Analysis of some "insoluble" problems of determining the binding parameters of ligand-receptor interaction and methods of their solving

Some problems of the estimation of the parameters of ligand-receptor interaction (affinity, rate constants, valency, etc.) were considered. It was demonstrated that not only the Scatchard plot but also Klotz plot could be used for determining the parameters of ligand-receptor interaction for two types of binding sites of different affinity. A new approach and new coordinate systems for the estimation of the parameters of ligand-receptor interaction were suggested. It was shown that for the estimation of the affinity of putative monovalent antibodies by ELISA various equations, which are more precise and convenient than the Friguet et al. equations, could be obtained by the transformation of mass action law equation. The problem solution for the estimation by ELISA the affinity of two types of bivalent antibodies with different affinity and their concentrations for the case of the mixture of these antibodies was also suggested. The application of the proposed coordinate of dilution allows to solve the problem of determination of the parameters of ligand-receptor interaction (including antigen-antibody system) for the pre-existing ligand-receptor mixture without their preliminary separation and purification. This approach is especially important for the cases when the receptor is not stable enough to be isolated in the intact form from this mixture. It was shown that the well-known phenomenon of the prozone often observed under the titration of serum antibodies by the method of agglutination may get a mathematical explanation. Analytical solution of the problem of determining the velocity constant and the amount of the end product of the first order irreversible and reversible reaction kinetics was suggested, despite the fact that the process is described by the system of irrational equations. Mehods of asymptotic solution of transcendental irrational equations which describe the dynamics of reactions which mechanisms are subject to the so-called heterogeneous, successive, or competitive models have been considered. These methods permit the finding of the reaction rate constants and the amount of the end product, if the kinetics of the transformation of either initial, or end product of the reaction is known.     

Determination of the binding parameters for a pre-existing antigen-antibody mixture

A new method, which allows to evaluate parameters of interaction between antibodies (or receptors) and an antigen (or ligand) is suggested. The method is based on the use of so-called coordinates of dilution suggested by the author earlier. Representation of the data of the titration curves for the mixtures of antibodies (or receptors) and antigen (or ligand) in these coordinates allows one to determine the affinity of interaction and the concentration of antigen (or ligand), which can reversibly block antibodies (or receptors). Simple formulas, which allow to estimate which part of paratopes or bivalent antibodies is free and which part is blocked by the antigen, depending on dilution of the considered system, are also suggested. Such a method could be useful for characterization of infection and autoimmune processes when the antigen and antibodies circulate together in the bloodstream.     

A new method for the evaluation of antibody affinity based on serial dilutions of studied antibody-antigen mixture

A new method for the evaluation of the affinity of bivalent antibodies were suggested. This method is based on the previously published by the author the idea of using so-called coordinates of dilutions. It was shown that the suggested method allows to evaluate the affinity of antibodies with high accuracy using this simple approach. It is supposed that at some conditions the suggested method could have substantial advantages in comparison to the traditional methods. This method allows to analyze situations when antibodies are already in a mixture with antigen, for example in the bloodstream in the case of infections or autoimmune diseases. The method provides useful approach for the evaluation not only antibody affinity, but also the concentration of circulated antigen.     

Avidity of bivalent antibodies. Problems of its experimental determination and theoretical evaluation

Some problems of experimental determination or theoretical evaluation of antibody avidity are considered. It was shown that in order to determine the fraction of nonoccupied antibodies in their mixture with the excess of the corresponding antigen which is required to estimate avidity the methods should be used which are more sensitive than ELISA. The available methods did not allow determining the avidity of bivalent antibodies because of many reasons. However, in the recent years new methods were suggested that make it possible to evaluate the avidity of bivalent antibodies and that of the receptors which consist of two binding sites connected by a flexible linker of the known length. Thus, there are all possibilities now for determining the avidity of bivalent antibodies in experiments or by theoretical methods.     

Determination of antibody affinity by ELISA. Theory

New approaches for the measurement of antibody affinity by ELISA are suggested and considered theoretically. It was shown that not only more precise and more convenient in comparison to that suggested earlier, but also more informative graphical representation of the experimental data in the appropriate coordinate could be used for evaluation of antibody affinity. The following cases were considered: (i) determination of antibody affinity for one kind of univalent antibodies, (ii) determination of antibody affinity for one kind of bivalent antibodies, (iii) determination of antibody affinity for two kinds of univalent antibodies, which are in a mixture, and (iv) determination of antibody affinity for two kinds of bivalent antibodies, which are in a mixture. Advantages and disadvantages of the different approaches are discussed.     

ELISA-based method for determining the affinity of bivalent antibodies of two specificities in a mixture

The problem of the evaluation of the affinity for two types of bivalent antibodies in a mixture is considered. It is shown that the binding curve in appropriate coordinates can be used to compose either a system of four equations with four unknowns or a system of two equations with two unknown variables. The numerical solution of these equation systems yields affinity constants for both antibodies and the relationship between concentrations of antibodies studied in the mixture.     

Determination of the affinity of high- and low-affinity antibodies, which are in a mixture, using ELISA and the method of non-linear regression

It was shown that application of the method of non-linear regression for the solution of the equation, which relates the fraction of free antibodies in a mixture and antigen concentrations, allows to determine the affinity constants for two antibodies in a mixture. Such method is easier and more accurate than the suggested by us earlier method, which use the numerical solution of the appropriate four equations, that describe the relations between the experimental data obtained by ELISA, competing antigen concentration, and values of antibody affinity. In addition, the proposed method allows using much less quantity of experimental measurements without diminishing of the accuracy for the affinity constants evaluations.     

Determination of the concentration of ligand-specific molecules, found in mixtures with ligand-nonspecific molecules

A new method, which allows determination of the concentration of ligand-specific molecules in a mixture of these molecules with biochemically similar but ligand-unspecific molecules, is suggested. The method is based on a partial exhaustion of the mixture on a column with immobilized ligand and determination of the part of ligand-specific molecules presented in exhausted mixture. The concentration of monoclonal antibodies specific to bovine serum albumin in a commercial "Sigma" preparation and concentration of polyreactive immunoglobulins in a commercial "Sigma" preparation of bovine immunoglobulins were determined by suggested method.     

Determining the parameters for receptor-ligand interaction by serial dilution method for the case when the ligand and receptor are in a pre-existing mixture

New methods of determining the binding parameters for ligand-receptor interaction are considered. The considered approaches are based on the earlier suggested method of serial dilution and application of so-called coordinates of dilution. It was shown that the suggested methods allow to evaluate affinity constant and ligand concentration even for the case, when the receptor and corresponding ligand of unknown concentration are in a mixture and their separation from each other is impossible. In this connection the suggested methods are especially useful for studying the ligand-receptor interaction if the receptor is very liable and its purification from the ligand would cause drastic changes of its binding properties.     

Genetic regulation of the expression of antigen specificity H-2K.31 on mouse erythrocytes

In titration of anti-H-2K.31 antiserum by hemagglutination, erythrocytes of some mice show “standard” titration curves without a detectable prozone, whereas erythrocytes of other mice show a marked prozone or midzone phenomenon. Genetic studies have shown that a single, dominant gene identical with or closely lined to theEa-4 ^b allele of C57BL-related mouse strains is responsible for this prozone. The anti-H-2K.31 serum (A anti-BALB/c sarcoma Meth A) also contains a low titer of anti-Ea-6.2 antibodies, the first reported occurrence of these antibodies.     

Pitfalls in the Dextran-coated charcoal assay of estrogen receptors in breast cancer tissue

This study investigated the influence of the degree of concentration of breast tumor cytosols on the apparent estrogen receptor content as measured by the Dextran-charcoal assay. It was found that the dilution of cytosols to 1-2 mg protein/ml frequently but not always causes highly underestimated receptor concentrations. This could not be explained by the protein loss through adsorption to the charcoal. The effect was also studied in the presence of gelatin, sodium molybdate or with limited trypsinization of the incubation mixture. Addition of 1 mg/ml gelatin in the Dextran-charcoal suspension was very useful in most cases in preventing dilution induced losses in receptor sites. Both trypsinization and addition of sodium molybdate produced increases in receptor concentrations that were not as susceptible to inactivation through dilution of the cytosol. These data suggest that the observed high variability in the dilution induced receptor losses can be explained by receptor heterogeneity: some receptor form(s) are either readily absorbed to or "stripped" by the charcoal particles. As a conclusion we recommend that in order to optimize the estrogen receptor assay as regards both binding sites and affinities the cytosol concentrations should be maintained as high as possible and a protein expander be included in the Dextran-charcoal suspension. Though sodium molybdate frequently gives considerable increases in estrogen binding sites it occasionally has an opposite effect. For this reason we hesitate to recommend its use in routine assays of estrogen receptors.     

New capabilities in determining the binding parameters for ligand-receptor interaction

A new method for determining the binding parameters of ligand-receptor interaction is suggested. The method is based on the application of the so-called coordinate of dilution, suggested by us earlier. We demonstrated that it is possible to determine the binding characteristics of ligand-receptor interaction using either the measurement of the concentration of the ligand-receptor complex at a state of equilibrium or the concentration of free receptors at different dilutions of the studying ligand-receptor mixture. The method also allows the determination of the concentration of the ligand in a pre-existing ligand-receptor mixture without preliminary separation of the interacting counterparts. For this reason the suggested method could be especially useful when the studying very labile receptors for which purification from the corresponding ligand is very difficult or impossible.     

Display of the alveolar plateau of single-breath tests in "dilution index" format

In 1949, Fowler (J. Appl. Physiol. 2: 283-299) advocated calculation of a "dilution index" from data of the alveolar plateau of single-breath tests; the calculation provides an estimate of the dilution of resident gas in the lung that gave rise to the observed concentrations. In this communication, we show that the calculation can be applied to conventional single-breath tests where O2 is inhaled by air-breathing persons, and we illustrate the principle with vital capacity breaths of a mixture that contained a low concentration of neon. The dilution was approximately 3:1 in young subjects (20-30 yr), as if a vital capacity of 6 liters were mixed with a residual volume of 2 liters. The dilution was less, 2:1, in older subjects (56 yr) and tended to become as low as 1:1 during emptying of the closing volume. In addition to being more informative, the dilution index format allows common sense comparison of alveolar plateau levels and slopes when single-breath tests are done by various methods.     

New approach in evaluating affinity of bivalent antibodies by the method of surface plasmon resonance. Theory

Theoretical aspects of the affinity evaluation for the interaction between bivalent receptors (or antibodies) and corresponding ligands (or antigens) are considered. It was shown that the ligand presence in the solution at the stage when the receptor dissociation occurs leads to the increase of the affinity evaluation accuracy. We demonstrated that the analysis of the dissociative curve of the receptor from the chip is not necessary for affinity determination; the analysis of associative curve is sufficient for this purpose. We also suggested a new approach for evaluating the affinity of bivalent receptors (or antibodies) when these reagents are present in the studied solution and the correspondent ligand (or antigen) is immobilized on the chip.     

Melting of DNA-total histone complexes in the presence of noradrenaline]

Study is presented of the effect of noradrenaline on thermic denaturation of DNA-total histone complexes within the range of protein concentrations which corresponds to c1/c2 0-1.7 in solutions of 10(-3) M Na+ ionic strength (c1 and c2 being the weight concentrations of protein and nucleic acid, respectively). Denaturation of these systems has been found to be strongly affected by bivalent metals contained in DNA samples. Their presence accounts for the high temperature and wide melting range of DNA and diminution of the latter with an increase of the protein concentration in DNA-histone complexes. The denaturation parametres obtained for the studied systems are in fair agreement with predictions from the clip thermodynamic theory. Noradrenaline is shown to be capable of destabilizing DNA-total histon complexes. This is due to the inactivation of bivalent metals bound with DNA by noradrenaline. It is also suggested that noradrenaline does not weaken the histone binding with a nucleic acid.     

Membrane protein reconstitution and crystallization by controlled dilution

Efficient reconstitution of membrane proteins for functional analyses can be achieved by dilution of a ternary mixture containing proteins, lipids and detergents. Once the dilution reaches the point where the free detergent concentration would become lower than the critical micellar concentration, detergent is recruited from the bound detergent pool, and association of proteins and lipids is initiated. Here we show that dilution is also suitable for the assembly of two-dimensional crystals. A device has been designed that allows controlled dilution of a protein-lipid-detergent mixture to induce formation of densely packed or crystalline proteoliposomes. Turbidity is used to monitor the progress of reconstitution on-line, while dilution is achieved by computer-controlled addition of buffer solution in sub-microliter steps. This system has mainly been tested with porin OmpF, a typical beta-barrel protein, and aquaporin-1, a typical alpha-helical protein. The results demonstrate that large, highly ordered two-dimensional crystals can be produced by the dilution method.     

Characterization of protection afforded by a bivalent virus-like particle vaccine against bluetongue virus serotypes 1 and 4 in sheep

Background

Bluetongue virus (BTV) is an economically important, arthropod borne, emerging pathogen in Europe, causing disease mainly in sheep and cattle. Routine vaccination for bluetongue would require the ability to distinguish between vaccinated and infected individuals (DIVA). Current vaccines are effective but are not DIVA. Virus-like particles (VLPs) are highly immunogenic structural mimics of virus particles, that only contain a subset of the proteins present in a natural infection. VLPs therefore offer the potential for the development of DIVA compatible bluetongue vaccines.

Methodology/Principal Findings

Merino sheep were vaccinated with either monovalent BTV-1 VLPs or a bivalent mixture of BTV-1 VLPs and BTV-4 VLPs, and challenged with virulent BTV-1 or BTV-4. Animals were monitored for clinical signs, antibody responses, and viral RNA. 19/20 animals vaccinated with BTV-1 VLPs either alone or in combination with BTV-4 VLPs developed neutralizing antibodies to BTV-1, and group specific antibodies to BTV VP7. The one animal that showed no detectable neutralizing antibodies, or group specific antibodies, had detectable viral RNA following challenge but did not display any clinical signs on challenge with virulent BTV-1. In contrast, all control animals'' demonstrated classical clinical signs for bluetongue on challenge with the same virus. Six animals were vaccinated with bivalent vaccine and challenged with virulent BTV-4, two of these animals had detectable viral levels of viral RNA, and one of these showed clinical signs consistent with BTV infection and died.

Conclusions

There is good evidence that BTV-1 VLPs delivered as monovalent or bivalent immunogen protect from bluetongue disease on challenge with virulent BTV-1. However, it is possible that there is some interference in protective response for BTV-4 in the bivalent BTV-1 and BTV-4 VLP vaccine. This raises the question of whether all combinations of bivalent BTV vaccines are possible, or if immunodominance of particular serotypes could interfere with vaccine efficacy.     

印楝素农药与虫生真菌混用防治红树林鳞翅目害虫

采用2种印楝素农药1%印楝素苦参碱乳油和0.3%印楝素乳油,以及2个虫生真菌绿僵菌菌株和白僵菌菌株对桐花长卷蛾、棉古毒蛾和广州小斑螟等3种红树林叶面和种子害虫的室内毒力测定结果表明,两种印楝素农药的单剂(500～1000倍)和与虫生真菌的复配剂(700倍),均对害虫有较强的毒性,一周内害虫死亡率达78.6～100%.两种印楝素农药与虫生真菌混合使用均比各自单独使用的杀虫效果好,其中与虫生真菌的复配剂700倍液的杀虫最快,效果最好,第3天柑橘长卷蛾和广州小斑螟的死亡率达100%,棉古毒蛾的死亡率达93.3%.应用1%印楝素苦参碱乳油和0.3%印楝素乳油与绿僵菌和白僵菌的复配剂500倍液进行林间防治危害桐花树的柑橘长卷蛾的试验,防治效果达65.4%～100%,该复配剂具有内吸传导作用、高效、低毒和安全等优点,值得大力推广应用.     

The antigen-antibody reaction and its inhibition

The sera of intact and immune animals contain factors capable of inhibiting the interaction of antibodies with the homologous antigen. These agglutination inhibiting (AI) factors not only block the antigen, thus competing with antibodies, but may induce the dissociation of the antigen-antibody complex. Heating of antisera at 60-63 degrees C leads to an increase in the activity of AI factors. The phenomenon of "prozone" in the agglutination test appears to be explained by the presence of AI factors in sera.