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

Modeling termination kinetics of non-stationary free-radical polymerizations

Pulsed-laser induced polymerization is modeled via an approach presented in a previous paper. An equation for the time dependence of free-radical concentration is derived. It is shown that the termination rate coefficient may vary significantly as a function of time after applying the laser pulse despite of the fact that the change in monomer concentration during one experiment is negligible. For the limiting case of t ≫ c-1 (kpM)-1, where c is a dimensionless chain-transfer constant, kp the propagation rate coefficient and M the monomer concentration, an analytical expression for kt is derived. It is also shown that time-resolved single pulsed-laser polymerization (SP-PLP) experiments can yield the parameters that allow the modeling of kt in quasi-stationary polymerization. The influence of inhibitors is also considered. The conditions are analyzed under which M (t) curves recorded at different extents of laser-induced photo-initiator decomposition intersect. It is shown that such type of behavior is associated with chain-length dependence of kt

Critically evaluated termination rate coefficients for free-radical polymerization, 1 - The current situation

This is the first publication of an IUPAC-sponsored Task Group on "Critically evaluated termination rate coefficients for free-radical polymerization." The paper summarizes the current situation with regard to the reliability of values of termination rate coefficients k(t). It begins by illustrating the stark reality that there is large and unacceptable scatter in literature values of k(t), and it is pointed out that some reasons for this are relatively easily, remedied. However, the major reason for this situation is the inherent complexity of the phenomenon of termination in free-radical polymerization. It is our impression that this complexity is only incompletely grasped by many workers in the field, and a consequence of this tendency to oversimplify is that misunderstanding of and disagreement about termination are rampant. Therefore this paper presents a full discussion of the intricacies of k(t): sections deal with diffusion control, conversion dependence, chain-length, dependence, steady state and non-steady state measurements, activation energies and activation volumes, combination and disproportionation, and theories. All the presented concepts are developed from first principles, and only rigorous, fully-documented experimental results and theoretical investigations are cited as evidence. For this reason it can be said that this paper summarizes all that we, as a cross-section of workers in the, field, agree on about termination in free-radical polymerization. Our discussion naturally leads to a series of recommendations regarding measurement of k(t) and reaching a more satisfactory understanding of this very important rate coefficient. Variation of termination. rate coefficient k(t) with inverse absolute temperature T-1 for bulk, polymerization of methyl methacrylate at ambient pressure.([6]) The plot contains all methacrylate at ambient pressure. tabulated values([6]) (including those categorized as "recalculated") except ones from polymerizations noted as involving. solvent or above-ambient pressures