The Intratumoral Heterogeneity Reflects the Intertumoral Subtypes of Glioblastoma Multiforme: A Regional Immunohistochemistry Analysis.

Glioblastoma multiforme (GBM) is the most frequent and aggressive primary brain tumor in adults. Despite extensive therapy the prognosis for GBM patients remains poor and the extraordinary therapy resistance has been attributed to intertumoral heterogeneity of glioblastoma. Different prognostic relevant GBM tumor subtypes have been identified based on their molecular profile. This approach, however, neglects the heterogeneity within individual tumors, that is, the intratumoral heterogeneity. Here, we detected the regional immunoreactivity by immunohistochemistry and immunofluorescence using nine different markers on resected GBM specimens (IDH wildtype, WHO grade IV). We found repetitive expression profiles, that could be classified into clusters. These clusters could then be assigned to five pathophysiologically relevant groups that reflect the previously described subclasses of GBM, including mesenchymal, classical, and proneural subtype. Our data indicate the presence of tumor differentiations and tumor subclasses that occur within individual tumors, and might therefore contribute to develop adapted, individual-based therapies.

Information directionality in coupled time series using transcripts.

In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations among information measures of the symbolic representations of time series. These theoretical results are then applied for the assessment of coupling directionality in dynamical systems, where suitable coupling directionality measures are introduced depending only on transcripts. These measures improve the reliability of the information flow estimates and reduce to well-established coupling directionality quantifiers when some general conditions are satisfied. Furthermore, by generalizing the definition of transcript to ordinal patterns of different lengths, several of the commonly used information directionality measures can be encompassed within the same framework.

Transcripts: an algebraic approach to coupled time series.

Ordinal symbolic dynamics is based on ordinal patterns. Its tools include permutation entropy (in metric and topological versions), forbidden patterns, and a number of mathematical results that make this sort of symbolic dynamics appealing both for theoreticians and practitioners. In particular, ordinal symbolic dynamics is robust against observational noise and can be implemented with low computational cost, which explains its increasing popularity in time series analysis. In this paper, we study the perhaps less exploited aspect so far of ordinal patterns: their algebraic structure. In a first part, we revisit the concept of transcript between two symbolic representations, generalize it to N representations, and derive some general properties. In a second part, we use transcripts to define two complexity indicators of coupled dynamics. Their performance is tested with numerical and real world data.

Label-free live-cell imaging with confocal Raman microscopy.

Confocal Raman spectroscopy is a noninvasive alternative to established cell imaging methods because it does not require chemical fixation, the use of fluorescent markers, or genetic engineering. In particular, single live-cell, high-resolution imaging by confocal Raman microscopy is desirable because it allows further experiments concerning the individually investigated cells. However, to derive meaningful images from the spectroscopic data, one must identify cell components within the dataset. Using immunofluorescence images as a reference, we derive Raman spectral signatures by means of information measures to identify cell components such as the nucleus, the endoplasmic reticulum, the Golgi apparatus, and mitochondria. The extracted signatures allow us to generate representations equivalent to conventional (immuno)fluorescence images with more than three cell components at a time, exploiting the Raman spectral information alone.

Characterizing synchronization in time series using information measures extracted from symbolic representations.

We present a methodology to characterize synchronization in time series based on symbolic representations. Each time series is mapped onto a sequence of p -dimensional delay vectors that are subsequently transformed into symbols by means of a rank-ordering of their values. Based on these representations, we propose a transcription scheme between symbols of the respective time series to study synchronization properties. Group-theoretical considerations and the use of information measures allow us to classify regimes of synchronization and to assess its strength. We apply our method to a prototype nonlinear system, which reveals a rich variety of coupled dynamics. We investigate in detail the robustness of the derived synchronization measure against noise and compare its value with that of the established measures.