A Web-Based, Calculator-Skills Tutorial and Self-Test for General Chemistry Students

We describe the creation and utilization of a collection of Internet-based materials as supplemental instruction for students enrolled in the first-semester course of a general chemistry sequence. These tutorial and self-assessment materials are intended for asynchronous use as a review of mathematical concepts and skills including functional performance with calculators.     

The emulsifying properties of β-lactoglobulin genetic variants A, B and C

The emulsifying properties of three genetic variants of β-lactoglobulin (β-lac) (the A, B and C variants) are investigated as a function of protein concentration. Differences in the emulsifying properties and emulsion stability are explained in view of the known differences in physico-chemical and structural/conformational properties of the β-lac variants. β-lac A forms the finest emulsion droplets, and β-lac C the largest droplets. The order of decreasing emulsifying ability (A>B>C) can be explained in terms of differences in the molecular structure, and conformational stability of the variant proteins. The creaming stability, when compared at the same particle size, is greatest for β-lac C, with β-lac A and B having a similar and lower stability. The differences in creaming stability may arise from a higher surface coverage for the β-lac C droplets at an equivalent particle size. The storage stability is lower for β-lac A than for β-lac B and C, which both show a similar behaviour. Storage stability differences are discussed in terms of differences in molecular structure, conformational stability, interfacial viscosity and surface coverage for the three variants.     

Interpreting the catalytic voltammetry of an adsorbed enzyme by considering substrate mass transfer, enzyme turnover, and interfacial electron transport

Redox active enzymes can be adsorbed onto electrode surfaces to catalyze the interconversion of oxidized and reduced substrates in solution, driven by the supply or removal of electrons by the electrode. The catalytic current is directly proportional to the rate of enzyme turnover, and its dependence on the electrode potential can be exploited to define both the kinetics and thermodynamics of the enzyme's catalytic cycle. However, observed electrocatalytic voltammograms are often complex because the identity of the rate limiting step changes with the electrode potential and under different experimental conditions. Consequently, extracting mechanistic information requires that accurate models be constructed to deconvolute and analyze the observed behavior. Here, a basic model for catalysis by an adsorbed enzyme is described. It incorporates substrate mass transport, enzyme kinetics, and interfacial electron transport, and it accurately reproduces experimentally recorded voltammograms from the oxidation of NADH by subcomplex Ilambda (the hydrophilic subcomplex of NADH:ubiquinone oxidoreductase), under a range of conditions. Mass transport is imposed by a rotating disk electrode and described by the Levich equation. Interfacial electron transport is controlled by the electrode potential and characterized by a dispersion of rate constants, according to the model of Léger and co-workers. Here, the Michaelis-Menten equation is used for the enzyme kinetics, but our methodology can also be readily applied to derive and apply analogous equations relating to alternative enzyme mechanisms. Therefore, our results are highly relevant to the interpretation of electrocatalytic voltammograms for adsorbed enzymes in general.     

Embeddings of countable closed sets and reverse mathematics

Summary If there is a homeomorphic embedding of one set into another, the sets are said to be topologically comparable. Friedman and Hirst have shown that the topological comparability of countable closed subsets of the reals is equivalent to the subsystem of second order arithmetic denoted byATR ₀. Here, this result is extended to countable closed locally compact subsets of arbitrary complete separable metric spaces. The extension uses an analogue of the one point compactification of .     

The Inducibility of Graphs on Four Vertices

We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H. The exact value of this quantity is known only for a handful of small graphs and a specific set of complete multipartite graphs. Answering questions of Brown–Sidorenko and Exoo, we determine the inducibility of K_{1, 1, 2} and the paw graph. The proof is obtained using semidefinite programming techniques based on a modern language of extremal graph theory, which we describe in full detail in an accessible setting.     

Molecular Compton profiles from SCF-MO wavefunctions

This paper considers the dependence of Compton profiles calculated from molecular wavefunctions on the atomic basis set used. For fluoromethane there is no significant difference between profiles calculated with a Slater minimal basis set and with STO-3G, STO-4G and STO-5G sets. A Slater double-zeta set and Dunning's gaussian basis give essentially the same profile and the addition of polarization functions to the Dunning basis has little effect. For methanol, methylamine and ethane there is a significant difference between the STO-3G profiles and those calculated from extended basis sets but again the addition of polarization functions has little effect. The use of Dunning's basis would seem to be adequate for Compton profile calculations for molecules of medium size. As one goes along the series from ethane to fluoromethane the Compton profile becomes broader.     

Rotating ellipses of varying shape

This article describes an investigation carried out while the second author was an undergraduate. The article gives an account of the way the work evolved, to give insight into the learning processes, as well as the mathematical issues encountered.     

Water order profiles on phospholipid/cholesterol membrane bilayer surfaces

Water is pivotal in the stabilization of macromolecular biological structures, although the dynamic ensemble structure of water near to molecular surfaces has yet to be fully understood. We show, through molecular simulation and fluorescence measurements, that water at the membrane surface is substantially more ordered than bulk water, due to a loss of hydrogen bonding between water molecules, coupled with an alignment of lipid and water dipole moments. Ordering of the water leads to a gradient in the effective dielectric permittivity, which is evident in both the molecular simulations and the fluorescence measurements. A lower effective dielectric permittivity was correlated with a decreasing degree of hydrogen bonding over the same spatial range. The water molecules closest to the lipid headgroup oxygen atoms form hydrogen bonds which exhibit a mean lifetime of 6.3 ps, compared with a mean lifetime of water-water hydrogen bonds of less than 2 ps. Membranes made up purely of phosphatidylcholine (PC) were compared with those made with a PC/cholesterol ratio relevant to cell membranes. Clear differences were found between these membrane configurations. These observations point to molecular structural differences in the surface environments of membranes and may underlie regional differences in the surface biophysical properties of membrane microdomains.     

Quantitative structure-activity relationships by neural networks and inductive logic programming. I. The inhibition of dihydrofolate reductase by pyrimidines

Summary Neural networks and inductive logic programming (ILP) have been compared to linear regression for modelling the QSAR of the inhibition of E. coli dihydrofolate reductase (DHFR) by 2,4-diamino-5-(substitured benzyl)pyrimidines, and, in the subsequent paper [Hirst, J.D., King, R.D. and Sternberg, M.J.E., J. Comput.-Aided Mol. Design, 8 (1994) 421], the inhibition of rodent DHFR by 2,4-diamino-6,6-dimethyl-5-phenyl-dihydrotriazines. Cross-validation trials provide a statistically rigorous assessment of the predictive capabilities of the methods, with training and testing data selected randomly and all the methods developed using identical training data. For the ILP analysis, molecules are represented by attributes other than Hansch parameters. Neural networks and ILP perform better than linear regression using the attribute representation, but the difference is not statistically significant. The major benefit from the ILP analysis is the formulation of understandable rules relating the activity of the inhibitors to their chemical structure.