Lipase-catalyzed reaction in the packed-bed reactor with continuous extraction column to overcome a product inhibition

The resolution of rac-α-methyl-β-propiothiolactone (rac-MPTL) was performed in a packed-bed reactor (PBR) using Pseudomonas cepacia lipase (PCL) in organic media to produce enantiopure (R)-MPTL. By comparing enzyme stability of three enzyme forms, i.e. commercial PCL powder, Celite-immobilized PCL, and cross-linked enzyme crystals of PCL (CLECs-PCL), Celite-immobilized PCL was chosen for the construction of PBR because of its comparable stability to that of CLEC and easy handling. Owing to the severe product inhibition by 3-mercapto-α-methylpropionic acid (MMPA), the batch reaction system was inappropriate for the hydrolysis with PCL at high concentration of rac-MPTL. To overcome these problems, PBR with a continuous extraction column was used. The product inhibition was successfully overcome by incorporating an aqueous extraction unit. However, the yield of (R)-MPTL (enantiomeric excess, ee>99%) was only about 20% based upon the initial concentration of rac-MPTL, due to the concomitant partitioning of rac-MPTL to the aqueous phase in the extraction column as well as the subsequent auto-hydrolysis of rac-MPTL to rac-MMPA during extraction. To reduce the undesired partitioning of rac-MPTL to aqueous phase, various salts were screened to modulate the partitioning coefficient of the reaction components. Using 1 M ammonium sulfate solution as the aqueous phase of the extraction column, the yield of (R)-MPTL (ee>99%) was enhanced to 40%.     

Use of charcoal to minimize end product inhibition in enzymatic hydrolysis of cellulose

Summary Tests made to improve saccharification of cellulose byTrichoderma cellulases showed that charcoal used as an adsorbent minimized the end product inhibition. Charcoal adsorbed both cellobiose and glucose and did not affect the enzymatic hydrolysis of cellulose. Results showed that charcoal is as effective as -glucosidase in improving the enzymatic saccharification of cellulose.     

Bifurcation analysis of a product inhibition model of a continuous fermentation process

Summary A product inhibition model of a continuous fermentation process is considered. If the yield term is a variable function of ethanol concentration, oscillation in the cell and ethanol concentrations is shown to be a Hopf bifurcation in the underlying system of nonlinear, ordinary differential equations which comprises the model.     

Scalar modeling and analysis of a 3D biochemical reaction model

For many systems it is advantageous if analysis and modeling can be accomplished from a scalar time series because this greatly facilitates the experimental setup. Moreover, in real-life systems it is hardly true that all the state variables are available for analysis and modeling. Since the late 1980s, techniques have been put forward for building mathematical models from a scalar time series. One of the objectives of this paper is to verify if it is possible to obtain global non-linear models (non-linear differential equations) from scalar time series. Such data are obtained using a model of biochemical reaction with aperiodic (chaotic) oscillations as recently observed in the case of a glycolytic reaction (Nielsen, K., Sorensen, P.G., Hynne, F., 1997. Chaos in glycolysis. J Theor. Biol. 186, 303-306.). The main objective, however, is to investigate which state variable is more convenient for the task in practice. It is shown that observability indices seem to quantify quite well which variable should be preferred as the observable. The validity of the results are established performing rigorous topological analysis on the original system and the obtained models. The influence of noise, always present in experimental time series, on the dynamics underlying such a system is also investigated.     

Tyrosine hydroxylase. Activation by protein phosphorylation and end product inhibition.

Protein phosphorylation activates tyrosine hydroxylase in crude extracts of rat striatum, hypothalamus, and adrenal glands by a reduction in the apparent Km value for 6-methyltetrahydropterin. Removal of endogenous catecholamines by gel filtration or cation exchange results in a similar activation. Phosphorylation causes only a small additional reduction in the apparent Km for reduced pterin in striatal extracts from which catecholamines have been removed. Kinetic analysis indicates that protein phosphorylation causes a significant increase in the Ki for end product dopamine, whereas gel filtration or cation exchange treatment has little effect on the dopamine Ki value. None of the above treatments appears to change the molecular weight of the enzyme. At physiological concentrations of dopamine, the increase in Ki by phosphorylation would effectively release tyrosine hydroxylase from end product feedback inhibition.     

Optimization of a stagewise biochemical reactor system with product feedback

A consecutive, first-order, irreversible, biochemical reaction, \documentclass{article}\pagestyle{empty}\begin{document}$ A{\textstyle{{k(\theta)} \over {{\rm Enzyme }1}}} \to B{\textstyle{{k(\theta)} \over {{\rm Enzyme 2}}}} \to C $\end{document}, taking place in a series of N reactors with product recycle is considered. A discrete version of the maximum principle is used to derive general equations necessary for maximizing the production of (1) the final product, C, by choosing the temperature or the pH value in each reactor, and (2) the intermediate product, B, by choosing the reactor volume. A numerical computation for a series of three reactors with recycle is illustrated. The effects of varying the recycle rates on the optimal state and decision variables are also presented.     

Kinetic model for membrane transport. 2. Time lag and overshoot

A lag time during the period of variation in solute concentration in the receiver phase and overshoot in that in the membrane phase have been predicted to occur with a kinetic model for membrane transport which takes into account both the membrane volume and the partitioning kinetics (Makino et al., Biophys. Chem. 35 (1990) 85). The duration of the lag time becomes longest when the donor and receiver phases have the same volume. This maximum grows in length with increase in the partition coefficient, tending to be proportional to the volume fraction of the receiver phase. Moreover, it displays an increase in length with decreasing membrane volume fraction. Overshoot occurs only when the volume fraction of the receiver phase is greater than that of the donor. Overshoot is observed during the earlier stages of membrane transport when the partition coefficient is smaller or the volume fraction of the receiver phase is larger.     

Advanced glycation end product ligands for the receptor for advanced glycation end products: biochemical characterization and formation kinetics

Advanced glycation end products (AGEs) accumulate with age and at an accelerated rate in diabetes. AGEs bind cell-surface receptors including the receptor for advanced glycation end products (RAGE). The dependence of RAGE binding on specific biochemical characteristics of AGEs is currently unknown. Using standardized procedures and a variety of AGE measures, the present study aimed to characterize the AGEs that bind to RAGE and their formation kinetics in vitro. To produce AGEs with varying RAGE binding affinity, bovine serum albumin (BSA) AGEs were prepared with 0.5M glucose, fructose, or ribose at times of incubation from 0 to 12 weeks or for up to 3 days with glycolaldehyde or glyoxylic acid. The AGE-BSAs were characterized for RAGE binding affinity, fluorescence, absorbance, carbonyl content, reactive free amine content, molecular weight, pentosidine content, and N-epsilon-carboxymethyl lysine content. Ribose-AGEs bound RAGE with high affinity within 1 week of incubation in contrast to glucose- and fructose-AGE, which required 12 and 6 weeks, respectively, to generate equivalent RAGE ligands (IC50=0.66, 0.93, and 1.7 microM, respectively). Over time, all of the measured AGE characteristics increased. However, only free amine content robustly correlated with RAGE binding affinity. In addition, detailed protocols for the generation of AGEs that reproducibly bind RAGE with high affinity were developed, which will allow for further study of the RAGE-AGE interaction.     

A biochemical model of matrix metalloproteinase 9 activation and inhibition

Matrix metalloproteinases (MMPs) are a class of extracellular and membrane-bound proteases involved in an array of physiological processes, including angiogenesis. We present a detailed computational model of MMP9 activation and inhibition. Our model is validated to existing biochemical experimental data. We determine kinetic rate constants for the processes of MMP9 activation by MMP3, MMP10, MMP13, and trypsin; inhibition by the tissue inhibitors of metalloproteinases (TIMPs) 1 and 2; and MMP9 deactivation. This computational approach allows us to investigate discrepancies in our understanding of the interaction of MMP9 with TIMP1. Specifically, we find that inhibition due to a single binding event cannot describe MMP9 inhibition by TIMP1. Temporally accurate biphasic inhibition requires either an additional isomerization step or a second lower affinity isoform of MMP9. We also theoretically characterize the MMP3/TIMP2/pro-MMP9 and MMP3/TIMP1/pro-MMP9 systems. We speculate that these systems differ significantly in their time scales of activation and inhibition such that MMP9 is able to temporarily overshoot its final equilibrium value in the latter. Our numerical simulations suggest that the ability of pro-MMP9 to complex TIMP1 increases this overshoot. In all, our analysis serves as a summary of existing kinetic data for MMP9 and a foundation for future models utilizing MMP9 or other MMPs under physiologically well defined microenvironments.     

Time discrete model of recurrent inhibition in hippocampal dentate gyrus

A time discrete model of recurrent inhibition in the hippocampal dentate gyrus is made and analyzed. This model assumes that (1) each granule cell can generate only one action potential in response to a single stimulation of the perforant path, (2) each interneuron receives synaptic inputs from many granule cells, and (3) an output of the interneuron is inhibitory for granule cells. Although each granule cell generates an action potential in the all-or-none fashion, the population spike is shown to be approximated by a piecewise linear function of the population excitatory post-synaptic potential (EPSP). From this model six patterns in the population spike responses to the paired-pulse stimulation are deduced. Each pattern is composed of some broken lines whose slopes and intercepts are explicitly expressed by the average and variance of the microscopic parameters and the population size of the cells. This model clarifies the relation between the measured quantity in the field potential experiment and the microscopic quantities peculiar to the granule cell and to the interneuron.     

A study for multiple steady states of biochemical reactions under substrate and product inhibition

This paper combines Sturm's method with the tangent analysis method to solve a biochemical reaction involving multiplicity. This method can easily derive the necessary conditions for multiplicity. In addition, we find a starting bifurcation point for multiplicity which cannot be obtained by the tangent method alone. Moreover, a start-up strategy is suggested to obtain a high conversion and unique steady state in four selected kinetic models of biochemical reactions, with inhibition.     

31P NMR studies of Clostridium thermocellum. Mechanism of end product inhibition by ethanol

31P NMR studies of intact cells and perchloric acid extracts are used to investigate the effect of ethanol on the bioenergetics and glycolysis of Clostridium thermocellum, an anaerobic bacterium potentially useful for the single step conversion of biomass to ethanol. Whole cells suspended in phosphate buffer and given a carbon source (cellobiose) at 60 degrees C rapidly establish a pH gradient across the membrane that can be monitored by the chemical shifts of inorganic phosphate in the exterior buffer and in the cytoplasm. Peak intensities can be related to phosphate active transport rates. Wild type bacteria and cells grown in inhibiting concentrations of ethanol establish similar pH gradients, but with slower kinetics and slower phosphate transport rates for the cells adapted to growth in ethanol. Direct addition of ethanol does not affect the rate of pH gradient formation or phosphate transport. Thus, while ethanol does not directly affect processes for energy conservation carried out by the membrane, adaptation to ethanol does alter membrane functions such as phosphate transport. 31P NMR spectra of perchloric acid extracts show that when wild type cells are adapted to grow in inhibiting concentrations of ethanol and then energized with cellobiose, sugar phosphate content is increased and the steady state distribution of glycolytic intermediates is altered. Nucleotide triphosphate/nucleotide diphosphate ratios are unaltered in these cells. These results strongly indicate that in C. thermocellum growth inhibition by ethanol is related to a blockage in glycolysis.     

The mechanism of end product inhibition of serine biosynthesis. V. Mechanism of serim inhibition of phosphoglycerate dehydrogenases.

The reduction of enzyme-bound DPN constitutes a half-reaction of phosphoglycerate dehydrogenase and has been investigated fluorometrically. Serine was found to inhibit the half-reaction to the same extent and with the same degree of cooperation as the steady state reaction. This finding identifies the ternary complex conversion as the point in the reaction sequence at which serine inhibition occurs. Delta H determinations for the half-reaction showed no difference whether serine was or was not present and led to the conclusion that the inhibitory effect of serine could only manifest itself through the delta S term in the expression for the formation of the activated transition state complex. DL-3-P[2-2H]glyceric acid showed no primary isotope effect in the half-reaction. This result excludes hydrogen transfer as the rate-limiting step in the half-reaction and confirms that an isomerization step, affected by serine, exists in the ternary complex conversion scheme. The deuterated 3-P-glyceric acid shows an isotope effect of 2 in the steady state reaction.     

Mouse transthyretin-related protein is a hydrolase which degrades 5-hydroxyisourate, the end product of the uricase reaction

Uric acid is the end product of the purine degradation pathway in humans. It is catabolized to allantoin by urate oxidase or uricase (E.C. 1.7.3.3.) in most vertebrates except humans, some primates, birds, and certain species of reptiles. Here we provide evidence that mouse transthyretin-related protein facilitates the hydrolysis of 5-hydroxyisourate, the end product of the uricase reaction. Mutagenesis experiments showed that the residues that are absolutely conserved across the TRP family, including His11, Arg51, His102, and the C-terminal Tyr-Arg-Gly-Ser, may constitute the active site of mTRP. Based on these results, we propose that the transthyretin-related proteins present in diverse organisms are not functionally related to transthyretin but actually function as hydroxyisourate hydrolases.     

The behaviour of coupled biochemical oscillators as a model of contact inhibition of cellular division

Intercellular communication of molecules between normal cells by tight junctions, and lack of this in some cancer cells (Loewenstein), can explain contact inhibition of cellular division in tissues. A general theory has been based on assuming the continual rise and fall (intrinsic oscillation) of a key substance x in each cell, with the period of the cell cycle. Periods are asynchronous in different cells, and x is exchanged between cells in contact by diffusion. A reduction in the resultant amplitude of fluctuation of x results, so that it does not reach the threshold x_t required for division to ensue; hence contact inhibition.The mathematical model is defined in its simplest form, and the sets of differential equations for arrays of cells are solved, from the isolated cell to the cell in an infinite sheet. The relative probability of division, P, is computed by numerical analysis from the area of resultant curves of x that lies above the threshold x_t. P depends on four dimensionless parameters, the order of coupling n (the number of cells directly communicating with a given cell), the total number of cells N in the aggregate, the communication constant K, and x_t, as a fraction of the amplitude of the intrinsic oscillation. The degree of synchrony, measured by the coefficient of variation σ of the periods, is important. If σ < ± 4%, contact inhibition is much reduced. The theory predicts that a paradoxical “contact-facilitation” is possible for very small aggregates of cells. For a cell in an infinite sheet, the amplitude of oscillation of x is reduced approximately by the factor $\text{1}\text{nK}$. For normal cells K is probably > 1, for cancer cells that lack communication, K is probably «< 1. However, two other basic causes for lack of regulation of tissue growth (cancer) could be excessive intrinsic oscillation of x, cf. x_t, and partial or complete synchronization of groups of cells by some unknown mechanism.     

A simulation study of a time lag population model

The lack of terms representing time lags is a widely recognized weakness of the Volterra-Gause formulations of population growth and interaction. A number of analytical attempts to include time lag terms have been made in the past, but they have provided relatively little ecological insight.     

The kinetic effect of product instability in a Michaelis-Menten mechanism with competitive inhibition

In most kinetic studies it is assumed that both the reactant and the products are stable. However, under certain conditions spontaneous decomposition or deterioration caused by one of the participating species occurs. Studies, in which a species (the free enzyme, the enzyme-substrate complex, an inhibitor or the product of the reaction) is unstable, have appeared in the literature. However, to our knowledge, the enzymatic systems, in which a competitive inhibition and a decomposition or transformation of the products take place simultaneously, have not been studied so far. In this paper, we present a kinetic analysis of an enzyme reaction that follows a Michaelis-Menten mechanism, in which the free enzyme suffers a competitive inhibition simultaneously with the decomposition of the immediate product. In this study, we have linearised the differential equations that describe the kinetics of the process. Under the assumption of limiting concentration of enzyme, we have obtained and tested the explicit equation describing the time dependence of the product concentration using numerical calculus. With this equation and the experimental progress curve of the product, we constructed an easy procedure for the evaluation of the principal kinetic parameters of the process.     

Persistent behavior in a phase-shift sequence of periodical biochemical oscillations

We present the analysis of a phase-shift sequence obtained from random transitions between periodic solutions of a biochemical dynamical model, formed by a system of three differential equations and which represent an instability-generating multienzymatic mechanism. The phase-shift series was studied in terms of Hurst’s rescaled range analysis. We found that the data were characterized by a Hurst exponent H = 0.69, which was clearly indicative of long-term trends. This result had a high significance level, as was confirmed through Monte Carlo simulations in which the data were scrambled in the series, destroying its original ordering. For these series we obtained a Hurst exponent which was consistent with the expectation of H = 0.5 for a random independent process. This clearly showed that, although the transitions between the periodic solutions were provoked randomly, the stochastic process obtained exhibited long-term persistence. The fractal dimension was also estimated and found to be consistent with the value of the Hurst exponent.     

Characteristic reaction paths of biochemical reaction systems with time scale separation

A technique has been developed for characterizing the in vivo behavior of key enzymes from intermediate measurements. The technique is based on the identification of characteristic reaction paths, and it depends on the time scale separation characteristics of the systems. It is shown that useful information can be obtained from the phase plots of properly selected intermediate pairs or combinations which typically show process insensitive algebraic relations approached on time scales short compared to those of most practical interest. These characteristic reaction paths provide useful global measures of enzyme activity. The mathematical basis of reaction path analysis is investigated using linear transformation techniques. General theorems are developed predicting the existence of characteristic reaction paths as asymptotic limits whenever there is effective time scale separation. These limits are reached when fast reactions are relaxed, and available evidence suggests that these conditions will occur for the majority of reaction networks.