Reversible Michaelis-Menten Kinetics Research Articles

Can models adequately reflect how long-term nitrogen enrichment alters the forest soil carbon cycle?

Abstract. Changes in the nitrogen (N) status of forest ecosystems can directly and indirectly influence their carbon (C) sequestration potential by altering soil organic matter (SOM) decomposition, soil enzyme activity, and plant–soil interactions. However, model representations of linked C–N cycles and SOM decay are not well validated against experimental data. Here, we use extensive data from the Fernow Experimental Forest long-term whole-watershed N fertilization study to compare the response to N perturbations of two soil models that represent decomposition dynamics differently (first-order decay versus microbially explicit reverse Michaelis–Menten kinetics). These two soil models were coupled to a common vegetation model which provided identical input data. Key responses to N additions measured at the study site included a shift in plant allocation to favor woody biomass over belowground carbon inputs, reductions in soil respiration, accumulation of particulate organic matter (POM), and an increase in soil C:N ratios. The vegetation model did not capture the often-observed shift in plant C allocation with N additions, which resulted in poor predictions of the soil responses. We modified the parameterization of the plant C allocation scheme to favor wood production over fine-root production with N additions, which significantly improved the vegetation and soil respiration responses. Additionally, to elicit an increase in the soil C stocks and C:N ratios with N additions, as observed, we modified the decay rates of the POM in the soil models. With these modifications, both models captured negative soil respiration and positive soil C stock responses in line with observations, but only the microbially explicit model captured an increase in soil C:N. Our results highlight the need for further model development to accurately represent plant–soil interactions, such as rhizosphere priming, and their responses to environmental change.

Analytical Expression of Effectiveness Factor for Immobilized Enzymes System with Reversible Michaelis Menten Kinetics

The mathematical model of immobilized enzyme system in porous spherical particle is presented. This model is based on a non-stationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of enzymatic reaction. A general and closed form of an analytical expression pertaining to the substrate concentration profile and effectiveness factor are reported for all possible values of Thiele modules φ andα . However, we have employed New Homotopy Perturbation Method (NHPM) to solve the nonlinear reaction/diffusion equation in immobilized enzymes system. Therefore, analytical results were found to be in an appropriate agreement with simulation result.

Competitor and substrate sizes and diffusion together define enzymatic depolymerization and microbial substrate uptake rates

Diffusion limitations of extracellular enzymes and soluble monomers have been recognized as important mechanisms controlling soil organic matter (SOM) dynamics. Here we combine diffusion limitation with the geometric sizes of extracellular enzymes, polymer particles, monomers, and bacterial cells to derive testable relationships of SOM kinetic parameters, including (1) maximum reaction rates and (2) binding half saturation constants (also known as substrate affinity parameters). We integrate the relevant mechanisms with the Equilibrium Chemistry Approximation (ECA) kinetics, which has been shown to reasonably represent these complex competitive interactions in soils, and then evaluate the reverse and forward Michaelis-Menten kinetics approximations under different conditions. We found: (1) due to the size contrast between larger organic polymer particles and smaller enzyme molecules, depolymerization is limited by the abundance of enzyme binding sites supplied by polymer particles, making the reverse Michaelis-Menten kinetics a better approximation to the ECA kinetics for depolymerization, and (2) due to the size contrast between larger microbial cells and smaller monomer molecules, monomer uptake is limited by accessible microbial cell transporters, making the forward Michaelis-Menten kinetics a better approximation to ECA kinetics for microbial monomer substrate uptake. These results may explain conflicting applications in the literature associated with using reverse and forward Michaelis-Menten kinetics to represent SOM dynamics. Further, the size contrast between litter particles and extracellular enzymes suggests that litter fragmentation by soil fauna and fungi is an important process to be included in models of organic matter decomposition and challenges soil enzyme assays to accurately measure enzyme abundances in order to properly derive the kinetic parameters.

Particle-Based Simulation Reveals Macromolecular Crowding Effects on the Michaelis-Menten Mechanism

Many computational models for analyzing and predicting cell physiology rely on in vitro data collected in dilute and controlled buffer solutions. However, this can mislead models because up to 40% of the intracellular volume—depending on the organism, the physiology, and the cellular compartment—is occupied by a dense mixture of proteins, lipids, polysaccharides, RNA, and DNA. These intracellular macromolecules interfere with the interactions of enzymes and their reactants and thus affect the kinetics of biochemical reactions, making in vivo reactions considerably more complex than the in vitro data indicates. In this work, we present a new, to our knowledge, type of kinetics that captures and quantifies the effect of volume exclusion and other spatial phenomena on the kinetics of elementary reactions. We further developed a framework that allows for the efficient parameterization of these kinetics using particle simulations. Our formulation, entitled generalized elementary kinetics, can be used to analyze and predict the effect of intracellular crowding on enzymatic reactions and was herein applied to investigate the influence of crowding on phosphoglycerate mutase in Escherichia coli, which exhibits prototypical reversible Michaelis-Menten kinetics. Current research indicates that many enzymes are reaction limited and not diffusion limited, and our results suggest that the influence of fractal diffusion is minimal for these reaction-limited enzymes. Instead, increased association rates and decreased dissociation rates lead to a strong decrease in the effective maximal velocities Vmax and the effective Michaelis-Menten constants KM under physiologically relevant volume occupancies. Finally, the effects of crowding were explored in the context of a linear pathway, with the finding that crowding can have a redistributing effect on the effective flux responses in the case of twofold enzyme overexpression. We suggest that this framework, in combination with detailed kinetics models, will improve our understanding of enzyme reaction networks under nonideal conditions.

Integration of simulated moving bed chromatography and enzymatic racemization for the production of single enantiomers

Integration of enantioseparation by simulated moving bed (SMB) and mild enzymatic racemization enables the production of single enantiomers from a racemic mixture in theoretically 100% yield and hence overcomes the 50% yield limitation of conventional SMB processes. We implemented such a process consisting of a Chirobiotic TAG column-SMB, an amino acid racemase-containing enzyme membrane reactor, and a nanofiltration unit for concentration of the distomer-enriched SMB raffinate prior to racemization on lab-scale for the production of enantiopure D-methionine. The integrated process scheme was operated continuously for over 30h without significant variations in product concentration and purity and with a yield of 93.5%, demonstrating the feasibility of this integrated process concept. Furthermore, a rational analysis of the integrated process on the basis of a short-cut model was conducted. The process model consists of a true moving bed equilibrium stage model to represent the SMB, a continuous stirred tank reactor model with reversible Michaelis–Menten kinetics to represent the enzyme membrane reactor, a nanofiltration model and feed node mass balances, and enabled the identification of optimal operating points (flow rate ratios, enzyme concentration) at a variety of process specifications and objectives. Optimal operating points were calculated for different cost distributions between the applied materials such as stationary phase, enzyme, solvent, and nanofiltration membrane. By assigning plausible pricing data and lifetimes to the respective materials, variable costs for the specific process considered in this work were estimated.

Responses of two nonlinear microbial models to warming and increased carbon input

Abstract. A number of nonlinear microbial models of soil carbon decomposition have been developed. Some of them have been applied globally but have yet to be shown to realistically represent soil carbon dynamics in the field. A thorough analysis of their key differences is needed to inform future model developments. Here we compare two nonlinear microbial models of soil carbon decomposition: one based on reverse Michaelis–Menten kinetics (model A) and the other on regular Michaelis–Menten kinetics (model B). Using analytic approximations and numerical solutions, we find that the oscillatory responses of carbon pools to a small perturbation in their initial pool sizes dampen faster in model A than in model B. Soil warming always decreases carbon storage in model A, but in model B it predominantly decreases carbon storage in cool regions and increases carbon storage in warm regions. For both models, the CO2 efflux from soil carbon decomposition reaches a maximum value some time after increased carbon input (as in priming experiments). This maximum CO2 efflux (Fmax) decreases with an increase in soil temperature in both models. However, the sensitivity of Fmax to the increased amount of carbon input increases with soil temperature in model A but decreases monotonically with an increase in soil temperature in model B. These differences in the responses to soil warming and carbon input between the two nonlinear models can be used to discern which model is more realistic when compared to results from field or laboratory experiments. These insights will contribute to an improved understanding of the significance of soil microbial processes in soil carbon responses to future climate change.

On the relationships between the Michaelis–Menten kinetics, reverse Michaelis–Menten kinetics, equilibrium chemistry approximation kinetics, and quadratic kinetics

Abstract. The Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics are two popular mathematical formulations used in many land biogeochemical models to describe how microbes and plants would respond to changes in substrate abundance. However, the criteria of when to use either of the two are often ambiguous. Here I show that these two kinetics are special approximations to the equilibrium chemistry approximation (ECA) kinetics, which is the first-order approximation to the quadratic kinetics that solves the equation of an enzyme–substrate complex exactly for a single-enzyme and single-substrate biogeochemical reaction with the law of mass action and the assumption of a quasi-steady state for the enzyme–substrate complex and that the product genesis from enzyme–substrate complex is much slower than the equilibration between enzyme–substrate complexes, substrates, and enzymes. In particular, I show that the derivation of the Michaelis–Menten kinetics does not consider the mass balance constraint of the substrate, and the reverse Michaelis–Menten kinetics does not consider the mass balance constraint of the enzyme, whereas both of these constraints are taken into account in deriving the equilibrium chemistry approximation kinetics. By benchmarking against predictions from the quadratic kinetics for a wide range of substrate and enzyme concentrations, the Michaelis–Menten kinetics was found to persistently underpredict the normalized sensitivity ∂ ln v / ∂ ln k2+ of the reaction velocity v with respect to the maximum product genesis rate k2+, persistently overpredict the normalized sensitivity ∂ ln v / ∂ ln k1+ of v with respect to the intrinsic substrate affinity k1+, persistently overpredict the normalized sensitivity ∂ ln v / ∂ ln [E]T of v with respect the total enzyme concentration [E]T, and persistently underpredict the normalized sensitivity ∂ ln v / ∂ ln [S]T of v with respect to the total substrate concentration [S]T. Meanwhile, the reverse Michaelis–Menten kinetics persistently underpredicts ∂ ln v / ∂ ln k2+ and ∂ ln v / ∂ ln [E]T, and persistently overpredicts ∂ ln v / ∂ ln k1+ and ∂ ln v / ∂ ln [S]T. In contrast, the equilibrium chemistry approximation kinetics always gives consistent predictions of ∂ ln v / ∂ ln k2+, ∂ ln v / ∂ ln k1+, ∂ ln v / ∂ ln [E]T, and ∂ ln v / ∂ ln [S]T, indicating that ECA-based models will be more calibratable if the modeled processes do obey the law of mass action. Since the equilibrium chemistry approximation kinetics includes advantages from both the Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics and it is applicable for almost the whole range of substrate and enzyme abundances, land biogeochemical modelers therefore no longer need to choose when to use the Michaelis–Menten kinetics or the reverse Michaelis–Menten kinetics. I expect that removing this choice ambiguity will make it easier to formulate more robust and consistent land biogeochemical models.

Model-based cost optimization of a reaction–separation integrated process for the enzymatic production of the rare sugar d-psicose at elevated temperatures

The integration of biocatalysis with continuous separation of product and substrate constitutes an attractive option for overcoming the intrinsic yield limitation in enzymatic reactions that suffer from an unfavourable position of the equilibrium. One example is the recently established continuous process combining enzymatic epimerization in an enzyme membrane reactor (EMR), simulated moving bed (SMB) chromatography and nanofiltration for the high-yield production of the rare sugar d-psicose from its bulk epimer d-fructose with recycling of the unused epimer to the EMR. In this work, we present a first, comprehensive analysis of this novel reaction-separation process concept on the basis of an integrated process model. Therefore, a process model consisting of a continuous stirred tank reactor model with reversible Michaelis–Menten kinetics for representation of EMR operation, a transport-dispersive true moving bed model for representation of SMB operation and an ideal filtration model was constructed. As enzyme costs are particularly difficult to estimate due to their strong dependence on the reactor temperature, we further established a model-based procedure for characterizing the biocatalyst in terms of operational stability and activation as a function of the reactor operating temperature. The integrated process model then enabled the identification of optimum operating points for a fully integrated process operation. First, the established design procedure was used to implement a highly productive run on our existing lab-scale plant (i.e. 2.3kg of d-psicose per L of SMB column volume and day and 4.5kg d-psicose per g enzyme and day), where Dpsicose was produced both at high purity (≈ 98%) and at remarkable yield (96%). Next, the established process model was used for the optimization of the overall process economics. Therefore, a comprehensive analysis of the process in terms of suitable reactor temperatures was performed based on a multi-objective function addressing important cost contributions in the integrated process (i.e. enzyme, desorbent, solid phase, substrate). The presented integrated process scheme can be easily adapted to a number of similar isomerization and epimerization reactions enabling economic production of (almost) the complete set of C6 sugars.

A model reduction method for biochemical reaction networks.

BackgroundIn this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.ResultsWe apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.ConclusionsThe method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches

The Michaelis-Menten (MM) function is a fractional linear function depending on two positive parameters. These can be estimated by nonlinear or linear least squares methods. The non-linear methods, based directly on the defect of the MM function, can fail and not produce any minimizer. The linear methods always produce a unique minimizer which, however, may not be positive. Here we give sufficient conditions on the data such that the nonlinear problem has at least one positive minimizer and also conditions for the minimizer of the linear problem to be positive. We discuss in detail the models and equilibrium relations of a classical operator-repressor system, and we extend our approach to the MM problem with leakage and to reversible MM kinetics. The arrangement of the sufficient conditions exhibits the important role of data that have a concavity property (chemically feasible data).

A note on the reverse Michaelis–Menten kinetics

We theoretically derived a general equation describing the enzyme kinetics that could be further simplified to the typical Michaelis–Menten (M–M) kinetics or the reverse M–M equation (RM–M) under the condition of S ≈ S1 >> E0 or S1 << E0, respectively, where E0 and S1 (=S + ES) are the concentrations of total enzyme and substrate including free substrate (S) and enzyme–substrate complex (ES). We showed that the related Schimel and Weintraub RM–M equation (RM–M–SW) can be derived from the Langmuir adsorption isotherm theory with S >> E0. Both the M–M and the RM-M-SW are appropriate to field soil conditions with S >> E0 given different values of specific reaction rate (k3) and half-saturation constant (Ks). In contrast to M–M and RM–M–SW models, the RM–M model is not applicable to field conditions because of its limited application to one substrate with a simple enzyme system. However, we demonstrate that the best formulation for the process of enzyme-mediated decomposition may vary depending on whether the process is limited by substrate or enzyme availability.

PS1 - 3. The relationship between plasma and brain glucose levels under hypoglycemic conditions in humans

Since glucose is the main source of energy for the brain, understanding the kinetics of brain glucose uptake under hypoglycemic conditions is highly important. Under normo- and hyperglycemic conditions the relationship between plasma and brain glucose levels is linear and behaves according to reversible Michaelis-Menten (MM) kinetics. In the present study brain glucose levels during hypoglycemia were measured by 13C magnetic resonance spectroscopy (MRS).

A short recursive procedure for evaluating effectiveness factors for immobilized enzymes with reversible Michaelis–Menten kinetics

A short recursive procedure for calculating the effectiveness factor for enzymes immobilized in porous spherical particles is presented. The method is mathematically simple and very precise; it is valid for reversible Michaelis–Menten kinetics including, as particular situations, simple Michaelis–Menten and product competitive inhibition kinetics. The procedure is a modification of the two-parameter model previously published by the authors. The definition of an auxiliary dimensionless concentration leads to a recursive equation which simplifies the resolution of the model by means of elementary numerical methods. The solution algorithm has been transformed into a computer program, whose source code is appended. The exact values of the effectiveness factors for zero and first order kinetics, as a function of the Thiele module, were compared with those obtained with the numerical procedure proposed in this work. The good agreement between both results demonstrates the validity of the method.

Model‐based characterization of an amino acid racemase from Pseudomonas putida DSM 3263 for application in medium‐constrained continuous processes

The amino acid racemase with broad substrate specificity from Pseudomonas putida DSM 3263 was overproduced and characterized with respect to application in an integrated multi-step process (e.g., dynamic kinetic resolution) that--theoretically--would allow for 100% chemical yield and 100% enantiomeric excess. Overexpression of the racemase gene in Escherichia coli delivered cell free extract with easily sufficient activity (20-50 U mg(-1) total protein) for application in an enzyme membrane reactor (EMR) setting. Model-based experimental analysis of a set of enzyme assays clearly indicated that racemization of the model substrates D- or L-methionine could be accurately described by reversible Michaelis-Menten kinetics. The corresponding kinetic parameters were determined from progress curves for the entire suitable set of aqueous-organic mixtures (up to 60% methanol and 40% acetonitrile) that are eligible for an integrated process scheme. The resulting kinetic expression could be successfully applied to describe enzyme membrane reactor performance under a large variety of settings. Model-based calculations suggested that a methanol content of 10% and an acetonitrile content of 20% provide maximum productivity in EMR operations. However product concentrations were decreased in comparison to purely aqueous operation due to decreasing solubility of methionine with increasing organic solvent content. Finally, biocatalyst stability was investigated in different solvent compositions following a model-based approach. Buffer without organic content provided excellent stability at moderate temperatures (20-35 degrees C) while addition of 20% acetonitrile or methanol drastically reduced the half-life of the racemase.

Two-parameter model for evaluating effectiveness factor for immobilized enzymes with reversible Michaelis–Menten kinetics

A two-parameter mathematical model was developed to calculate the effectiveness factor for immobilized enzymes in porous spherical particles. The model was resolved for reversible Michaelis–Menten kinetics, including simple Michaelis–Menten and product competitive inhibition kinetics. Since only two dimensionless moduli are involved in the model, the effectiveness factor for the three kinetic equations considered can be estimated by using only one generalized graph.

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.

The effect of insulin on in vivo cerebral glucose concentrations and rates of glucose transport/metabolism in humans.

The continuous delivery of glucose to the brain is critically important to the maintenance of normal metabolic function. However, elucidation of the hormonal regulation of in vivo cerebral glucose metabolism in humans has been limited by the lack of direct, noninvasive methods with which to measure brain glucose. In this study, we sought to directly examine the effect of insulin on glucose concentrations and rates of glucose transport/metabolism in human brain using (1)H-magnetic resonance spectroscopy at 4 Tesla. Seven subjects participated in paired hyperglycemic (16.3 +/- 0.3 mmol/l) clamp studies performed with and without insulin. Brain glucose remained constant throughout (5.3 +/- 0.3 micromol/g wet wt when serum insulin = 16 +/- 7 pmol/l vs. 5.5 +/- 0.3 micromol/g wet wt when serum insulin = 668 +/- 81 pmol/l, P = NS). Glucose concentrations in gray matter-rich occipital cortex and white matter-rich periventricular tissue were then simultaneously measured in clamps, where plasma glucose ranged from 4.4 to 24.5 mmol/l and insulin was infused at 0.5 mU. kg(-1). min(-1). The relationship between plasma and brain glucose was linear in both regions. Reversible Michaelis-Menten kinetics fit these data best, and no differences were found in the kinetic constants calculated for each region. These data support the hypothesis that the majority of cerebral glucose uptake/metabolism is an insulin-independent process in humans.

Differentiation of glucose transport in human brain gray and white matter.

Localized 1H nuclear magnetic resonance spectroscopy has been applied to determine human brain gray matter and white matter glucose transport kinetics by measuring the steady-state glucose concentration under normoglycemia and two levels of hyperglycemia. Nuclear magnetic resonance spectroscopic measurements were simultaneously performed on three 12-mL volumes, containing predominantly gray or white matter. The exact volume compositions were determined from quantitative T1 relaxation magnetic resonance images. The absolute brain glucose concentration as a function of the plasma glucose level was fitted with two kinetic transport models, based on standard (irreversible) or reversible Michaelis-Menten kinetics. The steady-state brain glucose levels were similar for cerebral gray and white matter, although the white matter levels were consistently 15% to 20% higher. The ratio of the maximum glucose transport rate, V(max), to the cerebral metabolic utilization rate of glucose, CMR(Glc), was 3.2 +/- 0.10 and 3.9 +/- 0.15 for gray matter and white matter using the standard transport model and 1.8 +/- 0.10 and 2.2 +/- 0.12 for gray matter and white matter using the reversible transport model. The Michaelis-Menten constant K(m) was 6.2 +/- 0.85 and 7.3 +/- 1.1 mmol/L for gray matter and white matter in the standard model and 1.1 +/- 0.66 and 1.7 +/- 0.88 mmol/L in the reversible model. Taking into account the threefold lower rate of CMR(Glc) in white matter, this finding suggests that blood--brain barrier glucose transport activity is lower by a similar amount in white matter. The regulation of glucose transport activity at the blood--brain barrier may be an important mechanism for maintaining glucose homeostasis throughout the cerebral cortex.

Optimum design of a series of CSTRs performing reversible Michaelis-Menten kinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversible Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the feed stream to the first reactor, as well as the effect of the product intermediate concentrations in the downstream reactors on the reaction rate are investi- gated. For a given number of N CSTRs required to perform a certain degree of substrate conversion and under steady state operation and constant volumetric flow rate, the re- actor optimization problem is posed as a constrained nonlinear programming problem (NLP). The reactor op- timization is based on the minimum overall residence time (volume) of N reactors in series. When all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optimum overall residence time is obtained. Also, the necessary and sufficient conditions for the minimum overall residence time of N CSTRs are derived analytically. In the presence of product in the feed stream, the re- versible Michaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K 0 that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (w 0 ) of product to sub- strate concentrations in the feed stream increases. The isomerization of glucose to fructose, which follows a re- versible Michaelis-Menten kinetics, is chosen as a model for the numerical examples. List of symbols CE;0 (mg/l) initial concentration of active enzyme

Steady-state cerebral glucose concentrations and transport in the human brain.

Understanding the mechanism of brain glucose transport across the blood-brain barrier is of importance to understanding brain energy metabolism. The specific kinetics of glucose transport have been generally described using standard Michaelis-Menten kinetics. These models predict that the steady-state glucose concentration approaches an upper limit in the human brain when the plasma glucose level is well above the Michaelis-Menten constant for half-maximal transport, Kt. In experiments where steady-state plasma glucose content was varied from 4 to 30 mM, the brain glucose level was a linear function of plasma glucose concentration. At plasma concentrations nearing 30 mM, the brain glucose level approached 9 mM, which was significantly higher than predicted from the previously reported Kt of approximately 4 mM (p < 0.05). The high brain glucose concentration measured in the human brain suggests that ablumenal brain glucose may compete with lumenal glucose for transport. We developed a model based on a reversible Michaelis-Menten kinetic formulation of unidirectional transport rates. Fitting this model to brain glucose level as a function of plasma glucose level gave a substantially lower Kt of 0.6 +/- 2.0 mM, which was consistent with the previously reported millimolar Km of GLUT-1 in erythrocyte model systems. Previously reported and reanalyzed quantification provided consistent kinetic parameters. We conclude that cerebral glucose transport is most consistently described when using reversible Michaelis-Menten kinetics.