Theory and simulation of diffusion-controlled Michaelis-Menten kinetics for a static enzyme in solution

We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes.     

Off-line form of the Michaelis-Menten equation for studying the reaction kinetics in a polymer microchip integrated with enzyme microreactor

We firstly transformed the traditional Michaelis-Menten equation into an off-line form which can be used for evaluating the Michaelis-Menten constant after the enzymatic reaction. For experimental estimation of the kinetics of enzymatic reactions, we have developed a facile and effective method by integrating an enzyme microreactor into direct-printing polymer microchips. Strong nonspecific adsorption of proteins was utilized to effectively immobilize enzymes onto the microchannel wall, forming the integrated on-column enzyme microreactor in a microchip. The properties of the integrated enzyme microreactor were evaluated by using the enzymatic reaction of glucose oxidase (GOx) with its substrate glucose as a model system. The reaction product, hydrogen peroxide, was electrochemically (EC) analyzed using a Pt microelectrode. The data for enzyme kinetics using our off-line form of the Michaelis-Menten equation was obtained (K(m) = 2.64 mM), which is much smaller than that reported in solution (K(m) = 6.0 mM). Due to the hydrophobic property and the native mesoscopic structure of the poly(ethylene terephthalate) film, the immobilized enzyme in the microreactor shows good stability and bioactivity under the flowing conditions.     

The kinetics laws for polymer collapse and biopolymer folding

We discuss some recent ideas relating to the folding and other conformational transitions of polymers. In particular we emphasize that it is possible to conceive the accompanying kinetic processes as a problem in non-equilibrium statistical mechanics. In this sense it should be possible to develop such methods to deduce the kinetic laws in the vicinity of various conformational transitions. To establish the ideas we first study the well known problem of the collapse transition of a homopolymer. We then turn to conformational transitions in periodic and random copolymers. We offer a brief survey of the status of these ideas in applications to biopolymeric conformational kinetics.     

From Langmuir kinetics to first- and second-order rate equations for adsorption

So far, the first- and second-order kinetic equations have been most frequently employed to interpret adsorption data obtained under various conditions, whereas the theoretical origins of these two equations still remain unknown. Using the Langmuir kinetics as a theoretical basis, this study showed that the Langmuir kinetics can be transformed to a polynomial expression of dtheta t /d t = k 1(theta e - theta t ) + k 2(theta e - theta t ) (2), a varying-order rate equation. The sufficient and necessary conditions for simplification of the Langmuir kinetics to the first- and second-order rate equations were put forward, which suggested that the relative magnitude of theta e over k 1/ k 2 governs the simplification of the Langmuir kinetics. In cases where k 1/ k 2 is greater than theta e or k 1/ k 2 is very close to theta e, adsorption kinetics would be reasonably described by the first-order rate equation, whereas the Langmuir kinetics would be reduced to the second-order equation only at k 1/ k 2 < theta e. It was further demonstrated that both theta e and k 1/ k 2 are the function of initial adsorbate concentration ( C 0) at a given dosage of adsorbent, indicating that simplification of the Langmuir kinetics indeed is determined by C 0. Detailed C 0-depedent boundary conditions for simplifying the Langmuir kinetics were also established and were verified by experimental data.     

Graphic rule for non-steady-state enzyme kinetics and protein folding kinetics

When going more deeply into the principles of enzyme action as well as protein folding, one is often confronted with transient process systems. Based on the recent progress in graphic methods of enzyme kinetics, in this article a graphic rule is described, which can be used to deal with transient processes occurring in both enzyme-catalyzed reaction systems and protein folding systems. Introducing the graphic method to nonsteady-state systems can raise the efficiency of the calculations and provide an intuitive picture, helping the analysis of the mechanisms concerned. For instance, using the current graphic rule, one can immediately write out the phase concentrations of enzyme species or protein folding states. Calculation work such as setting up differential equations, making Laplace transformations, and expanding determinants, which is both tedious and liable to error, is completely avoided. The mathematical proof of the non-steady-state graphic rule is given in the appendix.Presented at the Symposium on Applied Graph Theory and Discrete Mathematics in Chemistry held at the University of Saskatchewan, Saskatoon, Canada, September 12-14, 1991, in honor of Professor Frank Harary on the occasion of his 70th birthday.     

Surface pressure isotherm for the fluid state of Langmuir monolayers

The equation of state for the monolayer comprised of the molecules of different sizes (water and biopolymers) is modified to describe the fluid (liquid-expanded and gaseous) state of the insoluble molecules monolayer. In contrast to the equation of state derived previously in ref 1, this equation does not involve either the Gibbs' adsorption equation or the differential equation for the chemical potential of the insoluble component, but it is based only on the equations for the chemical potential of the solvent in the bulk and in the surface layer. The results calculated from the proposed equations are in perfect agreement with the experimental Pi-A isotherms of the liquid-expanded state obtained for Langmuir monolayers of various types of amphiphilic compounds. The values of molecular areas of amphiphilic molecules estimated from the fitting of experimental data to the proposed equation are found to be quite similar to those measured in independent grazing incidence X-ray diffraction (GIXD) experiments.     

Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach

This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy.     

Scanning electrochemical microscopy as a probe of Ag+ binding kinetics at Langmuir phospholipid monolayers

A new method has been developed for measuring local adsorption rates of metal ions at interfaces based on scanning electrochemical microscopy (SECM). The technique is illustrated with the example of Ag+ binding at Langmuir phospholipid monolayers formed at the water/air interface. Specifically, an inverted 25 microm diameter silver disc ultramicroelectrode (UME) was positioned in the subphase of a Langmuir trough, close to a dipalmitoyl phosphatidic acid (DPPA) monolayer, and used to generate Ag+ via Ag electro-oxidation. The method involved measuring the transient current-time response at the UME when the electrode was switched to a potential to electrogenerate Ag+. Since the Ag+/Ag couple is reversible, the response is highly sensitive to local mass transfer of Ag+ away from the electrode, which, in turn, is governed by the interaction of Ag+ with the monolayer. The methodology has been used to determine the influence of surface pressure on the adsorption of Ag+ ions at a phospholipid (dipalmitoyl phosphatidic acid) Langmuir monolayer. It is shown that the capacity for metal ion adsorption at the monolayer increased as the density of surface adsorption sites increased (by increasing the surface pressure). A model for mass transport and adsorption in this geometry has been developed to explain and characterise the adsorption process.     

Modeling of a control induced system for product formation in enzyme kinetics

Double substrate enzyme kinetics has a leading role for product quantification and optimization in different chemical and biochemical sectors. Mathematical approach for controlling these reactions in different stages by suitable parameters adds a new dimension in this interdisciplinary field of research. Applying control theoretic approach in the reversible backward stages of double substrate enzymatic model, time economization with regard to product formation is significant. In this article, we formulate a double substrate mathematical model of enzymatic dynamical reaction system with control measures with a view to observe the effect of changes of these measures with respect to the concentration of substrates, enzyme, complexes and finally product. Here, Pontryagin Minimum Principle is used for observing the effect of control measures in the system dynamics with the help of Hamiltonian. We compare the relevant numerical solutions for the substrates, enzyme, complexes and product concentration profile for a specified time interval with respect to control factors.     

Single-substrate enzyme kinetics: the quasi-steady-state approximation and beyond

We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios by adopting a different scaling scheme and computational procedure. The regions of validity of the quasi-steady-state approximation are noted. Certain prevalent conditions are checked and compared against the actual findings. Efficacies of a few other measures, obtained from the present work, are highlighted. Some recent observations are rationalized, particularly at moderate and high enzyme concentrations.     

Modified Langmuir Isotherm for the Description of Cluster Adsorption on Surface Lyophilic Centers

An adsorption isotherm that generalizes the Langmuir equation for the cluster adsorption of several interacting molecules at one center is proposed. In the case of the adsorption of water molecules at surface hydroxyl groups on modified silica it was shown that the energy and structure characteristics of such a system, determined by the ab initio method, agree with the experimental data and lead to satisfactory agreement with the parameters of the proposed isotherm. __________ Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 41, No. 5, pp. 283–289, September–October, 2005.     

Immbolization of uricase enzyme in Langmuir and Langmuir-Blodgett films of fatty acids: possible use as a uric acid sensor

Preserving the enzyme structure in solid films is key for producing various bioelectronic devices, including biosensors, which has normally been performed with nanostructured films that allow for control of molecular architectures. In this paper, we investigate the adsorption of uricase onto Langmuir monolayers of stearic acid (SA), and their transfer to solid supports as Langmuir-Blodgett (LB) films. Structuring of the enzyme in β-sheets was preserved in the form of 1-layer LB film, which was corroborated with a higher catalytic activity than for other uricase-containing LB film architectures where the β-sheets structuring was not preserved. The optimized architecture was also used to detect uric acid within a range covering typical concentrations in the human blood. The approach presented here not only allows for an optimized catalytic activity toward uric acid but also permits one to explain why some film architectures exhibit a superior performance.     

Study of Michaelis-Menten kinetics with linear-type product inhibition in ultrafiltration membrane reactors: Mathematical model,experimental and data

A method is proposed for the study of enzymatic reactions affected by product inhibition. The use of continuous and stirred ultrafiltration membrane reA mathematical model has been defined which depicts Michaelis-Menten kinetics with a linear-type product inhibition for all competitive, non-competitivThe experimental procedure needed to identify the inhibition pattern and to evaluate the set of kinetic constants is detailed. Two model systems, the h     

Surface properties of "jellyfish": Langmuir monolayer and Langmuir-Blodgett film studies of recombinant aequorin

In this paper, we studied the surface properties of recombinant aequorin at the air-water interface. Using the Langmuir monolayer technique, the surface properties of aequorin were studied, including the surface pressure and surface potential-area isotherms, compression-decompression cycles, and stability on Trizma Base (Tris/HCl) buffer at pH 7.6. The results showed that aequorin formed a stable Langmuir monolayer and the surface pressure-area isotherms were dependent on both pH and ionic strength. At a pH higher or lower than 7.6, the limiting molecular area decreased. The circular dichroism (CD) spectra of aequorin in aqueous solutions explained this result: when the pH was higher than 7.6, the alpha-helix conformation changed to unordered structures, whereas at a pH lower than 7.6, the alpha-helix conformation changed to beta-sheet. The addition of calcium chloride to the Tris/HCl buffer subphase (pH 7.6) caused an increase of the limiting molecular area of the aequorin Langmuir monolayer. The fluorescence spectra of a Langmuir-Blodgett (LB) film of aequorin in the presence of calcium chloride indicated that the aequorin transformed to the apoaequorin.     

Surface chemkin: A general formalism and software for analyzing heterogeneous chemical kinetics at a gas-surface interface

This article describes a general kinetic formalism for treating the details of heterogeneous reactions at a gas-solid interface. We develop a nomenclature for treating reactions between the gas phase and surface species residing on any number of surface site types and bulk-phase species residing in bulk-phase mixtures or in pure bulk phases. The rate of progress of surface reactions follows the law of mass-action. We discuss the relationship between macroscopic conservation laws for mass and energy and the microscopic surface reaction rates as they might appear in boundary conditions for a chemically reacting flow. The formalism developed has been implemented in a general package of Fortran computer codes for the evaluation of complex surface-reaction kinetics called Surface Chemkin.     

Modeling of electrocatalysis at chemically modified electrodes: a combination of second-order and Michaelis-type chemical kinetics

The model presented accounts for the diffusion of a reactant and of charge carriers within the modifier layer placed at electrode surface, and redox interaction between reactant and an active center bearing charge carriers. The study extends our previous model by the use of a combination of two kinds of redox interaction—a simple chemical second-order reaction, and Michaelis-type redox reaction. Depending on relative increments from these two kinetic models, either linear, or hyperbolic dependencies of electric current on reactant concentration were obtained. The results obtained have been analyzed in terms of current-concentration interdependencies.     

Rational design of combination enzyme therapy for celiac sprue

Celiac sprue (also known as celiac disease) is an inheritable, gluten-induced enteropathy of the upper small intestine with an estimated prevalence of 0.5%-1% in most parts of the world. The ubiquitous nature of food gluten, coupled with inadequate labeling regulations in most countries, constantly poses a threat of disease exacerbation and relapse for patients. Here, we demonstrate that a two-enzyme cocktail comprised of a glutamine-specific cysteine protease (EP-B2) that functions under gastric conditions and a PEP, which acts in concert with pancreatic proteases under duodenal conditions, is a particularly potent candidate for celiac sprue therapy. At a gluten:EP-B2:PEP weight ratio of 75:3:1, grocery store gluten is fully detoxified within 10 min of simulated duodenal conditions, as judged by chromatographic analysis, biopsy-derived T cell proliferation assays, and a commercial antigluten antibody test.     

Lectin microarrays: a powerful tool for glycan-based biomarker discovery

Cell surfaces, especially mammalian cell surfaces, are heavily coated with complex poly- and oligosaccharides, and these glycans have been implicated in many functions, such as cell-to-cell communication, host-pathogen interactions and cell matrix interactions. Not surprisingly then, the aberrations of glycosylation are usually indicative of the onset of specific diseases, such as cancer. Therefore, glycans are expected to serve as important biomarkers for disease diagnosis and/or prognosis. Recent development of the lectin microarray technology has allowed researchers to profile the glycans in complex biological samples in a high throughput fashion. This relatively new tool is highly suitable for both live cell and cell lysate analyses and has the potential for rapid discovery of glycan-based biomarkers. In this review, we will focus on the basic concepts and the latest advances of lectin microarray technology. We will also emphasize the application of lectin microarrays for biomarker discovery, and then discuss the challenges faced by this technology and potential future directions. Based on the tremendous progress already achieved, it seems apparent that lectin microarrays will soon become an indispensible tool for glycosylation biomarker discovery.