Transport effects on surface–volume biological reactions

Many cellular reactions involve a reactant in solution binding to or dissociating from a reactant confined to a surface. This is true as well for a BIAcore, an optical biosensor that is widely used to study the interaction of biomolecules. In the flow cell of this instrument, one of the reactants is immobilized on a flat sensor surface while the other reactant flows past the surface. Both diffusion and convection play important roles in bringing the reactants into contact. Usually BIAcore binding data are analyzed using well known expressions that are valid only in the reaction-limited case when the Damk?hler number Da is small. Asymptotic and singular perturbation techniques are used to analyze dissociation of the bound state when Da is small and O(1). Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. In addition, effective rate constants are derived that illustrate the effects of transport on the measured rate constants. All these expressions provide a direct way to estimate the rate constants from BIAcore binding data.     

A Theoretical and Experimental Study of Competition Between Solution and Surface Receptors for Ligand in a Biacore Flow Cell

Rate constants that characterize the kinetics of binding and dissociation between biomolecules carry fundamental information about the biological processes these molecules are involved in. An instrument that is widely used to determine these rate constants is the Biacore. In a Biacore experiment, one of the reactants, which we will call the receptor, is immobilized on a sensor chip. During the binding phase of the experiment the other reactant flows past the chip. After binding, buffer alone is introduced into the flow cell and dissociation is monitored. Often surface-based binding assays are influenced by the transport of the reactant in solution, complicating the determination of the chemical rate constants from the observed binding kinetics. We propose a new way to determine the dissociation rate constant by adding soluble receptor during dissociation. The method is tested first on simulated data and then on Biacore experiments where the lac repressor protein binds and dissociates from a stretch of double stranded DNA containing the lac repressor binding site. With this method we find a dissociation rate constant k_d=0.075 ± 0.005s^-1, a value that is faster than previously obtained from Biacore experiments. In developing our method to analyze these experiments we obtain an expression for the transport limited rate constant for a Biacore experiment when soluble receptor is present during dissociation.     

Effective rate models for receptors distributed in a layer above a surface: application to cells and Biacore

In the Biacore biosensor, a widely used tool for studying the kinetics of ligand/receptor binding, receptors are commonly localized to the sensor surface through attachment to polymers that extend from the surface to form a layer. The importance of the polymeric layer in analyzing data is controversial. The question of the effect of a binding layer also arises in the case of ligands interacting with binding sites distributed in the extracellular matrix of cells. To identify and quantify the effects of a binding layer on the estimation of association and dissociation rate constants, we derived effective rate coefficients. The expressions show that rate constants determined under the standard assumption that binding takes place on a two-dimensional surface underestimate the true reaction rate constants by a factor that depends on the ratio of the height of the layer to the mean free path of the ligand within the layer. We show that, for typical biological ligands, receptors, cells, and Biacore conditions, the binding layer will affect the interpretation of data only if transport of the ligand in the layer is slowed substantially--by one or two orders of magnitude--relative to transport outside the layer. From existing experiments and theory, it is not clear which Biacore experiments, if any, have transport within the dextran layer reduced to such an extent. We propose a method, based on the effective rate coefficients we have derived, for the experimental determination of ligand diffusion coefficients in a polymeric matrix.     

Convection Effects in the BIAcore Dextran Layer: Surface Reaction Model

The BIAcore is a surface plasmon resonance (SPR) device used to measure rate constants, primarily for biochemical reactions. It consists of a flow channel containing one reactant adjoining a dextran gel containing the other. In order to explain anomalous measurements from the device, it has been proposed that some flow penetrates into the dextran layer, thus enhancing transport. A model is presented that accounts for such behavior, and typical velocity fields in the dextran are constructed. The system is analyzed in the limit of the surface reaction model, which corresponds to the limit of thin dextran layers. Asymptotic and singular perturbation techniques are used to analyze association and dissociation kinetics. Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. The results indicate that the effects of such penetration are bound to be small, regardless of the flow model used.     

Stochastic model of chemoattractant receptor dynamics in leukocyte chemosensory movement

Mammalian white blood cells are known to bias the direction of their movement along concentration gradients of specific chemical stimuli, a phenomenon called chemotaxis. Chemotaxis of leukocyte cells is central to the acute inflammatory response in living organisms and other critical physiological functions. On a molecular level, these cells sense the stimuli termed chemotactic factor (CF) through specific cell surface receptors that bind CF molecules. This triggers a complex signal transduction process involving intracellular biochemical pathways and biophysical events, eventually leading to the observable chemotactic response. Several investigators have shown theoretically that statistical fluctuations in receptor binding lead to “noisy” intracellular signals, which may explain the observed imperfect chemotactic response to a CF gradient. The most recent dynamic model (Tranquillo and Lauffenburger,J. Math. Biol. 25, 229–262. 1987) couples a scheme for intracellular signal transduction and cell motility response with fluctuations in receptor binding. However, this model employs several assumptions regarding receptor dynamics that are now known to be oversimplifications. We extend the earlier model by accounting for several known and speculated chemotactic receptor dynamics, namely, transient G-protein signaling, cytoskeletal association, and receptor internalization and recycling, including statistical fluctuations in the numbers of receptors among the various states. Published studies are used to estimate associated constants and ensure the predicted receptor distribution is accurate. Model analysis indicates that directional persistence in uniform CF concentrations is enhanced by increasing rate constants for receptor cytoskeletal inactivation, ternary complex dissociation, and binary complex dissociation, and by decreasing rate constants for receptor internalization and recycling. For most rate constants, we have detected an optimal range that maximizes orientation bias in CF gradients. We have also examined different desensitization and receptor recycling mechanisms that yield experimentally documented orientation behavior. These yield novel insights into the relationship between receptor dynamics and leukocyte chemosensory movement behavior.     

A high sensitivity assay for the inflammatory marker C-Reactive protein employing acoustic biosensing

C-Reactive Protein (CRP) is an acute phase reactant routinely used as a biomarker to assess either infection or inflammatory processes such as autoimmune diseases. CRP also has demonstrated utility as a predictive marker of future risk of cardiovascular disease. A new method of immunoassay for the detection of C-Reactive Protein has been developed using Resonant Acoustic Profiling™ (RAP™) with comparable sensitivity to a high sensitivity CRP ELISA (hsCRP) but with considerable time efficiency (12 minutes turnaround time to result). In one method, standard solutions of CRP (0 to 231 ng/mL) or diluted spiked horse serum sample are injected through two sensor channels of a RAP™ biosensor. One contains a surface with sheep antibody to CRP, the other a control surface containing purified Sheep IgG. At the end of a 5-minute injection the initial rate of change in resonant frequency was proportional to CRP concentration. The initial rates of a second sandwich step of anti-CRP binding were also proportional to the sample CRP concentration and provided a more sensitive method for quantification of CRP. The lower limit of detection for the direct assay and the homogenous sandwich assay were both 20 ng/mL whereas for the direct sandwich assay the lower limit was 3 ng/mL. In a step towards a rapid clinical assay, diluted horse blood spiked with human CRP was passed over one sensor channel whilst a reference standard solution at the borderline cardiovascular risk level was passed over the other. A semi-quantities ratio was thus obtained indicative of sample CRP status. Overall, the present study revealed that CRP concentrations in serum that might be expected in both normal and pathological conditions can be detected in a time-efficient, label-free immunoassay with RAP™ detection technology with determined CRP concentrations in close agreement with those determined using a commercially available high sensitivity ELISA.     

Methyltransferase CheR binds to its chemoreceptor substrates independent of their signaling conformation yet modifies them differentially

Methylation of specific chemoreceptor glutamyl residues by methyltransferase CheR mediates sensory adaptation and gradient sensing in bacterial chemotaxis. Enzyme action is a function of chemoreceptor signaling conformation: kinase‐off receptors are more readily methylated than kinase‐on, a feature central to adaptational and gradient‐sensing mechanisms. Differential enzyme action could reflect differential binding, catalysis or both. We investigated by measuring CheR binding to kinase‐off and kinase‐on forms of Escherichia coli aspartate receptor Tar deleted of its CheR‐tethering, carboxyl terminus pentapeptide. This allowed characterization of the low‐affinity binding of enzyme to the substrate receptor body, otherwise masked by high‐affinity interaction with pentapeptide. We quantified the low‐affinity protein–protein interactions by determining kinetic rate constants of association and dissociation using bio‐layer interferometry and from those values calculating equilibrium constants. Whether Tar signaling conformations were shifted by ligand occupancy or adaptational modification, there was little or no difference between the two signaling conformations in kinetic or equilibrium parameters of enzyme‐receptor binding. Thus, differential methyltransferase action does not reflect differential binding. Instead, the predominant determinants of binding must be common to different signaling conformations. Characterization of the dependence of association rate constants on Deybe length, a measure of the influence of electrostatics, implicated electrostatic interactions as a common binding determinant. Taken together, our observations indicate that differential action of methyltransferase on kinase‐off and kinase‐on chemoreceptors is not the result of differential binding and suggest it reflects differential catalytic propensity. Differential catalysis rather than binding could well be central to other enzymes distinguishing alternative conformations of protein substrates.     

A fractal analysis of protein to DNA binding kinetics using biosensors

A fractal analysis of a confirmative nature only is presented for the binding of estrogen receptor (ER) in solution to its corresponding DNA (estrogen response element, ERE) immobilized on a sensor chip surface [J. Biol. Chem. 272 (1997) 11384], and for the cooperative binding of human 1,25-dihydroxyvitamin D(3) receptor (VDR) to DNA with the 9-cis-retinoic acid receptor (RXR) [Biochemistry 35 (1996) 3309]. Ligands were also used to modulate the first reaction. Data taken from the literature may be modeled by using a single- or a dual-fractal analysis. Relationships are presented for the binding rate coefficient as a function of either the analyte concentration in solution or the fractal dimension that exists on the biosensor surface. The binding rate expressions developed exhibit a wide range of dependence on the degree of heterogeneity that exists on the surface, ranging from sensitive (order of dependence equal to 1.202) to very sensitive (order of dependence equal to 12.239). In general, the binding rate coefficient increases as the degree of heterogeneity or the fractal dimension of the surface increases. The predictive relationships presented provide further physical insights into the reactions occurring on the biosensor surface. Even though these reactions are occurring on the biosensor surface, the relationships presented should assist in understanding and in possibly manipulating the reactions occurring on cellular surfaces.     

Monte Carlo simulation of diffusion and reaction in water radiolysis – a study of reactant `jump through' and jump distances

In Monte Carlo simulations of water radiolysis, the diffusion of reactants can be approximated by “jumping” all species randomly, to represent the passage of a short period of time, and then checking their separations. If, at the end of a jump, two reactant species are within a distance equal to the reaction radius for the pair, they are allowed to react in the model. In principle, the possibility exists that two reactants could “jump through” one another and end up with a separation larger than the reaction radius with no reaction being scored. Ignoring this possibility would thus reduce the rate of reaction below that intended by such a model. By making the jump times and jump distances shorter, any error introduced by `jump through' is made smaller. This paper reports numerical results of a systematic study of `jump through' in Monte Carlo simulations of water radiolysis. With a nominal jump time of 3 ps, it is found that more than 40% of the reactions of the hydrated electron with itself and of the H atom with itself occur when reactions during `jump through' are allowed. For all other reactions, for which the effect is smaller, the contributions of `jump through' lie in the range l%–16% of the total. Corrections to computed rate constants for two reactions are evaluated for jump times between 0.1 and 30 ps. It is concluded that jump-through corrections are desirable in such models for jump times that exceed about 1 ps or even less. In a separate study, we find that giving all species of a given type the same size jump in a random direction yields results that are indistinguishable from those when the jump sizes are selected from a Gaussian distribution. In this comparison, the constant jump size is taken to be the root-mean-square jump size from the Gaussian distribution. Received: 8 September 1997 / Accepted in revised form: 27 October 1997     

Opiate Receptor: Multiple Effects of Metal Ions

Abstract: The opiate antagonist [³H]diprenorphine ([³H]dip), a universal ligand at the μ, δ, and k opiate receptor subtypes, was used to study the effects of Ca-II, Cu-II, Mg-II, Mn-II, and Na⁺ on the rat cerebral opiate receptor. Two categories of effects were observed: (a) those on the binding rate constants and (b) those on binding capacity. (a) Sodium ions increased on- and off-rates on [³H]dip with a rather small net change in receptor affinity. The effects of Na⁺ and the divalent ions Ca-II, Mg-II, and Mn-II were antagonistic to each other. Ca-II, Mg-II, and the more effective Mn-II decreased receptor association and dissociation rates, again with minimal changes in the overall binding affinity in washed membrane homogenates. Previous studies using equilibrium binding analysis alone failed to detect changes in [³H]dip binding kinetics caused by these metal ions. In untreated rat brain homogenates, however, Ca-II (and to a lesser extent Mg-II) decreased [³H]dip binding, an effect distinct from that on the binding rate constants in washed membrane homogenates. (b) In untreated, Tris-buffer homogenates not containing external metal ions, a gradual decline in [³H]dip binding was observed. Cu-II or an equivalent endogenous divalent metal ion was identified as a causative factor, and Mn-II partially reversed this effect. Moreover, the addition of Mn-II stabilized the [³H]dip binding sites at very low concentrations of the metal (nM to μM range) that did not change the binding rate constants and that were in the physiological range of Mn-II in rat brain. This unique effect of Mn-II may represent a physiological function in the regulation of the opiate receptor that is not shared by Mg-II and Ca-II. The opposite effects of Cu-II and Mn-II on the in vitro receptor stability may be related to their opposite pharmacological effect in vivo. Finally, multiple changes of the effects of the tested metal ions on [³H]dip binding were observed during in vitro membrane homogenate dilution, centrifugation, and washing. These changes indicate that the opiate receptor complex as it exists in vivo may lose some of its functions and control mechanisms in vitro.     

On the validity of the quasi-steady state approximation of bimolecular reactions in solution

Two-step binding kinetics are extensively used to study the relative importance of diffusion in biochemical reactions. Classical analysis of this problem assumes ad hoc that the encounter complex is at quasi-steady state (QSS). Using scaling arguments we derive a criterion for the validity of this assumption in the limit of irreversible product formation. We find that the QSS approximation (QSSA) of two-step binding is only valid if the total ligand and receptor concentrations are much smaller than (k2+k-1)/k1, where k1 and k-1 are, respectively, the forward and reverse diffusion encounter rate constants and k2 is the chemical association rate constant. This criterion can be shown to imply that the average time between encounters is much longer than the half-life of the encounter complex and also guarantees that the concentration of the encounter complex is negligible compared to the reactant and product concentrations. Numerical examples of irreversible and reversible cases corroborate our analysis and illustrate that the QSS may be invalid even if k-2相似文献   

Study of Receptor-Chaperone Interactions Using the Optical Technique of Spectroscopic Ellipsometry

This work describes a detailed quantitative interaction study between the novel plastidial chaperone receptor OEP61 and isoforms of the chaperone types Hsp70 and Hsp90 using the optical method of total internal reflection ellipsometry (TIRE). The receptor OEP61 was electrostatically immobilized on a gold surface via an intermediate layer of polycations. The TIRE measurements allowed the evaluation of thickness changes in the adsorbed molecular layers as a result of chaperone binding to receptor proteins. Hsp70 chaperone isoforms but not Hsp90 were shown to be capable of binding OEP61. Dynamic TIRE measurements were carried out to evaluate the affinity constants of the above reactions and resulted in clear discrimination between specific and nonspecific binding of chaperones as well as differences in binding properties between the highly similar Hsp70 isoforms.     

Determination of thermodynamics and kinetics of RNA reactions by force

Single-molecule methods have made it possible to apply force to an individual RNA molecule. Two beads are attached to the RNA; one is on a micropipette, the other is in a laser trap. The force on the RNA and the distance between the beads are measured. Force can change the equilibrium and the rate of any reaction in which the product has a different extension from the reactant. This review describes use of laser tweezers to measure thermodynamics and kinetics of unfolding/refolding RNA. For a reversible reaction the work directly provides the free energy; for irreversible reactions the free energy is obtained from the distribution of work values. The rate constants for the folding and unfolding reactions can be measured by several methods. The effect of pulling rate on the distribution of force-unfolding values leads to rate constants for unfolding. Hopping of the RNA between folded and unfolded states at constant force provides both unfolding and folding rates. Force-jumps and force-drops, similar to the temperature jump method, provide direct measurement of reaction rates over a wide range of forces. The advantages of applying force and using single-molecule methods are discussed. These methods, for example, allow reactions to be studied in non-denaturing solvents at physiological temperatures; they also simplify analysis of kinetic mechanisms because only one intermediate at a time is present. Unfolding of RNA in biological cells by helicases, or ribosomes, has similarities to unfolding by force.     

A single-fractal analysis of cellular analyte-receptor binding kinetics utilizing biosensors

A fractal analysis of a confirmative nature only is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using a single-fractal analysis. Relationships are presented for the binding rate coefficient as a function of the fractal dimension and for the analyte concentration in solution. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. It is of interest to note that examples are presented where the binding coefficient, k exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficient (or affinity). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensor or other surfaces.     

Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction A⇌B

Many biochemical reactions consist of the spontaneous fluctuation between two states: A⇌B. For example these two states could be a ligand bound to an enzyme and the ligand and the enzyme separated from each other. A typical case would be the unbinding of CO from myoglobin (Mb), namely, MbCO⇌Mb+CO. Another example is the fluctuation in the ion channel protein in the cell membrane between conformations that are closed to the passage of ions and those that are open to the passage of ions, namely, closed⇌open. Such chemical reactions can be described as two energy levels corresponding to the two states, separated by a distribution of activation energy barriers. Since a kinetic rate can be associated with each energy barrier, this is also equivalent to a distribution of kinetic rate constants. We derive the distribution of the kinetic rates that produces the stretched exponential probability distribution, exp(−at ^b ) where 0<b≤1, which has been observed for such reactions. We also derive the form of the cumulative probability distribution when the pathways connecting the states have minimum or maximum rate constants.     

Relaxation methods for the determination of drug receptor affinities

According to the occupation theory of drug receptor interaction, the response is a functionf of the number of receptors occupied by drug molecules. Considerable controversy exists regarding assumptions about this function. Without knowledge of the nature of the function, it is not possible to determine directly the rate constants, and hence the affinity constant, in the reaction between the receptor and an agonist drug. Instead, indirect determinations involving the use of antagonists have been employed, limiting the determination of affinity to those agents for which specific antagonists exist. The present paper discusses a method for the direct determination of affinity of an agonist drug. It is a “relaxation method,” i.e., the equilibrium is perturbed and the kinetics of the restoration process are studied. Assuming only thatf is non-decreasing and approximately linear over a limited domain of concentrations, it is shown that the change in response obeys first order kinetics, permitting a determination of the rate constants from the time course of the restoration process.     

Two-Step Mechanism of Phlorizin Binding to the SGLT1 Protein in the Kidney

The relationships between phlorizin binding and Na⁺-glucose cotransport were addressed in rabbit renal brush-border membrane vesicles. At pH 6.0 and 8.6, high affinity phlorizin binding followed single exponential kinetics. With regard to phlorizin concentrations, the binding data conformed to simple Scatchard kinetics with lower apparent affinities of onset binding (K _di = 12–30 μm) compared to steady-state binding (K _de = 2–5 μm), and the first-order rate constants demonstrated a Michaelis-Menten type of dependence with K _m values identical to K _di . Phlorizin dissociation from its receptor sites also followed single exponential kinetics with time constants insensitive to saturating concentrations of unlabeled phlorizin or d-glucose, but directly proportional to Na⁺ concentrations. These results prove compatible with homogeneous binding to SGLT1 whereby fast Na⁺ and phlorizin addition on the protein is followed by a slow conformation change preceding further Na⁺ attachment, thus occluding part of the phlorizin-bound receptor complexes. This two-step mechanism of inhibitor binding invalidates the recruitment concept as a possible explanation of the fast-acting slow-binding paradigm of phlorizin, which can otherwise be resolved as follows: the rapid formation of an initial collision complex explains the fast-acting behavior of phlorizin with regard to its inhibition of glucose transport; however, because this complex also rapidly dissociates in a rapid filtration assay, the slow kinetics of phlorizin binding are only apparent and reflect its slow isomerization into more stable forms. Received: 22 June 2000/Revised: 1 November 2000     

Kinetics of ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor. I. A computer simulation of the influence of mass transport.

The influence of mass transport on ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor, was investigated. A one-dimensional computer model for the mass transport of ligand between the bulk solution and the polymer gel and within the gel was employed, and the influence of the diffusion coefficient, the partition coefficient, the thickness of the matrix, and the distribution of immobilized receptor were studied for a variety of conditions. Under conditions that may apply to many published experimental studies, diffusion within the matrix was found to decrease the overall ligand transport significantly. For relatively slow reactions, small spatial gradients of free and bound ligand in the gel are found, whereas for relatively rapid reactions strong inhomogeneities of ligand within the gel occur before establishment of equilibrium. Several types of deviations from ideal pseudo-first-order binding progress curves are described that resemble those of published experimental data. Extremely transport limited reactions can in some cases be fitted with apparently ideal binding progress curves, although with apparent reaction rates that are much lower than the true reaction rates. Nevertheless, the ratio of the apparent rate constants can be semiquantitatively consistent with the true equilibrium constant. Apparently "cooperative" binding can result from high chemical on rates at high receptor saturation. Dissociation in the presence of transport limitation was found to be well described empirically by a single or a double exponential, with both apparent rate constants considerably lower than the intrinsic chemical rate constant. Transport limitations in the gel can introduce many generally unknown factors into the binding progress curve. The simulations suggest that unexpected deviations from ideal binding progress curves may be due to highly transport influenced binding kinetics. The use of a thinner polymer matrix could significantly increase the range of detectable rate constants.