The generalised Riesz-Fischer theorem states that ifis convergent, with 1 < p ≤ 2, thenis the Fourier series of a function of class . When p > 2 the series (2) is not necessarily a Fourier series; neither is it necessarily a Fourier D-series. It will be shown below that it must however be what may be called a “Fourier Stieltjes” series. That is to say, the condition (1) with (p > 1) implies that there is a continuous function F (x) such that
The proteinase from the extremely thermophilic Bacillus strain EA.1 exhibits maximum stability at a pH of approx. 6.5. In the presence of calcium ions the half-life at 95 degrees C of the enzyme at this pH was 17 min, and loss of activity followed first-order decay kinetics. The role of metal ions in the activity and stability of the enzyme was studied using the holoenzyme, the metal-depleted apoenzyme, and a zinc-enriched apoenzyme preparation. Zinc and calcium ions were the preferred bivalent cations for the active site and stabilization site(s) respectively. Stabilization by metal ions was not in itself a highly stringent process, but ions other than calcium which stabilized the enzyme generally had a concomitant inhibitory effect on activity. Inhibition and stabilization of the enzyme by cations were concentration-dependent effects and certain ions activated the apoenzyme but not the holoenzyme. Manganese(II) ions conferred some stability and also activated the enzyme, but in the latter case were not as effective as zinc ions. The results are discussed with reference to the ionic radii, co-ordination number and preferred ligand donors of the ions. Mercury(II) ions severely compromised enzyme activity and stability, and the effects of thiol-reactive agents suggest that thiol groups also have a role in enzyme integrity.
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