Global existence and controllability to a stochastic integro-differential equation

In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter is given to illustrate the theory

Shotgun lipidomics identifies a paired rule for the presence of isomeric ether phospholipid molecular species

BACKGROUND: Ether phospholipids are abundant membrane constituents present in electrically active tissues (e.g., heart and the brain) that play important roles in cellular function. Alterations of ether phospholipid molecular species contents are associated with a number of genetic disorders and human diseases. METHODOLOGY/PRINCIPAL FINDINGS: Herein, the power of shotgun lipidomics, in combination with high mass accuracy/high resolution mass spectrometry, was explored to identify a paired rule for the presence of isomeric ether phospholipid molecular species in cellular lipidomes. The rule predicts that if an ether phospholipid A′-B is present in a lipidome, its isomeric counterpart B′-A is also present (where the ′ represents an ether linkage). The biochemical basis of this rule results from the fact that the enzymes which participate in either the sequential oxidation of aliphatic alcohols to fatty acids, or the reduction of long chain fatty acids to aliphatic alcohols (metabolic precursors of ether lipid synthesis), are not entirely selective with respect to acyl chain length or degree of unsaturation. Moreover, the enzymatic selectivity for the incorporation of different aliphatic chains into the obligatory precursor of ether lipids (i.e., 1-O-alkyl-glycero-3-phosphate) is also limited. CONCLUSIONS/SIGNIFICANCE: This intrinsic amplification of the number of lipid molecular species present in biological membranes predicted by this rule and demonstrated in this study greatly expands the number of ether lipid molecular species present in cellular lipidomes. Application of this rule to mass spectrometric analyses provides predictive clues to the presence of specific molecular species and greatly expands the number of identifiable and quantifiable ether lipid species present in biological samples. Through appropriate alterations in the database, use of the paired rule increases the number of identifiable metabolites in metabolic networks, thereby facilitating identification of biomarkers presaging disease states