The correction of reaction rates in continuous fluorometric assays of enzymes

The kinetic data obtained from the action of a cathepsin D-like enzyme from Biomphalaria glabrata hepatopancreas (digestive gland) on MOCAc-Gly-Lys-Pro-Ile-Leu-Phe-Phe-Arg-Leu-Lys(DNp)-D-Arg-NH(2), was studied as a data prototype, generated by means of a fluorogenic substrate. An initial fluorescence, due to incomplete energy transfer, of about 8% of the values attained after complete substrate hydrolysis; a non-linear standard curve even at microM concentrations and an exponential decay of the steady state fluorescence of reaction product of the order of 10(-4) x s(-1) were the main analytical problems encountered. The standard curves for fluorescence of the substrate reaction product after 48 h of hydrolysis, and the reference compound MOCAc-Pro-Leu-Gly-NH(2), were fitted by polynomial approximation and the point derivates used as calibration factors. Time dependence of the calibration factor for the reaction product was -2.96 x 10(-4) a.u microM(-1) x s(-1) that is, in the same order of observed enzymic reaction rates. A mathematical treatment was devised for obtaining rates corrected for errors derived from the three analytical problems indicated. The method is of general application in continuous fluorometric assays, irrespective of the particular enzyme used, but of special value for substrates that present significant initial fluorescence. The reaction rates were 11% higher; as calculated by means of the calibration factor [substrate]/(final-initial fluorescence intensities), which is the prevalent procedure in the literature; leading to underestimation of K(m) and overestimation of V(max).     

Coupled,continuous and discontinuous fluorometric assays for trehalase activity

Continuous and discontinuous coupled fluorometric assays which couple trehalose hydrolysis to peroxidation of the fluorogenic compounds eugenol (4-allyl-2-methoxyphenol) or p-hydroxyphenylacetic acid using glucose oxidase (EC 1.1.3.4) and peroxidase (EC 1.11.1.7) as ancillary enzymes have been developed for the measurement of trehalase (α,α′-trehalose-1-d-glucohydrolase, EC 3.2.1.28) activity from the cellular slime mold, Dictyostelium discoideum. With these methods, product formation was linear with time and the coupled reaction rate was directly proportional to the level of enzyme assayed. The validity of both the discontinuous and continuous fluorometric assays was confirmed by comparative studies with discontinuous spectrophotometric assays for glucose. Levels of glucose as low as 0.02 nmol were measurable with the discontinuous fluorometric procedures, thereby making the latter about 500-fold more sensitive than routine spectrophotometric assays. With the continuous fluorometric trehalase assays, the lower limits of sensitivity correspond to enzyme levels of the order of 5 to 25 μunits. The high level of sensitivity achieved with these assays makes them ideally well suited for: (i) elucidation of the regulatory mechanisms underlying the dramatic changes in trehalase activity that occur during spore germination and cellular aggregation in Dictyostelium and (ii) characterization studies involving electrophoresis or isoelectric focusing of trehalase in solid matrices in which enzymatic activity is measured either quantitatively in gel eluates or qualitatively by the in situ localization of the enzyme histochemically.     

Substrate specificity of the human matrix metalloproteinase stromelysin and the development of continuous fluorometric assays.

To probe the specificity of the metalloendoproteinase stromelysin toward peptide substrates, we determined kc/Km values for the stromelysin-catalyzed hydrolyses of peptides whose design was based loosely on the structure of a known SLN substrate, substance P (Arg-Pro-Lys-Pro-Gln-Gln-Phe-Phe-Gly-Leu-MetNH2, hydrolysis at Gln-Phe, kc/Km = 1700 M-1 s-1). Several noteworthy points emerge from this study: (i) Catalytic efficiency is dependent on peptide chain length with N-terminal truncation of substance P resulting in more pronounced rate-constant reductions than C-terminal truncation. These results suggest the existence of an extended active site for stromelysin. (ii) Preferences at positions P3, P2, P1, P1', and P2' are for the hydrophobic amino acids Pro, Leu, Ala, Nva, and Trp, respectively. (iii) Investigation of specificity at P3' supports our earlier hypothesis that SLN has a requirement for a hydrogen-bond donor at this position in its substrates. Based on these observations, we designed and had synthesized the fluorogenic substrate N-(2,4-dinitrophenyl)Arg-Pro-Lys-Pro-Leu-Ala-Nva-TrpNH2, whose stromelysin-catalyzed hydrolysis can be monitored continuously (kc/Km = 45,000 M-1 s-1).     

An evaluation of fluorometric proteinase assays which employ fluorescamine

The sensitivity and utility of proteinase assays employing fluorescamine, a compound which reacts with primary amines to form a fluorescent adduct, was assessed. As little as 1 ng of purified trypsin or clostridiopeptidase A could be detected within 3 h of incubation at 37 degrees C, using casein or gelatin as substrates. Increasing the incubation period to 18 h permitted the detection of 250 pg of each enzyme. When gelled collagen was utilized as substrate, the sensitivity to clostridiopeptidase A was reduced to 2.5 ng at 3 h and 500 pg at 18 h. The techniques could be used to measure the gelatinase, caseinase, and collagenase activities of culture media conditioned by synovial tissue. The main disadvantage of this assay is its susceptibility to interference by compounds which fluoresce or quench. This, in turn, necessitates additional blanks, which may render the assay tedious.     

Two time-resolved fluorometric high-throughput assays for quantitation of GDP-L-fucose

Two rapid and simple procedures for the quantitative analysis of GDP-l-fucose (GDP-Fuc) are described. The methods are based on time-resolved fluorescence and microplate assay technology. The first assay relies on measuring the enzyme activity of alpha1, 3-fucosyltransferase. In this assay, transfer of fucose from GDP-Fuc converts sialyllactosamine to sialyl Lewis x tetrasaccharide, which is detected and quantified by relevant antibodies on a microplate. The formation of the reaction product is directly dependent on the presence of GDP-Fuc in the concentration range of 10-10,000 nM. In the second method GDP-Fuc inhibits the binding of fucose-specific Aleuria aurantia lectin to fucosylated glycan on a microwell. The lectin-based assay is less sensitive than the enzyme assay, but it is cheaper and faster. We used these assays in monitoring the amount of GDP-Fuc in crude lysates of transgenic yeast, which expresses the enzymes producing GDP-Fuc. The newly developed assays are versatile and applicable to measure also other nucleotide sugars or glycosyltransferase activities in a high-throughput manner.     

Immobilized enzymes: electrokinetic effects on reaction rates in a porous medium

The effect of the internal diffusion and electrical surface charge on the overall rate of a reaction catalyzed by an enzyme immobilized on a porous medium are examined. Effectiveness factors have been calculated which compare the global reaction rate to that existing in the absence of the internal diffusion and/or the electrical field. The surface charge, assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme, generates an electrical double layer at the pore surface. The double-layer potential is governed by the Poisson-Boltzmann equation. It is shown that the diffusion potential can be characterized by a modulus which depends upon the surface reaction rate, the charges and diffusivities of the substrate and products, the ionic strength, and the pore dimensions. The flux of a charged species in the pore occurs under the influences of the concentration gradient and the electrical potential gradient. The governing equations are solved by an iterative numerical method. The effects of pH, enzyme concentration, and substrate concentration on the rates of two different hydrolysis reactions catalyzed by immobilized papain are examined. The release of H(+) in one of the reactions causes the lowering of internal pH, and also a constancy of the internal pH when the external pH in creases beyond a certain value. The latter reaction also shows a maximum in the reaction rate with respect to enzyme concentration. The reaction not involving H(+) as a product shows a maximum in the reaction rate with respect to external pH, but a monotonic increase in the reaction rate as the enzyme concentration increases.     

Immobilized enzymes: Electrokinetic effects on reaction rates under external diffusion

The rates of reactions catalyzed by enzymes immobilized on a nonporous solid surface have been computed employing a Nernst film model. The Nernst-Planck equations for the transport of the charged substrate and product species in the film and the Poisson equation for the distribution of electrical potential are solved numerically with the appropriate boundary conditions. The electrical charge at the surface is assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme. The pH at the surface affects both the surface charge as well as the intrinsic kinetics of the enzyme-catalyzed reaction. Factors which determine the pH at the surface include the pH in the bulk solution and the release of H(+) ions in the enzyme-catalyzed reaction. The latter causes a lowering of pH at the surface, causing the reaction rate to differ from that computed assuming an equilibrium distribution of electrical potential. Another kind of nonequilibrium contribution is caused by unequal charges or diffusivities of the substrate and products, which results in a diffusion potential being set up. Two moduli are introduced to evaluate the significance of the reaction-generated lowering of pH and the diffusion potential effect. The effect of changing various parameters, e.g., reaction rate constant, substrate concentration, enzyme concentration, pH, etc., on the overall reaction rate are studied.     

Microbial production of enzymes: Nonlinear state and kinetic reaction rates estimation

The nonlinearity of the biotechnological processes and the absence of cheap and reliable instrumentation require an enhanced modelling effort and estimation strategies for the state and the kinetic parameters. This work approaches nonlinear estimation strategies for microbial production of enzymes, exemplified by using a process of lipase production from olive oil by Candida rugosa. First, by using a dynamical mathematical model of this process, an asymptotic observer which reconstructs the unavailable state variables is proposed. The design of this kind of observers is based on mass and energy balances without the knowledge of kinetics being necessary; only minimal information concerning the measured concentrations is used. Second, a nonlinear high-gain observer is designed for the estimation of imprecisely known kinetics of the bioprocess. An important advantage of this high-gain estimator is that the tuning is reduced to the calibration of a single parameter. Numerical simulations in various scenarios are provided in order to test the behaviour and performances of the proposed nonlinear estimation strategies.     

Quantitative genetics of continuous reaction norms: thermal sensitivity of caterpillar growth rates

A continuous reaction norm or performance curve represents a phenotypic trait of an individual or genotype in which the trait value may vary with some continuous environmental variable. We explore patterns of genetic variation in thermal performance curves of short-term caterpillar growth rate in a population of Pieris rapae. We compare multivariate methods, which treat performance at each test temperature as a distinct trait, with function-valued methods that treat a performance curve as a continuous function. Mean growth rate increased with increasing temperatures from 8 to 35 degrees C, was highest at 35 degrees C, and declined at 40 degrees C. There was substantial and significant variation among full-sib families in their thermal performance curves. Estimates of broad-sense genetic variances and covariances showed that genetic variance in growth rate increased more than 30-fold from low (8-11 degrees C) to high (35-40 degrees C) temperatures, even after differences in mean growth rate across temperatures were removed. Growth rate at 35 and 40 degrees C was negatively correlated genetically, suggesting a genetic trade-off in growth rate at these temperatures; this trade-off may represent either a generalist-specialist trade-off and/or variation in the optimal temperature for growth. The estimated genetic variance-covariance function (G function), the function-valued analog of the variance-covariance matrix (G matrix), was quite bumpy compared with the estimated G matrix; and results of principal component analyses of the G function were difficult to interpret. The use of orthogonal polynomials as the basis functions in current function-valued estimation methods may generate artifacts when the true G function has prominent local features, such as strong negative covariances at nearby temperatures (e.g. at 35 and 40 degrees C); this may be a particular issue for thermal performance curves and other highly nonlinear reaction norms.     

Diffusion controlled reaction rates in spheroidal geometry. Application to repressor--operator association and membrane bound enzymes

The von Smoluchowski-Debye formulae for diffusion controlled reaction rates are extended to the more general case of spheroidal geometry. Their application to the association of represser and operator is thoroughly discussed in the light of recent experiments on the lac system by Riggs et al. The conclusions suggest that the surprisingly high association rate is not essentially due to electrostatic attraction but rather to unspecific binding of represser to nonoperator DNA with subsequent diffusion along the chain.     

Production of extracellular enzymes in continuous culture

The production of bacterial enzymes in batch fermentations is compared with results obtained in continuous culture. When studying the production of α-amylase inBacillus subtilis it was found that instability of the enzyme synthesis was due to nonhomogeneity of the population rather than to “the culture’s history” (i.e. succession of several physiological states necessary for the enzyme production). The plasmid contained in the production clone was found to be the factor responsible for the α-amylase production. Predominance of the production clone or of the nonproduction one depends on the cultivation conditions used. As compared with batch cultivation the continuous production yields higher enzyme concentrations under optimal conditions and the fermentor productivity may be four to five times higher.     

The characterization of complex continuous norms of reaction

Recent focus on the array of phenotypes expressed under differing environmental conditions, or phenotypic plasticity, has led to increased understanding of its genetic basis as well as its adaptive significance. However, the quantification of plasticity has proven difficult, hampered by both the limited number of environments over which plasticity may typically be assessed and by the need to assume, a priori, the general form of reaction norms under study. Our understanding of the shapes of continuous norms of reaction and, consequently, the subtle differences that may exist in shapes among genotypes or populations is rudimentary. Here, we propose the use of the loess smoothing function to analyze complex norms of reaction and to quantify total plasticity over many environments. A thermogradient incubator offers an ideal means to provide many environments for a demonstration of the use of the loess method. We test seed germination in three populations of two monocarpic plant species for population differentiation in plasticity to temperature. First, we test for differentiation in norms of reaction to 30 temperature environments among three populations of the monocarpic perennial, Lobelia inflata . The second demonstration assesses plasticity to eight temperature environments of three populations of the arctic-alpine annual, Koenigia islandica . Our demonstration shows that the loess technique can detect significant genetic differentiation among populations in complex norms of reaction for both species studied, and suggests that the use of this procedure should be considered where the form of norms of reaction might be complex. The general applicability of the approach is discussed.     

A continuous fluorometric assay for the assessment of MazF ribonuclease activity

Plasmids maintain themselves in their bacterial host through several different mechanisms, one of which involves the synthesis of plasmid-encoded toxin and antitoxin proteins. When the plasmid is present, the antitoxin binds to and neutralizes the toxin. If a plasmid-free daughter cell arises, however, the labile antitoxin is degraded (and not replenished) and the toxin kills the cell from within. These toxin-antitoxin (TA) systems thereby function as postsegregational killing systems, and the disruption of the TA interaction represents an intriguing antibacterial strategy. It was recently discovered that the genes for one particular TA system, MazEF, are ubiquitous on plasmids isolated from clinical vancomycin-resistant enterococci (VRE) strains. Thus, it appears that small molecule disruptors of the MazEF interaction have potential as antibacterial agents. The MazF toxin protein is known to be a ribonuclease. Unfortunately, traditional methods for the assessment of MazF activity rely on the use of radiolabeled substrates followed by analysis with polyacrylamide gel electrophoresis. This article describes a simple and convenient continuous assay for the assessment of MazF activity. The assay uses an oligonucleotide with a fluorophore on the 5' end and a quencher on the 3' end, and processing of this substrate by MazF results in a large increase in the fluorescence signal. Through this assay, we have for the first time determined K(M) and V(max) values for this enzyme and have also found that MazF is not inhibited by standard ribonuclease inhibitors. This assay will be useful to those interested in the biochemistry of the MazF family of toxins and the disruption of MazE/MazF.     

Comparative sensitivities of electrophoretic assays for human enzymes

The sensitivities of 26 starch gel electrophoretic enzyme assays have been compared using HeLa human cells and A9 mouse cells grown in vitro.This research was supported by National Institutes of Health Grant No. USPHS GM 09966.