An explicit expression for determining cometabolism kinetics using progress curve analysis

We present an explicit expression for describing the kinetics of cometabolic biotransformation of environmental pollutants. This expression is based on the Lambert W function and explicitly relates the substrate concentration, S, to time, t, the two experimentally measured variables. This explicit relationship simplifies kinetic parameter estimation as differential equation solution and iterative estimation of the substrate concentration are eliminated. The applicability of this new expression for nonlinear kinetic parameter estimation was first demonstrated using noise containing synthetic data where final estimates of the kinetic parameters were very close to their actual values. Subsequently 1.1.1-trichloroethane degradation data at initial concentrations of 750 and 375 μM were described using the explicit expression resulting in r and K(s) estimates of 0.26 μM/mg d and 28.08 μM and 0.30 μM/mg d and 28.70 μM, respectively, very similar to 0.276 μM/mg d and 31.2 μM, respectively, that were reported in the original study. The new explicit expression presented in this study simplifies estimation of cometabolic kinetic parameters and can be easily used across all computational platforms thereby providing an attractive alternative for progress curve analysis.     

NMR for direct determination of K(m) and V(max) of enzyme reactions based on the Lambert W function-analysis of progress curves

(1)H NMR spectroscopy was used to follow the cleavage of sucrose by invertase. The parameters of the enzyme's kinetics, K(m) and V(max), were directly determined from progress curves at only one concentration of the substrate. For comparison with the classical Michaelis-Menten analysis, the reaction progress was also monitored at various initial concentrations of 3.5 to 41.8mM. Using the Lambert W function the parameters K(m) and V(max) were fitted to obtain the experimental progress curve and resulted in K(m)=28mM and V(max)=13μM/s. The result is almost identical to an initial rate analysis that, however, costs much more time and experimental effort. The effect of product inhibition was also investigated. Furthermore, we analyzed a much more complex reaction, the conversion of farnesyl diphosphate into (+)-germacrene D by the enzyme germacrene D synthase, yielding K(m)=379μM and k(cat)=0.04s(-1). The reaction involves an amphiphilic substrate forming micelles and a water insoluble product; using proper controls, the conversion can well be analyzed by the progress curve approach using the Lambert W function.     

Simultaneous analysis of microbial identity and function using NanoSIMS

Identifying the function of uncultured microbes in their environments today remains one of the main challenges for microbial ecologists. In this article, we describe a new method allowing simultaneous analysis of microbial identity and function. This method is based on the visualization of oligonucleotide probe-conferred hybridization signal in single microbial cells and isotopic measurement using high-resolution ion microprobe (NanoSIMS). In order to characterize the potential of the method, an oligonucleotide containing iodized cytidine was hybridized on fixed cells of Escherichia coli cultured on media containing different levels of ¹³C or ¹⁵N. Iodine signals could clearly be localized on targeted cells and the isotopic enrichment could be monitored at the single-cell level. The applicability of this new technique to the study of in situ ecophysiology of uncultured microorganisms within complex microbial communities is illustrated.     

A convenient analysis of Michaelis enzyme kinetic progress curves based on second derivatives

A simple method is described for the estimation of the Michaelis parameters, K_m and V_m, from a single progress curve at a single substrate concentration without the need to follow the reaction to completion. By measuring the substrate concentration and the time when the second derivative is at a minimum, K_m and V_m can be easily obtained.     

Experimental design for optimal parameter estimation of an enzyme kinetic process based on the analysis of the Fisher information matrix

The investigation of enzyme kinetics is increasingly important, especially for finding active substances and understanding intracellular behaviors. Therefore, the determination of an enzyme's kinetic parameters is crucial. For this a systematic experimental design procedure is necessary to avoid wasting time and resources. The parameter estimation error of a Michaelis-Menten enzyme kinetic process is analysed analytically to reduce the search area as well as numerically to specify the optimum for parameter estimation. From analytical analysis of the Fisher information matrix the fact is obtained, that an enzyme feed will not improve the estimation process, but substrate feeding is favorable with small volume flow. Unconstrained and constrained process conditions are considered. If substrate fed-batch process design is used instead of pure batch experiments the improvements of the Cramer-Rao lower bound of the variance of parameter estimation error reduces to 82% for mu(max) and to 60% for K(m) of the batch values in average.     

A new plot for the kinetic analysis of dead-end enzyme inhibitors

A new procedure to characterize reversible dead-end inhibitors is presented. Preliminary identification of the inhibitor type is made by plotting vo/vi against the inhibitor concentration at different substrate concentrations. The inhibition constants for competitive, uncompetitive and mixed dead-end inhibitors are determined by secondary plots of l/(slope) vs [S], l/(slope) vs l/[S] and (slope)(Ks + [S] vs [S] respectively. These secondary plots render straight lines only for their corresponding type of inhibitor. For noncompetitive inhibitors all the secondary plots used yield straight lines. Therefore, the application of this plotting procedure leads to unambiguous diagnosis of the inhibitor type. An important feature of the procedure presented here is that the variable used (vo/vi) is independent on Vmax values. Therefore, experimental values obtained from enzyme preparations showing significant differences in their specific activities -i.e. enzyme coming from different purification steps- can be used.     

Mechanistic and kinetic analysis of the DcpS scavenger decapping enzyme

Decapping is an important process in the control of eukaryotic mRNA degradation. The scavenger decapping enzyme DcpS functions to clear the cell of cap structure following decay of the RNA body by catalyzing the hydrolysis of m(7)GpppN to m(7)Gp and ppN. Structural analysis has revealed that DcpS is a dimeric protein with a domain-swapped amino terminus. The protein dimer contains two cap binding/hydrolysis sites and displays a symmetric structure with both binding sites in the open conformation in the ligand-free state and an asymmetric conformation with one site open and one site closed in the ligand-bound state. The structural data are suggestive of a dynamic decapping mechanism where each monomer could alternate between an open and closed state. Using transient state kinetic studies, we show that both the rate-limiting step and rate of decapping are regulated by cap substrate. A regulatory mechanism is established by the intrinsic domain-swapped structure of the DcpS dimer such that the decapping reaction is very efficient at low cap substrate concentrations yet regulated with excess cap substrate. These data provide biochemical evidence to verify experimentally a dynamic and mutually exclusive cap hydrolysis activity of the two cap binding sites of DcpS and provide key insights into its regulation.     

Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model

Journal of Mathematical Biology - Despite numerous studies of epidemiological systems, the role of seasonality in the recurrent epidemics is not entirely understood. During certain periods of the...     

ENZO: a web tool for derivation and evaluation of kinetic models of enzyme catalyzed reactions

We describe a web tool ENZO (Enzyme Kinetics), a graphical interface for building kinetic models of enzyme catalyzed reactions. ENZO automatically generates the corresponding differential equations from a stipulated enzyme reaction scheme. These differential equations are processed by a numerical solver and a regression algorithm which fits the coefficients of differential equations to experimentally observed time course curves. ENZO allows rapid evaluation of rival reaction schemes and can be used for routine tests in enzyme kinetics. It is freely available as a web tool, at http://enzo.cmm.ki.si.     

pH dependence of kinetic parameters for oxalacetate decarboxylation and pyruvate reduction reactions catalyzed by malic enzyme

Both chicken liver NADP-malic enzyme and Ascaris suum NAD-malic enzyme catalyze the metal-dependent decarboxylation of oxalacetate. Both enzymes catalyze the reaction either in the presence or in the absence of dinucleotide. The presence of dinucleotide increases the affinity of oxalacetate for the chicken liver NADP-malic enzyme, but this information could not be obtained in the case of A. suum NAD-malic enzyme because of the low affinity of free enzyme for NAD. The kinetic mechanism for oxalacetate decarboxylation by the chicken liver NADP-malic enzyme is equilibrium ordered at pH values below 5.0 with NADP adding to enzyme first. The Ki for NADP increases by a factor of 10 per pH unit below pH 5.0. An enzyme residue is required protonated for oxalacetate decarboxylation (by both enzymes) and pyruvate reduction (by the NAD-malic enzyme), but the beta-carboxyl of oxalacetate must be unprotonated for reaction (by both enzymes). The pK of the enzyme residue of the chicken liver NADP-malic enzyme decreases from a value of 6.4 in the absence of NADP to about 5.5 with Mg2+ and 4.8 with Mn2+ in the presence of NADP. The pK value of the enzyme residue required protonated for either oxalacetate decarboxylation or pyruvate reduction for the A. suum NAD-malic enzyme is about 5.5-6.0. Although oxalacetate binds equally well to protonated and unprotonated forms of the NADP-enzyme, the NAD-enzyme requires that oxalacetate or pyruvate selectively bind to the protonated form of the enzyme. Both enzymes prefer Mn2+ over Mg2+ for oxalacetate decarboxylation.(ABSTRACT TRUNCATED AT 250 WORDS)     

An on-line method for the collection and analysis of quasi-steady-state kinetic data for enzyme-catalyzed reactions.

A special mixing device for initiating enzyme-catalyzed reactions is used to rapidly achieve an unperturbed quasi-steady state. An on-line computer is employed to sample the initial conditions, the mixing time, and concentrations that change as a function of time during this quasi-steady state phase. A statistical method for estimating initial, quasi-steady state rates from the time course of the enzyme-catalyzed reaction is described. Practical considerations for using this parameter estimation system lead to the conclusion that for the enzyme-catalyzed reaction tested, the extent overall reaction should be above .2% for high initial substrate concentrations, and above 1% for initial substrate concentrations in the range of the Michaelis constant. Application of this method to a typical enzyme-catalyzed reaction suggests that objective estimates of initial rates from a given set of concentrations and corresponding times can be obtained with a standard error in the range of 2–3%, but that reproducibility is not better than about 10%. When this procedure was used to estimate initial rates for the glycerol dehydrogenase-catalyzed oxidation of glycerol by NAD, it was found that this enzyme did not behave according to the classical “Michaelis-Menten” mechanism of enzyme action.     

A luminol chemiluminescence method for sensing histidine and lysine using enzyme reactions

The analysis of free amino acids in urine and plasma is useful for estimating disease status in clinical diagnoses. Changes in the concentration of free amino acids in foods are also useful markers of freshness, nutrition, and taste. In this study, the specific interaction between aminoacyl–tRNA synthetase (aaRS) and its corresponding amino acid was used to measure amino acid concentrations. Pyrophosphate released by the amino acid–aaRS binding reaction was detected by luminol chemiluminescence; the method provided selective quantitation of 1.0–30 μM histidine and 1.0–60 μM lysine.     

Simple kinetic models explaining critical phenomena in enzymatic reactions with isomerization of the enzyme and substrate

Kinetic models for enzyme reactions are considered which take into account enzyme and substrate isomerization. Application of graph-theoretic methods allows to reveal fragments in schemes which may induce multiple stead-states or concentrational selfoscillations. The role of substrate isomers in the inhibition of enzyme isomers to produce critical phenomena is considered. The boundaries of parameter domains for critical phenomena are estimated. It is shown that the controlled change in concentrations of substrate and enzyme isomers may be important in regulation of enzyme systems, if different enzyme isomers are inhibited mainly by different substrate isomers. The models are used for interpretation of possible critical phenomena in the open reaction catalyzed by lactate dehydrogenase. It is shown that lactate dehydrogenase may act as a trigger in carbohydrate metabolism by changing "critically" its activity in relation to changes in pH and pyruvate fluxes. Slow enzyme inhibition by enolpyruvate is suggested as a possible reason for glycolytic oscillations.     

Intestinal function and body growth of broiler chickens on diets based on maize dried at different temperatures and supplemented with a microbial enzyme

A study was conducted to evaluate the effects of varying drying temperature (Fresh, 85, 95 or 105 degrees C) on the nutritive value of maize and response of broiler chickens to diets based on such grain, and supplemented with a microbial enzyme (Avizyme 1500). The chemical composition of the grain was affected by drying temperature. Starch and amylopectin contents were increased while there was a reduction in amylose content. These changes were expected to underlie the response of chicks to the diets. Total feed intake over 28 days was increased (P < 0.05) as a result of heat-treating the maize up to 95 degrees C. The final body weight of chicks on the diet based on fresh maize was improved (P < 0.05) by the microbial enzyme supplement (MES). There was no effect of the enzyme supplement on body weight when assessed at earlier ages. Over the entire feeding period, feed conversion efficiency (FCE) declined (P < 0.001) with increasing oven temperature, regardless of the supplementation with the microbial enzyme. Body weight was influenced (P < 0.05) by the microbial enzyme only when assessed over the entire trial period. The weight of visceral organs, protein content and activities of pancreatic and jejunal digestive enzymes were unaffected by grain heat treatment or MES. The ileal digestibility of calcium was reduced (P < 0.001) on diets based on fresh maize and maize that was oven-dried at 105 degrees C. Heat-treatment also improved (P < 0.05) the ileal digestibility of phosphorus in chicks on the diets without MES. There were no effects of grain heat treatment or MES on the ileal digestibility of energy, protein, Ca and amino acids. The results indicate some variations in grain quality as a result of heat treatment but the differences were not significant enough to stimulate major responses to the MES. Further studies should examine samples from commercial drying processes or samples obtained from a closer simulation of commercial conditions, to arrive at more practical conclusions.     

Evidence for discrete cell kinetic subpopulations in mouse epidermis based on mathematical analysis

Abstract. Continuous (repeated) labelling studies in mouse epidermis indicate that nearly all cells are labelled after about 100 hr. Percentage labelled mitoses studies ([³H]TdR at 15.00 and 03.00 hours) have a first peak that does not reach 100% and has a half-width of about 10 hr. Small second and third peaks can be detected at about 90 and 180 hr, respectively. The changes with time in the number of labelled cells show a difference dependent on the time of day of [³H]TdR administration. Both curves show an early doubling in labelled cells which then decline, forming a peak of labelled cells. A second peak occurs at about 120 hr. This is followed by a progressive decline with no further peaks until values of about 1% labelling are obtained at 340 hr.
These experiments have been investigated mathematically. A computer programme has been devized that permits all three types of experiments to be analysed simultaneously. More importantly, it can analyse situations with a heterogeneity in cell cycle parameters in all proliferative subpopulations.
Various models for epidermal cell replacement have been considered. The data as a whole can best be explained if the basal layer contains at least two distinct subpopulations of cells and an exponentially decaying post-mitotic population with a half-life of about 30 hr. The proliferative sub-populations must be characterized by near integer differences in the length of cycle, the precursor (stem) compartment having the longer cycle. An inverse relationship is required for the length of S, i.e. the shortest time for the stem cells.
A full range of cell kinetic parameters can be calculated and are tabulated for the most appropriate model system which is one involving three transit proliferating subpopulations.