The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

The Electromagnetic Lorentz Condition Problem and Symplectic Properties of Maxwell and Yang-Mills Type Dynamical Systems

Symplectic structures associated to connection forms on certain types of principal fiber bundles are constructed via analysis of reduced geometric structures on fibered manifolds invariant under naturally related symmetry groups. This approach is then applied to nonstandard Hamiltonian analysis of of dynamical systems of Maxwell and Yang-Mills type. A symplectic reduction theory of the classical Maxwell equations is formulated so as to naturally include the Lorentz condition (ensuring the existence of electromagnetic waves), thereby solving the well known Dirac -Fock - Podolsky problem. Symplectically reduced Poissonian structures and the related classical minimal interaction principle for the Yang-Mills equations are also considered. 1

Classical R-matrix theory for bi-Hamiltonian field systems

The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The theory is developed for (1+1)-dimensional case where the space variable belongs either to R or to various discrete sets. Then, the extension onto (2+1)-dimensional case is made, when the second space variable belongs to R. The formalism presented contains many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.Comment: review article, 39 page

New insights into the synergism of nucleoside analogs with radiotherapy

Nucleoside analogs have been frequently used in combination with radiotherapy in the clinical setting, as it has long been understood that inhibition of DNA repair pathways is an important means by which many nucleoside analogs synergize. Recent advances in our understanding of the structure and function of deoxycytidine kinase (dCK), a critical enzyme required for the anti-tumor activity for many nucleoside analogs, have clarified the mechanistic role this kinase plays in chemo- and radio-sensitization. A heretofore unrecognized role of dCK in the DNA damage response and cell cycle machinery has helped explain the synergistic effect of these agents with radiotherapy. Since most currently employed nucleoside analogs are primarily activated by dCK, these findings lend fresh impetus to efforts focused on profiling and modulating dCK expression and activity in tumors. In this review we will briefly review the pharmacology and biochemistry of the major nucleoside analogs in clinical use that are activated by dCK. This will be followed by discussions of recent advances in our understanding of dCK activation via post-translational modifications in response to radiation and current strategies aimed at enhancing this activity in cancer cells

Cholesterol Homeostasis in Two Commonly Used Human Prostate Cancer Cell-Lines, LNCaP and PC-3

BACKGROUND:Recently, there has been renewed interest in the link between cholesterol and prostate cancer. It has been previously reported that in vitro, prostate cancer cells lack sterol-mediated feedback regulation of the major transcription factor in cholesterol homeostasis, sterol-regulatory element binding protein 2 (SREBP-2). This could explain the accumulation of cholesterol observed in clinical prostate cancers. Consequently, perturbed feedback regulation to increased sterol levels has become a pervasive concept in the prostate cancer setting. Here, we aimed to explore this in greater depth. METHODOLOGY/PRINCIPAL FINDINGS:After altering the cellular cholesterol status in LNCaP and PC-3 prostate cancer cells, we examined SREBP-2 processing, downstream effects on promoter activity and expression of SREBP-2 target genes, and functional activity (low-density lipoprotein uptake, cholesterol synthesis). In doing so, we observed that LNCaP and PC-3 cells were sensitive to increased sterol levels. In contrast, lowering cholesterol levels via statin treatment generated a greater response in LNCaP cells than PC-3 cells. This highlighted an important difference between these cell-lines: basal SREBP-2 activity appeared to be higher in PC-3 cells, reducing sensitivity to decreased cholesterol levels. CONCLUSION/SIGNIFICANCE:Thus, prostate cancer cells are sensitive to changing sterol levels in vitro, but the extent of this regulation differs between prostate cancer cell-lines. These results shed new light on the regulation of cholesterol metabolism in two commonly used prostate cancer cell-lines, and emphasize the importance of establishing whether or not cholesterol homeostasis is perturbed in prostate cancer in vivo

Designing a broad-spectrum integrative approach for cancer prevention and treatment

Targeted therapies and the consequent adoption of "personalized" oncology have achieved notablesuccesses in some cancers; however, significant problems remain with this approach. Many targetedtherapies are highly toxic, costs are extremely high, and most patients experience relapse after a fewdisease-free months. Relapses arise from genetic heterogeneity in tumors, which harbor therapy-resistantimmortalized cells that have adopted alternate and compensatory pathways (i.e., pathways that are notreliant upon the same mechanisms as those which have been targeted). To address these limitations, aninternational task force of 180 scientists was assembled to explore the concept of a low-toxicity "broad-spectrum" therapeutic approach that could simultaneously target many key pathways and mechanisms. Using cancer hallmark phenotypes and the tumor microenvironment to account for the various aspectsof relevant cancer biology, interdisciplinary teams reviewed each hallmark area and nominated a widerange of high-priority targets (74 in total) that could be modified to improve patient outcomes. For thesetargets, corresponding low-toxicity therapeutic approaches were then suggested, many of which werephytochemicals. Proposed actions on each target and all of the approaches were further reviewed forknown effects on other hallmark areas and the tumor microenvironment. Potential contrary or procar-cinogenic effects were found for 3.9% of the relationships between targets and hallmarks, and mixedevidence of complementary and contrary relationships was found for 7.1%. Approximately 67% of therelationships revealed potentially complementary effects, and the remainder had no known relationship. Among the approaches, 1.1% had contrary, 2.8% had mixed and 62.1% had complementary relationships. These results suggest that a broad-spectrum approach should be feasible from a safety standpoint. Thisnovel approach has potential to be relatively inexpensive, it should help us address stages and types ofcancer that lack conventional treatment, and it may reduce relapse risks. A proposed agenda for futureresearch is offered