A new graphical method for determining parameters in Michaelis-Menten-type kinetics for enzymatic lactose hydrolysis

A new graphical method was developed to determine the kinetic parameters in the Michaelis-Menten-type equation. This method was then applied to studying the kinetics of lactose hydrolysis by Aspergillus niger beta-galactosidase. In this study, the reaction temperature ranged between 8 and 60 degrees C, and the initial lactose concentration ranged between 2.5 and 20%. A kinetic model similar to the conventional Michaelis-Menten equation with competitive product inhibition by galactose was tested using this graphical method as well as a nonlinear computer regression method. The experimental data and the model fit together fairly well at 50 degrees C. However, a relative large disparity was found for reactions at 30 degrees C. A three-parameter integrated model derived from the reversible reaction mechanism simulates the experimental data very well at all temperatures studied. However, this reversible reaction model does not follow the Arrhenius temperature dependence. Nevertheless, reaction rate constants for the proposed model involving the enzyme-galactose complex (in addition to the Michaelis complex) as an intermediate in lactose hydrolysis follow the Arrhenius temperature dependence fairly well, suggesting that this model can be best used for describing the enzymatic lactose hydrolysis. The lack of fit between the model predictions and data may be largely attributed to the effects of galactose mutarotation and oligosaccharide formation during lactose hydrolysis.     

Kinetic Analysis of Self-Replicating Peptides: Possibility of Chiral Amplification in Open Systems

A simplified kinetic model scheme is presented that addresses the main reactions of two recently reported peptide self-replicators. Experimentally observed differences in the autocatalytic efficiency between these two systems-- caused by variations in the peptide sequences--and the possible effect of chiral amplification under heterochiral reaction conditions were evaluated. Our numerical simulations indicated that differences in the catalytic performance are exclusively due to pronounced variations in the rate parameters that control the reversible and hydrophobic interactions in the reaction system but neither to alterations in the underlying reaction network nor to changes in the stoichiometry of the involved aggregation processes. Model predictions further demonstrated the possible existence of chiral amplification if peptide self-replication is performed under heterochiral reaction conditions. Pointing into the direction of a possible cause for biomolecular homochirality, it was found that in open flow reactors, keeping the system under non-equilibrium conditions, a remarkable amplification of enantiomeric excess could be achieved. According to our modeling, this is due to a chiroselective autocatalytic effect and a meso-type separation process both of which are assumed to be intrinsic for the underlying dynamics of heterochiral peptide self-replication.     

Kinetic analysis of artificial peptide self-replication. Part I: the homochiral case

Computational kinetic analysis of a lately discovered homochiral peptide self-replicator is presented. A 6-step kinetic model was designed that addresses the main reactions and hydrophobic interactions involved in this template-directed, autocatalytic system and that gave rise to excellent fitting of 4 previously published independent experimental series. The model sheds light on the mechanistic principle of the reaction system and illustrates directly a number of dynamic properties such as the observed autocatalytic efficiency. It was found that the dynamics are basically governed by two reversible hydrophobic interactions: between the template and a peptide fragment and between two template species. The later association was determined to be considerably more favored, which leads to the predominant presence of the catalytically inactive template dimer in the reaction system. Our results show that the involvement of a template trimer is not necessary to obtain the observed fittings.     

Kinetics of Ca2+-induced fusion of cardiolipin-phosphatidylcholine vesicles: correlation between vesicle aggregation, bilayer destabilization, and fusion

We have investigated the kinetics of Ca2+-induced aggregation and fusion of large unilamellar vesicles composed of an equimolar mixture of bovine heart cardiolipin and dioleoylphosphatidylcholine. Mixing of bilayer lipids was monitored with an assay based on resonance energy transfer (RET) and mixing of aqueous vesicle contents with the Tb/dipicolinate assay. The results obtained with either assay were analyzed in terms of a mass action kinetic model, providing separate rate constants for vesicle aggregation and for the fusion reaction proper. At different Ca2+ concentrations, either at 25 degrees C or at 37 degrees C, aggregation rate constants derived from the data obtained with the RET assay were the same as those derived from the Tb/dipicolinate data, indicating that mixing of bilayer lipids occurred only during vesicle aggregation events that resulted in mixing of aqueous contents as well. At 25 degrees C, identical fusion rate constants were obtained with either assay, indicating that at this temperature the probability of lipid mixing and that of aqueous contents mixing, occurring after vesicle aggregation, were the same. The fusion rate constants for the RET assay increased more steeply with increasing temperature than the fusion rate constants derived from the Tb/dipicolinate data. As a result, at 37 degrees C the tendency of the vesicles, after aggregation, to mix lipids was slightly higher than their tendency to mix aqueous contents. The aggregation rate constants increased steeply with Ca2+ concentrations increasing in a narrow range (9.5-11 mM), indicating that, in addition to a Ca2+-dependent charge neutralization on the vesicle surface, structural changes in the lipid bilayer are involved in the aggregation process.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetics of pressure inactivation at subzero and elevated temperature of lipoxygenase in crude green bean (Phaseolus vulgaris L.) extract

Lipoxygenase (LOX) in crude green bean extract was irreversibly inactivated by pressure treatments combined with subzero or elevated temperature. LOX inactivation was described accurately assuming a first-order reaction. In the entire pressure-temperature domain studied (200 to 700 MPa and -10 to 60 degrees C), an increase in pressure at constant temperature enhanced the LOX inactivation rate, whereas at constant pressure, an increase in reaction rate was obtained by either increasing or decreasing temperature at 20 degrees C. At elevated pressure, LOX exhibited the greatest stability around 20 degrees C. Also the pressure dependence of the inactivation rate constants for LOX was the highest around 20 degrees C. On the basis of the estimated LOX inactivation rate constants, an iso-rate contour diagram as a function of pressure and temperature was constructed, and an empirical mathematical model describing the combined pressure-temperature dependence of the LOX inactivation rate constants was formulated.     

Evaluation of the kinetic parameters of the activation of trypsinogen by trypsin

Kinetic analysis of the mechanism of trypsinogen activation by trypsin under rapid equilibrium conditions and certain relationships between the rate constants are presented. The kinetic equations are valid from the beginning of the reaction. In addition, we suggest a procedure, based on the above equations, for the evaluation of the kinetic parameters of the reaction. This procedure is applied to a set of experimental data collected during the activation of bovine trypsinogen by trypsin at 30 degrees C (pH 8.1) in 0.01 M CaCl2. In this system, the amount of active enzyme increases exponentially, as expected from an autocatalytic process. The apparent rate constant, delta, governing this increase would vary linearly with the trypsinogen concentration, [Z]0, if no Michaelis complex was detectable. However, the increase in delta with [Z]0 is clearly non-linear and fits a hyperbola (delta = k2[Z]0/(Kz + [Z]0)) well.     

Reaction kinetics and modeling of the enzyme-catalyzed production of lactosucrose using beta-fructofuranosidase from Arthrobacter sp. K-1

Lactosucrose synthesis from sucrose and lactose was carried out by using beta-fructofuranosidase from Arthrobacter sp. K-1. The transfructosylation mechanism was found to be of an ordered bi-bi type in which sucrose was bound first to the enzyme and lactosucrose was released last. Hydrolysis side-reaction experiments indicated that the reactions were uncompetitively inhibited by glucose and lactose, while no inhibition by fructose was apparent. The overall reaction rates were formulated. The reaction rate constants, equilibrium constant, and dissociation and Michaelis constants were determined at 35 degrees C and 50 degrees C by fitting the experimental concentration changes with the calculated values by a nonlinear least-square method. The average relative derivation for the concentrations was 9.67%. The kinetic parameters were also calculated for 43 degrees C and 60 degrees C by assuming the Arrhenius law, and the course of reaction was predicted. The obtained reaction rate equations well represented the concentration changes during the experiment at all temperatures.     

Fusion of influenza virus with cardiolipin liposomes at low pH: mass action analysis of kinetics and extent

The kinetics and extent of low pH induced fusion between influenza virus and large unilamellar cardiolipin liposomes were investigated with an assay for lipid mixing based on fluorescence resonance energy transfer. The results were analyzed in terms of a mass action kinetic model, which views the overall fusion reaction as a sequence of a second-order process of virus-liposome adhesion or aggregation followed by the first-order fusion reaction itself. The fluorescence development during the course of the fusion process was calculated by numerical integration, employing separate rate constants for the initial aggregation step and for the subsequent fusion reaction. Analytical solutions were found for several limiting cases. Deaggregation of virus--liposome aggregates was explicitly taken into account but was found to be a minor effect under the conditions studied. The calculations gave good simulations and predictions for the kinetics and extent of fusion at different virus/liposome concentrations and ratios. At pH 5.0 and 37 degrees C, very high rate constants for aggregation and fusion were obtained, and essentially all of the virus particles were involved in the fusion process. Experiments at different virus/liposome ratios showed that fusion products may consist of a single virus particle and several liposomes but not of a single liposome and several virus particles. At pH 6.0, the rate constant for aggregation was the same as at pH 5.0, but the rate constant of fusion was about 5-fold lower, and only 25-40% of the virus particles were capable of fusing with the liposomes. The analytical procedure presented enables elucidation of the crucial role of the composition of target membrane vesicles in the initial adhesion and subsequent fusion of the virus at various pH values.     

Catalytic activity of α-chymotrypsin in enzymatic peptide synthesis in ionic liquids

The catalytic activity of α-chymotrypsin in the enzymatic peptide synthesis of N-acetyl-l-tryptophan ethyl ester with glycyl glycinamide was examined in ionic liquids and organic solvents. The water content in 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide ([emim][FSI]) affected the initial rates of peptide synthesis and hydrolysis. The activity of α-chymotrypsin was influenced by a kind of anions consisting of the same cation, [emim], when an ionic liquid was used as a solvent. The initial rate of peptide synthesis was improved 16-fold by changing from an organic solvent, acetonitrile, to an ionic liquid, [emim][FSI], at 25 °C. The activity of α-chymotrypsin in the peptide synthesis in [emim][FSI] was 17 times greater than that in acetonitrile at 60 °C, although the activity of α-chymotrypsin in the peptide synthesis gradually decreased with an increase in reaction temperature in [emim][FSI], similar to organic solvents. Moreover, α-chymotrypsin exhibited activity in [emim][FSI] and [emim][PF₆] at 80 °C.     

Effect of increased temperatures on RNA and protein synthesis in the cells of a synchronous Candida utilis culture

The rate of incorporation of labeled precursors for RNA ([14C]uracil) and protein ([14C]DL-leucine) into the cells of the synchronous culture of Candida utilis VKMY-1668 (the optimum temperature of growth, 31--32 degrees C) was studied as a function of different temperatures (28, 31, 32, 34, 36, 38, and 41 decrees C). The yeast was grown on a simple mineral medium containing glycerol. RNA synthesis was found to be more susceptible to elevated temperature than protein synthesis: the maximum rate of incorporation was registered at 32--34 degrees C for [14C]DL-leucine and only at 32 degrees C for [14C]uracil (the rate of its incorporation at 34 degrees C decreased by 50% as compared to that at 32 degrees C). The rate of incorporation of [14C]uracil at 34 degrees C reached 100% (the rate at 32 degrees C) when yeast autolysate was added to the medium, and 75 and 70%, respectively, upon the addition of DL-methionine or Mg2+ (as compared to 50% without them).     

A density functional theory study on peptide bond cleavage at aspartic residues: direct vs cyclic intermediate hydrolysis

In this work, peptide bond cleavages at carboxy- and amino-sides of the aspartic residue in a peptide model via direct (concerted and step-wise) and cyclic intermediate hydrolysis reaction pathways were explored computationally. The energetics, thermodynamic properties, rate constants, and equilibrium constants of all hydrolysis reactions, as well as their energy profiles were computed at the B3LYP/6-311++G(d,p) level of theory. The result indicated that peptide bond cleavage of the Asp residue occurred most preferentially via the cyclic intermediate hydrolysis pathway. In all reaction pathways, cleavage of the peptide bond at the amino-side occurred less preferentially than at the carboxy-side. The overall reaction rate constants of peptide bond cleavage of the Asp residue at the carboxy-side for the assisted system were, in increasing order: concerted < step-wise < cyclic intermediate.     

Soluble high molecular weight derivatives of pancreatic inhibitors. Kinetic-thermodynamic studies of inhibitors linked to differently charged matrices]

The effects of electrostatic charge of the matrix on the pH-dependence of interactions of commercial trypsin with preparations of pancreatic inhibitor modified by soluble polysaccharide coupling were studied. It was shown that the rate constants of trypsin association with native and modified pancreatic inhibitor preparations as well as the rate constants of dissociation of their complexes and, consequently, the inhibition constants are identical. The invariability of the rate constants for the association reaction after the increase in the molecular weight of pancreatic inhibitor may be probably accounted for by the fact that the limiting step of a stable trypsin-inhibitor complex formation is not controlled by diffusion. Thermal denaturation of pancreatic inhibitor preparations modified by binding to polysaccharides (pH 4.7--8.0, 97 degrees C) suggests an essential role of the negative charge of matrix in stabilization of the protein inhibitor globule.     

An autocatalytic model for bacterial spore germination.

The sigmoidal response observed in kinetic studies of germinating bacterial spores, using nephelometric techniques and phase contrast microscope photometry, is analysed by postulating an autocatalytic process. A scheme A to B to C, where B catalyses the degradation of A, is applied to describe the response accurately by three rate constants. The autocatalytic model is compared with previous proposals for quantifying germination studies and for interpreting the effect of different experimental conditions on initiation of germination. Its effectiveness is demonstrated by quantifying published results for a germinating single spore determined by phase contrast microscopy, and nephelometric results for spore suspensions, including the effect of temperature on the rate of initiation of germination. Although developed for quantitative analysis of spore germination, the model is applicable to other autocatalytic phenomena. To assist the experimentalist, a simple accurate method for deriving the three constants specifying the sigmoidal characteristic is described.     

Ca2+-induced fusion of phosphatidylserine vesicles: mass action kinetic analysis of membrane lipid mixing and aqueous contents mixing

We have investigated the initial kinetics of Ca2+-induced aggregation and fusion of phosphatidylserine large unilamellar vesicles at 3, 5 and 10 mM Ca2+ and 15, 25 and 35 degrees C, utilizing the Tb/dipicolinate (Tb/DPA) assay for mixing of aqueous vesicle contents and a resonance energy transfer (RET) assay for mixing of bilayer lipids. Separate rate constants for vesicle aggregation as well as deaggregation and for the fusion reaction itself were determined by analysis of the data in terms of a mass action kinetic model. At 15 degrees C the aggregation rate constants for either assay are the same, indicating that at this temperature all vesicle aggregation events that result in lipid mixing lead to mixing of aqueous contents as well. By contrast, at 35 degrees C the RET aggregation rate constants are higher than the Tb/DPA aggregation rate constants, indicating a significant frequency of reversible vesicle aggregation events that do result in mixing of bilayer lipids, but not in mixing of aqueous vesicle contents. In any conditions, the RET fusion rate constants are considerably higher than the Tb/DPA fusion rate constants, demonstrating the higher tendency of the vesicles, once aggregated, to mix lipids than to mix aqueous contents. This possibly reflects the formation of an intermediate fusion structure. With increasing Ca2+ concentrations the RET and the Tb/DPA fusion rate constants increase in parallel with the respective aggregation rate constants. This suggests that fusion susceptibility is conferred on the vesicles during the process of vesicle aggregation and not solely as a result of the interaction of Ca2+ with isolated vesicles. Aggregation of the vesicles in the presence of Mg2+ produces neither mixing of aqueous vesicle contents nor mixing of bilayer lipids.     

Kinetics and modeling of temperature effects on batch xanthan gum fermentation

Batch fermentation kinetics of xanthan gum production from glucose by Xanthomonas campestris at temperatures between 22 degrees C and 35 degrees C were studied to evaluate temperature effects on cell growth and xanthan formation. These batch xanthan fermentations were modeled by the logistic equation for cell growth, the Luedeking-Piret equation for xanthan production, and a modified Luedeking-Piret equation for glucose consumption. Temperature dependence of the parameters in this model was evaluated. Growth-associated rate constants increased to a maximum at approximately 30 degrees C and then decreased to zero at approximately 35 degrees C. This temperature effect can be modeled using a square-root model. On the contrary, non-growth-associated rate constants increased with increasing temperature, following the Arrhenius relationship, in the entire temperature range studied. The model developed in this work fits the experimental data very well and can be used in a simulation study. However, due to the empirical nature of the model, the parameter values need to be reevaluated if the model is to be applied to different growth conditions.     

Synthesis of aromatic nitrogen mustard agents and analysis of their alkylation activity at physiological pH and temperature

A Structure Activity Relationship (SAR) study was accomplished with six aromatic compounds which have a nitrogen mustard (N-mustard) substituent. N-mustard agents are very important for the clinical treatment of many types of cancers. All N-mustard agents synthesized alkylated a nucleophilic primary amine (p-chloroaniline) in aqueous solvent at pH 7.4 and 37 degrees C. Rate constants and rate equations were determined for the alkylation reactions by monitoring the formation of a fluorescent complex formed when fluorescamine complexes the unreacted p-chloroaniline. Fluorescamine complexation of the unreacted primary amine halts the alkylation reaction and allows the determination of remaining unreacted primary amine, which in turn permits the determination of rate constants and rate equations. The fluorescamine-amine complex shows a strong absorbance peak at a wavelength of 400 nanometers in aqueous solvent. The molar absorptivity (epsilon) was calculated to be 18.37 L/(mole x cm). First order rate constants ranged from 0.513E-2 minute(-1) to 1.32E-2 minute(-1) with second order rate constants from 2.85E-2 (M x minute)(-1) to 4.78E-2 (M x minute)(-1). The aromatic compounds included benzoic acid, m-chlorobenzoic acid, hydrocinnamic acid, m-toluic acid, and 3,4-dimethoxybenzoic acid. The synthesis procedure produced the N-mustard agents at > or = 90% yield and high purity. Partition coefficient Log(Kow)Log P values ranged from 2.66 to 4.18. The N-mustard agents consisted of greyish-yellow crystals which retained alkylation activity for more than ten weeks when stored at -10 degrees C and were soluble in water at 25 degrees C and 37 degrees C.     

Thermodynamic extremal principles in evolution

Summary An evolutionary ecosystem may be described in terms of a quasi autocatalytic model, i.e. in terms of a sequence of different autocatalytic systems. Such a sequence can exhibit considerable evolutionary change (for example, adjustment of various rate constants) even if the dissipation function remains essentially the same. Under these conditions the dissipation is always a monotonically increasing function of the concentration of catalyst (biomass) and certain rate constants (the catalytic capacity). Biomass and catalytic capacity are complementary in the sense that the quasi autocatalytic system always assumes a steady state by varying these quantities in the opposite direction (all other conditions remaining constant). This means that evolutionary systems cannot exhibit orthogenetic increases in both rate of operation and biomass, at least within any given evolutionary epoch. This has implications for the importance of spatial heterogeneity in stabilizing the behavior of evolutionary systems.     

Reactivity of thiols towards derivatives of 2- and 6-methyl-1,4-naphthoquinone bioreductive alkylating agents

The stoichiometry and kinetics of the anaerobic reactions between some thiols and derivatives of 2- and 6-methyl-1,4-naphthoquinones in water were measured using stopped flow spectrophotometry. The stoichiometry of the reaction with representative compounds was 1:2 thiol:quinone, a finding consistent with the formation of a hydroquinone as well as a thioether in the reaction. The first-order dependence of rate on thiol concentration, and the pH-dependent rate constants indicated that the thiolate anion was involved in the rate-limiting step, with rate constants at pH 7.6 generally increasing in the order glutathione (GSH) less than cysteamine less than dithiothreitol (DTT) less than cysteine. Despite the lower reactivity of GSH, the half-lives of the uncatalyzed conjugation reaction of these quinones at typical biological concentrations of GSH (e.g. 2 mM) ranged from about 2.0 to 20 s at pH 7.6 and 25 degrees C. The implications of these reactions in the use of naphthoquinones as potential bioreductive alkylating agents and as hypoxic cell radiosensitizers are discussed.     

Catalytic activity of beta-amylase from barley in different pressure/temperature domains

The depolymerization of starch by beta-amylase during exposure to hydrostatic pressure up to 700 MPa and within a temperature range from 20 to 70 degrees C has been investigated. Inactivation of the enzyme as well as alterations in conversion speed in response to combined pressure-temperature treatments were assessed by analyzing the kinetic rate constants. At 200 MPa a significant stabilization of the enzyme against heat inactivation was observed. However, high pressure also impedes the catalytic reaction and a progressive reduction of the conversion rate constants with increasing pressure was found at all temperatures investigated. For the overall reaction of maltose liberation from soluble starch in ACES buffer at pH 5.6 an optimum was identified at 106 MPa and at 63 degrees C, which is approximately 7 degrees C above the local maximum at ambient pressure (0.1 MPa). Gelatinization of nonsoluble starch granules in response to pressure-temperature (p-T) treatment has been inspected by phase-contrast microscopy and yielded circular curves of identical effect in the p-T plane.     

Inhibition of cell surface receptor-bound plasmin by alpha 2-antiplasmin and alpha 2-macroglobulin.

The purpose of this investigation was to characterize the reaction of alpha 2-antiplasmin (alpha 2AP) and alpha 2-macroglobulin (alpha 2M) with human plasmin bound to rat C6 glioma cells and human umbilical vein endothelial cells (HUVECs). Binding of plasmin (0.1 microM) to C6 cells at 4 degrees C did not cause cell detachment, decrease viability or change cell morphology. The KD and Bmax for the binding of diisopropyl phosphoryl plasmin (DIP-plasmin) to C6 cells were 0.9 microM and 2.6 x 10(6) sites/cell. The dissociation rate constants (koff) for 125I-plasmin were 9.7 x 10(-4) and 4.0 x 10(-4) s-1 at 4 degrees C in the presence and absence of 0.3 microM DIP-plasmin, respectively. Similar constants were determined for 125I-plasminogen and 125I-DIP-plasmin. Neither alpha 2AP nor alpha 2M affected the dissociation of DIP-plasmin. C6 cell-associated 125I-plasmin reacted slowly with alpha 2AP; however, the inhibition rate constants exceeded the koff. alpha 2AP-plasmin complex formed after the plasmin dissociated into solution (reaction pathway 1) and by direct reaction of alpha 2AP with cell-associated enzyme (reaction pathway 2). High concentrations of alpha 2AP favored pathway 2. C6 cell-associated plasmin was also protected from inhibition by alpha 2M. While the same pathways were probably involved in this reaction, alpha 2M was less effective than alpha 2AP as an inhibitor of nondissociated plasmin (pathway 2). When C6 cell-bound plasmin reacted with alpha 2AP, alpha 2AP-plasmin complex was recovered primarily in the medium, suggesting dissociation of complexes formed on the cell surface. Plasmin-receptor dissociation and inhibition experiments were performed at 22 degrees and 37 degrees C, confirming the conclusions of the 4 degrees C studies. Comparable results were also obtained using HUVEC cultures. These studies demonstrate that cell-associated plasmin is protected from inhibition by alpha 2M as well as alpha 2AP. At least two reaction pathways may be demonstrated for the inhibition of plasmin that is initially receptor-bound; however, neither pathway is highly effective, accounting for the "plasmin-protective" activity of the cell surface.