The effects of media properties on the horseradish peroxidase-catalyzed fluorogenic reaction

The effects of media properties including buffers, acidity, solvents and surfactant on horseradish peroxidase-catalyzed fluorogenic reaction were investigated. The results showed that the so-called non-fluorescent hydrogen donors were in fact fluorescent. There existed an acid—base equilibrium in the fluorescent dimer product. For p -hydroxyphenylpropionic acid, a pK_a value of 8.0 for the product was obtained from its titration curve. The product fluorescence increased with higher pH, however, a longer time was needed to reach the reaction equilibrium due to the pH mismatch problem. Cationic micelles cetyltrimethylammonium bromide and cetyltrimethylammonium chloride could reduce the pH mismatch and offered a way to further increase the determination sensitivity. Finally, a micelle-enhanced flow-injection analysis of horseradish peroxidase is suggested.     

The distribution of 4-full numbers

Let Q(x) denote the number of 4-full numbers not exceeding x. It is well known that $$Q(x) = \sum\limits_{j = 4}^7 {r_j x^{1/j} + R(x)}$$ where $$r_j = \mathop {res}\limits_{s = 1/j} (F(s)/s), F(s) = \mathop \prod \limits_P \left( {1 + \frac{{p^{ - 4s} }}{{1 - p^{ - s} }}} \right)$$ and R(x) is the remainder. This paper proves that $$R(x) \ll x^{3626/35461 + \varepsilon }$$ where ε is any positive number.     

Exact solution of a vertex model ind dimensions

We consider a class of vertex models describing directed lines on a lattice in arbitraryd dimensions, and solve the model exactly for the Cartesian lattice and in the case that each loop of lines carries a fugacity - 1. Our analysis, which can be carried out for arbitrary lattices, is based on an equivalence of the vertex model with a dimer problem. The dimer problem is, in turn, solved using the method of Pfaffians. It is found that the system is frozen below a critical temperatureT _cwith the critical exponent = (3 –d)/2.