Diffusional effects on the heterogeneous kinetics of two-substrate enzymic reactions.

When a two-substrate reaction is catalyzed by a surface bound enzyme, the diffusion of both substrates can considerably modify the kinetic properties of the reaction. According to this theoretical analysis, limitations in substrate diffusion yield very different effects depending whether the two substrates have similar or different affinities for the enzyme. With two substrates of comparable affinities the diffusion of the two substrates can be limiting, and similar activity dependences on the two substrate concentrations are obtained. Under these conditions, diffusional limitations may only slightly influence half-maximal-activity substrate concentrations. With two substrates of widely different affinities, on the contrary, the rate of the enzymic reaction can only be limited by the diffusion of the high-affinity substrate, used at the lower concentration. Under these conditions, in the presence of diffusional limitations the activity dependence on the two substrate concentrations are highly different, and the half-maximal-activity concentration is increased and decreased for the high- and low-affinity substrates, respectively. The theoretical results are verified by experimental data previously obtained with collagen-bound aspartate aminotransferase and sorbitol dehydrogenase.     

A quantum model for controlled enzymic reactions

A quantum model for the general enzymic reaction,E+S ⇌ ES → P, is presented, starting with the assumptions that any chemical substanceS, which may be a substrate for a particularE _(S)-enzyme is a microphysical system and any enzymeE-molecule, capable of interacting with anS-substrate is a “measuring system” which will “measure” one or more of theS-observables. According to the above assumptions a stochastic model of the reaction is constructed and a computer simulation of the steady state performed. The results thus obtained predicted fluctuations in the enzymic reaction rate, function of the substrate “perturbation”. On an experimental basis it is demonstrated that the irradiation of an enzymic substrate with low energies results in the inducement of a dose-dependent oscillatory behavior in the corresponding enzymic reaction rate. In the reaction type, the oscillations thus induced in theE-activity by the corresponding substrates are out-of-phase, realizing a biochemical discriminating net. Likewise, in an reaction type, the oscillations induced by the irradiatedS-substrate in the activities of the respective enzyme, realize a biochemical switching net.     

Modeling the kinetics of enzymic reactions in mainly solid reaction mixtures

There is currently considerable interest in using mainly solid reaction mixtures for enzymic catalysis. In these reactions starting materials dissolve into, and product materials crystalize out of, a small amount of liquid phase in which the catalytic reaction occurs. An initial mathematical model for mass transfer effects in such systems is constructed using some physically reasonable approximations. The model equations are solved numerically to determine how the reactant concentrations vary with time and position. To evaluate the extent to which mass transfer limits the overall rate of product formation, an effectiveness factor is defined as the ratio of the observed total reaction rate to the total reaction rate in the reaction limited limit. As expected, the value of the effectiveness factor in steady state is strongly dependent on the Thiele modulus. However, it is also observed that the effectiveness factor can vary widely as a result of changes in the other dimensionless groups characterizing the system. For example, there are situations with Thiele modulus equal to unity in which the value of the effectiveness factor varies between approximately 0.1 and 0.8 as the other parameters are varied in physically reasonable ranges. Analytical asymptotic solutions that provide good approximations to the numerically calculated results in various physically important limiting cases are also presented.     

Mechanism and stereochemistry of enzymic reactions involved in porphyrin biosynthesis.

5-Aminolaevulinate synthetase cataylses the condensation of glycine and succinyl-CoA to give 5-aminolaevulinic acid. At least two broad pathways may be considered for the initial C--C bond forming step in the reaction. In pathway A the Schiff base of glycine and enzyme bound pyridoxal phosphate (a) undergoes decarboxylation to give the carbanion (b) which then condenses with succinyl-CoA with the retention of both the original C2 hydrogen atoms of glycine. In pathway B, loss of a C2 hydrogen atom gives another type of carbanion (c) that reacts with succinyl-CoA. Evidence has been presented to show that the initial C--C bond forming event occurs via pathway B which involves the removal of the pro R hydrogen atom of glycine. Subsequent mechanistic and stereochemical events occurring at the carbon atom destined to become C5 of 5-aminolaevulinate have also been delineated.(Carticle) Several mechanistic alternatices for the formation of the two vinyl groups of haem from the propionate residues of the precursor, coproporphyrinogen III, have been examined. (see article). It is shown that during the biosynthesis both the hydrogen atoms resident at the alpha positions of the propionate side chains remain undisturbed thus eliminating mechanisms which predict the involvement of acrylic acid intermediates. Biosynthetic experiments performed with precursors containing stereospecific labels have shown that the two vinyl groups of haem are formed through the loss of pro S hydrogen atoms from the beta-positions of the propionate side chains. In the light of these results, three related mechanisms for the conversion, propionate leads to vinyl, have been considered. In order to study the mechanism of porphyrinogen carboxy-lyase reaction, stereo-specifically deuterated, tritiated-succinate was incorporated into the acetate residues of uroporphyrinogen III which on decarboxylation generated asymmetric methyl groups in coproporphyrinogen III and then in haem. Degradation of the latter yielded chiral acetate deriving from C and D rings of haem. Configurational analysis of this derivate acetate shows that the carboxy-lyase reaction proceeds with a retention of configuration.     

A vector method of representation of enzymic reactions: 1. Parametric classification of types of enzymic reaction

A new “parametric” classification of the types of single-substrate enzymic reactions is proposed that includes 15 different types: seven inhibited, seven activated and one initial (uninhibited, i=0 and nonactivated, a=0). The new classification takes into account both the “parametricity” of these reactions and the mechanisms of their action. It unites all the types in an original symmetric system which vividly demonstrates the interconnection between separate (strictly definite) types of inhibited and activated enzymic reactions. The proposed classification permits the revision and some corrections to traditional “competitive” terminology as well as the application of these ideas and mathematical approaches pertinent to the calculation of reactions of enzyme inhibition for data analysis of enzyme activation.     

A probabilistic approach to compact steady-state kinetic equations for enzymic reactions

We describe a method for deriving kinetic equations based on the simplification of a complex graphical scheme of steady-state enzymic reactions to one that is comprised of an unbranched pathway. It entails compressing unbranched multi-step sequences into one step, and fusing some graph nodes into a single node. The final form of the equations is compact and well structured, and it simplifies the choice of independent kinetic parameters. The approach is illustrated by an analysis of representative two- and three-substrate reactions.     

Determination of initial velocities of enzymic reactions from progress curves.

The present communication describes a novel method for estimating initial velocities (v) of enzyme-catalysed reactions. It is based on an approximation of experimental data obtained by the cubic spline function. The initial velocity of a reaction is calculated as a derivative of the approximating function at a time value equal to zero. The proposed method is usable on a computer with a FORTRAN IV program. The method can be successfully used in such cases as substantial extents of substrate conversion, the inactivation of an enzyme in the course of a reaction, the existence of large experimental error or when the reaction mechanism is unknown.     

Performance of a hollow fibre beaker device for continuous enzymic reactions

The performance of the beaker-type hollow fibre dialyser as a continuous enzymatic reactor has been examined for two operational modes: (A) enzyme inside the fibres and substrate outside the fibres, (B) enzyme outside the fibres and substrate inside the fibres. On the basis of simple mathematical models, it is demonstrated that the superiority of mode (B) over (A) appears as the system approaches membrane permeation control. This conclusion is confirmed experimentally in the hydrolysis of urea.     

Concerning the intermediacy of organic radicals in vitamin B12-dependent enzymic reactions

The vitamin B12 coenzyme adenosylcobalamin assists the enzymic catalysis of molecular rearrangements of the type (formula; see text) in which the migrating group X can be OH, NH2 or a suitable substituted carbon atom such as C(=CH2)CO2H. This paper discusses evidence for the participation of organic radicals as intermediates in these reactions. Theoretical and model studies supporting the intermediacy of radicals in the reactions catalysed by the enzymes diol dehydratase and alpha-methyleneglutarate mutase are described. For the model studies, alkyl radicals, alkylcobaloximes (alkyl represents, for example, ethoxycarbonyl substituted, but-3-enyl and cyclopropylmethyl) and also dihydroxyalkylcobalamins have been investigated. The Co-C alpha-C beta angle of 125 degrees in adenosylcobalamin is shown to be an 'especial' angle by analysis of the crystal structures of R- and S-2,3-dihydroxypropylcobalamin.