Metabolites of Purine Nucleoside Phosphorylase (NP) in Serum Have the Potential to Delineate Pancreatic Adenocarcinoma

Pancreatic Adenocarcinoma (PDAC), the fourth highest cause of cancer related deaths in the United States, has the most aggressive presentation resulting in a very short median survival time for the affected patients. Early detection of PDAC is confounded by lack of specific markers that has motivated the use of high throughput molecular approaches to delineate potential biomarkers. To pursue identification of a distinct marker, this study profiled the secretory proteome in 16 PDAC, 2 carcinoma in situ (CIS) and 7 benign patients using label-free mass spectrometry coupled to 1D-SDS-PAGE and Strong Cation-Exchange Chromatography (SCX). A total of 431 proteins were detected of which 56 were found to be significantly elevated in PDAC. Included in this differential set were Parkinson disease autosomal recessive, early onset 7 (PARK 7) and Alpha Synuclein (aSyn), both of which are known to be pathognomonic to Parkinson's disease as well as metabolic enzymes like Purine Nucleoside Phosphorylase (NP) which has been exploited as therapeutic target in cancers. Tissue Microarray analysis confirmed higher expression of aSyn and NP in ductal epithelia of pancreatic tumors compared to benign ducts. Furthermore, extent of both aSyn and NP staining positively correlated with tumor stage and perineural invasion while their intensity of staining correlated with the existence of metastatic lesions in the PDAC tissues. From the biomarker perspective, NP protein levels were higher in PDAC sera and furthermore serum levels of its downstream metabolites guanosine and adenosine were able to distinguish PDAC from benign in an unsupervised hierarchical classification model. Overall, this study for the first time describes elevated levels of aSyn in PDAC as well as highlights the potential of evaluating NP protein expression and levels of its downstream metabolites to develop a multiplex panel for non-invasive detection of PDAC

Infinite horizon differential games for abstract evolution equations

Berkovitz's notion of strategy and payoff for differential games is extended to study two player zero-sum infinite dimensional differential games on the infinite horizon with discounted payoff. After proving dynamic programming inequalities in this framework, we establish the existence and characterization of value. We also construct a saddle point for the game

Differential games with continuous, switching and impulse controls

A two-person zero-sum differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching, and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott-Kalton, the authors prove the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities

Existence of Value and Saddle Point in Infinite-Dimensional Differential Games

We study two-player zero-sum differential games of finite duration in a Hilbert space. Following the Berkovitz notion of strategies, we prove the existence of value and saddle-point equilibrium. We characterize the value as the unique viscosity solution of the associated Hamilton–Jacobi–Isaacs equation using dynamic programming inequalities

Evolutionary Stability Against Multiple Mutations

It is known (see, e. g., Weibull in Evolutionary Game Theory, MIT Press, 1995) that an evolutionarily stable strategy is not necessarily robust against multiple mutations. Precise definition and analysis of "evolutionarily stable strategy against multiple mutations" are not available in the literature. In this article, we formalize evolutionarily robustness against multiple mutations. Our main result shows that such a robust strategy is necessarily a pure strategy. Further, we study some equivalent formulations and properties of evolutionary stability against multiple mutations. In particular, we characterize completely the robustness against multiple mutations in 2 x 2 games