Crystallization and Preliminary X-Ray Diffraction Study of the C-Terminal Fragment of Myomesin-2

Crystallography Reports - The recombinant С-terminal fragment of myomesin-2 was purified to a homogeneous state. The crystallization conditions for the С-terminal fragment of myomesin-2...     

The Klein–Gordon Equation in a Domain with Time‐Dependent Boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time‐dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.     

Second SH3 domain of ponsin solved from powder diffraction

Determination of protein crystal structures is dependent on the growth of high-quality single crystals, a process that is not always successful. Optimum crystallization conditions must be systematically sought for, and microcrystalline powders are frequently obtained in failed attempts to grow the desired crystal. In materials science, structures of samples ranging from ceramics, pharmaceuticals, zeolites, etc., can nowadays be solved, almost routinely, from powdered samples, and there seems to be no fundamental reason, except the sheer size and complexity of the structures involved, why powder diffraction should not be employed to solve structures of small proteins. Indeed, recent work has shown that the high-quality powder diffraction data can be used in the study of protein crystal structures. We report the solution, model building, and refinement of a 67-residue protein domain crystal structure, with a cell volume of 64 879 A3, from powder diffraction. The second SH3 domain of ponsin, a protein of high biological significance due to its role in cellular processes, is determined and refined to resolution limits comparable to single-crystal techniques. Our results demonstrate the power and future applicability of the powder technique in structural biology.     

Chemiluminometric determination of reserpine and related alkaloids

The determination of the alkaloids reserpine, rescinnamine and yohimbine based on a chemiluminogenic reaction with potassium permanganate in the presence of polyphosphoric acid is described. The investigation was carried out using a batch and a flow injection chemiluminometer. Both approaches were accurate and precise, allowing the measurement of reserpine within the ranges 0.100-3.00 and 0.050-3.00 micrograms ml-1 with RSD values for 1.00 microgram ml-1 of 1.91 and 0.33% (n = 8) with the batch and the flow injection manifold, respectively. The procedure was successfully applied to formulations after extraction of reserpine with chloroform, with recoveries from commercial formulations within the range 95.2-99.0%.     

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a≠0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.     

Quaternions and applications

This note gives an overview of two novel applications of Quaternions which appeared in [1]–[3]: First, the evaluation of certain three dimensional real integrals without integrating with respect to the real variables. This is the generalisation of the well-known Cauchy Residue Theorem from the case of two dimensions to the case of four dimensions. Second, the solution of boundary value problems for linear elliptic PDEs in four dimensions. This is the extension of some of the results of [4] from two to four dimensions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)