Spherulitic growth of hen egg-white lysozyme crystals

In protein crystallography, spherulites are considered the result of a failed crystallization experiment. Understanding the formation of these structures may contribute to finding methods to prevent their formation. Here, we present an in situ study on lysozyme spherulites grown from sodium nitrate and sodium thiocyanate solutions, investigating their morphology and growth kinetics using optical microscopy. In a morphodrom, we indicate the conditions at which spherulites form for the lysozyme-nitrate system, showing that liquid-liquid phase separation is not a prerequisite to form sheaflike spherulites and that supersaturation is not the only factor determining their creation. Despite their sheaflike morphology, the spherulites all appear to be formed through heterogeneous nucleation. The spherulites are of a new polymorphic form and are less stable than the monoclinic form. For a single needle, growth kinetics indicate surface processes to be the rate-limiting step during growth, but for an entire spherulite volume, diffusion still plays a role. Spherulites simulated by using a time-dependent, tip-splitting model are found to compare well to experimentally observed spherulites.     

The difference between doubly nonnegative and completely positive matrices

The convex cone of n×n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, for n4 only, every DNN matrix is CP. In this paper, we investigate the difference between 5×5 DNN and CP matrices. Defining a bad matrix to be one which is DNN but not CP, we: (i) design a finite procedure to decompose any n×n DNN matrix into the sum of a CP matrix and a bad matrix, which itself cannot be further decomposed; (ii) show that every bad 5×5 DNN matrix is the sum of a CP matrix and a single bad extreme matrix; and (iii) demonstrate how to separate bad extreme matrices from the cone of 5×5 CP matrices.     

A novel microfluidics-based method for probing weak protein-protein interactions

We report the use of a novel microfluidics-based method to detect weak protein-protein interactions between membrane proteins. The tight junction protein, claudin-2, synthesised in vitro using a cell-free expression system in the presence of polymer vesicles as membrane scaffolds, was used as a model membrane protein. Individual claudin-2 molecules interact weakly, although the cumulative effect of these interactions is significant. This effect results in a transient decrease of average vesicle dispersivity and reduction in transport speed of claudin-2-functionalised vesicles. Polymer vesicles functionalised with claudin-2 were perfused through a microfluidic channel and the time taken to traverse a defined distance within the channel was measured. Functionalised vesicles took 1.19 to 1.69 times longer to traverse this distance than unfunctionalised ones. Coating the channel walls with protein A and incubating the vesicles with anti-claudin-2 antibodies prior to perfusion resulted in the functionalised vesicles taking 1.75 to 2.5 times longer to traverse this distance compared to the controls. The data show that our system is able to detect weak as well as strong protein-protein interactions. This system offers researchers a portable, easily operated and customizable platform for the study of weak protein-protein interactions, particularly between membrane proteins.     

A network modelling approach for assessing the efficiency of prevention strategies

Survey data and a simulation model based on a stochastic pair formation process are used to construct networks of sexual contacts. We model heterosexual partnerships which can be steady or casual depending on their average duration. Transmission of an infectious disease can take place in pairs of a susceptible and an infected individual. We study networks of sexual contacts accumulated during 1 year for different types of mixing patterns. The networks are constructed on the basis of data from a survey in The Netherlands. We analyze the network structure for different mixing patterns and investigate the relationship between network structure and disease spread; furthermore we study the effect of prevention measures on the structure of the network.     

Ionization energies of LinX (n = 2, 3; X = Cl, Br, I) molecules

Molecules of Li(n)X (n = 2, 3; X = Cl, Br, I) were examined with a magnetic sector mass spectrometer by surface ionization using a triple rhenium filament impregnated with fullerene (C60). The ionization energies obtained for Li(2)Cl, Li(2)Br and Li(2)I molecules are 3.8 +/- 0.1, 3.9 +/- 0.1 and 4.0 +/- 0.1 eV, respectively. The first ionization energy of Li(2)Cl is documented, while there are no literature data for the ionization energies of Li(2)Br and Li(2)I. The molecules of Li(3)Cl, Li(3)Br and Li(3)I were detected experimentally for the first time with ionization energies of 4.0 +/- 0.1, 4.1 +/- 0.1 and 4.1 +/- 0.1 eV, respectively. The ionization energies of Li(n)X (n = 2, 3; X = Cl, Br, I) are in correlation with the theoretical prediction of their hyperlithiated configurations.     

Conditions Characterizing Minima of the Difference of Functions

 Optimization problems involving differences of functions arouse interest as generalizations of so-called d.c. problems, i.e. problems involving the difference of two convex functions. The class of d.c. functions is very rich, so d.c. problems are rather general optimization problems. Several global optimality conditions for these d.c. problems have been proposed in the optimization literature. We provide a survey of these conditions and try to detect their common basis. This enables us to give generalizations of the conditions to situations when the objective function is no longer a difference of convex functions, but the difference of two functions which are representable as the upper envelope of an arbitrary family of functions. (Received 6 February 2001; in revised form 11 October 2001)