Chronocoulometric techniques in the study of computerized enzyme electrode systems

The electrochemical transient of a two-substrate enzyme electrode was studied theoretically and experimentally. Operation of such electrodes in the chronocoulometric mode leads to increased electrode sensitivity and makes possible the retrieval of useful information on transport and kinetics parameters. Digital simulation was used to solve the kinetics and transport equations and to produce the theoretical chronocoulometric response. A glucose electrode based on glucose oxidase crosslinked to different matrices was tested with air oxygen and p-benzoquinone as the cosubstrate. A computerized electrochemical system was employed for electrode potential control and data acquistion and analysis.     

Analysis and optimization of a two-substrate fermentation for xylitol production using Candida tropicalis

Xylitol, a functional sweetener, was produced from xylose using Candida tropicalisATCC 13803. A two-substrate fermentation was designed in order to increase xylitol yield and volumetric productivity. Glucose was used initially for cell growth followed by conversion of xylose to xylitol without cell growth and by-product formation after complete depletion of glucose. High glucose concentrations increased volumetric productivity by reducing conversion time due to high cell mass, but also led to production of ethanol, which, in turn, inhibited cell growth and xylitol production. Computer simulation was undertaken to optimize an initial glucose concentration using kinetic equations describing rates of cell growth and xylose bioconversion as a function of ethanol concentration. Kinetic constants involved in the equations were estimated from the experimental results. Glucose at 32 g L⁻¹ was estimated to be an optimum initial glucose concentration with a final xylose concentration of 86 g L⁻¹ and a volumetric productivity of 5.15 g-xylitol L⁻¹ h⁻¹. The two-substrate fermentation was performed under optimum conditions to verify the computer simulation results. The experimental results were in good agreement with the predicted values of simulation with a xylitol yield of 0.81 g-xylitol g-xylose⁻¹ and a volumetric productivity of 5.06 g-xylitol L⁻¹ h⁻¹. Received 16 June 1998/ Accepted in revised form 28 February 1999     

Equations of Substrate-inhibition Kinetics Applied to Pig Kidney Diamine Oxidase (DAO,E.C. 1.4.3.6)

Pig kidney diamine oxidase (DAO) and other semicarbazide-sensitive amine oxidases (SSAO) show clear substrate-inhibition kinetics and a reaction-scheme mechanism based on two substrate binding sites. We evaluated several reaction scheme mechanisms with a non-linear regression program (NCSS), estimating R², the constants of the equations and their standard errors and we determined the deviation of experimental data from theoretical equations. The best fit was obtained with a “dead end” mechanism with two binding sites. Based on this scheme, other schemes for a two-substrate reaction and for mechanisms of inhibition were constructed. These reaction schemes, even at low substrate concentration, fitted experimental data better than Michaelis-Menten kinetics, and provided information on the mechanisms of action of inhibitors. The presence of two substrate-binding sites on pig kidney DAO was confirmed by all experimental data.     

Equations of substrate-inhibition kinetics applied to pig kidney diamine oxidase (DAO, E.C. 1.4.3.6)

Pig kidney diamine oxidase (DAO) and other semicarbazide-sensitive amine oxidases (SSAO) show clear substrate-inhibition kinetics and a reaction-scheme mechanism based on two substrate binding sites. We evaluated several reaction scheme mechanisms with a non-linear regression program (NCSS), estimating R2, the constants of the equations and their standard errors and we determined the deviation of experimental data from theoretical equations. The best fit was obtained with a "dead end" mechanism with two binding sites. Based on this scheme, other schemes for a two-substrate reaction and for mechanisms of inhibition were constructed. These reaction schemes, even at low substrate concentration, fitted experimental data better than Michaelis-Menten kinetics, and provided information on the mechanisms of action of inhibitors. The presence of two substrate-binding sites on pig kidney DAO was confirmed by all experimental data.     

Lipase reaction in AOT-isooctane reversed micelles: effect of water on equilibria

The effect of water on equilibria for hydrolytic reaction in reversed micelles has been investigated using lipase as a model enzyme. The effect of water on equilibria has been ignored for hydrolase reactions in an aqueous phase. In a reversed micellar system, however, the equilibrium of the lipase reaction was changed when water was added during the hydrolytic reaction. Furthermore, equilibrium fractional conversion is affected by the initial water concentration, being shifted to higher values with higher water concentrations, with other reaction conditions being held constant, indicating that the reaction should be regarded as a two-substrate process. Equations corresponding to a two-substrate, second-order reversible model are derived and used for further analysis. The progress curves predicted from the rate equations agree very well with the experimental results under various reaction conditions. The values of the molar ratio of water to surfactant (R) which maximize the initial reaction rate and maximum fractional conversion is predictable from the derived rate equations and the resulting relationship between R and the kinetic constants.     

Qualitative analysis of a mathematical model of a open enzyme reaction

A general case of the set of two differential equations, describing an open reaction v1 leads to S v reversible E P v2 leads to, has been considered. The requirements to the character of the functions v1([S]), v2([P]) and v([S], [P]) were formulated for the case of existence and absence of alternative steady states and sustained oscillations. The formulae were derived to determine the slope of the unstable portion of the quasi-steady state characteristic. The generalized model of Monod, Wyman and Changeux has been considered as an example of v([S], [P]). It has been shown that with monotonically decreasing v1 and monotonically increasing v2, the alternative steady states and oscillations are possible only in the presence of substrate inhibition or product activation. However, under the joint action of substrate inhibition and product activation, the system will exhibit bistability rather than an oscillatory behavior. In the case of an irreversible two-substrate reaction which can be described by a similar mathematical model, inhibition by the first and second substrate is equivalent to substrate inhibition and product activation.     

Improved assay and mechanism of the reaction catalyzed by the chitin synthase from Saccharomyces cerevisiae

1. An improved filtration method is introduced to perform kinetic investigations on the chitin synthase reaction. This method is especially suited for the assay of a large number of samples necessary in enzyme kinetic studies. 2. From initial rate data the possibility could be excluded that the two-substrate reactions occurs by a random or a ping-pong mechanism. 3. Investigations of product inhibition exclude a rapid random mechanism but favour an ordered mechanism with UDP-N-acetylglucosamine as the first substrate. 4. This result was confirmed by isotope exchange studies.     

Kinetics of the selective fermentation of glucose from glucose/fructose mixtures using Saccharomyces cerevisiae ATCC 36859

The kinetics of batch fermentation during the growth of S. cerevisiae ATCC 36859 was studied in various glucose/fructose mixtures. It was found that the growth is inhibited equally by glucose and fructose even though fructose is not consumed to any large extent by the yeast under the conditions tested here. The inhibition of growth by the substrate and ethanol is represented by linear equations. These equations were combined with the MONOD expression in order to formulate equations for the biomass growth, glucose and fructose consumption and ethanol production. Parameter estimates were obtained by fitting these equations to batch fermentation data and so developing models which indicate that the growth is completely inhibited when 62 g/l ethanol is produced by the yeast, while glucose consumption and ethanol production continue up to an ethanol concentration of 152 g/l. Products containing a high concentration of fructose are best produced by using a high initial biomass concentration.     

Molecular mass determination by sedimentation velocity experiments and direct fitting of the concentration profiles.

A new method for the direct molecular mass determination from sedimentation velocity experiments is presented. It is based on a nonlinear least squares fitting procedure of the concentration profiles and simultaneous estimation of the sedimentation and diffusion coefficients using approximate solutions of the Lamm equation. A computer program, LAMM, was written by using five different model functions derived by Fujita (1962, 1975) to describe the sedimentation of macromolecules during centrifugation. To compare the usefulness of these equations for the analysis of hydrodynamic results, the approach was tested on data sets of Claverie simulations as well as experimental curves of some proteins. A modification for one of the model functions is suggested, leading to more reliable sedimentation and diffusion coefficients estimated by the fitting procedure. The method seems useful for the rapid molecular mass determination of proteins larger than 10 kDa. One of the equations of the Archibald type is also suitable for compounds of low molecular mass, probably less than 10 kDa, because this model function requires neither the plateau region nor a meniscus free of solute.     

II. Transient phase of two-substrate enzyme systems

The time dependence in the transient phase of the two-substrate enzyme systems which evolve according to the random ternary-complex, ordered ternary-complex, ping-pong bi-bi and Theorell-Chance mechanisms has been studied. With this purpose, the equations derived in paper I have been applied. This has allowed to propose a method in order to obtain the rate constant values of these enzyme reactions. In addition, we show that, from experimental knowledge of the induction periods of the ligand species, it is possible to give a method which allows to discriminate between these mechanisms.     

NMMD: Efficient Cryo-EM Flexible Fitting Based on Simultaneous Normal Mode and Molecular Dynamics atomic displacements

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.     

Moment arms and musculotendon lengths estimation for a three-dimensional lower-limb model

This paper presents a set of polynomial expressions that can be used as regression equations to estimate length and three-dimensional moment arms of 43 lower-limb musculotendon actuators. These equations allow one to find, at a low computational cost, the musculotendon geometric parameters required for numerical simulation of large musculoskeletal models. Nominal values for these biomechanical parameters were established using a public-domain musculoskeletal model of the lower limb (IEEE Trans. Biomed. Eng. 37 (1990) 757). To fit these nominal values, regression equations with different levels of complexity were generated, based on the number of generalized coordinates of the joints spanned by each musculotendon actuator. Least squares fitting was used to identify regression equation coefficients. The goodness of the fit and confidence intervals were assessed, and the best fitting equations selected.     

Kinetic modelling of aldolase-catalyzed addition between dihydroxyacetone phosphate and (S)-alaninal

This paper is focused on the development of a kinetic model for an aldolase-catalyzed reaction. The aldol addition between dihydroxyacetone phosphate (DHAP) and (S)-benzyloxycarbonyl-alaninal ((S)-Cbz-alaninal) catalyzed by the four DHAP-dependent aldolases is a promising way for the synthesis of four complementary diastereoisomers with potential biological activity. The reaction catalyzed by fuculose-1-phosphate aldolase (FucA) conducts to a synthesis product with a 100% diastereomeric excess. A kinetic model has been proposed including both the synthesis and a parallel non-desired secondary reaction. The model involved an ordered two-substrate mechanism for the synthesis and non-competitive inhibition by (S)-Cbz-alaninal and competitive inhibition by methylglyoxal byproduct in both reactions. The values of the model kinetic parameters were determined and the model validated in batch and fed-batch synthesis reactions. The obtained model could be extended to explain the behavior of other class II DHAP-dependent aldolases and exploited in simulation for reactor design purposes.     

A mathematical model of actin filament turnover for fitting FRAP data

A novel mathematical model of the actin dynamics in living cells under steady-state conditions has been developed for fluorescence recovery after photobleaching (FRAP) experiments. As opposed to other FRAP fitting models, which use the average lifetime of actins in filaments and the actin turnover rate as fitting parameters, our model operates with unbiased actin association/dissociation rate constants and accounts for the filament length. The mathematical formalism is based on a system of stochastic differential equations. The derived equations were validated on synthetic theoretical data generated by a stochastic simulation algorithm adapted for the simulation of FRAP experiments. Consistent with experimental findings, the results of this work showed that (1) fluorescence recovery is a function of the average filament length, (2) the F-actin turnover and the FRAP are accelerated in the presence of actin nucleating proteins, (3) the FRAP curves may exhibit both a linear and non-linear behaviour depending on the parameters of actin polymerisation, and (4) our model resulted in more accurate parameter estimations of actin dynamics as compared with other FRAP fitting models. Additionally, we provide a computational tool that integrates the model and that can be used for interpretation of FRAP data on actin cytoskeleton.     

Studies on the mechanism and kinetics of the 2-oxoglutarate dehydrogenase system from pig heart.

1. The kinetic properties of the 2-oxoglutarate dehydrogenase system were investigated. To this end, initial-velocity studies were carried out by the method of Fromm [(1967) Biochim. Biophys. Acta 139, 221-230]. Reciprocal plots of the results did not agree with those expected for the Hexa Uni Ping Pong mechanism previously proposed for the system. 2. The measured initial velocities were fitted to initial-rate equations corresponding to several possible mechanisms by using a computer optimization technique. Statistical analyses performed on the results of the optimization studies indicated that one mechanism was a significantly better fit to the experimental data than the other mechanisms tested. This mechanism is one in which there is a random order of binding of NAD+ and CoA and release of succinyl-CoA, although the binding of 2-oxoglutarate and release of CO2 is still given a Ping Pong mechanism, which precedes the binding of the other substrates. These conclusions were supported by NADH-inhibition studies. 3. The usefulness of the method of fitting initial-rate data to rate equations and the applicability of the proposed enzymic mechanism to the enzyme complex are discussed.     

Diagnosis of enzyme inhibition based on the degree of inhibition

In this work, a method for the diagnosis of kinetic inhibition, based on the dependence of the degree of inhibition (epsilon(i)) on the inhibitor concentration [I] and on the substrate concentration [S], is presented. Because the degree of inhibition is a ratio between rates, kinetic data are normalized by the introduction of an internal control-the rate of the uninhibited reaction. Therefore, the error associated with the kinetic measurements decreases and less experimental measurements are necessary to achieve the diagnosis. The process described, which uses graphical and/or non-linear fitting procedures, allows distinguishing between 20 different kinds of inhibition, including not only linear and hyperbolic, but also parabolic and rational 2,2 inhibitions. Rational 2,2 indicates a new type of inhibition corresponding to an incomplete parabolic inhibition, i.e. mechanistically it corresponds to an inhibitor that binds to two inhibition sites producing enzymatic complexes that are still active. In spite of its comprehensiveness, the diagnosis process is greatly facilitated by the division of the diagnosis of the inhibition in a step-by-step procedure, where only two rival models are evaluated in each step. In the non-linear fittings, the choice between rival models uses a test based on information statistics theory, the Akaike information criterion test, in order to penalize complex models that tend to be favoured in fittings. Finally, equations that allow the determination of inhibition kinetic constants were also deduced. The formalism presented was tested by examining inhibition of acid phosphatase by phosphate (a linear competitive inhibitor).     

Mathematical modelling of ethanol production from glucose/xylose mixtures by recombinant Zymomonas mobilis

A model has been developed for the fermentation of mixtures of glucose and xylose by recombinant Zymomonas mobilis strain ZM4(pZB5), containing additional genes for xylose assimilation and metabolism. A two-substrate model based on substrate limitation, substrate inhibition, and product (ethanol) inhibition was evaluated, and experimental data was compared with model simulations using a Microsoft EXCEL based program and methods of statistical analysis for error minimization. From the results it was established that the model provides good predictions of experimental batch culture data for 25/25, 50/50, and 65/65 g l^–1 glucose/xylose media.     

Role of catabolite regulatory mechanisms in control of carbohydrate utilization by the rumen anaerobic fungus Neocallimastix frontalis.

Neocallimastix frontalis PN-1 utilized the soluble sugars D-glucose, D-cellobiose, D-fructose, maltose, sucrose, and D-xylose for growth. L-Arabinose, D-galactose, D-mannose, and D-xylitol did not support growth of the fungus. Paired substrate test systems were used to determine whether any two sugars were utilized simultaneously or sequentially. Of the paired monosaccharides tested, glucose was found to be preferentially utilized compared with fructose and xylose. The disaccharides cellobiose and sucrose were preferentially utilized compared with fructose and glucose, respectively, an cellobiose was also the preferred substrate compared with xylose. Xylose was the preferred substrate compared with maltose. In further incubations, the fungus was grown on the substrate utilized last in the two-substrate tests. After moderate growth was attained, the preferred substrate was added to the culture medium. Inhibition of nonpreferred substrate utilization by the addition of the preferred substrate was taken as evidence of catabolite regulation. For the various combinations of substrates tested, fructose and xylose utilization was found to be inhibited in the presence of glucose, indicating that catabolite regulation was involved. No clear-cut inhibition was observed with any of the other substrate combinations tested. The significance of these findings in relation to rumen microbial interactions and competitions is discussed.     

Role of catabolite regulatory mechanisms in control of carbohydrate utilization by the rumen anaerobic fungus Neocallimastix frontalis

Neocallimastix frontalis PN-1 utilized the soluble sugars D-glucose, D-cellobiose, D-fructose, maltose, sucrose, and D-xylose for growth. L-Arabinose, D-galactose, D-mannose, and D-xylitol did not support growth of the fungus. Paired substrate test systems were used to determine whether any two sugars were utilized simultaneously or sequentially. Of the paired monosaccharides tested, glucose was found to be preferentially utilized compared with fructose and xylose. The disaccharides cellobiose and sucrose were preferentially utilized compared with fructose and glucose, respectively, an cellobiose was also the preferred substrate compared with xylose. Xylose was the preferred substrate compared with maltose. In further incubations, the fungus was grown on the substrate utilized last in the two-substrate tests. After moderate growth was attained, the preferred substrate was added to the culture medium. Inhibition of nonpreferred substrate utilization by the addition of the preferred substrate was taken as evidence of catabolite regulation. For the various combinations of substrates tested, fructose and xylose utilization was found to be inhibited in the presence of glucose, indicating that catabolite regulation was involved. No clear-cut inhibition was observed with any of the other substrate combinations tested. The significance of these findings in relation to rumen microbial interactions and competitions is discussed.