Consecutive immobilized enzymatic reactions with and without enzyme denaturation

Consecutive biochemical reactions in an immobilized enzyme particle under the effects of internal and external diffusional resistances are analyzed. A rigorous nonlinear reaction kinetics is employed and the steady state effectiveness factor with negligible enzyme denaturation compared with the previous prediction by the first-order kinetics. It is found that the difference between them is rather substantial under most circumstances. The cases with significant enzyme denaturation are also investigated by using an unsteady state model. The substrate concentration responses to variation of the physical and kinetic parameters reveal many interesting characteristics of the reaction system.     

Protein dynamics and reactions of photosystem II

The kinetics of charge recombination by electron transfer from Q(A)(*-) to P680(*+) on the reducing branch of PSII is likely to be strongly dependent on protein dynamics, in analogy with the kinetics of the corresponding reaction in the reaction center of purple bacteria [Biophys. J. 74 (1998) 2567]. On the oxidizing branch of PSII, the kinetics of electron hole transfer from P680(*+) to Y(Z) is known to be multiexponential. This transfer is in the Babcock model of the reactions of the water-oxidizing complex coupled with proton transfer from Y(Z). The proton is via switching hydrogen bonds in the protein transferred to the thylakoid lumen. The demand for successive proton transfers requires rearrangement of the hydrogen bonds, which in turn requires a flexible protein making fluctuating excursions among all its conformations. In the equilibrated protein, only a fractional part of the molecules is in a conformation that is able to support the proton transfer from Y(Z). The kinetics of the rearrangement to this active conformation will be multiexponential and dependent on the distribution among all conformations, which is likely to be sensitive to various influences, in particular from changes in the protein coordination to the (Mn)(4) cluster between the different S states.     

Protein microchips: use for immunoassay and enzymatic reactions

Different proteins such as antibodies, antigens, and enzymes were immobilized within the 100 x 100 x 20-microm gel pads of protein microchips. A modified polyacrylamide gel has been developed to accommodate proteins of a size up to 400,000 daltons. Electrophoresis in the microchip reaction chamber speeded up antigen-antibody interactions within the gel. Protein microchips were used in immunoassays for detection of antigens or antibodies, as well as to carry out enzymatic reactions and to measure their kinetics in the absence or presence of an inhibitor. A protein microchip can be used several times in different immunoassays and enzymatic kinetic measurements.     

Protein dynamics and enzyme catalysis: insights from simulations

The role of protein dynamics in enzyme catalysis is one of the most active and controversial areas in enzymology today. Some researchers claim that protein dynamics are at the heart of enzyme catalytic efficiency, while others state that dynamics make no significant contribution to catalysis. What is the biochemist - or student - to make of the ferocious arguments in this area? Protein dynamics are complex and fascinating, as molecular dynamics simulations and experiments have shown. The essential question is: do these complex motions have functional significance? In particular, how do they affect or relate to chemical reactions within enzymes, and how are chemical and conformational changes coupled together? Biomolecular simulations can analyse enzyme reactions and dynamics in atomic detail, beyond that achievable in experiments: accurate atomistic modelling has an essential part to play in clarifying these issues. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

Allosterically gated enzyme dynamics in the cysteine synthase complex regulate cysteine biosynthesis in Arabidopsis thaliana

Plants and bacteria assimilate sulfur into cysteine. Cysteine biosynthesis involves a bienzyme complex, the cysteine synthase complex (CSC), which consists of serine-acetyl-transferase (SAT) and O-acetyl-serine-(thiol)-lyase (OAS-TL) enzymes. The activity of OAS-TL is reduced by formation of the CSC. Although this reduction is an inherent part of the self-regulation cycle of cysteine biosynthesis, there has until now been no explanation as to how OAS-TL loses activity in plants. Complexation of SAT and OAS-TL involves binding of the C-terminal tail of SAT in one of the active sites of the homodimeric OAS-TL. We here explore the flexibility of the unoccupied active site in Arabidopsis thaliana cytosolic and mitochondrial OAS-TLs. Our results reveal two gates in the OAS-TL active site that define its accessibility. The observed dynamics of the gates show allosteric closure of the unoccupied active site of OAS-TL in the CSC, which can hinder substrate binding, abolishing its turnover to cysteine.     

A simplified approach to derive Cleland model for enzymatic reactions

Metabolic modeling can suggest which is the key enzyme activity that needs to be controlled or its activity enhanced for the required production of a metabolite in a pathway. It also helps to find possible drug targets (enzymes to be inhibited). In metabolic modeling, knowing the kinetics of the enzymes involved in a pathway is mandatory. Most enzymatic reactions involve multi-substrates and follow an ordered sequential or ping–pong mechanism. The kinetic parameters involved in the model are obtained by fitting experimental data using a model based on the mechanism. The Cleland model has been used for some years. The grouping of parameters, such as dissociation constant and Michaelis–Menten constant, makes the strategy meaningful and hence the Cleland model is still in use. Although other alternate methods, e.g., the King-Altman method, are available, derivation by determinants can be used to derive a rate expression for the sequential or ping–pong mechanism, they are tedious. Hence, a meaningful modification is suggested in this communication for deriving the enzyme mechanism which is based on Thilakavathi et al. (Biotech Lett 28:1889–1894, 2006) to obtain the Cleland model in an easier way.     

A steady state model of sequential irreversible enzyme reactions

Summary One of the questions which arises in the study of certain inborn errors of metabolism as well as in the field of enzyme kinetics is: what are the quantitative relationships between parameters of enzyme activity and substrate pool sizes in a metabolic pathway? A steady state model has been devised to answer this question for a homogeneous system of non-branched sequential irreversible enzyme reactions which follow Michaelis-Menten kinetics. The concentration of a substrate in such a pathway, [S_i], is a function of 5 variables: (a) the K_M of the enzyme which forms the substrate (K_{M (i–1)}), (b) the K_M of the enzyme which utilizes the substrate (K_{M i}), (c) the V_max of the enzyme which forms the substrate (V_{m (i–1)}), (d) the V_max of the enzyme which utilizes the substrate (V_{m i}) and (e) the immediate precursor concentration [S_(i–1)] where [S_i] = K_{M i} V_{m (i–1)} [S_(i–1)]/[S_(i–1)] (V_mi -V_{m (i–1)}) + K_{M (i–1)}) V_mi The model introduces and defines the concept of and conditions for amplification. An input in the form of a steady state concentration of precursor [S_(i–1)] may be amplified as an output in the form of an increased steady state concentration of product [S_i]. The model also defines the values of the above 5 parameters which do not allow attainment of a steady state for the type of pathway considered.From the Metabolism Branch, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20014.     

Effective activation energy of enzymatic and nonenzymatic reactions. Evolution-imposed requirements to enzyme structure

The difference of the activation energies in a protein globule and water has been treated in terms of the theory of an elementary act of charge transfer reaction with regards to the energy spent on the transfer of charged reactants from water into the protein. The protein was treated as a structureless dielectric with a given optical and static dielectric constants surrounded by the aqueous phase. Reactions of different types (charge exchange between reactants, charge separation, neutralization, etc.) have been analyzed both under prevalence of purely electrostatic effects and under considerable nonelectrostatic contributions to the activation energies. It is shown that for all one-electron and most multi-electron reactions involving two reaction centres the energy spent for charged reactant transfer from water into protein is greater than the concomitant activation energy gain. The same effect takes place in a number of cases for multi-centre processes as well. To overcome the entropy hindrances, the reactants and catalysts must combine into multiparticle complexes, i.e. form microscopic regions of low dielectric constant. This results in increased effective activation energy as compared to reactions in water. It has been hypothesized that in order to make up for this loss the evolution has selected the proteins which are characterized by considerable intraglobular permanent electric fields. The presence in proteins of high concentrations of strongly polar peptide groups renders them advantageous in this respect over other polymers that are less polar.     

Protein dynamics studied by NMR

The results of NMR studies using several nuclei indicate that proteins have considerable internal mobility. The most obvious is the mobility of side-chains. This mobility is general on the exterior surfaces but extends internally in a differential way. The functional value of surface mobility concerns both on and off rates of ligand binding (e.g. metal ions and parts of substrates) and protein/protein interactions. The mobility, which indicates that recognition is more in the hand-in-glove class than in the lock-in-key class, makes for a modified view of the specificity of protein interactions. Thus, fast on/off systems cannot be as selective as slower systems. Segmental mobility of proteins is considered in the context of protein secondary structure. The least mobile segments are the -sheet and the tight -turn. Mobility is always possible for, but not within, rod-like helices and in loose turns. Many examples are given and the importance of mobility in molecular machines is described. Finally, examples are given of virtually random-coil proteins, segments, and linker regions between domains and the functional value of such extremely dynamic regions of proteins is discussed.This work is based on a lecture at the EBSA Symposium, organised by the Italian Biophysical Society (S.I.B.P.A.), Tabiano Terme, September 1992     

The condition for pseudo-first-order kinetics in enzymatic reactions is independent of the initial enzyme concentration

The linearization of the Michaelis-Menten reaction by pseudo-first-order kinetics is revised. A phase-plane analysis allows the derivation of a new condition for its validity that is directly linked to the reaction efficiency, and contrary to widely established knowledge, is independent of the initial enzyme concentration.     

The use of the inverted linear model of enzyme decay to plan a strategy for enzymatic batch reactions and to assess the industrial applicability of immobilized enzyme preparations

This article is concerned with the development of a model to plan a strategy for an enzymatic batch process where enzyme is subjected to deactivation described by the inverted linear decay model. The particular system studied is the enzymatic hydrolysis of penicillin to 6-amino penicillanic acid (6 APA), but the model can be utilized with other batch systems as long as the decay of the immobilized enzyme (IME) preparation is described by the inverted linear decay model. The model developed is eminently practical and simple and several example of its application are shown. Experimental data obtained in a small pilot plant batch recirculated reactor on the average are well fitted by this model. For IME systems whose decay is best described by the first-order decay model, it is not possible to use the same approach.     

On a model and the kinetics of photo-enhanced enzyme reactions

The recently observed enhancement, by laser irradiation, of the specific activity of the enzyme chymotrypsin (which hydrolyses Benzoyl-L-tyrosine-ethyl ester) at low enzyme concentration is considered. The enhancement of the reaction rate is attributed to a coherently excited state of the enzyme molecule (activated through Raman scattering of the laser light) following a prediction due to Fröhlich. The model is described, the kinetics of the process is framed and the observed enzyme-concentration dependence of the specific activity is reproduced. Predictions of the model are delineated to urge verification of the main contentions through further experimentation.     

Effect of molecular confinement on internal enzyme dynamics: frequency domain fluorometry and molecular dynamics simulation studies

The tryptophanyl emission decay of the mesophilic beta-galactosidase from Aspergillus oryzae free in buffer and entrapped in agarose gel is investigated as a function of temperature and compared to that of the hyperthermophilic enzyme from Sulfolobus solfataricus. Both enzymes are tetrameric proteins with a large number of tryptophanyl residues, so the fluorescence emission can provide information on the conformational dynamics of the overall protein structure rather than that of the local environment. The tryptophanyl emission decays are best fitted by bimodal Lorentzian distributions. The long-lived component is ascribed to close, deeply buried tryptophanyl residues with reduced mobility; the short-lived one arises from tryptophanyl residues located in more flexible external regions of each subunit, some of which are involved in forming the catalytic site. The center of both lifetime distribution components at each temperature increases when going from the free in solution mesophilic enzyme to the gel-entrapped and hyperthermophilic enzyme, thus indicating that confinement of the mesophilic enzyme in the agarose gel limits the freedom of the polypeptide chain. A more complex dependence is observed for the distribution widths. Computer modeling techniques are used to recognize that the catalytic sites are similar for the mesophilic and hyperthermophilic beta-galactosidases. The effect due to gel entrapment is considered in dynamic simulations by imposing harmonic restraints to solvent-exposed atoms of the protein with the exclusion of those around the active site. The temperature dependence of the tryptophanyl fluorescence emission decay and the dynamic simulation confirm that more rigid structures, as in the case of the immobilized and/or hyperthermophilic enzyme, require higher temperatures to achieve the requisite conformational dynamics for an effective catalytic action and strongly suggest a link between conformational rigidity and enhanced thermal stability.