AFFINOGEN--a program for affinity spectrum reconstruction

Quantitative analyses of bifunctional molecules

Small molecules can be discovered or engineered to bind tightly to biologically relevant proteins, and these molecules have proven to be powerful tools for both basic research and therapeutic applications. In many cases, detailed biophysical analyses of the intermolecular binding events are essential for improving the activity of the small molecules. These interactions can often be characterized as straightforward bimolecular binding events, and a variety of experimental and analytical techniques have been developed and refined to facilitate these analyses. Several investigators have recently synthesized heterodimeric molecules that are designed to bind simultaneously with two different proteins to form ternary complexes. These heterodimeric molecules often display compelling biological activity; however, they are difficult to characterize. The bimolecular interaction between one protein and the heterodimeric ligand (primary dissociation constant) can be determined by a number of methods. However, the interaction between that protein-ligand complex and the second protein (secondary dissociation constant) is more difficult to measure due to the noncovalent nature of the original protein-ligand complex. Consequently, these heterodimeric compounds are often characterized in terms of their activity, which is an experimentally dependent metric. We have developed a general quantitative mathematical model that can be used to measure both the primary (protein + ligand) and secondary (protein-ligand + protein) dissociation constants for heterodimeric small molecules. These values are largely independent of the experimental technique used and furthermore provide a direct measure of the thermodynamic stability of the ternary complexes that are formed. Fluorescence polarization and this model were used to characterize the heterodimeric molecule, SLFpYEEI, which binds to both FKBP12 and the Fyn SH2 domain, demonstrating that the model is useful for both predictive as well as ex post facto analytical applications.

Computational models in immunological methods: an historical review

The utilization of computational models in immunology dates from the birth of the science. From the description of antibody-antigen binding to the structural models of receptors, models are utilized to bring fundamental understandings of the processes together with laboratory measurements to uncover implications of these data. In this review, an historical view of the role of computational models in the immunology laboratory is presented, and short mathematical descriptions are given of fundamental assays. In addition, the range of current uses of models is explored -- especially as seen through papers which have appeared in the Journal of Immunological Methods from volume 1 (1971/1972) to volume 208 (1997). Each paper which introduced a new mathematical, statistical, or computer simulation model, or introduced an enhancement to an instrument through a model in those volumes is cited and the type of computational model noted.

Interaction between antibodies and hapten-protein conjugates of different composition: theoretical predictions and experimental data

Mathematical models of competitive ELISAs with labelled antibody and with labelled antigen taking into account bivalent interactions between antibodies and hapten-protein conjugates were developed and analyzed. It was shown that in the kinetic model of the immunochemical reaction the conjugate composition influenced the amplitude of detected signal but not ELISA sensitivity. In the equilibrium model decreased sensitivity correlated with bivalent complexes formation. The predictions were tested experimentally using 2,4-dichlorophenoxyacetic acid (2,4-D) and testosterone as haptens. It was confirmed that increasing of the hapten : protein ratio resulted in formation of bivalent complexes with antibodies. The equilibrium binding constants for these complexes were two orders of magnitude higher than for monovalent ones. Optimal conjugate compositions have been chosen for ELISA of these haptens.

Multiple receptor populations: binding isotherms and their numerical analysis

This paper reviews present models and methods of parameter estimation in relationships describing receptor-ligand interactions in equilibrium, as used in the author's laboratory. The state-of-the-art and the present experience can be summarized as follows: 1) Binding isotherms (relationships of bound and free/total ligand concentrations) are superpositions of several elementary terms describing the ligand binding to individual binding sites (receptors) present in the biological material investigated. The "nonspecific binding" is usually represented by a linear term. 2) The elementary terms are most frequently described by a rectangular hyperbola, Hill (power) function, or a rational function (binding of several ligand molecules to one molecule of receptor). Heterologous displacement requires specific functions which, however, can be transformed into one of the elementary terms. 3) Parameters (binding capacities, dissociation constants, Hill coefficients, etc.) can most reliably be estimated by nonlinear regression methods. However, these methods frequently fail to yield physically relevant values if initial estimates are far from "real" values, or if the data are strongly scattered. Some of the available routines (e.g., LIGAND) offer manifold tools to solve these difficulties. 4) The "affinity spectrum", a relationship between binding capacities and equilibrium constants, shows the presence of individual binding sites in the binding system in question. The spectrum can be constructed either by Fourier analysis, or by a stepwise procedure (computation of binding capacity for several dissociation constants). The former way of analysis is demanding; software tools are rare. 5) The "STEP" routine based on Hill/Scatchard linearization routines yields profiles similar to affinity spectra, but offers, in addition, values of Hill coefficients of individual binding populations. Values obtained can be used as initial estimates for nonlinear regression. 6) Selection of a suitable model, its testing, numerical procedures, statistical estimates, etc. frequently entail severe difficulties which are approached in the available software packages in different ways, none of them is usually optimal.