Sedimentation of generalized systems of interacting particles. I. Solution of systems of complete Lamm equations.

A very general approach to the chemical equilibria between many interacting molecules during sedimentation (boundary, band, or active enzyme) taking into account boundary conditions, cell geometry, equilibrium constants, diffusion, enzyme kinetics, etc., is presented. Through a Fortran program, the method has been applied to two very simple but typical cases. With only minor adjustments, the method presented here for sedimentation studies can be extended to all sorts of problems in which “pools” of various species are interacting with each other.     

Transient-time analysis of substrate-channelling in interacting enzyme systems.

The kinetics of dynamically interacting enzyme systems is examined, in the light of increasing evidence attesting to the widespread occurrence of this mode of organization in vivo. The transient time, a key phenomenological parameter for the coupled reaction, is expressed as a function of the lifetime of the intermediate substrate. The relationships between the transient time and the pseudo-first-order rate constants for the coupled reaction by the complexed and uncomplexed enzyme species are indicative of the mechanism of intermediate transfer ('channelling'). In a dynamically interacting enzyme system these kinetic parameters are composite functions of those for the processes catalysed by the complex and by the separated enzymes. The mathematical paradigm can be extended to a linear sequence of N coupled reactions catalysed by dynamically (pair-wise) interacting enzymes.     

Isoelectric focusing of interacting systems. II. pH-dependent conformational transitions.

Transient and equilibrium isoelectric focusing patterns have been computed for pH-dependent conformational transitions in the limits of complete cooperativity and instantaneous chemical equilibration. Transitions induced by the binding of a relatively large number of hydrogen ions by the macromolecule give well resolved bimodal equilibrium patterns, provided that the resulting conformer has the lower isoelectric point. The corresponding transient patterns may be either bimodal or virtually unimodal for practical times of operation depending upon the point of insertion of the sample into the pH gradient and the stoichiometry of the interaction. A macromolecule undergoing sequential transitions can give multimodal isoelectric focussing patterns.     

Active enzyme gel chromatography: II. Computer simulations

The behavior of an enzyme undergoing reaction while on a gel chromatography column has been studied by computer simulation using the steady state assumption for a system with a single enzyme—substrate complex. The profiles of the enzyme—substrate complex, product, and substrate were examined varying the parameters of k_cat, flow rate, partition coefficient, dispersion coefficient, and time. These investigations confirm that much information about both the active enzyme and the product may be obtained by examining the product profile alone, varying the power of applying scanning gel chromatography to active enzyme systems.     

II. Transient phase of two-substrate enzyme systems

The time dependence in the transient phase of the two-substrate enzyme systems which evolve according to the random ternary-complex, ordered ternary-complex, ping-pong bi-bi and Theorell-Chance mechanisms has been studied. With this purpose, the equations derived in paper I have been applied. This has allowed to propose a method in order to obtain the rate constant values of these enzyme reactions. In addition, we show that, from experimental knowledge of the induction periods of the ligand species, it is possible to give a method which allows to discriminate between these mechanisms.     

The perfection of substrate-channelling in interacting enzyme systems: energetics and evolution

Some implications of substrate channelling in interacting enzyme systems are considered, with regard to the energetics and evolution of enzyme action. The transient time, a key analytical parameter relating to the phenomenon of channelling, is the basis of our kinetic study. Bounds on the kinetics of multienzyme complexes are established using (apparent) rate constants emanating from the transient-time formulation of coupled reactions. From a transition state representation of the rate process, it is shown how dynamically and statically organized enzyme systems lead to the modification of current ideas on the evolutionary optimization of the energy profile of enzyme catalysis in situ.     

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.

This paper contains extensions of results from a previous paper regarding structured one enzyme systems to a more complicated structured two enzyme system. A stochastic model and a deterministic model are developed for such systems and their steady state reaction kinetics are compared. These comparisons are in the form of graphs of the reaction kinetics versus substrate concentration. Two quantities are proposed as indications of lack of agreement between the two models. This lack of agreement corresponds to situations in which the model systems are more highly non-linear, in accord with Jensen's inequalities. Implications of these results, relative to experimental procedures are briefly discussed.     

African Hepatics. XXXI. Some new or little-known Lejeuneaceae and extensions of range

Abstract

Lejeunea brenanii sp. nov. and Microlejeunea ankasica sp. nov. are described. Lejeunea autoica Schuster and Pycnolejeunea contigua (Nees) Grolle are described and recorded as new to Africa. Lejeunea longirostris (Steph.) E.W. Jones, nom. inval., is a synonym of L. grossecristata (Steph.) E.W. Jones. Critical notes and/or new localities are provided for Colura digitalis (Mitt.) Steph., C. dusenii Steph., C. humbertii S. Jovet-Ast, C. sp. ad inornata Jovet-Ast, Marchesinia moelleriana Pearson.     

African Hepatics XXIX. Some new or little-known species and extensions of range

Abstract

Calypogeia afrocaernlea E. W. Jones, sp. nov. is described (type, from Kilimanjaro, in BM). Critical notes are provided on Cylindrocolea chevalieri (Steph.) Schuster, Simia S. Arnell, Syzygiella ruwenzorensis Steph., and Taxilejeunea pulchriflora Pearson. The following are new combinations: Cheilolejeunea surrepens (Mitt.) (basionym Lejeunea surrepens), Stictolejeunea balfourii (Mitt.) (basionym Lejeunea balfouri). Calypogeia fusca (Lehm.) Steph. is recorded from Cameroun and Ruanda; C. longifolia Steph. from Sierra Leone.     

Isoprenoid enzyme systems of silkworm. II. Formation of the juvenile hormone skeletons by farnesyl pyrophosphate synthetase II

Comparative substrate specificities of farnesyl pyrophosphate synthetases I and II purified from larvae of silkworm, Bombyx mori, were studied by use of the possible biosynthetic intermediates of juvenile hormones in the insect. In the presence of Mn2+ ions farnesyl pyrophosphate synthetase II showed higher activity than synthetase I and the corresponding enzyme from pig liver with the following substrate homologues: (Z)-3-methyl-2-pentenyl-, 3-ethyl-3-butenyl-, (2E,6Z)-3,7-dimethyl-2,6-nonadienyl-, and (2E,6Z)-3-ethyl-7-methyl-2,6-nonadienyl pyrophosphate. When (Z)-3-methyl-2-pentenyl-, 3-ethyl-3-butenyl-, and isopentenyl pyrophosphate were mixed and incubated with farnesyl pyrophosphate synthetase II, (2E,6E,10Z)-3,11-dimethyl-7-ethyl-2,6,10-tridecatrienyl-, (2E,6E,10Z)-3,7,11-trimethyl-2,6,10-tridecatrienyl, and a trace amount of (2E,6E,10Z)-3,7-diethyl-11-methyl-2,6,10-tridecatrienyl pyrophosphate, whose carbon skeletons were the same as those of juvenile hormone I, II, and O, respectively, were formed. (Z)-3-Methyl-2-pentenyl pyrophosphate was produced from 3-ethyl-3-butenyl pyrophosphate as a single product by the action of silkworm isopentenyl pyrophosphate isomerase, though the enzyme activity was much lower with this substrate than with the usual substrate, isopentenyl pyrophosphate.