Cancer Biomarker Discovery: The Entropic Hallmark

Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases

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This chapter describes lasers and other sources of coherent light that operate in a wide wavelength range. First, the general principles for the generation of coherent continuous-wave and pulsed radiation are treated including the interaction of radiation with matter, the properties of optical resonators and their modes as well as such processes as Q-switching and mode-locking. The general introduction is followed by sections on numerous types of lasers, the emphasis being on todayʼs most important sources of coherent light, in particular on solid-state lasers and several types of gas lasers. An important part of the chapter is devoted to the generation of coherent radiation by nonlinear processes with optical parametric oscillators, difference- and sum-frequency generation, and high-order harmonics. Radiation in the extended ultraviolet (EUV) and x-ray ranges can be generated by free electron lasers (FEL) and advanced x-ray sources. Ultrahigh light intensities up to 1021 W/cm2 open the door to studies of relativistic laser–matter interaction and laser particle acceleration. The chapter closes with a section on laser stabilization