Mathematical description of microbiological reactions involving intermediates

Stoichiometric relationships for biological reactions involving intermediate formation are developed from microbial reaction fundamentals and thermodynamic principles. Biological reactions proceed through intermediates, which sequester carbon and electrons whenever their degradation is relatively slow. Modeling intermediate formation and subsequent utilization requires evaluation of the distribution of electrons, energy, and macronutrients (C and N) between energy-generating pathways and cell-synthesis pathways for each step in the mineralization of the primary electron-donor substrate. We describe how energy and electron balances are utilized to predict the stoichiometry for each step of a multi-step degradation process. Each stoichiometric relationship developed predicts substrate utilization, cell growth, and the formation of other products (e.g., H(2)CO(3) or H(+)) for one step in the pathway to full mineralization. A modeling example demonstrates how different kinetics for each step in the degradation of nitrilotriacetic acid (NTA) leads to observed patterns in experimental results, such as a delay in the release of H(2)CO(3) after NTA is removed from solution.     

A simple and rapid micro-Kjeldahl method for total nitrogen analysis

Summary A fast and simple micro-method for total nitrogen analysis in complex fermentation media is presented. Samples containing up to 50 ug nitrogen are digested in tubes with sodium selenite (in sulphuric-phosphoric mixture) plus hydrogen peroxide during one hour at 380°C. Ammonium liberated is measured without extraction by Berthelot colorimetric reaction.     

Time-dependent closed form solutions for fully competitive enzyme reactions

An analytic formalism developed earlier to describe the time evolution of the basic enzyme reaction is extended to fully competitive systems. Time-dependent closed form solutions are derived for the three nominal cases of competition: even, slow and fast inhibitors, allowing for the first time the complete characterization of the reactions. In agreement with previous work, the time-independent Michaelis-Menten approach is shown to be inaccurate when a fast inhibitor is present. The validity of the quasi-steady-state approximation on which the present framework is based is also revised.     

Time-dependent kinetic complexities in cholinesterase-catalyzed reactions

Cholinesterases (ChEs) display a hysteretic behavior with certain substrates and inhibitors. Kinetic cooperativity in hysteresis of ChE-catalyzed reactions is characterized by a lag or burst phase in the approach to steady state. With some substrates damped oscillations are shown to superimpose on hysteretic lags. These time dependent peculiarities are observed for both butyrylcholinesterase and acetylcholinesterase from different sources. Hysteresis in ChE-catalyzed reactions can be interpreted in terms of slow transitions between two enzyme conformers E and E′. Substrate can bind to E and/or E′, both Michaelian complexes ES and E’s can be catalytically competent, or only one of them can make products. The formal reaction pathway depends on both the chemical structure of the substrate and the type of enzyme. In particular, damped oscillations develop when substrate exists in different, slowly interconvertible, conformational, and/or micellar forms, of which only the minor form is capable of binding and reacting with the enzyme. Biphasic pseudo-first-order progressive inhibition of ChEs by certain carbamates and organophosphates also fits with a slow equilibrium between two reactive enzyme forms. Hysteresis can be modulated by medium parameters (pH, chaotropic and kosmotropic salts, organic solvents, temperature, osmotic pressure, and hydrostatic pressure). These studies showed that water structure plays a role in hysteretic behavior of ChEs. Attempts to provide a molecular mechanism for ChE hysteresis from mutagenesis studies or crystallographic studies failed so far. In fact, several lines of evidence suggest that hysteresis is controlled by the conformation of His438, a key residue in the catalytic triad of cholinesterases. Induction time may depend on the probability of His438 to adopt the operative conformation in the catalytic triad. The functional significance of ChE hysteresis is puzzling. However, the accepted view that proteins are in equilibrium between preexisting functional and non-functional conformers, and that binding of a ligand to the functional form shifts equilibrium towards the functional conformation, suggests that slow equilibrium between two conformational states of these enzymes may have a regulatory function in damping out the response to certain ligands and irreversible inhibitors. This is particularly true for immobilized (membrane bound) enzymes where the local substrate and/or inhibitor concentrations depend on influx in crowded organellar systems, e.g. cholinergic synaptic clefts. Therefore, physiological or toxicological relevance of the hysteretic behavior and damped oscillations in ChE-catalyzed reactions and inhibition cannot be ruled out.     

Equilibrium protein folding-unfolding process involving multiple intermediates

Mathematical models for the protein folding-unfolding process involving multiple intermediates have been derived. Computer fitting of the experimental data to this model generates various thermodynamic parameters for the folding-unfolding process. In this way, the complex folding-unfolding process of the multi-domain proteins can be analysed in a quantitative way. The application of the folding-unfolding model involving seven stages in human placental alkaline phosphatase is described. These authors contributed equally to this paper.     

Tunneling of intermediates in enzyme-catalyzed reactions

A fascinating group of enzymes has been shown to possess multiple active sites connected by intramolecular tunnels for the passage of reactive intermediates from the site of production to the site of utilization. In most of the examples studied to date, the binding of substrates at one active site enhances the formation of a reaction intermediate at an adjacent active site. The most common intermediate is ammonia, derived from the hydrolysis of glutamine, but molecular tunnels for the passage of indole, carbon monoxide, acetaldehyde and carbamate have also been identified. The architectural features of these molecular tunnels are quite different from one another, suggesting that they evolved independently.     

Covalent enzyme-substrate intermediates in transferase reactions

Enzymatic transfer reactions are often depicted as occurring on the surface of the enzyme by direct transfer of a chemical group from a donor substrate molecule to an acceptor, in a single-displacement reaction without covalent participation of the enzyme. This picture of enzyme action is purely speculative, because no positive evidence in support of it exists. The kinetic argument, which formerly afforded the sole support for the single-displacement mechanism, is now known to be in error. Contrasting sharply with this dearth of proof is the substantial and growing body of evidence which upholds the double-displacement mechanism of enzymatic transfer. In this mechanism, a catalytic group (or atom) within the active site of the enzyme links covalently with one of the substrates, or some fragment of it, at some stage of the reaction. Through use of the covalent enzyme-substrate intermediate it may be that the enzyme is enabled to overcome certain entropic difficulties, thus accounting in part for the well-known speed of enzymatic reactions. Covalent participation by the enzyme also brings enzymatic catalysis into closer accord with homogenous and heterogeneous catalysis, in which the key reaction is the transient formation of a covalent bond between substrate and catalyst.     

Thiol exchange reactions involving selenotrisulfides

The occurrence of in vitro thiol exchange reactions involving selenotrisulfides has been documented by HPLC analyses of reaction solutions. Asymmetric selenotrisulfide (RSSeSR') (R,R' = penicillamine, cysteine, glutathione) was formed by the reactions between (i) a mixture of thiols and selenite, (ii) thiol (R'SH) and symmetric selenotrisulfide (RSSeSR), and (iii) symmetric selenotrisulfides (RSSeSR and R'SSeSR'). Further reaction of an asymmetric selenotrisulfide with thiol (R'SH) produced another symmetric selenotrisulfide (R'SSeSR'). These thiol exchange reactions may offer significant information to elucidate intake and metabolism of selenium in vivo.     

Theoretical studies of enzyme mechanisms involving high-valent iron intermediates

Recent theoretical contributions to the elucidation of mechanisms for iron containing enzymes are reviewed. The method used in most of these studies is hybrid density functional theory with the B3LYP functional. Three classes of enzymes are considered, the mononuclear non-heme enzymes, enzymes containing iron dimers, and heme-containing enzymes. Mechanisms for both dioxygen and substrate activations are discussed. The reactions usually go through two half-cycles, where a high-valent intermediate Fe(IV)O species is created in the first half-cycle, and the substrate reactions involving this intermediate occur in the second half-cycle. Similarities between the three classes of enzymes dominate, but significant differences also exist.     

Sulfate-reducing pathway in Escherichia coli involving bound intermediates.

Although a sulfate-reducing pathway in Escherichia coli involving free sulfite and sulfide has been suggested, it is shown that, as in Chlorella, a pathway involving bound intermediates is also present. E. coli extracts contained a sulfotransferase that transferred the sulfonyl group from a nucleosidephosphosulfate to an acceptor to form an organic thiosulfate. This enzyme was specific for adenosine 3'-phosphate 5'-phosphosulfate, did not utilize adenine 5'-phosphosulfate, and transferred to a carrier molecule that was identical with thioredoxin in molecular weight and amino acid composition. In the absence of thioredoxin, only very low levels of the transfer of the sulfo group to thiols was observed. As in Chlorella, thiosulfonate reductase activity that reduced glutathione-S-SO3- to bound sulfide could be detected. In E. coli, this enzyme used reduced nicotinamide adenine dinucleotide phosphate and Mg2+, but did not require the addition of ferredoxin or ferredoxin nicotinamide adenine dinucleotide phosphate reductase. Although in Chlorella the thiosulfonate reductase appears to be a different enzyme from the sulfite reductase, the E. coli thiosulfonate reductase and sulfite reductase may be activities of the same enzyme.     

A simple competition model involving selection

Asimple model system of two self-reproducing objects is considered. A set of equations, similar to Eigen's equation, describing competition of these objects is derived and analyzed under the effect of an ‘ecological constraint’. The relation with other constraints used in the literature is discussed.     

Lignin intermediates and simple phenolics as feeding stimulants for Scolytus multistriatus

Comparative stimulation of Scolytus multistriatus feeding by tested dihydroxybenzenes and benzaldehydes showed that molecules with 1,4 substitutions on the benzene ring were most active; 1,3 and 1,2 substitutions were progressively less active. Methoxyl substitution adjacent to the 4-hydroxyl group on benzaldehydes reduced feeding and replacement of a hydroxyl by a methoxyl group on 1,2 disubstituted phenols destroyed the feeding response. Methoxyl substitution on benzaldehydes increased volatility and short-range attraction, but reduced feeding activity in the laboratory bioassays.     

Oxidizing intermediates in cytochrome P450 model reactions

Oxoiron(IV) porphyrin -cation radicals have been considered as the sole reactive species in the catalytic oxidation of organic substrates by cytochromes P450 and their iron porphyrin models over the past two decades. Recent studies from several laboratories, however, have provided experimental evidence that multiple oxidizing species are involved in the oxygen transfer reactions and that the mechanism of oxygen transfer is much more complex than initially believed. In this Commentary, reactive intermediates that have been shown or proposed to be involved in iron porphyrin complex-catalyzed oxidation reactions are reviewed. Particularly, the current controversy on the oxoiron(IV) porphyrin -cation radical as a sole reactive species versus the involvement of multiple oxidizing species in oxygen transfer reactions is discussed.Abbreviations F₅PhIO pentafluoroiodosylbenzene - m-CPBA m-chloroperbenzoic acid - OEP dianion of octaethylporphyrin - PhIO iodosylbenzene - PPAA peroxyphenylacetic acid - TDCPP dianion of meso-tetrakis(2,6-dichlorophenyl)porphyrin - TMP dianion of meso-tetramesitylporphyrin - TPFPP dianion of meso-tetrakis(pentafluorophenyl)porphyrin - TPP dianion of meso-tetraphenylporphyrin - TTPPP dianion of meso-tetrakis(2,4,6-triphenylphenyl)porphyrin     

Stabilization of noncovalent intermediates in enzymatically catalyzed reactions

Reactive intermediate enzyme complexes are difficult to study directly and the use of physical methods requiring observation periods of more than a second has not been possible heretofore. Here we introduce a simple approach, the "Le Chatelier forcing method" which does for the first time produce significant concentrations of such kinetically competent central intermediates observable for extended periods of time. The method involves only the forcing of the accumulation of intermediate complexes at thermodynamic equilibrium by the use of high reactant concentrations working against a high concentration of a product, combined with a valid and applicable method of analysis. We demonstrate this approach using the glutamate dehydrogenase catalyzed reaction with the reaction product ammonia as a "dam" to oppose the forward driving force of NADP and l-glutamate. We demonstrate the accumulation of substantial amounts measurable amounts of stable enzyme-NADPH-alpha-carbinolamine and alpha-iminoglutarate complexes in three different alpha-amino acid dehydrogenases. We describe the manipulation of such Le Chatelier forced equilibria to increase the prominence of particular species and discuss the implications of these findings for previously unattainable experimental approaches.