Avoiding abelian squares in partial words

Erd?s raised the question whether there exist infinite abelian square-free words over a given alphabet, that is, words in which no two adjacent subwords are permutations of each other. It can easily be checked that no such word exists over a three-letter alphabet. However, infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words, or sequences that may contain some holes. In particular, we give lower and upper bounds for the number of letters needed to construct infinite abelian square-free partial words with finitely or infinitely many holes. Several of our constructions are based on iterating morphisms. In the case of one hole, we prove that the minimal alphabet size is four, while in the case of more than one hole, we prove that it is five. We also investigate the number of partial words of length n with a fixed number of holes over a five-letter alphabet that avoid abelian squares and show that this number grows exponentially with n.     

Capillary size exclusion chromatography with picogram sensitivity for analysis of monoclonal antibodies purified from harvested cell culture fluid

Size exclusion chromatography (SEC) is widely used in the characterization and quality control of therapeutic proteins to detect aggregates. Aggregation is a carefully monitored quality attribute from the earliest stages of clinical development owing to the possibility of eliciting an immunogenic response in the patient. During early stage molecule assessment for cell culture production, small-scale screening experiments are performed to permit rapid turn-around of results so as to not delay timelines. We report the development of a capillary SEC methodology for preliminary molecule assessment to support the evaluation of therapeutic candidates at an early stage of development. By making several key modifications to a commercially available liquid chromatography system, we demonstrate a platform process to perform capillary SEC with excellent precision, picogram sensitivity and good ruggedness. The limit of quantitation was determined to be approximately 15 pg; picogram sensitivity for SEC analysis of monoclonal antibodies had not been achieved prior to this work. In addition, we have developed a method to capture low levels of antibody (1 μg/mL) from harvested cell culture fluid (HCCF) for capillary SEC analysis. Up to 40% recovery efficiency was achieved using this micro-recovery method on 3 mL HCCF samples. Using early stage cell culture transient transfection samples, which typically have much lower titers than stable cell line samples, we demonstrate a consistent method for analyzing aggregates in low protein concentration HCCF samples for molecule assessment and early stage candidate screening.     

Microstructure determination of AOT + phenol organogels utilizing small-angle X-ray scattering and atomic force microscopy.

Dry reverse micelles of the anionic twin-tailed surfactant bis(2-ethylhexyl) sulfosuccinate (AOT) dissolved in nonpolar solvents spontaneously form an organogel when p-chlorophenol is added in a 1:1 AOT:phenol molar ratio. The solvents used were benzene, toluene, m-xylene, 2,2,4-trimethylpentane (isooctane), decane, dodecane, tetradecane, hexadecane, and 2,6,10,14-tetramethylpentadecane (TMPD). The proposed microstructure of the gel is based on strands of stacked phenols linked to AOT through hydrogen bonding. Small-angle X-ray scattering (SAXS) spectra of the organogels suggest a characteristic length scale for these phenol-AOT strands that is independent of concentration but dependent on the chemical nature of the nonpolar solvent used. Correlation lengths determined from the SAXS spectra indicate that the strands self-assemble into fibers. Direct visualization of the gel in its native state is accomplished by using tapping mode atomic force microscopy (AFM). It is shown that these organogels consist of fiber bundle assemblies. The SAXS and AFM data reinforce the theory of a molecular architecture consisting of three length scales-AOT/phenolic strands (ca. 2 nm in diameter) that self-assemble into fibers (ca. 10 nm in diameter), which then aggregate into fiber bundles (ca. 20-100 nm in diameter) and form the organogel.     

Analysis of fluorescently labeled substance P analogs: binding, imaging and receptor activation

Background  

Substance P (SP) is a peptide neurotransmitter found in central and peripheral nerves. SP is involved in the control of smooth muscle, inflammation and nociception. The amino acid sequence of SP is Arg-Pro-Lys-Pro-Gln-Gln-Phe-Phe-Gly-Leu-Met-NH₂. Five different forms of fluorescently labeled SP have recently been synthesized, in which Alexa 488, BODIPY Fl, fluorescein, Oregon Green 488 or tetramethylrhodamine has been covalently linked to SP at Lys³. Here, these novel analogs are characterized as to their ligand binding, receptor activation and fluorescence labeling properties.     

Phase Transfer Catalysis Preparation of Arvl,Thiocyanates

Phase transfer catalvsis, PTC, has become a common preparative method in organic chemistry. Numerous aliphatic substitution reactions have been performed yielding cvanides,¹ azides,² thiocyanates,³ ethers,⁴ and many other types of substitution products.¹     

Phase Transfer Catalysis Preparation of Acyl Isothiocyanates

The use of phase transfer catalysis, PTC, for nucleophillic substitution reactions is well documented.^1,2 Included among these reactions is the preparation of both alkyl³ and aryl⁴ thiocyanates. However, PTC reactions at an acyl carbon are much less common. Brándstróm⁵ has reported the preparation of acyl azides and Weber⁶ has used PTC to prepare benzoyl cyanide. Recently Illi⁷ has used PTC to acylate sterically crowded phenols.     

The hall effect in some liquid alloys

The Hall coefficient has been measured for (a) liquid CuTe, AgTe and AuTe₂ and (b) liquid Cu-Sn alloy. The results are discussed in terms of the possible semiconducting nature of liquids comprising group (a) and in terms of bound state formation around the Sn atoms for those in group (b).     

A Mössbauer spectroscopy and neutron diffraction study of magnetostrictive,melt-spun Fe–Ga alloy ribbons

Ribbons of Fe_100−xGa_x (x=15, 17.5, 19.5 and 22.5) were prepared by rapid solidification from the melt. ⁵⁷Fe Mössbauer spectroscopy and high resolution neutron diffraction have revealed that Fe_100−xGa_x alloys with x=15 and 17.5 have the disordered bcc (A2) structure even after annealing, but the alloy with x=19.5 developed the short-range ordered D0₃ phase when annealed. The x=22.5 alloys showed mainly D0₃ phase with a fraction of bcc phase. A fraction of the bcc phase transformed into D0₃ phase and the long-range ordering of D0₃ phase was improved after annealing. ⁵⁷Fe Mössbauer spectra showed no observable L1₂ phase in any samples even though less than 1% volume of L1₂ phases has been found in the annealed samples by neutron diffraction. The additional absorption at hyperfine field of 25 T in x=22.5 samples was regarded as a result of imperfect D0₃ structure, rather than L1₂ phase.