The equipotential surfaces of cubic lattices

The areas of zero electrostatic potential within an array of electric charges in an ionic crystal can be represented as a zero equipotential surface (ZEPS), which separates space into domains of positive and negative potential. ZEPS are conventionally expressed in terms of nodal surfaces. We express the coordinates and charge distribution of several ZEPS in terms of the Jacobi theta functions, and provide their graphical visualisation.     

A general method for affinity-based proteomic profiling of exo-α-glycosidases

Synthesis of iminosugar-based affinity-based proteomics probes for use in probing exo-α-glycosidase activity.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.     

Optimizing a Particular Real Root of a Polynomial by a Special Cylindrical Algebraic Decomposition

We study the problem of optimizing over parameters a particular real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic decomposition into cells in terms of number-of-roots-invariance.     

Assignment of the quadrupolar splittings in fully deuteriated alkyl chains of liquid crystalline compounds The case of 4-n-hexyloxy-4'-cyanobiphenyl

There have been disagreements about the assignment of the quadrupolar splittings in the deuteriated n-hexyl chain in 4-n-hexyloxy-4'-cyanobiphenyl (6OCB); these are resolved by comparing the splittings of the deuteron resonances in the fully deuteriated chain compound with those in the material with a selectively deuteriated chain. The methods available for assigning the quadrupolar splittings in fully deuteriated chains are then applied to 6OCB and it is concluded that measurement of spin-lattice relaxation times, T₁, is the best method.