Solvent Ingress in Polymers.

The understanding of solvent ingress into polymers is of vital importance in a plethora of applications that embrace such diverse technologies as dental resins and food systems. Two limiting regimes of small molecule diffusion in polymers are widely acknowledged: Fickian and Case II. Fickian diffusion is associated with solvent uptake proceeding with the square root of time and with smooth concentration profiles. Case II ingress is characterised by uptake that is linear with time and by concentration profiles with sharp fronts. This thesis describes new insight into both these transport mechanisms. Binary mixtures of good (methyl ethyl ketone) and bad (ethanol) solvents ingressing polystyrene with Fickian dynamics are investigated. Using both 2H magnetic resonance imaging (MRI) with selectively deuterated solvents and 13C-1H cyclic cross-polarisation chemically selective imaging of normal solvents, the individual components are separately measured. The two solvents are found to ingress together but they have different spatial concentration profiles. These results are explained in terms of a simple model. In a further study using both MRI and ellipsometry, no polymer molecular weight dependence is observed for Fickian solvent ingress. Powerful evidence of a new rate-limiting step to give Case II diffusion is demonstrated. We show that the rate-limiting step can be the solvent flux at the polymer surface as well as the visco-elastic polymer swelling. Numerical simulations of a simple phenomenological model demonstrating these effects are presented. They are supported by experimental measurements of liquid and vapour toluene ingress into polystyrene using MRI and stray field imaging. One problem with ellipsometry for measuring Fickian ingress is that it is difficult to unambiguously fit the and data to the smooth refractive index profile through the swelling sample. Two methods have been implemented to overcome this problem: a Born approximation and a Bayesian inference technique. The latter has shown that ellipsometry can now, in theory, be described as a model independent technique

Regulation of Kir Channels by Intracellular pH and Extracellular K+: Mechanisms of Coupling

ROMK channels are regulated by internal pH (pHi) and extracellular K+ (K+o). The mechanisms underlying this regulation were studied in these channels after expression in Xenopus oocytes. Replacement of the COOH-terminal portion of ROMK2 (Kir1.1b) with the corresponding region of the pH-insensitive channel IRK1 (Kir 2.1) produced a chimeric channel (termed C13) with enhanced sensitivity to inhibition by intracellular H+, increasing the apparent pKa for inhibition by ∼0.9 pH units. Three amino acid substitutions at the COOH-terminal end of the second transmembrane helix (I159V, L160M, and I163M) accounted for these effects. These substitutions also made the channels more sensitive to reduction in K+o, consistent with coupling between the responses to pHi and K+o. The ion selectivity sequence of the activation of the channel by cations was K+ ≅ Rb+ > NH4+ >> Na+, similar to that for ion permeability, suggesting an interaction with the selectivity filter. We tested a model of coupling in which a pH-sensitive gate can close the pore from the inside, preventing access of K+ from the cytoplasm and increasing sensitivity of the selectivity filter to removal of K+o. We mimicked closure of this gate using positive membrane potentials to elicit block by intracellular cations. With K+o between 10 and 110 mM, this resulted in a slow, reversible decrease in conductance. However, additional channel constructs, in which inward rectification was maintained but the pH sensor was abolished, failed to respond to voltage under the same conditions. This indicates that blocking access of intracellular K+ to the selectivity filter cannot account for coupling. The C13 chimera was 10 times more sensitive to extracellular Ba2+ block than was ROMK2, indicating that changes in the COOH terminus affect ion binding to the outer part of the pore. This effect correlated with the sensitivity to inactivation by H+. We conclude that decreasing pHI increases the sensitivity of ROMK2 channels to K+o by altering the properties of the selectivity filter

A new balance index for phylogenetic trees

Several indices that measure the degree of balance of a rooted phylogenetic tree have been proposed so far in the literature. In this work we define and study a new index of this kind, which we call the total cophenetic index: the sum, over all pairs of different leaves, of the depth of their least common ancestor. This index makes sense for arbitrary trees, can be computed in linear time and it has a larger range of values and a greater resolution power than other indices like Colless' or Sackin's. We compute its maximum and minimum values for arbitrary and binary trees, as well as exact formulas for its expected value for binary trees under the Yule and the uniform models of evolution. As a byproduct of this study, we obtain an exact formula for the expected value of the Sackin index under the uniform model, a result that seems to be new in the literature.Comment: 24 pages, 2 figures, preliminary version presented at the JBI 201

Clades and clans: a comparison study of two evolutionary models

The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under these two models provides valuable insights into macro-evolutionary processes, and is important in hypothesis testing and Bayesian analyses in phylogenetics. Here we show that these distributions are log-convex, which implies that very large clades or very small clades are more likely to occur under these two models. Moreover, we prove that there exists a critical value $\kappa(n)$ for each $n\geqslant 4$ such that for a given clade with size $k$, the probability that this clade is contained in a random tree with $n$ leaves generated under the YHK model is higher than that under the PDA model if $1<k<\kappa(n)$, and lower if $\kappa(n)<k<n$. Finally, we extend our results to binary unrooted trees, and obtain similar results for the distributions of clan sizes.Comment: 21page