Heteroclinic cycling and extinction in May–Leonard models with demographic stochasticity

Journal of Mathematical Biology - Reactions involving three or more reactants, called higher-molecular reactions, play an important role in mathematical modelling in systems and synthetic biology....     

The chemistry of protein catalysis

We report, for the first time, on the statistics of chemical mechanisms and amino acid residue functions that occur in enzyme reaction sequences using the MACiE database of 202 distinct enzyme reaction mechanisms as a knowledge base. MACiE currently holds representatives from each Enzyme Commission sub-subclass where there is an available crystal structure and sufficient evidence in the primary literature for a mechanism. Each catalytic step of every reaction sequence in MACiE is fully annotated, so that it includes the function of the catalytic residues involved in the reaction and the chemical mechanisms by which substrates are transformed into products. We show that the most catalytic amino acid residues are histidine, cysteine and aspartate, which are also the residues whose side-chains are more likely to serve as reactants, and that have the greatest versatility of function. We show that electrophilic reactions in enzymes are very rare, and the majority of enzyme reactions rely upon nucleophilic and general acid/base chemistry. However, although rare, radical (homolytic) reactions are much more common than electrophilic reactions. Thus, the majority of amino acid residues perform stabilisation roles (as spectators) or proton shuttling roles (as reactants). The analysis presented provides a better understanding of the mechanisms of enzyme catalysis and may act as an initial step in the validation and prediction of mechanism in an enzyme active site.     

Homochiral Selectivity in RNA Synthesis: Montmorillonite-catalyzed Quaternary Reactions of D,L-Purine with D,L- Pyrimidine Nucleotides

Selective adsorption of D, L-ImpA with D, L-ImpU on the platelets of montmorillonite demonstrates an important reaction pathway for the origin of homochirality in RNA synthesis. Our earlier studies have shown that the individual reactions of D, L-ImpA or D, L-ImpU on montmorillonite catalyst produced oligomers which were only partially inhibited by the incorporation of both D- and L-enantiomers. Homochirality in these reactions was largely due to the formation of cyclic dimers that cannot elongate. We investigated the quaternary reactions of D, L-ImpA with D, L-ImpU on montmorillonite. The chain length of these oligomers increased from 9-mer to 11-mer as observed by HPLC, with a concominant increase in the yield of linear dimers and higher oligomers in the reactions involving D, L-ImpA with D, L-ImpU as compared to the similar reactions carried out with D-enantiomers only. The formation of cyclic dimers of U was completely inhibited in the quaternary reactions. The yield of cyclic dimers of A was reduced from 60% to 10% within the dimer fraction. 12 linear dimers and 3 cyclic dimers were isolated and characterized from the quaternary reaction. The homochirality and regioselectivity of dimers were 64.1% and 71.7%, respectively. Their sequence selectivity was shown by the formation of purine-pyrimidine (54–59%) linkages, followed by purine-purine (29–32%) linkages and pyrimidine-pyrimidine (9–13%) linkages. Of the 16 trimers detected, 10 were homochiral with an overall homochirality of 73–76%. In view of the greater homochirality, sequence- and regio- selectivity, the quaternary reactions on montmorillonite demonstrate an unexpectedly favorable route for the prebiotic synthesis of homochiral RNA compared with the separate reactions of enantiomeric activated mononucleotides.     

The rate enhancement produced by the ribosome: an improved model

As a model for mechanistic comparison with peptidyl transfer within the ribosome, the reaction of aqueous glycinamide with N-formylphenylalanine trifluoroethyl ester (fPhe-TFE) represents an improvement over earlier model reactions involving Tris. The acidity of trifluoroethanol (pKa 12.4) resembles that of tRNA (12.98) more closely than do the acidities of model reactants described earlier, and the reactivity of the simple nucleophile glycinamide is free of potential complications that arise from alternative reaction pathways available to Tris. At 25 degrees C, the uncatalyzed reaction of glycinamide with fPhe-TFE proceeds with a second-order rate constant of 3 x 10(-5) M-1 s-1; DeltaH(++) = +7.8 kcal/mol; TDeltaS(++)= -15.7 kcal/mol. The ribosomal reaction of puromycin with fMet-tRNA proceeds 3 x 107-fold more rapidly, with a second-order rate constant (kcat/Km) of 1 x 10(3) M-1 s-1; DeltaH(++) = +16.0 kcal/mol; TDeltaS(++)= +2.0 kcal/mol. That rate enhancement, an order of magnitude larger than estimated earlier, is fully explained by the more favorable entropy of activation of the ribosomal reaction. Experiments involving ethylene glycol esters suggest that neighboring -OH group effects are negligible in the presence of solvent water, which itself acts as a general base catalyst. In the desolvated interior of the ribosome, the vicinal 2'-OH group of aminoacyl-tRNA probably replaces water as a general base catalyst. But the catalytic effect of the ribosome itself is overwhelmingly entropic in origin, suggesting that the ribosome achieves its effect by physical desolvation and/or juxtaposition of the reactants in a manner conducive to peptidyl transfer.     

Phosphoryl group transfer: evolution of a catalytic scaffold

It is proposed that enzymic phosphoryl-transfer reactions occur by concerted, step-wise, associative (phosphorane-intermediate) or dissociative (metaphosphate-intermediate) mechanisms, as dictated by the catalytic scaffold and the reactants. During the evolution of a phosphotransferase family, the mechanism of the phosphoryl-transfer reaction is in constant flux, potentially changing with each adaptation of the catalytic scaffold to a new phosphoryl-donor-acceptor pair. Phosphotransferases of the recently discovered haloacid dehalogenase superfamily of enzymes, one of the largest and most ubiquitous of the phosphotransferase families characterized to date, are described in the context of the co-evolution of the catalytic scaffold and mechanism.     

Catalytic mechanism of enzymes: preorganization, short strong hydrogen bond, and charge buffering

During the past decade, there has been much debate about the enormous catalytic rate enhancement observed in enzymatic reactions involving carbanion intermediates. Our recent theoretical study has demonstrated the importance of the short strong hydrogen bond (SSHB) in the enzymatic reactions. Nevertheless, other recent theoretical studies espouse the role of preorganization over that of the SSHB. To achieve a consensus on this issue and to find the truth, a more clarified explanation must be given. To this end, we have carried out an elaborate analysis of these enzymatic reactions. We here clarify that the catalytic mechanism needs to be explained with three important factors, viz., SSHB, preorganization, and charge buffering/dissipation. Since the charge buffering role is different from the commonly used concepts of the SSHB and preorganization (unless these definitions are expanded), we stress that the charge buffering role of the catalytic residues is an important ingredient of the enzymatic reaction in reducing the level of accumulation of the negative charge on the substrate during the reaction process. This charge reduction is critical to the lowering of activation barriers and the stabilization of intermediates.     

Classical catalase: ancient and modern

This review describes the historical difficulties in devising a kinetically satisfactory mechanism for the classical catalase after its identification as a unique catalytic entity in 1902 and prior to the breakthrough 1947 analysis by Chance and co-workers which led to the identification of peroxide compounds I and II. The role of protons in the formation of these two ferryl complexes is discussed and current problems of inhibitory ligand and hydrogen donor binding at the active site are outlined, especially the multiple roles involving formate or formic acid. A previous mechanism of NADPH-dependent catalase protection against substrate inhibition is defended. A revised model linking the catalytic ('catalatic') action and the one-electron side reactions involving compound II is suggested. And it is concluded that, contrary to an idea proposed in 1963 that eukaryotic catalase might be a 'fossil enzyme', current thinking gives it a central role in the redox protective processes of long term importance for human and other eukaryotic and prokaryotic life.     

Diffusion and reaction in the cell glycocalyx and the extracellular matrix

Many biologically important macromolecular reactions are assembled and catalyzed at the cell lipid-surface and thus, the extracellular matrix and the glycocalyx layer mediate transfer and exchange of reactants and products between the flowing blood and the catalytic lipid-surface. This paper presents a mathematical model of reaction–diffusion equations that simply describes the transfer process and explores its influence on surface reactivity for a prototypical pathway, the tissue factor (Tf) pathway of blood coagulation. The progressively increasing friction offered by the matrix and glycocalyx to reactants and to the product (coagulation factors X, VIIa and Xa) approaching the reactive surface is simulated and tested by solving the equations numerically with both, monotonically decreasing and constant diffusion profiles. Numerical results show that compared to isotropic transfer media, the anisotropic structure of the matrix and glycocalyx sharply decreases overall reaction rates and significantly increases the mean transit time of reactants; this implies that the anisotropy modifies the distribution of reactants. Results also show that the diffusional transfer, whether isotropic or anisotropic, influences reaction rates according to the order at which the reactants arrive at the boundary. Faster rates are observed when at least one of the reactants is homogeneously distributed before the other arrives at the boundary than when both reactants transfer simultaneously from the boundary.     

Non-empirical study of the phosphorylation reaction catalyzed by 4-methyl-5-β-hydroxyethylthiazole kinase: relevance of the theory of intermolecular interactions

The subject of this study was an analysis of the role of active site residues in the phosphoryl transfer reaction catalyzed by 4-methyl-5-β-hydroxyethylthiazole kinase (ThiK). The ThiK-catalyzed reaction is of special interest due to the lack of a highly conserved aspartate residue serving as a catalytic base. ONIOM(B3LYP:PM3) models of stationary points along the reaction pathway consisted of reactants, two magnesium ions and several highly conserved ThiK active site residues. The results indicate that an S_N2-like mechanism of ThiK, with γ-phosphate acting as an alcohol-activating base is reasonable. Geometries of substrates, transition state and products were utilized in the non-empirical analysis of the physical nature of catalytic interactions taking place in the ThiK active site. The role of particular residues was investigated in terms of their ability to preferentially stabilize the transition state relative to substrates (differential transition state stabilization, DTSS) or products (differential product stabilization, DPS). It seems that Mg2, Glu126 and Cys198 play a major catalytic role, whereas Mg1 and the same Cys198 are responsible for product release. It is remarkable that no dominant role of an electrostatic term in the interactions involved in catalytic activity is observed for product release. Determination of catalytic fields expressing differential electrostatic potential of the transition state with respect to substrates revealed the optimal electrostatic features of an ideal catalyst for the studied reaction. The predicted catalytic environment is in agreement with experimental data showing increased catalytic activity of ThiK upon mutation of Cys198 to aspartate. Figure Catalytic fields for ThiK-catalyzed reaction juxtaposed with the positions of active site residues of a model system. Magnesium ions are considered part of the transition state/reactants. The surface of constant electronic density is colored according to differential electrostatic potential of transition state with respect to reactants. The sign of the differential potential reflects the electrostatic properties of a complementary molecular environment. Red (green) color denotes regions where a negative (positive) charge would be optimal for catalytic activity     

Design of turbulent tangential micro-mixers that mix liquids on the nanosecond time scale

Unravelling (bio)chemical reaction mechanisms and macromolecular folding pathways on the (sub)microsecond time scale is limited by the time resolution of kinetic instruments for mixing reactants and observation of the progress of the reaction. To improve the mixing time resolution, turbulent four- and two-jet tangential micro-mixers were designed and characterized for their mixing and (unwanted) premixing performances employing acid–base reactions monitored by a pH-sensitive fluorescent dye. The mixing performances of the micro-mixers were determined after the mixing chamber in a free-flowing jet. The premixing behavior in the vortex chamber was assessed in an optically transparent glass–silicon replica of a previously well-characterized stainless-steel four-jet tangential micro-mixer. At the highest flow rates, complete mixing was achieved in 160 ns with only approximately 9% premixing of the reactants. The mixing time of 160 ns is at least 50 times shorter than estimated for other fast mixing devices. Key aspects to the design of ultrafast turbulent micro-mixers are discussed. The integration of these micro-mixers with an optical flow cell would enable the study of the very onset of chemical reactions in general and of enzyme catalytic reactions in particular.     

CarbonCarbon Bond Formation by Lewis Superacid Catalysis

Diverse intramolecular cyclizations involving the formation of C? C bonds are described using catalytic methodologies based on Lewis superacids. Examples are presented on 1,6‐diene cyclizations to gem‐dimethylcyclohexane structures. Tandem cyclization of trienes are described to afford bicyclic structures in reactions involving rearrangements. Hydroarylation of olefins and of allenes is developed in catalytic Friedel? Crafts‐type coupling processes, which can give rise to tandem reactions. The olfactory evaluation of the series of prepared compounds is also presented.     

A theory of polar medium electron transfer reactions through bridge groups with a quasicontinuous energy spectrum

A theory has been developed for outer sphere non-adiabatic electron transfer reactions in polar media, involving transfer from one reactant to another via a third species having many closely spaced electronic energy levels. Expressions have been developed for the overall probability of electron transfer per unit time, and it is shown that for suitable positions of the electronic terms a pronounced increase in the rate constants, compared with the direct electron transfer between the reactants, can be expected.     

Cytochrome c oxidase: Intermediates of the catalytic cycle and their energy-coupled interconversion

Several issues relevant to the current studies of cytochrome c oxidase catalytic mechanism are discussed. The following points are raised. (1) The terminology currently used to describe the catalytic cycle of cytochrome oxidase is outdated and rather confusing. Presumably, it would be revised so as to share nomenclature of the intermediates with other oxygen-reactive heme enzymes like P450 or peroxidases. (2) A "catalytic cycle" of cytochrome oxidase involving complete reduction of the enzyme by 4 electrons followed by oxidation by O(2) is a chimera composed artificially from two partial reactions, reductive and oxidative phases, that never operate together as a true multi-turnover catalytic cycle. The 4e(-) reduction-oxidation cycle would not serve a paradigm for oxygen reduction mechanism and protonmotive function of cytochrome oxidase. (3) The foremost role of the K-proton channel in the catalytic cycle may consist in securing faultless delivery of protons for heterolytic O-O bond cleavage in the oxygen-reducing site, minimizing the danger of homolytic scission reaction route. (4) Protonmotive mechanism of cytochrome oxidase may vary notably for the different single-electron steps in the catalytic cycle.     

Chemical evolution 40. clay-mediated oxidation of diaminomaleonitrile

Summary The previously reported inhibition of the oligomerization of HCN by montmorillonite clays was investigated. The inhibition is due to the oxidation of diaminomaleonitrile (DAMN) by the Fe³⁺ in the clay lattice. Fe²⁺ and oxalic acid were shown to be the reaction products. From these reaction products and the previous report that two equivalents of HCN are formed per equivalent ofDAMN, it was established that diiminosuccinonitrile (DISN) is the initial reaction product, which is rapidly hydrolyzed to oxalic acid and HCN. The same oxidative transformations are effected by Fe³⁺ bound to Dowex 50, Fe³⁺ in solution and Ni(NH₃)₆ ²⁺. The rate of reaction of DAMN decreased in the order Fe³⁺ > Fe³⁺-Dowex > montmorillonite, indicating no catalytic role for the clay in the oxidation of DAMN. Little reaction of DAMN was observed with montmorillonite in which the bulk of the iron was in the Fe²⁺ oxidation state. The possible significance of these redox reactions to chemical evolution is discussed.For the previous papers in this series see Ferris JP, Alwis KW, Edelson EH, Mount N, Hagan Jr J (1980) Origin of Life Wolman Y (ed) Reidel, Dordrecht, p 125–128 Ferris JP, Edelson EH, Auyeung JM, Joshi PC (1981) J Mol Evol 17:69-77     

Atomic motion in enzymatic reaction coordinates

Atomic excursions of reactants in enzymatic catalytic sites can be estimated from high-resolution crystal structures of enzyme complexes with substrates, transition state analog inhibitors and products. Transition state structures, defined from kinetic isotope effect studies, are compared to crystallographic structures to validate the properties of the transition state analog. Atomic excursions in enzymatic catalytic sites can differ from those in solution and define the role of the enzymatic catalyst in directing atomic motion.     

Development of biofuel cells based on gold nanoparticle decorated multi-walled carbon nanotubes

This study focused on developing the synthesis of Au nanoparticle-decorated functionalized multi-walled carbon nanotubes (Au-NPs/f-MWCNTs) for monosaccharide (bio-fuel) oxidation reactions and practical application in air-biofuel cells. We developed a scalable and straightforward method to synthesize Au-NPs/f-MWCNTs which allow us to control the loading and size of the Au-NPs. The Au-NPs/f-MWCNTs exhibited better catalytic activities and stability than the Au sheet and subsequently resulted in a threefold increase in the power density of the air-glucose fuel cell with an exceptionally high open circuit voltage (∼1.3 V). The catalytic efficiency was confirmed by high performance liquid chromatography with the superior of the Au-NPs/f-MWCNTs over a bare gold electrode. In addition, the application of this advanced catalyst to other monosaccharide oxidation reactions figured out that the configuration of –OH groups at C₂ and C₃ of the reactants plays an important role in the initial adsorption process, and thus, affects the required activation energy for further oxidation. The different monosaccharides lead to significantly different fuel cell performances in terms of power density, which coherently corresponds to the difference in the configuration of C₂ and C₃. Because two small air-glucose fuel cells using Au-NPs/f-MWCNTs can run a LED lamp, further applications of other monosaccharides as fuel in biofuel cells for equivalent required power devices may be possible.     

Structured fiber supports for gas phase biocatalysis

Pseudomonas cepaciae lipase adsorbed onto non-porous structured fiber supports in the form of woven fabrics, was used to catalyze hydrolysis and transesterification reactions in the gas phase. The enzyme adsorbed onto carbon fiber support exhibited much higher catalytic activity compared to the enzyme immobilized onto glass fiber carrier. The effect of temperature and relative humidity on reactions catalyzed by P. cepaciae lipase adsorbed onto structured fiber carbon support was studied in the gas system. Under the conditions investigated (up to 60 °C and 80% relative humidity), the immobilized enzyme showed a high thermostability and could be efficiently used to catalyze hydrolytic and transesterification reactions in continuous mode. Structured fiber supports, with a high specific surface area and a high mechanical resistance, showed a low-pressure drop during the passage of reactants through a reactor. The approach proposed in this study could be suitable for immobilization of a wide variety of enzymes.     

Selectivity of montmorillonite catalyzed prebiotic reactions of D,L-nucleotides

The montmorillonite-catalyzed reactions of the 5′-phosphorimidazolides of D, L-adenosine (D, L-ImpA) (Figure 1a. N = A, R = H) and D, L-uridine (Figure 1a., N = U, R = H) yields oligomers that were as long as 7 mers and 6 mers, respectively. The reactions of dilute solutions of D-ImpA and D-ImpU under the same conditions gave oligomers as long as 9 and 8 mers respectively. This demonstrated that oligomer formation is only partially inhibited by incorporation of both the D- and L-enantiomers. The structures of the dimers, trimers and tetramer fractions formed from D, L-ImpA was investigated by selective enzymatic hydrolysis, comparison with authentic samples and mass spectrometry. Homochiral products were present in greater amounts than would be expected if theoretical amounts of each were formed. The ratio of the proportion of homochiral products to that of the amount of each expected for the dimers (cyclic and linear), trimers and tetramers, was 1.3, 1.6, and 2.1, respectively. In the D, L-ImpU reaction homochiral products did not predominate with ratios of dimers (cyclic and linear), trimers and tetramers 0.8, 0.44, and 1.4, respectively. The proportions of cyclic dimers in the dimer fraction were 52–66% with D, L-ImpA and 44–69% with D, L-ImpU. No cyclic dimers were formed in the absence of montmorillonite. The differences in the reaction products of D, L-ImpA and D, L-ImpU are likely to be due to the difference in the orientations of the activated monomers when bound to the catalytic sites on montmorillonite. The consequences of the selectivity of montmorillonite as a prebiotic catalyst are discussed.     

Detailed kinetics and regulation of mammalian NAD-linked isocitrate dehydrogenase

A mathematical model is presented to describe the catalytic mechanism of mammalian NAD-linked isocitrate dehydrogenase (NAD-IDH), a highly regulated enzyme in the tricarboxylic acid cycle, a crucial pathway in energy metabolism and biosynthesis. The mechanism accounts for allosteric regulation by magnesium-bound isocitrate and EGTA and calcium-bound ATP and ADP. The developed model is used to analyze kinetic data for the cardiac enzyme and to estimate kinetic parameter values. Since the kinetic mechanism is expressed in terms of chemical species (rather than biochemical reactants), the model explicitly accounts for the effects of biochemical state (ionic strength, pH, temperature, and metal cation concentration) on the kinetics. Because the substrate isocitrate competes with allosteric activators (ATP and ADP) and an inhibitor (EGTA) for metal ion cofactors (Ca(2+) and Mg(2+)), the observed kinetic relationships between reactants, activator and inhibitor concentrations, and catalytic flux are complex. Our analysis reveals that under physiological conditions, the ADP/ATP ratio plays a more significant role than Ca(2+) concentration in regulating the enzyme's activity. In addition, the enzyme is highly sensitive to Mg(2+) concentration in the physiological range, pointing to a potential regulatory role of [Mg(2+)] in mitochondrial energy metabolism.     

Rapid reaction studies on the reduction and oxidation of chicken liver xanthine dehydrogenase by the xanthine/urate and NAD/NADH couples

Chicken liver xanthine dehydrogenase can be partially reduced by either xanthine or NADH. Reduction to approximately the 2-electron-reduced level occurs with NADH, and reduction beyond the 2-electron level occurs with xanthine. In both cases, the reaction is triphasic. The first and third phases are dependent on reductant concentration, whereas the second phase is not. Oxidation of fully (6-electron) reduced xanthine dehydrogenase by either urate or NAD is monophasic and dependent on the oxidant concentration. Oxidation stops at about the same level of reduction that was reached by the corresponding reductant. The position of this end point is sensitive to the potential of the reactants but is relatively insensitive to excess concentrations of oxidant or reductant. NADH binding to 2-electron-reduced enzyme is implicated in fixing the end point position in those reactions involving pyridine nucleotides, whereas urate binding is involved in fixing the end point of those reactions involving xanthine and urate.