Equilibrium expert: an add-in to Microsoft Excel for multiple binding equilibrium simulations and parameter estimations (original) (raw)
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A Practical Guide for the Determination of Binding Constants
When working in the field of host–guest chemistry, the binding constants have to be determined on many occasions. Here is a detailed document of how to determine the binding constants which covers both the basic principle and the practical issue: a practical experimental guideline, a representativemethod for the determination of stoichiometry and for the evaluation of a complex concentration, precautions to be taken on setting up concentration conditions of the titration experiment, practical data-treatment methods and estimation of statistical errors. This document is described in detail using the basic level of mathematics, statistics, and programs of spreadsheet software. Especially, the titration experiments by means of UV-visible and NMR spectroscopy are carried out and described.
Talanta, 1998
An algorithm is proposed for the estimation of binding parameters for the interaction of biologically important macromolecules with smaller ones from electrometric titration data. The mathematical model is based on the representation of equilibria in terms of probability concepts of statistical molecular thermodynamics. The refinement of equilibrium concentrations of the components and estimation of binding parameters (log site constant and cooperativity factor) is performed using singular value decomposition, a chemometric technique which overcomes the general obstacles due to near singularity. The present software is validated with a number of biochemical systems of varying number of sites and cooperativity factors. The effect of random errors of realistic magnitude in experimental data is studied using the simulated primary data for some typical systems. The safe area within which approximate binding parameters ensure convergence has been reported for the non-self starting optimization algorithms.
Journal of Immunological Methods, 2007
A new 4-parameter nonlinear equation based on the standard multiple independent binding site model (MIBS) is presented for fitting cell-based ligand titration data in order to calculate the ligand/cell receptor equilibrium dissociation constant and the number of receptors/cell. The most commonly used linear (Scatchard Plot) or nonlinear 2-parameter model (a single binding site model found in commercial programs like Prism®) used for analysis of ligand/receptor binding data assumes only the K D influences the shape of the titration curve. We demonstrate using simulated data sets that, depending upon the cell surface receptor expression level, the number of cells titrated, and the magnitude of the K D being measured, this assumption of always being under K Dcontrolled conditions can be erroneous and can lead to unreliable estimates for the binding parameters. We also compare and contrast the fitting of simulated data sets to the commonly used cell-based binding equation versus our more rigorous 4-parameter nonlinear MIBS model. It is shown through these simulations that the new 4-parameter MIBS model, when used for cell-based titrations under optimal conditions, yields highly accurate estimates of all binding parameters and hence should be the preferred model to fit cell-based experimental nonlinear titration data.
Journal of Medicinal Chemistry, 2002
The prediction of the binding affinity between a protein and ligands is one of the most challenging issues for computational biochemistry and drug discovery. While the enthalpic contribution to binding is routinely available with molecular mechanics methods, the entropic contribution is more difficult to estimate. We describe and apply a relatively simple and intuitive calculation procedure for estimating the free energy of binding for 53 protein-ligand complexes formed by 17 proteins of known three-dimensional structure and characterized by different active site polarity. HINT, a software model based on experimental LogP o/w values for small organic molecules, was used to evaluate and score all atom-atom hydropathic interactions between the protein and the ligands. These total scores (H TOTAL ), which have been previously shown to correlate with ∆G interaction for protein-protein interactions, correlate with ∆G binding for protein-ligand complexes in the present study with a standard error of (2.6 kcal mol -1 from the equation ∆G binding ) -0.001 95 H TOTAL -5.543. A more sophisticated model, utilizing categorized (by interaction class) HINT scores, produces a superior standard error of (1.8 kcal mol -1 . It is shown that within families of ligands for the same protein binding site, better models can be obtained with standard errors approaching (1.0 kcal mol -1 . Standardized methods for preparing crystallographic models for hydropathic analysis are also described. Particular attention is paid to the relationship between the ionization state of the ligands and the pH conditions under which the binding measurements are made. Sources and potential remedies of experimental and modeling errors affecting prediction of ∆G binding are discussed.
Analytical biochemistry, 2008
BIOEQS is a global analysis and simulations program for complex biomolecular interaction data developed in the 1990's [1,2]. Its continued usefulness derives from the fact that it is based on a numerical solver for complex coupled biological equilibria, rather than on closed-form analytical equations for the binding isotherms. It is therefore quite versatile, allowing easy testing of multiple binding models and analysis of systems too complex for closed form solutions. However, a major drawback to a generalized use of this program has been the lack of a graphical user interface (GUI) for setting up the binding models and experimental conditions, as well as visualizing the results. We present here a new GUI for BIOEQS that should be useful in both research and teaching applications.
Journal of General Physiology, 2016
A critical but often overlooked question in the study of ligands binding to proteins is whether the parameters obtained from analyzing binding data are practically identifiable (PI), i.e., whether the estimates obtained from fitting models to noisy data are accurate and unique. Here we report a general approach to assess and understand binding parameter identifiability, which provides a toolkit to assist experimentalists in the design of binding studies and in the analysis of binding data. The partial fraction (PF) expansion technique is used to decompose binding curves for proteins with n ligand-binding sites exactly and uniquely into n components, each of which has the form of a one-site binding curve. The association constants of the PF component curves, being the roots of an n-th order polynomial, may be real or complex. We demonstrate a fundamental connection between binding parameter identifiability and the nature of these one-site association constants: all binding parameters...
Analytical expressions for the homotropic binding of ligand to protein dimers and trimers
Analytical Biochemistry, 2012
Cooperative binding of a ligand to multiple subsites on a protein is a common theme among enzymes and receptors. The analysis of cooperative binding data (either positive or negative) often relies on the assumption that free ligand concentration, L, can be approximated by the total ligand concentration, L T . When this approximation does not hold, such analyses result in inaccurate estimates of dissociation constants. Presented here are exact analytical expressions for equilibrium concentrations of all enzyme and ligand species (in terms of K d values and total concentrations of protein and ligand) for homotropic dimeric and trimeric protein-ligand systems. These equations circumvent the need to approximate L and are provided in Excel worksheets suitable for simulation and least-squares fitting. The equations and worksheets are expanded to treat cases where binding signals vary with distinct site occupancy.