Analysis of protamine peptides in insulin pharmaceutical formulations by capillary electrophoresis

Protamines are a group of highly basic peptides that are sometimes added to insulin formulations to prolong the pharmacological action. In this study, different methods were investigated to identify protamine in insulin formulations. Capillary electrophoresis in aqueous and non‐aqueous media was tested to separate these peptides with very close amino acid sequences. Different buffers (phosphate or formate, both acidified) and various additives (principally negatively charged and neutral surfactants) were investigated to optimize peptide separation. Finally, a micellar electrokinetic capillary chromatography method using a capillary of 120 cm effective length and an aqueous background electrolyte made up of 100 mM phosphate buffer (pH 2) and 50 mM Thesit® gave the best results, providing the separation of the four major protamine peptides within 25 min.     

On permutations of order dividing a given integer

We give a detailed analysis of the proportion of elements in the symmetric group on n points whose order divides m, for n sufficiently large and m≥n with m=O(n).      

The influence of aliphatic diols on the temperature of maximum density of water

The influence of various aliphatic diols on the temperature of maximum density (TMD) of water has been investigated. 1,2-Propanediol, 1,3-propanediol, 1,3-butanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, and 2,5-hexanediol were found to yield positive structural contributions to the solute-induced shift in the TMD, i.e., they are structure makers. Contrariwise, data from the literature indicate that 1,2-ethanediol is a structure breaker. Relationships between the structure making/breaking tendencies of the solutes and the relative positions of the two hydroxyl groups are discussed.     

Non-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes

For a positive integer n, does there exist a vertex-transitive graph Γ on n vertices which is not a Cayley graph, or, equivalently, a graph Γ on n vertices such that Aut Γ is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, Marusic and Scapellato, and McKay and the second author) has produced answers to this question if n is prime, or divisible by the square of some prime, or if n is the product of two distinct primes. In this paper we consider the simplest unresolved case for even integers, namely for integers of the form n = 2pq, where 2 < q < p, and p and q are primes. We give a new construction of an infinite family of vertex-transitive graphs on 2pq vertices which are not Cayley graphs in the case where p ≡ 1 (mod q). Further, if p ? 1 (mod q), p ≡ q ≡ 3(mod 4), and if every vertex-transitive graph of order pq is a Cayley graph, then it is shown that, either 2pq = 66, or every vertex-transitive graph of order 2pq admitting a transitive imprimitive group of automorphisms is a Cayley graph.