks are based on building a graph and determining the correlation scores between the nodes of the graph and then compare those values with a given threshold. for those exceeding the threshold an undirected edge is linked between the nodes. as a novel concept in this paper, we research, implement and test graph clustering techniques as an equivalent to standard correlation networks for the analysis of therapeutic outcomes for u mg glioblastoma cells. global multivariate approaches such as the proposed novel graph clustering correlation network are needed in order to understand the potential disregulation of normal cellular responses in disease and their response to various therapeutic interventions. moreover, because nano-lc/ms can find and assign hundred of lipids from glioma cells, it is possible to identify causal influence relationships involving multiple lipids. building upon lipid measurements such as those illustrated in figure for the group of gangliosides for two treatments, figure shows the schematic of the graph clustering network based on multidimensional lipidomic data. the correlation structure is explored by varying the threshold between different lipids and the important changes between treatments by clusters of nodes of different sizes and fan-out degrees. a graph model based on correlation networks the notion of networks has recently started to permeate diverse fields of science as well as numerous concepts in our everyday lives. this development roots particularly strong in social network analysis, an area which spawned many concepts and methods that today experience a renaissance empowered by the ubiquity and availability of social networks, especially in the internet. the driving force behind the rise of this concept is the fact that a network is a very apt and well-perceivable representation of the interrelation of things. for this reason, we advocate the use of network analysis in the field of lipidomics. generally speaking, any set of interrelated entities constitutes a network, and can thus be modeled as a graph, which is the mathematical formalization of the term network. the evidence that lipids are related in their reaction to treatments leads to the fact that exploration and visualization of co-regulations in glioblastoma data can be done based on correlation network analysis. such networks describe all dependencies between the domain variables. more precisely we define the simple, undirected and weighted graph g = as follows. the set v of nodes is the set of all measured lipids while the set e of edges describes the dependencies between these lipids by a weight function ω: e → which expresses the strength of the dependencies. in our case ω is based on a matrix of correlation coefficients which is computed based on the pair-wise correlation between the concentrations of lipids in a given sample. thus, for an edge e = {u, v}, the weight ω is a measure of correlation, i.e., similarity between lipids u and v, with a value of indicating identical measurements x and y, and values close to indicating very different measurements. we base our correlation matrix on measured values x normalized with the standard normalization function f = log. however, since this proved to be too non-discriminative for network analysis techniques, we actually used f′ = ) the correlation of two measurements x and y is then computed as cor = min{f′, f′}/max{f′, f′}, with the special case of cor = if x = y = since in this work we divide our studies up into different groups of lipids, i.e., gangliosides, phosphatidylinositol and phosphatidylglycerol, we construct three different base-networks for our exploratory clusterings, one for each group. actual lipid correlation graphs are then obtained by choosing a treatment and a threshold value for the correlation coefficient values, i.e., edges with insignificant weights are pruned. two nodes u and v that are connected by an edge are called adjacent, and an edge e and an end node v of e are called incident, abbreviated by u ~ v and e ~ v, respectively. figure is the network of phosphatidylglycerols. for the sake of readability we do not state full names of lipids in our graphs, but instead denote the index of the lipid in the corresponding chart. the layout is determined with so called force-directed graph-drawing techniques. roughly speaking, strong ties draw nodes together and weak ties let them drift apart. heavier edges are darker than lighter edges and larger nodes share many heavy edges with other nodes. we can now identify groups of lipids that exhibit a similar behavior. graph clustering on correlation networks we propose and tested a novel concept for analyzing correlation networks based on graph clustering. in figure we can easily perceive three rather densely knit groups of lipids, which share mostly weak links to the other groups. such a dense subset indicates that these lipids correlate strongly with each other wrt. to their reaction to the applied treatment, i.e., it is a cluster of similarly behaving lipids. while in a single small example this might be done by hand, this task is usually realized with graph clustering algorithms, which automatically identify a clustering. clustering methods discover natural concentration and large-scale inhomogeneities in relational data. a clustering c of a graph g = is a partition c={c...,ck} of the set v of nodes into clusters ci. clusterings always follow the paradigm of intra-cluster density vs. inter-cluster sparsity. in other words, the edge-connectivity inside clusters is to be strong, while between clusters there should only be few, or light-weighted edges. in our context this means that the pairwise correlations of nodes inside one cluster are all rather high, and those of nodes in different clusters are comparably low. it is important to note that the number of clusters to be found is not preset by a parameter, instead it is determined by the algorithm and the instance. since edge weights represent the strength of ties, our graph clustering algorithm takes these edge weights into account, which yields a higher precision than pruning light edges and then employing an un weighted algorithm. for the sake of readability, we still use the pruning only for our drawings. for actual clustering tasks, the informal notion of intra-cluster density vs. inter-cluster sparsity requires amathematical formalization. a very simple such formula is coverage, which measures the fraction of thetotal edge weight which is covered by clusters. while, for a given clustering, coverage is a simple, yet decent measure for clustering goodness, trying to maximize it is unreasonable, as an optimal coverage value of is attained by setting c={c1} with c = v, i.e., using only one cluster. among the established graph clustering algorithms that have successfully been applied to networks with similar structure in the past are algorithms that maximize the quality index modularity, which builds upon coverage. roughly speaking, this index measures the goodness of a clustering by comparing the coverage of a clustering to the expectation of this value if edges were rewired randomly. equations and give the formulas for coverage and modularity, respectively: cov:=∑intra–cluster edges eω∑e∈eω mod:=cov−14)2∑c∈c)2︸exp for the purpose of this article it is unnecessary to delve into the details of modularity, we refer the reader to and further references therein. the rationale behind modularity is as follows. given some clustering, a very low modularity tells us that even a purely random network would t the clustering better than the given graph, while a high modularity score means that the identified clustering captures very well how edges differ from randomness and constitute dense groups. the modularity of given clustering can be computed in linear time, however, identifying a clustering with a high modularity is harder. in fact it is np-hard to actually optimize modularity, thus heuristics are used, of which a localized agglomerative approach is the current state of the art, which we also use in this work. we repeated our experiments with other graph clustering algorithms such as orca, which is strong on very large graphs, minimum-cut tree clustering, which is able to guarantee certain bottleneck properties of clusters, and iterative conductance clustering, which features a parameterized clustering coarseness. however, the constructed graphs are not large and we do not impose any specific requirements on the clustering, instead we intend to learn from the clustering and get an impression of the network. for these reasons, a self-contained modularity-based algorithm worked best for our purpose. the algorithm we use initializes each node as a singleton cluster, i.e., containing only this one node. then, iteratively, each node explores its local graph neighborhood, leaves its current cluster and joins the best neighbor cluster, if such a swap yields an increase in modularity. this process usually merges many clusters. the iteration is repeated until annealed, which means that modularity can no further be improved by moving any single node to a different cluster. resulting clusters are then abstracted to super-nodes, which means that a new graph is constructed, where each node represents a cluster in the original graph, and edges between original nodes are summarized into super-edges in the abstracted graph. in this resulting graph, the above process is repeated. eventually, at some abstraction stage, modularity will attain its peak and no node will join any other's cluster, then the abstraction hierarchy is unfurled and the final super-nodes induce the clustering of the original graph. figure is an example clustering of treatment of the phosphatidylglycerols. difference graphs and visualization of lipidomic changes for each treatment and for each group of lipids we now design a correlation network as described in the previous section, and identify a graph clustering. each clustering reveals subsets of lipids which exhibit a very similar reaction to this treatment. thus, roughly speaking, lipids within the same cluster can be grouped in terms of their behavior and, on the other hand, are more or less well separated from lipids in other clusters in this respect. generally speaking, comparing a treatment to others, e.g., a control, is of particular interest. thus, in order to compare a first treatment a to a second treatment b of the same group of lipids, we combine two graphs and their clusterings in one new graph layout, the difference graph, as follows. a's clustering is represented by boxes, such that each box constitutes a cluster, and b's clustering by node colors, i.e., subsets of nodes with the same color constitute clusters. comparing these clusterings yields many insights, which are immediately observable in a readable layout. it shows us how differently the two treatments "correlated the lipids". a cluster of lipids that react almost identically wrt. a might be split into different clusters in b's clustering, which strongly indicates that the split apart nodes share a property that makes them sensitive to treatment b. this selectively leads us back to specific places in the raw data, where we now know what to look for. in particular, this might even point to some biochemical feature of these lipids, the relevance of which has not yet been known. we will demonstrate this in the illustration below. as a side note, there is some literature on quantitatively comparing clusterings of graphs or partitions of data points. a good overview of this field, with an emphasis on the peculiarities of graph clusterings, is given in. a multitude of difference measures for clusterings exists, with perhaps the most prominent one being the rand measure, which is the fraction of node pairs, which are co-classified in the same way by both clusterings, i.e., twice together or twice separated. technically speaking, for two clusterings c and c of graph g = set ntog. = |{{u, v}∈|∃c1∈c  c2∈c such that u, v ∈ c and u, v ∈ c2}|, and set nsep. analogously for u, v separated, then rand  =/|}|.. using such a measure of comparison in our application would give a vague impression about how much treatments differ in terms of correlation of lipid reaction without looking at the graphs or knowing how the difference manifests. using any such measure requires care and experience as they are prone to biases introduced by the size of a network and the coarseness of the clusterings. since, additionally, we clearly focus on qualitative differences, which, for small graphs such as those in our application, our figures give a good impression about, we do not use difference measures. since the edge structure of the two compared graphs are already transferred into clusterings, we have the edges of the new difference graph represent more pressing information. the weight of edge {u, v} in a difference graph is its weight wrt. a minus its weight wrt. b. the crucial observation is as follows. this weight shows how treatments a and b differ in terms of the behavior of u and v; if this weight is close to zero, then switching from a to b does not discriminate u and v, if it is positive, then u and v correlate stronger wrt. treatment a than wrt. b. we color edges on a linear hsv-scale by the absolute value of this new edge weight. thus, edge colors indicate whether switching between treatment a and b discriminates nodes. however, in order not to overburden the drawing, colors encode only the absolute difference between the a and b's correlations; this hints at where to look for interesting behavior, and detailed quantities can then be read o edge annotations or the raw data. furthermore, we size nodes proportionally to sum of their incident absolute edge weights. thus, in a difference-graph for a and b, a node is large if it differs strongly in its correlations to other nodes wrt. the two treatments, there should thus be several heavy incident edges on such a node. small nodes roughly preserve their correlation behavior in both treatments. illustration of the approach our approach is illustrated by computing the graph-correlation networks resulting from gene therapy for gangliosides, phosphatidylinositol and phosphatidylglycerol. in the following we illustrate what can be concluded from the networks constructed from these different groups of lipids, as shown in their respective figures. please note that we do not predetermine the numbers of clusters, thus different treatments can very well yield different numbers of clusters, this simply reflects that the numbers and sizes of lipids with similar behavior depend on which treatment is used. we exemplarily show the resulting correlation networks for the group of gangliosides from figure for the strong difference of the first two treatments from table and figure in figure the result of the control treatment one is summarized by the box-clustering, and the treatment two, is depicted by node colors. a first observation is that the control yields only two clusters of lipids, and adding p yields three, thus, treatment two discriminates the reaction of lipids more finely. the red cluster is striking as it contains many large nodes, i.e., lipids, which differ strongly in their correlations wrt. the two treatments. the fan-out degree of every single lipid component in these graphs shows us the modulation degree with a given treatment. the hot edges incident to the largest nodes show where these differences manifest most strongly, i.e., which other nodes are discriminated by such a node by moving from treatment one to treatment two. looking up the respective lipids in figure the graphical clustering thus confirms the experimental results by showing that the long chain gangliosides go down after p treatment. in a similar manner we can use our graphs of other groups of lipids and treatments for pointers to behavioral phenomena. for the ratio of the third and fourth treatment combinations and the fifth and sixth, respectively, from table we do not observe any relevant changes as shown in figure and for the phosphatidylinositol, we see in figure the experimental outcome for the first two treatments showing an abundance increase of hydroxilated pis. we can also see that the hydroxylated pi go up after p treatment as depicted from the difference network between the first two treatments in figure the highest increase from zero to one hundred for +o as shown in the experimental results is represented in the network as a distinct separate cluster. there are no significant changes between the treatments u87+sn38/24hr+di312/24hr versus u87+sn38/24hr+p53/24hr and u87+di312/24hr versus u87+p53/24hr. the biochemical observations are again confirmed by our analysis for the phosphatidylglycerol profiles. the results for the first two treatments only are visualized in figure showing an abundance increase of hydroxylated pgs. the correlation network confirming these results is shown in figure cluster includes only the two pgs +o and +o showing an increase in signal magnitude from for the first treatment to for the second one. there are again as with the pis, no significant changes between the treatments u87+sn38/24hr+di312/24hr versus u87+sn38/24hr+p53/24hr and u87+di312/24hr versus u87+p53/24hr. we want to emphasize - based on the achieved results - that graph clustering networks compared to traditional correlation networks represent a unique "fingerprint" in lipidomics by revealing analytic properties while displaying the graph structure. this term from the field of analytic visualizations signifies a superficial drawing on the one hand, as it masks or even ignores some aspects of the raw data, however, on the other hand, it implies that prominent and potentially unknown features of the data become visible in an easily recognizable way. the above investigations show how observations made with the help of our clusterings coincide with and corroborate findings and interpretations based on expert knowledge. graph clustering and visualizations certainly cannot replace traditional analysis, but they can be a powerful supporting tool.  in this paper, we analyzed and interpreted lipidomic data sets acquired by high-throughput measurements such as nano liquid chromatography separation followed by detection with high mass accuracy and high mass-resolving power ft-icr ms. the samples were taken from u cell line treated under seven different treatments. we hypothesize that the observed correlations between the gangliosides concentrations are a result of the underlying lipidomic reaction network. thus, lipidomic networks in glioblastoma represent highly dynamical processes continuously changing under the influence of fluctuations. these induce a specific pattern of correlations and are measured in the experiment as a result of network propagation. as seen in plant metabolism, the determined pair-wise correlations represent a snapshot or "finger print" of the biochemical state of the glioblastoma cell at a given point in time. we introduced a novel concept in correlation network, the so-called graph clustering approach, which results in finding not only the correlations but also the clusters in these networks providing thus based on the concept of modularity a better visualization and analysis in lipidomic data exploration. the simulations based on the novel theoretical concept have confirmed the experimental findings: a down-regulation for gangliosides and an up-regulation for sulfatides and phosphatidylinositol. furthermore, we could quantize the regulations across the whole lipidom showing additionally that hydroxylated phosphatidylglycerol is also up-regulated. among the seven possible treatments, we showed that most visible changes leading to apoptosis can be found in combination with adenovirus therapy. in summary, this paper revealed in an unique way the "fingerprints" in lipidomics showing us how gene therapy with wild type p followed by chemotherapy with the topoisomerase inhibitor sn induces 95% apoptosis. 
to identify distinct biomarkers and differences in therapeutic outcomes, we develop a novel technique based on graph-clustering. we investigate the changes in the correlation networks for different therapies and study the success of novel gene therapies targeting aggressive glioblastoma.
 intelligent and multitiered quantitative analysis of biological systems rapidly evolves to a key technique in studying biomolecular cancer aspects. newly emerging advances in both measurement as well as bio-inspired computational techniques have facilitated the development of lipidomics technologies and offer an excellent opportunity to understand regulation at the molecular level in many diseases.  we present computational approaches to study the response of glioblastoma u cells to gene- and chemo-therapy. to identify distinct biomarkers and differences in therapeutic outcomes, we develop a novel technique based on graph-clustering. this technique facilitates the exploration and visualization of co-regulations in glioblastoma lipid profiling data. we investigate the changes in the correlation networks for different therapies and study the success of novel gene therapies targeting aggressive glioblastoma.  the novel computational paradigm provides unique "fingerprints" by revealing the intricate interactions at the lipidome level in glioblastoma u cells with induced apoptosis and thus opens a new window to biomedical frontiers. 