Hilary S. Booth

Modelling and bioinformatics studies of the human Kappa-class glutathione transferase predict a novel third glutathione transferase family with similarity to prokaryotic 2-hydroxychromene-2-carboxylate isomerases

The Kappa class of GSTs (glutathione transferases) comprises soluble enzymes originally isolated from the mitochondrial matrix of rats. We have characterized a Kappa class cDNA from human breast. The cDNA is derived from a single gene comprising eight exons and seven introns located on chromosome 7q34-35. Recombinant hGSTK1-1 was expressed in Escherichia coli as a homodimer (subunit molecular mass approximately 25.5 kDa). Significant glutathione-conjugating activity was found only with the model substrate CDNB (1-chloro-2,4-ditnitrobenzene). Hyperbolic kinetics were obtained for GSH (parameters: K(m)app, 3.3+/-0.95 mM; V(max)app, 21.4+/-1.8 micromol/min per mg of enzyme), while sigmoidal kinetics were obtained for CDNB (parameters: S0.5app, 1.5+/-1.0 mM; V(max)app, 40.3+/-0.3 micromol/min per mg of enzyme; Hill coefficient, 1.3), reflecting low affinities for both substrates. Sequence analyses, homology modelling and secondary structure predictions show that hGSTK1 has (a) most similarity to bacterial HCCA (2-hydroxychromene-2-carboxylate) isomerases and (b) a predicted C-terminal domain structure that is almost identical to that of bacterial disulphide-bond-forming DsbA oxidoreductase (root mean square deviation 0.5-0.6 A). The structures of hGSTK1 and HCCA isomerase are predicted to possess a thioredoxin fold with a polyhelical domain (alpha(x)) embedded between the beta-strands (betaalphabetaalpha(x)betabetaalpha, where the underlined elements represent the N and C motifs of the thioredoxin fold), as occurs in the bacterial disulphide-bond-forming oxidoreductases. This is in contrast with the cytosolic GSTs, where the helical domain occurs exclusively at the C-terminus (betaalphabetaalphabetabetaalphaalpha(x)). Although hGSTK1-1 catalyses some typical GST reactions, we propose that it is structurally distinct from other classes of cytosolic GSTs. The present study suggests that the Kappa class may have arisen in prokaryotes well before the divergence of the cytosolic GSTs.

An Efficient Z-Score Algorithm for Assessing Sequence Alignments

We describe an alternative method for scoring of the pairwise alignment of two biological sequences. Designed to overcome the bias due to the composition of the alignment, it measures the distance (in standard deviations) between the given alignment and the mean value of all other alignments that can be obtained by a permutation of either sequence. We demonstrate that the standard deviation can be calculated efficiently. By concentrating upon the ungapped case, the mean and standard deviation can be calculated exactly and in two steps, the first being O(N) time, where N is the length of the sequence, the second in a fixed number of calculations, i.e., in O(1) time. We argue that this statistic is a more consistent measure than a similarity score based upon a standard scoring matrix. Even in the ungapped case, the statistic proves in many cases to be more accurate than the commonly used (FASTA) (Pearson and Lipman, 1988) gapped Z-score in which the sequence is matched against a random sample of the database. We demonstrate the use of the POZ-score as a secondary filter which screens out several well-known types of false positive, reducing the amount of manual screening to be done by the biologist.

Algebraic solution for the vector potential in the Dirac equation

The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford’s method of algebraically solving for the vector potential is reviewed, with attention to the additional constraints arising from non-maximality of the rank. The extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c- and a-number wavefunctions. PACS numbers: 0350D, 0210, 0220, 0365P, 1130P

A Stochastic Model of Gene Regulation Using the Chemical Master Equation

The chemical master equation in combination with chemical rate equations is used as a tool to study Markovian models of genetic regulatory networks in prokaryotes. States of the master equation represent the binding and unbinding of protein complexes to DNA, resulting in a gene being expressed or not expressed in a cell, while protein and substrate concentrations are represented by continuum variables which evolve via differential equations.

NONLINEAR ELECTRON SOLUTIONS AND THEIR CHARACTERISTICS AT INFINITY

The Maxwell-Dirac equations model an electron in an electromagnetic field. The two equations are coupled via the Dirac current which acts as a source in the Maxwell equation, resulting in a nonlinear system of partial differential equations (PDEs). Well-behaved solutions, within reasonable Sobolev spaces, have been shown to exist globally as recently as 1997 [12]. Exact solutions have not been found---except in some simple cases. We have shown analytically in [6, 18] that any spherical solution surrounds a Coulomb field and any cylindrical solution surrounds a central charged wire; and in [3] and [19] that in any stationary case, the surrounding electron field must be equal and opposite to the central (external) field. Here we extend the numerical solutions in [6] to a family of orbits all of which are well-behaved numerical solutions satisfying the analytic results in [6] and [11]. These solutions die off exponentially with increasing distance from the central axis of symmetry. The results in [18] can be extended in the same way. A third case is included, with dependence on z only yielding a related fourth-order ordinary differential equation (ODE) [3].