Morphogen gradient from a noisy source

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of robust gradient formation, and the results are confirmed by numerical simulation. It is shown that such deviations can disrupt robustness for sufficiently high noise levels, and the implications of these findings for more complex models of gradient-shaping pathways are discussed.     

Mie theory interpretations of light scattering from intact cells

We present a Mie theory-based analysis of angularly resolved light scattering from intact cells that involves the product of a particle size distribution rho and the scattering cross section sigma. The analysis shows that the ability to size intracellular organelles depends strongly upon the assumed functional form of the particle size distribution; however, the product sigma rho extracts the dominant light scatterers regardless of this choice. We examine goniometer measurements from our own and another laboratory and find that this analysis reconciles seemingly conflicting results and confirms that mitochondrial-sized organelles dominate scattering from intact cells in the angular range 50 degrees - 90 degrees.     

Attachment of glycosaminoglycan oligosaccharides to thiol-derivatised gold surfaces

Glycosaminoglycan oligosaccharides have been attached to thiol-derivatised gold surfaces, via the formation of mercury-sugar adducts at the non-reducing end, representing a new method of generating versatile glycoconjugates incorporating this class of biologically and medically important carbohydrate.     

Chemical shift anisotropy amplification

A new NMR experiment which allows a measurement of the chemical shift anisotropy (CSA) tensor under magic angle spinning (MAS) is described. This correlates a fast MAS spectrum in the omega2 dimension with a sideband pattern in omega1 in which the intensities mimic those for a sample spinning at a fraction of the rate omega r/N, and these sidebands result from an amplification by a factor N of the modulation caused by the CSA. Standard methods can be used to extract the principal tensor components from the omega1 sideband patterns, and the nature of the experiment is such that the use of a large number of t1 increments can be avoided without compromising the resolution of different chemical sites. The new experiment is useful for accurately measuring narrow shift anisotropies.     

Correlation between host-guest binding and host amplification in simulated dynamic combinatorial libraries

We present a versatile computer model of diverse dynamic combinatorial libraries, and examine how molecular recognition between library members and a template can be used to amplify the best binders. The correlation between host-guest binding and amplification was examined for a set of 50 libraries with >300 components each over a wide range of template and building block concentrations. Depending on these concentrations correlations vary from poor (when using a large excess of template) to good (for very dilute libraries and/or substoichiometric template concentrations), highlighting the need to choose the experimental conditions for dynamic combinatorial libraries thoughtfully.     

Studies on pyridazine azide cyclisation reactions

Reaction of sodium azide with 4-methyl-3,5,6-tribromopyridazine results in the formation of 3,5,6-triazide intermediate which could cyclise to give two possible bicyclic products while ab initio calculations show that the formation of a tricyclic compound is extremely energetically unfavourable. However, experimentally, only one major product is isolated. The structure of this unstable product has been conclusively established by X-ray crystallography as 3,5-diazido-4-methyl[1,5-b]tetrazolopyridazine confirming theoretical predictions.     

A Bailey lattice

We exhibit a technique for generating new Bailey pairs which leads to deformations of classical -series identities, multiple series identities of the Rogers-Ramanujan type, identities involving partial theta functions, and a variety of representations for -series by number-theoretic objects such as weight 3/2 modular forms, ternary quadratic forms, and weighted binary quadratic forms.

     

Overpartitions

We discuss a generalization of partitions, called overpartitions, which have proven useful in several combinatorial studies of basic hypergeometric series. After showing how a number of finite products occurring in -series have natural interpretations in terms of overpartitions, we present an introduction to their rich structure as revealed by -series identities.

     

All-forward semiclassical simulations of nonlinear response functions

We propose a quantum trajectory algorithm for computing nonlinear response functions of condensed phase molecular systems based on a time-ordered expansion of the density matrix. The nth-order response function is expressed as a sum of 2(n) impulsive response pathways representing trajectories involving zero, one, and up to n interactions with short external pulses. These are evaluated using a forward propagation algorithm based upon a Liouville space extension of the Bohmian propagation method.