Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

Prediction of Intrinsic kinetics in diffusion disguised immobilized enzyme systems

When immobilized enzyme kinetics are disguised by inter- and intraparticle diffusion effects, an approximate mathematical procedure is indicated whereby experimental data obtained in the limiting ranges of first- and zeroth-order Michaelis-Menten kinetics could be used for the prediction of the kinetic constants.

Studies on active site mutants of P-falciparum adenylosuccinate synthetase: Insights into enzyme catalysis and activation

Adenylosuccinate synthetase catalyzes a reversible reaction utilizing IMP, GTP and aspartate in the presence of Mg2+ to form adenylosuccinate, GDP and inorganic phosphate. Comparison of similarly liganded complexes of Plasmodium falciparum, mouse and Escherichia coil AdSS reveals H-bonding interactions involving nonconserved catalytic loop residues (Asn429, Lys62 and Thr307) that are unique to the parasite enzyme. Site-directed mutagenesis has been used to examine the role of these interactions in catalysis and structural organization of P. falciparum adenylosuccinate synthetase (PfAdSS). Mutation of Asn429 to Val, Lys62 to Leu and Thr307 to Val resulted in an increase in K-m values for IMP, GTP and aspartate, respectively along with a 5 fold drop in the k(cat) value for N429V mutant suggesting the role of these residues in ligand binding and/or catalysis. We have earlier shown that the glycolytic intermediate, fructose 1,6 bisphosphate, which is an inhibitor of mammalian AdSS is an activator of the parasite enzyme. Enzyme kinetics along with molecular docking suggests a mechanism for activation wherein F16BP seems to be binding to the Asp loop and inducing a conformation that facilitates aspartate binding to the enzyme active site. Like in other AdSS, a conserved arginine residue (Arg155) is involved in dimer crosstalk and interacts with IMP in the active site of the symmetry related subunit of PfAdSS. We also report on the iochemical characterization of the arginine mutants (R155L, R155K and R155A) which suggests that unlike in E. coil AdSS, Arg155 in PfAdSS influences both ligand binding and catalysis. (C) 2010 Elsevier B.V. All rights reserved.

Catalysis of tRNA Aminoacylation: Single Turnover to Steady-State Kinetics of tRNA Synthetases

Aminoacyl-tRNA synthetases (aaRS) catalyze the bimolecular association reaction between amino acid and tRNA by specifically and unerringly choosing the cognate amino acid and tRNA. There are two classes of such synthetases that perform tRNA-aminoacylation reaction. Interestingly, these two classes of aminoacyl-tRNA synthetases differ not only in their structures but they also exhibit remarkably distinct kinetics under pre-steady-state condition. The class I synthetases show initial burst of product formation followed by a slower steady-state rate. This has been argued to represent the influence of slow product release. In contrast, there is no burst in the case of class H enzymes. The tight binding of product with enzyme for class I enzymes is correlated with the enhancement of rate in presence of elongation factor. EF-TU. In spite of extensive experimental studies, there is no detailed theoretical analysis that can provide a quantitative understanding of this important problem. In this article, we present a theoretical investigation of enzyme kinetics for both classes of aminoacyl-tRNA synthetases. We present an augmented kinetic scheme and then employ the methods of time-dependent probability statistics to obtain expressions for the first passage time distribution that gives both the time-dependent and the steady-state rates. The present study quantitatively explains all the above experimental observations. We propose an alternative path way in the case of class II enzymes showing the tRNA-dependent amino acid activation and the discrepancy between the single-turnover and steady-state rate.

From anomalies in neat liquid to structure, dynamics and function in the biological world

Water brings its remarkable thermodynamic and dynamic anomalies in the pure liquid state to biological world where water molecules face a multitude of additional interactions that frustrate its hydrogen bond network. Yet the water molecules participate and control enormous number of biological processes in manners which are yet to be understood at a molecular level. We discuss thermodynamics, structure, dynamics and properties of water around proteins and DNA, along with those in reverse micelles. We discuss the roles of water in enzyme kinetics, in drug-DNA intercalation and in kinetic-proof reading ( the theory of lack of errors in biosynthesis). We also discuss how water may play an important role in the natural selection of biomolecules. (C) 2011 Elsevier B. V. All rights reserved.

On the Presumed Kinetic Consequences of Pre-equilibrium. Implications for the Michaelis-Menten Equation

The overall rate equation for a reaction sequence consisting of a pre-equilibrium and rate-determining steps should not be derived on the basis of the concentration of the intermediate product (X). This is apparently indicated by transition state theory (as the path followed to reach the highest energy transition state is irrelevant), but also proved by a straight-forward mathematical approach. The thesis is further supported by the equations of concurrent reactions as applied to the partitioning of X between the two competing routes (reversal of the pre-equilibrium and formation of product). The rate equation may only be derived rigorously on the basis of the law of mass action. It is proposed that the reactants acquire the overall activation energy prior to the pre-equilibrium, thus forming X in a high-energy state en route to the rate-determining transition state. (It is argued that conventional energy profile diagrams are misleading and need to be reinterpreted.) Also, these arguments invalidate the Michaelis-Menten equation of enzyme kinetics, and necessitate a fundamental revision of our present understanding of enzyme catalysis. (The observed ``saturation kinetics'' possibly arises from weak binding of a second molecule of substrate at the active site; analogous conclusions apply to reactions at surfaces).

Kinetic proofreading at single molecular level: aminoacylation of tRNA(Ile) and the role of water as an editor

Proofreading/editing in protein synthesis is essential for accurate translation of information from the genetic code. In this article we present a theoretical investigation of efficiency of a kinetic proofreading mechanism that employs hydrolysis of the wrong substrate as the discriminatory step in enzyme catalytic reactions. We consider aminoacylation of tRNA(Ile) which is a crucial step in protein synthesis and for which experimental results are now available. We present an augmented kinetic scheme and then employ methods of stochastic simulation algorithm to obtain time dependent concentrations of different substances involved in the reaction and their rates of formation. We obtain the rates of product formation and ATP hydrolysis for both correct and wrong substrates (isoleucine and valine in our case, respectively), in single molecular enzyme as well as ensemble enzyme kinetics. The present theoretical scheme correctly reproduces (i) the amplitude of the discrimination factor in the overall rates between isoleucine and valine which is obtained as (1.8x10(2)).(4.33x10(2)) = 7.8x10(4), (ii) the rates of ATP hydrolysis for both Ile and Val at different substrate concentrations in the aminoacylation of tRNA(Ile). The present study shows a non-michaelis type dependence of rate of reaction on tRNA(Ile) concentration in case of valine. The overall editing in steady state is found to be independent of amino acid concentration. Interestingly, the computed ATP hydrolysis rate for valine at high substrate concentration is same as the rate of formation of Ile-tRNA(Ile) whereas at intermediate substrate concentration the ATP hydrolysis rate is relatively low. We find that the presence of additional editing domain in class I editing enzyme makes the kinetic proofreading more efficient through enhanced hydrolysis of wrong product at the editing CP1 domain.

The crystal structure of a lectin from Butea monosperma: Insight into its glycosylation and binding of ligands

Crystal structure of a lectin purified from Butea monosperma seeds was determined by Molecular Replacement method. Its primary structure was determined by Tandem Mass Spectroscopy and electron density maps from X-ray diffraction data. Its quaternary structure was tetrameric, formed of two monomers, alpha and beta, beta appearing as truncated alpha. The occurrence of two tetramers in the asymmetric unit of the crystal might be a consequence of asymmetric contacts due to difference in glycosylation and variable loops structures, to form an `octamer-structure'. The crystal structure showed binding pockets for gamma Abu, having a proposed role in plant defense, at the interface of canonical dimer-partners. Hemagglutination studies, enzyme kinetics, isothermal titration calorimetry and molecular dynamics showed that the lectin is specific to N-acetyl D-galactosamine, galactose and lactose in decreasing order, and alpha-amylase inhibitor. (C) 2014 Elsevier B.V. All rights reserved.

A Model of Anomalous Enzyme-Catalyzed Gel Degradation Kinetics

We show that a model of target location involving n noninteracting particles moving subdiffusively along a line segment (a generalization of a model introduced by Sokolov et al. [Biophys. J. 2005, 89, 895.]) provides a basis for understanding recent experiments by Pelta et al. [Phys. Rev. Lett. 2007, 98, 228302.] on the kinetics of diffusion-limited gel degradation. These experiments find that the time t(c) taken by the enzyme thermolysin to completely hydrolyze a gel varies inversely as roughly the 3/2 power of the initial enzyme concentration [E]. In general, however, this time would be expected to vary either as [E](-1) or as [E](-2), depending on whether the Brownian diffusion of the enzyme to the site of cleavage took place along the network chains (1-d diffusion) or through the pore spaces (3-d diffusion). In our model, the unusual dependence of t(c) on [E] is explained in terms of a reaction-diffusion equation that is formulated in terms of fractional rather than ordinary time derivatives.

The carbon dioxide hydration activity of the sulfonamide-resistant carbonic anhydrase from the liver of male rat: pH independence of the steady-state kinetics

The steady-state kinetic constants for the catalysis of CO2 hydration by the sulfonamide-resistant and testosterone-induced carbonic anhydrase from the liver of the male rat has been determined by stopped-flow spectrophotometry. The turnover number was 2.6 ± 0.6 × 103 s− at 25 °C, and was invariant with pH ranging from 6.2 to 8.2 within experimental error. The Km at 25 °C was 5 ± 1 mImage , and was also pH independent. These data are in quantitative agreement with earlier findings of pH-independent CO2 hydration activity for the mammalian skeletal muscle carbonic anhydrase isozyme III. The turnover numbers for higher-activity isozymes I and II are strongly pH dependent in this pH range. Thus, the kinetic status of the male rat liver enzyme is that of carbonic anhydrase III. This finding is consistent with preliminary structural and immunologic data from other laboratories.

Effect of Ethanol Extract of Whole Plant of Trichosanthes cucumerina var. cucumerina L. on Gonadotropins, Ovarian Follicular Kinetics and Estrous Cycle for Screening of Antifertility Activity in Albino Rats

Ethanol extract of whole plant of Trichosanthes cucumerina L. var. cucumerina was evaluated for antiovulatory activity in adult rats. The ethanol extract at the doses 200 and 400mg/kg body weight (orally) affected the normal estrous cycle showing a significant increase in estrus and metestrus phases and decrease in diestrus and proestrus phases. The extract also significantly reduced the number of healthy follicles (Class I-Class VI) and corpora lutea and increased the number of regressing follicles (Stage IA, Stage IB, Stage IIA, and Stage IIB). The protein and glycogen content in the ovaries were significantly reduced in treated rats. The cholesterol level was significantly increased, whereas, the enzyme activities like 3b-HSD and 17b-HSD were significantly inhibited in the ovary of treated rats. Serum FSH and LH levels were significantly reduced in the treated groups were measured by RIA. In acute toxicity test, neither mortality nor change in the behavior or any other physiological activities in mice were observed in the treated groups. In chronic toxicity studies, no mortality was recorded and there were no significant differences in the body and organ weights were observed between controls and treated rats. Hematological analysis showed no significant differences in any of the parameters examined (RBC, WBC count and Hemoglobin estimation). These observations showed the antiovulatory activity of ethanol extract of whole plant of Trichosanthes cucumerina L. var. cucumerina in female albino rats.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.

Studies on Plant Aspartate Transcarbamylase Purification and Properties of the Enzyme from Mung-Bean (Phaseolus aureus) Seedlings

Aspartate transcarbamylase is purified from mung bean seedlings by a series of steps involving manganous sulphate treatment, ammonium sulphate fractionation, DEAE-cellulose chromatography, followed by a second ammonium sulphate fractionation and finally gel filtration on Sephadex-G 100. The enzyme is homogeneous on ultracentrifugation and on polyacrylamide gel electrophoresis. It functions optimally at 55°C. It has two pH optima, one at 8.0 and the other at 10.2. The enzyme follows Michaelis-Menten kinetics with l-aspartate as the variable substrate. However, it exhibits sigmoid saturation curves at both the pH optima when the concentration of carbamyl phosphate is varied. The enzyme is allosterically inhibited by UMP at both the pH optima. Increasing phosphorylation of the uridine nucleotide decreases the inhibitory effect. The enzyme is desensitized to inhibition by UMP on treatment with p-hydroxymercuribenzoate, gel electrophoresis indicating that the enzyme is dissociated by this treatment; the dissociated enzyme can be reassociated by treatment with 2-mercaptoethanol. The properties of the mung bean enzyme are compared with the enzyme from other sources.

Studies on Plant Aspartate Transcarbamylase Purification and Properties of the Enzyme from Mung-Bean (Phaseolus aureus) Seedlings

Aspartate transcarbamylase is purified from mung bean seedlings by a series of steps involving manganous sulphate treatment, ammonium sulphate fractionation, DEAE-cellulose chromatography, followed by a second ammonium sulphate fractionation and finally gel filtration on Sephadex-G 100. The enzyme is homogeneous on ultracentrifugation and on polyacrylamide gel electrophoresis. It functions optimally at 55°C. It has two pH optima, one at 8.0 and the other at 10.2. The enzyme follows Michaelis-Menten kinetics with l-aspartate as the variable substrate. However, it exhibits sigmoid saturation curves at both the pH optima when the concentration of carbamyl phosphate is varied. The enzyme is allosterically inhibited by UMP at both the pH optima. Increasing phosphorylation of the uridine nucleotide decreases the inhibitory effect. The enzyme is desensitized to inhibition by UMP on treatment with p-hydroxymercuribenzoate, gel electrophoresis indicating that the enzyme is dissociated by this treatment; the dissociated enzyme can be reassociated by treatment with 2-mercaptoethanol. The properties of the mung bean enzyme are compared with the enzyme from other sources.

Microbial L-phenylalanine ammonia-lyase. Purification, subunit structure and kinetic properties of the enzyme from Rhizoctonia solani

Phenylalanine ammonia-lyase (EC 4.3.1.5) was purified to homogeneity from the acetone-dried powders of the mycelial felts of the plant pathogenic fungus Rhizoctonia solani. 2. A useful modification in protamine sulphate treatment to get substantial purification of the enzyme in a single-step is described. 3. The purified enzyme shows bisubstrate activity towards L-phenylalanine and L-tyrosine. 4. It is sensitive to carbonyl reagents and the inhibition is not reversed by gel filtration. 5. The molecular weight of the enzyme as determined by Sephadex G-200 chromatography and sucrose-density-gradient centrifugation is around 330000. 6. The enzyme is made up of two pairs of unidentical subunits, with a molecular weight of 70000 (alpha) and 90000 (beta) respectively. 7. Studies on initial velocity versus substrate concentration have shown significant deviations from Michaelis-Menten kinetics. 8. The double-reciprocal plots are biphasic (concave downwards) and Hofstee plots show a curvilinear pattern. 9. The apparent Km value increases from 0.18 mM to as high as 5.0 mM with the increase in the concentration of the substrate and during this process the Vmax, increases by 2-2.5-fold. 10. The value of Hill coefficient is 0.5. 11. Steady-state rates of phenylalanine ammonia-lyase reaction in the presence of inhibitors like D-phenylalanine, cinnamic, p-coumaric, caffeic, dihydrocaffeic and phenylpyruvic acid have shown that only one molecule of each type of inhibitor binds to a molecule of the enzyme. These observations suggest the involvement of negative homotropic interactions in phenylalanine ammonia-lyase. 12. The enzyme could not be desensitized by treatment with HgCl2, p-chloromercuribenzoic acid or by repeated freezing and thawing.