Absolute reaction rate and kinetics of protein adsorption at solid-liquid interfaces.

Extents of adsorption of bovine serum albumin from aqueous solution to the surface of alumina, silica, carbon and chromium powder have been studied as function of time for various values of bulk protein concentration, pH, ionic strength and temperature. The rates of adsorption in all cases have been observed to fit in the first order rate equation with two different rate constants Ka1 and Ka2. Effects of addition of SDS, CTAB and neutral salts on values of Ka1 and Ka2 have also been studied. Using Arrhenius equation the activation energy values Ea1 and Ea2 have been evaluated from the values of Ka1 and Ka2 at three different temperatures, respectively. The corresponding values of enthalpy of activation (delta H*), entropy of activation (delta S*), and free energy of activation (delta G*) have been evaluated using Eyring's equation of absolute reaction rate. The mechanism of protein adsorption has been discussed in the light of basic principles of absolute reaction rate. It has been found that for Ka1 the delta H*1 greater than T delta S*1 and for Ka2 T delta S*2 greater than H*2, i.e. the anchorage and binding of protein to the surface are enthalpy controlled processes whereas the surface denaturation as well as rearrangement and folding is an entropy controlled process. The role of diffusion on rate of adsorption has also been discussed.     

The kinetics of hemolytic plaque formation. II. Inhibition of plaques by hapten.

We present a mathematical theory of hapten inhibition of hemolytic plaque formation. The treatment is based upon the mathematical model for plaque growth presented by DeLisi &; Bell (1974). The lymphocyte under consideration is embedded in an infinite three-dimensional medium, and is secreting antibodies isotropically at a constant rate. As the antibodies diffuse from the source they can bind reversibly to hapten, and in the most general case reversibly to red blood cell (RBC) epitope. The model leads to a non-linear diffusion equation coupled to a set of first order differential equations. The system must, in general, be solved numerically. However, in many cases of experimental interest simplifications arise which permit closed form solutions to be obtained. In this paper we have developed solutions for three special cases.In the first example antibodies can bind only univalently to RBCs, as would be expected if the epitopes are sparsely distributed. In this case reaction between antibody site and RBC epitope is rapid ( ⪆ 1 sec) and reversible and local equilibrium is assumed. This leads to a “pure” diffusion equation in the free antibody concentration, but with a reduced diffusion coefficient.In another example univalent attachment of an antibody site to a RBC epitope is followed by a rapid irreversible intramolecular reaction. This might be expected for example if the epitope density is large. An exact solution to the resulting diffusion equation was also found in this case. In order to assess an intermediate situation, we also solved the equations for a model in which intramolecular reaction is slow and irreversible.The theory predicts that the type of information one can obtain from inhibition experiments depends critically upon the preparation of the RBC. If the cell is sufficiently haptenated so that rapid irreversible multivalent attachment is favorable, a differential plot of the inhibition curve will reflect the affinity distribution of antibody sites for free hapten. If only univalent attachment with RBCs is possible, so that antibody sites bind to RBC hapten in the same way they bind to free hapten, then a differential plot of the inhibition curve will reflect the secretion rate distribution.     

Probing of the substrate binding domain of lactose permease by a proton pulse

The lactose permease of Escherichia coli coupled proton transfer across the bacterial inner membrane with the uptake of beta-galactosides. In the present study we have used the cysteine-less C148 mutant that was selectively labeled by fluorescein maleimide on the C148 residue, which is an active component of the substrate transporting cavity. Measurements of the protonation dynamics of the bound pH indicator in the time resolved domain allowed us to probe the binding site by a free diffusing proton. The measured signal was reconstructed by numeric integration of differential rate equations that comply with the detailed balance principle and account for all proton transfer reactions taking place in the reaction mixture. This analysis yields the rate constants and pK values of all residues participating in the fast proton transfer reaction between the bulk and the protein's surface, revealing the exposed residues that react with free protons in a diffusion controlled reaction and how they transfer protons among themselves. The magnitudes of these rate constants were finally evaluated by comparison with the rate predicted by the Debye-Smoluchowski equation. The analysis of the kinetic and pK values indicated that the protein-fluorescein adduct assumes two conformation states. One is dominant above pH 7.4, while the other exists only below 7.1. In the high pH range, the enzyme assumes a constrained configuration and the rate constant of the reaction of a free diffusing proton with the bound dye is 10 times slower than a diffusion controlled reaction. In this state, the carboxylate moiety of residue E126 is in close proximity to the dye and exchanges a proton with it at a very fast rate. Below pH 7.1, the substrate binding domain is in a relaxed configuration and freely accessed by bulk protons, and the rate of proton exchange between the dye and E126 is 100,000 times slower. The relevance of these observations to the catalytic cycle is discussed.     

Immobilized enzymes: Electrokinetic effects on reaction rates under external diffusion

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

Participation of oxygen in the reduction of methylviologen, photosensitized by chlorophyll, in an aqueous solution of detergent]

Dependence of chlorophyll "a" photosensitized reduction of methylviologene with tiourea on the temperature of reaction mixture was studied in aerobic conditions in triton X-100 aqueous solution. It was found that the reaction consisted of two stages: the light and dark ones. Photosensitized oxidation of tiourea with air oxygen proceeds at the temperatures up to -70 degrees C. Reduction of methylviologen is a dark stage for which diffusion processes are necessary. The role of hydrogen peroxide in the reaction studied has been investigated. It has been shown that hydrogen peroxide is not the "initiator" of the reaction which results in the reduction of methylviologen. Reduced glutation and the mixture of reduced and oxidized glutations were used as electron donors in photosensitized reaction in the presence of air oxygen. An increase of the depth and rate of the reduction of methylviologen under aerobic conditions as compared to anaerobic ones points to the formation of more active reducers than the initial electron donor.     

Open tubular heterogeneous enzyme reactors: preparation and kinetic behavior

Tubes with immobilized enzymes on the inner wall, called open tubular heterogeneous enzyme reactors, were prepared by binding enzymes either directly to the tube inside surface or to a layer of a porous matrix attached to the inner wall. Kinetic studies of the hydrolysis of N-benzoyl-L -arginine ethylester as a model reaction indicated that the reaction was kinetically controlled in reactors with surface bound trypsin and the kinetic parameters were evaluated by conventional methods. On the other hand, substrate diffusion in both the porous matrix and the bulk substrate solution strongly affected the rate of reaction in porous layer trypsin reactors. The highest overall rates of reaction were obtained when the reaction was bulk diffusion controlled and the measured rates were in agreement with those calculated from expressions derived from heat transfer theory. The design of reactors for the limiting cases of kinetic and bulk diffusion controlled reaction as well as a method for the determination of substrate diffusivity are outlined.     

Kinetic analysis of protonation of a specific site on a buffered surface of a macromolecular body

The kinetics of protonation of a specific site on a macromolecular structure (micelle) in buffered solution was studied with the purpose of evaluating the effect of buffer on the observed dynamics. The experimental system consisted of the following elements: Brij 58 micelles serving as homogeneous uncharged macromolecular bodies, bromocresol green, a well-adsorbed proton detector, and 2-naphthol-3,6-disulfonate as a proton emitter in the bulk. Imidazole was the mobile buffer while neutral red, which has a high affinity for the micellar surface, served as the immobile buffer. An intensive laser pulse ejects a proton from the proton emitter, and the subsequent proton-transfer reactions are measured by fast spectrophotometric methods. The dynamics of proton pulse in buffered solution are characterized by a very rapid trapping of the discharged protons by the abundant buffer molecules. This event has a major effect on the kinetic regime of the reaction. During the first 200 ns the proton flux is rate limited by free-proton diffusion. After this period, when the free-proton concentration decayed to the equilibrium level, the relaxation of the system is carried out by the diffusion of buffer. Thus in the buffered biochemical system, at neutral pH, most of proton flux between active sites and bulk is carried out by buffer molecules--not by diffusion of free protons. Surface groups on a high molecular weight body exchange protons among them at a very fast rate. This reaction has a major role on proton transfer from a specific site to the bulk.(ABSTRACT TRUNCATED AT 250 WORDS)     

An enzyme rate equation for the overall rate of reaction of gel-immobilized glucose oxidase particles under buffered conditions. I. Pseudo-one substrate conditions

The overall rate of reaction of buffered gel-immobilized glucose oxidase particles is described by means of an enzyme rate equation which relates the overall reaction rate of a particle to the free solution characteristics of the enzyme, the effective diffusivity of the limiting substrate in the gel, the characteristic particle size, and the limiting substrate concentration adjacent to the gel surface. This equation accounts quantitatively for the limitation of the overall rate of reaction by substrate diffusion, and it is used to illustrate the influence of the system parameters, i. e., particle size, enzyme concentration, and pH, on the extent of the diffusional resistance associated with gel-immobilized glucose oxidase particles. The enzyme rate equation is generally applicable to those enzymes whose kinetics approximately follow Michaelis-Menten form when in free solution.     

Transient response of encapsulated enzymes in hollow-fiber reactor

A mathematical model for the transient response of encapsulated enzymes is developed showing the effects of the outer boundary layer, the encapsulating membrane, the partition coefficient, and diffusion with reaction within the encapsulating medium. The model incorporates both first-order kinetics and Michaelis-Menten kinetics for the reaction rate. Using typical hollow-fiber or microcapsule parameters, the model shows that (a) the partition coefficient affects the overall rate only when the rate-limiting step is diffusion through the membrane, (b) the transient overall effectiveness factor rises sharply with time and approaches an asymptotic value for most situations, and (c) the first-order approximation to Michaelis-Menten kinetics is not valid when the initial outside bulk concentration is higher than the Michaelis constant and the overall rate is reaction limited. The model is compared with experimental data using uricase in a hollow-fiber enzyme reactor configuration. Batch assay and CSTUER (continuous-stirred ultrafiltration enzyme reactor) studies were conducted on the free enzyme to provide some of the parameters used in the model. The CSTUER data fit the case of substrate inhibition kinetics with the apparent Michaelis constant approaching zero. The hollow-fiber reactor was conducted with uricase dissolved in both a buffer solution and a concentrated hemoglobin solution. Diffusivities of the solute were measured in both solutions as was the osmotic pressure of the hemoglobin solution. While experimental data for uricase in buffer solution could easily be matched by the model, that in the concentrated hemoglobin solution could not.     

Sensitized photomodification of DNA with binary systems of oligonucleotide conjugates. IV. Photoinduced electron transfer

The photomodification of single-stranded DNA sensitized to visible light (450-580 nm) by a binary system of oligonucleotide conjugates complementary to adjacent DNA sequences was studied. One oligonucleotide carries a residue of the photoreagent p-azidotetrafluorobenzaldehyde hydrazone at its 3'-terminal phosphate, and the other has a residue of the sensitizer, perylene or 1,2-benzanthracene, at the 5'-terminal phosphate. The rate of photomodification sensitized by the perylene derivative is 300,000-fold higher than the rate of photomodification in the absence of the sensitizer. Since the excitation energy of perylene is lower than the energy necessary for the initiation of azide photodecomposition, it is likely that the sensitization in the complementary complex occurs by electron transfer from the azido group of the photoreagent to the excited sensitizer. The sensitization by the 1,2-benzanthracene oligonucleotide derivative occurs by means of singlet-singlet energy transfer, which enables this sensitizer to act as a unconsumable catalyst each molecule of which is able to initiate the photomodification of more than 20 DNA molecules. By both mechanisms, the photomodification occurs with high specificity on the G11 residue of the target DNA. The degree of sensitized photomodification reaches 72%.     

Kinetic studies of alpha-galactosidase-containing mold pellets on PNPG hydrolysis.

Little is known about techniques for applying untreated microbial cells containing enzymes directly to industrial processes as a biocatalyst. The kinetic behavior of alpha-galactosidase-containing spherical pellets which are formed naturally under given conditions in a submerged culture of Mortierella vinacea was studied on the hydrolysis of PNPG (p-nitrophenyl-alpha-D-galactopyranoside). The effect on intraparticle diffusion on the overall reaction rate was assessed by the use of an effectiveness factor, which was calculated by the approximate solution to the equation derived from the mass balance within a pellet. The experimental effectiveness factors were found to be represented as a single function of the modified Thiele modulus, including such parameters as pellet size, enzyme concentration in the pellet, and substrate concentration. As the diffusional effect became more significant, the marked substrate inhibition as seen for a free enzyme disappeared gradually. The effect of product inhibition on the pellets was much weaker than that for a free enzyme at a given substrate concentration. In the region of diffusion controlled reaction, it was found that the rate is proportional to the square root of the enzyme concentration in the pellet. In addition, similarly to what was reported previously for a free enzyme,the reaction in a batch system was found to be approximately representable as simple first-order kinetics in which the rate constant was dependent on the initial substrate concentration.     

Effects of lysophosphatidylcholine micelle and phosphatidylcholine liposome on photoreduction of methylviologen

Photoinduced reduction of methylviologen (MV2+) by ethylenediaminetetraacetate (EDTA3-), which was sensitized by thiacarbocyanine dyes having long alkyl chains (C+m-n) embedded in palmitoyl lysophosphatidylcholine micelle and dipalmitoyl phosphatidylcholine liposomal membrane, was carried out. The formation rate of reduced methylviologen cation radical (MV+.) decreased with the time of irradiation with visible light, and the deceleration was more pronounced in the micellar solution. In kinetic studies, we found that the sensitizer divalent cation radical (C2+.m-n) is formed through the reaction of photoexcited sensitizer (C+*m-n) with MV2+ as an intermediate in this reaction, and that the reduction of C2+.m-n with EDTA3- inhibits the back reaction of MV+. with C2+.m-n. The inhibition was greater in the liposomal solution than in the micellar solution. This was ascribed to a higher concentration of EDTA3- on the liposomal surfaces through the electrostatic interaction between EDTA3- and the liposomal surfaces, the charge of which is attributed to the univalent cation sensitizer embedded in the liposomal membrane. The difference in the positive charge density of the surface of these lipid aggregates was due to the difference in the curvature of the micelle and the liposome. These results suggest that the dipalmitoyl phosphatidylcholine liposome is a more effective carrier than the palmitoyl lysophosphatidylcholine micelle for the production of MV+. in the photoreduction studied here.     

Photosensitized transformation of adrenochrome

The methylene blue-sensitized photooxidation of adrenochrome was studied by steady-state kinetics. The buffered, aqueous system was irradiated with light longer than 600 nm, wavelengths at which only the sensitizer absorbs. During irradiation, disappearance of adrenochrome and the formation of adrenochrome-melanin was observed. Calculated rate constants were determined on the basis of spectroscopic measurements. It was found that the observed transformation reaction steps are pH dependent. The participation of two types of photosensitized mechanism has been evidenced. Type II, singlet oxygen mechanism, predominates at pH below 9, whereas above pH 9, Type I applies. We observed the so-called "isotope effect" and a decrease of photooxidation rate in the presence of azide ion, a well-known singlet oxygen quencher, indicating the participation of singlet oxygen.     

Reaction rate enhancement by surface diffusion of adsorbates.

Ligands can be captured by a surface target through either direct bulk diffusion or surface diffusion following reversible adsorption to the surface. We have solved a steady state boundary value problem for a perfect sink disk target in the surface, taking into account bulk and surface diffusion coefficients D and Ds and adsorption/desorption kinetic rate constants ka and kd at non-target regions. Solutions have been successfully found by numerical computation. The results show that the rate of capture from the surface depends non-linearly on Ds, D, ka, kd and geometrical dimensions. In particular, we demonstrate that not only is the non-target region equilibrium constant Keq (= ka/kd) important in determining the rate of capture from the surface, but so are the kinetic rate constants ka and kd separately. In all cases, the surface adsorption/diffusion combination enhances the total rate of capture. The results should be useful for predicting reaction rates of biological membrane bound receptor clusters and substrate-immobilized enzymes.     

The effect of flanking bases on direct and triplet sensitized cyclobutane pyrimidine dimer formation in DNA depends on the dipyrimidine,wavelength and the photosensitizer

Cyclobutane pyrimidine dimers (CPDs) are the major products of DNA produced by direct absorption of UV light, and result in C to T mutations linked to human skin cancers. Most recently a new pathway to CPDs in melanocytes has been discovered that has been proposed to arise from a chemisensitized pathway involving a triplet sensitizer that increases mutagenesis by increasing the percentage of C-containing CPDs. To investigate how triplet sensitization may differ from direct UV irradiation, CPD formation was quantified in a 129-mer DNA designed to contain all 64 possible NYYN sequences. CPD formation with UVB light varied about 2-fold between dipyrimidines and 12-fold with flanking sequence and was most frequent at YYYR and least frequent for GYYN sites in accord with a charge transfer quenching mechanism. In contrast, photosensitized CPD formation greatly favored TT over C-containing sites, more so for norfloxacin (NFX) than acetone, in accord with their differing triplet energies. While the sequence dependence for photosensitized TT CPD formation was similar to UVB light, there were significant differences, especially between NFX and acetone that could be largely explained by the ability of NFX to intercalate into DNA.     

Determination of effective diffusion coefficient of substrate in gel particles with immobilized biocatalyst

A method of determining of the effective diffusion coefficient of substrate in a particle, where the diffusion and consumption of substrate by biocatalytic reaction are present simultaneously, was designed and experimentally verified. The method is based on measuring the overall rate of heterogeneous biocatalytic reaction in particles of varying diameter. The effective diffusion coefficient, D_e, was determined by fitting the measured reaction rates with the solution of the reaction-diffusion equation. The method is tailored for cases where the enzyme reaction is governed by the Michaelis-Menten kinetics. The value of K_m required for the solution of the mathematical model was adopted from the measurement of the kinetics of free cells, whereas the rate parameter, k₂, was optimized together with D_e. As an experimental model, the sucrose hydrolysis catalyzed by Ca-alginate-entrapped yeast cells was examined. The particle diameter varied in the range of 1.2–3.9 mm and the initial reaction rates were measured in a batch-stirred reactor at a sucrose concentration of 100 m . The D_e of sucrose at 30°C was found to be 2.9 · 10⁻¹⁰ m²s⁻¹.     

Kinetics and thermodynamics of protein adsorption: a generalized molecular theoretical approach

The thermodynamics and kinetics of protein adsorption are studied using a molecular theoretical approach. The cases studied include competitive adsorption from mixtures and the effect of conformational changes upon adsorption. The kinetic theory is based on a generalized diffusion equation in which the driving force for motion is the gradient of chemical potentials of the proteins. The time-dependent chemical potentials, as well as the equilibrium behavior of the system, are obtained using a molecular mean-field theory. The theory provides, within the same theoretical formulation, the diffusion and the kinetic (activated) controlled regimes. By separation of ideal and nonideal contributions to the chemical potential, the equation of motion shows a purely diffusive part and the motion of the particles in the potential of mean force resulting from the intermolecular interactions. The theory enables the calculation of the time-dependent surface coverage of proteins, the dynamic surface tension, and the structure of the adsorbed layer in contact with the approaching proteins. For the case of competitive adsorption from a solution containing a mixture of large and small proteins, a variety of different adsorption patterns are observed depending upon the bulk composition, the strength of the interaction between the particles, and the surface and size of the proteins. It is found that the experimentally observed Vroman sequence is predicted in the case that the bulk solution is at a composition with an excess of the small protein, and that the interaction between the large protein and the surface is much larger than that of the smaller protein. The effect of surface conformational changes of the adsorbed proteins in the time-dependent adsorption is studied in detail. The theory predicts regimes of constant density and dynamic surface tension that are long lived but are only intermediates before the final approach to equilibrium. The implications of the findings to the interpretation of experimental observations is discussed.     

Reduction mechanism of L-cysteine on keratin fibers using microspectrophotometry and Raman spectroscopy

In order to investigate the reduction mechanism of L-cysteine (Cys) on keratin fibers, cross-sectional samples of virgin white human hair treated with Cys were prepared. The heterogeneous reaction between Cys and keratin fibers involving the diffusion of Cys into human hair was analyzed at the molecular level using microspectrophotometry and Raman spectroscopy. The diffusion pattern of Cys into human hair showed non-Fickian type characteristics, thus indicating the free amino groups of electrostatically interacted with the anionic ions of the fiber surface. The disconnected relative concentration of -SS- groups at various depths of the hair samples with pH 9.0 was less than the Cys relative concentration, indicating that the reaction rate (the disconnection of -SS- groups) was slower than the diffusion rate of Cys into human hair. From these experiments, we concluded that the free amino groups of Cys electrostatically interacted with the anionic ions of the fiber surface, thereby decreasing the reaction rate (the disconnection of -SS- groups) of Cys at pH 9.0.     

Proton transport via the membrane surface

Some proton pumps, such as cytochrome c oxidase (C(c)O), translocate protons across biological membranes at a rate that considerably exceeds the rate of proton transport to the entrance of the proton-conducting channel via bulk diffusion. This effect is usually ascribed to a proton-collecting antenna surrounding the channel entrance. In this paper, we consider a realistic phenomenological model of such an antenna. In our model, a homogeneous membrane surface, which can mediate proton diffusion toward the channel entrance, is populated with protolytic groups that are in dynamic equilibrium with the solution. Equations that describe coupled surface-bulk proton diffusion are derived and analyzed. A general expression for the rate constant of proton transport via such a coupled surface-bulk diffusion mechanism is obtained. A rigorous criterion is formulated of when proton diffusion along the surface enhances the transport. The enhancement factor is found to depend on the ratio of the surface and bulk diffusional constants, pK(a) values of surface protolytic groups, and their concentration. A capture radius for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton can migrate on the membrane surface between a source (such as CcO) and a sink (such as ATP synthase) without fully equilibrating with the bulk. In pure aqueous solutions, protons can travel over long distances (microns). In buffered solutions, the travel distance is much shorter (nanometers); still the enhancement effect of the surface diffusion on the proton flow to a target on the surface can be tens to hundreds at physiological buffer concentrations. These results are discussed in a general context of chemiosmotic theory.     

Diffusion-controlled reactions on spherical surfaces. Application to bacteriophage tail fiber attachment.

We have explored the kinetic implications of a model that may account for the acceleration of tail fiber (F) attachment to baseplates (B) by whiskers (W) on bacteriophage T4. The model assumes that a W-F complex is formed initially, and that the tethered fiber then undergoes rotational diffusion until a B-F encounter takes place. In the absence of whiskers, B-F complexes must form unassisted. Formation of a W-F intermediate will accelerate F attachment to B if (a) the bimolecular rate constant for W-F complex formation is larger than that for direct B-F interaction and (b) subsequent rotational diffusion of the tip of F to B is not much slower than the dissociation of W-F. Condition a was investigated by applying a recent theory of orientational effects on translational diffusion-controlled reactions. This theory suggests that substantial rate enhancement is expected if the reaction half-angle theta 0 is larger for W-F than for B-F complex formation. Condition b was investigated by calculating the mean and the variance of the time required for the diffusion of a molecule (the proximal tip of the fiber) on a spherical surface (whose radius is the distance from the tip to the whisker tethering point) into a circular sink (the baseplate site). The mean time is on the order of the inverse rotational diffusion coefficient, DR, of the fiber, but is sensitive to theta 0. Both conditions are satisfied for plausible choices of parameters. The solution to the diffusion equation we have obtained should have application to other physical situations, such as the rate of quenching of a fluorophore as it diffuses on the surface of a spherical membrane into proximity with a quencher.