A new analytical expression is proposed for the reduced influence parameter in Density Gradient Theory when combined with the Peng-Robinson equation of state for 32 n-alkanes. It contains the critical and triple point temperature values for each fluid as input and three adjustable coefficients. The new analytical expression contains the two-coefficients Zuo and Stenby and Miqueu et al.correlations as particular cases, and it is a modification of the previously published Cachadiña et al. correlation. Initially, the correlation coefficients for each fluid were obtained by fitting selected values for surface tension, and the results were comparable to other specific correlations reported in the literature. The overall mean absolute percentage deviation (OMAPD) between the selected and calculated data is just 0.79% Then, a general correlation including six adjustable coefficients valid for all the considered n-alkanes is proposed. It includes the radius of gyration as a new input parameter for each fluid. In this case, the OMAPD is 1.78\%. The use of other fluid properties as inputs is also briefly discussed.

Lipases, a versatile class of biocatalysts, have been shown to function in non-aqueous media/organic solvents and to possess promiscuous catalytic activity for a wide range of organic transformations. In this study, we explore the biocatalytic properties of a library of commercially available lipases by screening them for catalysis of a one-pot synthesis of Wieland-Miescher Ketone, an important intermediate in the synthesis of biologically active compounds such as steroids and terpenoids, from methyl vinyl ketone and 2-methyl-1,3-cyclohexanedione. As a direct outgrowth of this screen, we have created an optimized procedure for Wieland-Miescher Ketone (WMK) synthesis using crude lipase preparations, characterizing both reaction yield and enantiomeric excess. We have also identified principal components of the crude lipase mixture through proteomics and present evidence for a non-lipolytic origin of the observed catalysis. Finally, using the optimized conditions developed in this study, we propose a general absorbance-based screening methodology for assessing biocatalytic potential of crude enzyme preparations for synthesis of WMK.

Loss-of-function mutations of the spermine synthase gene (SMS) result in Snyder-Robinson Syndrome (SRS), a recessive X-linked syndrome characterized by intellectual disability, osteoporosis, hypotonia, speech abnormalities, kyphoscoliosis, and seizures. As SMS catalyzes the biosynthesis of the polyamine spermine from its precursor spermidine, SMS deficiency causes a lack of spermine with an accumulation of spermidine. As polyamines, spermine and spermidine play essential cellular roles that require tight homeostatic control to ensure normal cell growth, differentiation, and survival. Using patient-derived lymphoblast cell lines, we sought to comprehensively investigate the effects of SMS deficiency on polyamine homeostatic mechanisms including polyamine biosynthetic and catabolic enzymes, derivatives of the natural polyamines, and polyamine transport activity. In addition to decreased spermine and increased spermidine in SRS cells, ornithine decarboxylase activity and its product putrescine were significantly decreased. Treatment of SRS cells with exogenous spermine revealed that polyamine transport was active, as the cells accumulated spermine, decreased their spermidine level, and established a spermidine-to-spermine ratio within the range of wild type cells. SRS cells also demonstrated elevated levels of tissue transglutaminase, a change associated with certain neurodegenerative diseases. These studies form a basis for further investigations into the leading biochemical changes and properties of SMS-mutant cells that potentially represent therapeutic targets for the treatment of Snyder-Robinson Syndrome.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.