Ordering on multiple lengthscales in a series of side group liquid crystal block copolymers containing a cholesteryl-based mesogen

Hierarchical ordering in a side group liquid crystal block copolymer is investigated by differential scanning calorimetry, polarized optical microscopy, small-angle X-ray and neutron scattering (SAXS and SANS) and transmission electron microscopy (TEM). A series of block copolymers with a range of compositions was prepared by atom transfer radical polymerization, comprising a polystyrene block and a poly(methyl methacrylate) block bearing chiral cholesteryl mesogens. Smectic ordering is observed as well as microphase separation of the block copolymer. Lamellar structures were observed for far larger volume fractions than for coil-coil copolymers (up to a volume fraction of liquid crystal block, f(LC) = 0.8). A sample with f(LC) = 0.86 exhibited a hexagonal-packed cylinder morphology, as confirmed by SAXS and TEM. The matrix comprised the liquid crystal block, with the mesogens forming smectic layers. For the liquid crystal homopolymer and samples with high f(LC), a smectic-smectic phase transition was observed below the clearing point. At low temperature, the smectic phase comprises coexisting domains with monolayer S-A,S-1 coexisting with interdigitated S-A,S-d domains. At high temperature a SA,1 phase is observed. This is the only structure observed for samples with lower f(LC). These unprecedented results point to the influence of block copolymer microphase separation on the smectic ordering.

Chromatographic alignment of LC-MS and LC-MS/MS datasets by genetic algorithm feature extraction

Liquid chromatography-mass spectrometry (LC-MS) datasets can be compared or combined following chromatographic alignment. Here we describe a simple solution to the specific problem of aligning one LC-MS dataset and one LC-MS/MS dataset, acquired on separate instruments from an enzymatic digest of a protein mixture, using feature extraction and a genetic algorithm. First, the LC-MS dataset is searched within a few ppm of the calculated theoretical masses of peptides confidently identified by LC-MS/MS. A piecewise linear function is then fitted to these matched peptides using a genetic algorithm with a fitness function that is insensitive to incorrect matches but sufficiently flexible to adapt to the discrete shifts common when comparing LC datasets. We demonstrate the utility of this method by aligning ion trap LC-MS/MS data with accurate LC-MS data from an FTICR mass spectrometer and show how hybrid datasets can improve peptide and protein identification by combining the speed of the ion trap with the mass accuracy of the FTICR, similar to using a hybrid ion trap-FTICR instrument. We also show that the high resolving power of FTICR can improve precision and linear dynamic range in quantitative proteomics. The alignment software, msalign, is freely available as open source.

A preliminary comparative analysis of the H. sapiens saliva proteome between cysteine fractionation,performic acid oxidation LC/MALDI/MS/MS and LC/ESI/MS/MS

We present a comparative study between LC/MALDI/MS/MS and LC/ESI/MS/MS. Diagnostic biomarkers in saliva have been identified for monitoring caries, periodontitis, oral cancer, salivary gland diseases, and systemic disorders e.g. hepatitis and HIV[1]. Saliva is similar to serum in that there are a small number of highly abundant proteins and many low abundance proteins. There are 35 previously identified salivary proteins [1-4]. We prepared a representative sample of cysteine containing peptides and oxidised them to improve their fragmentation under MALDI conditions. In total 20 proteins were identified with 6 been identified by both methods. Surprisingly there was little overlap in the peptides used to identify the proteins between the two methods

First-dimension separation with the MicroRotoforTM cell prior to SDS-PAGE and LC-MS/MS analysis

Free-flow isoelectric focusing (IEF) is a gel-free method for separating proteins based on their isoelectric point (pl) in a liquid environment and in the presence of carrier ampholytes. this method has been used with the RotoforTM cell at the preparative scale to fractionate proteins from samples containing several hundred milligrams of protein; see the refeences listed in Bio-Rad bulletin 3152. the MicroRotofor cell applies the same method to much sl=maller protein samples without dilution, separating and recoverng milligram quantities of protein in a total volume of about 2 ml.

On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

LC-MS & DFT investigations of Cryptolepis sanginolenta root extracts

The roots of Crytolepis sanguinolenta, a medicinally important ethanobotanical source of the antimalarial cryptolepine, were soxhlet extracted in anaerobic conditions, using hexane then ethanol. Samples of each extract were fractioned using flash chromatography and preparative TLC and compound identity was established using gradient HPLC-positive ion electrospray mass spectrometry. The use of argon depressed the formation of quindoline and hydroxycrytolepine. In addition to known compounds such as cryptolepine, several as yet unidentified compounds remain to be characterised in this root extract.

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.