Deriving complex ligand-binding formulas

Quantitative analysis of protein-protein interactions

Numerous authors, including contributors to this volume, have described methods to detect protein-protein interactions. Many of these approaches are now accessible to the inexperienced investigator thanks to core facilities and/or affordable instrumentation. This chapter discusses some common design considerations that are necessary to obtain valid measurements, as well as the assumptions and analytical methods that are relevant to the quantitation of these interactions.

A simple model-free method for direct assessment of fluorescent ligand binding by linear spectral summation

Fluorescent tagged ligands are commonly used to determine binding to proteins. However, bound and free ligand concentrations are not directly determined. Instead the response in a fluorescent ligand titration experiment is considered to be proportional to the extent of binding and, therefore, the maximum value of binding is scaled to the total protein concentration. Here, a simple model-free method is presented to be performed in two steps. In the first step, normalized bound and free spectra of the ligand are determined. In the second step, these spectra are used to fit composite spectra as the sum of individual components or linear spectral summation. Using linear spectral summation, free and bound 1-Anilinonaphthalene-8-Sulfonic Acid (ANS) fluorescent ligand concentrations are directly calculated to determine ANS binding to tear lipocalin (TL), an archetypical ligand binding protein. Error analysis shows that the parameters that determine bound and free ligand concentrations were recovered with high certainty. The linear spectral summation method is feasible when fluorescence intensity is accompanied by a spectral shift upon protein binding. Computer simulations of the experiments of ANS binding to TL indicate that the method is feasible when the fluorescence spectral shift between bound and free forms of the ligand is just 8 nm. Ligands tagged with environmentally sensitive fluorescent dyes, e.g., dansyl chromophore, are particularly suitable for this method.

Differential binding models for isothermal titration calorimetry: moving beyond the Wiseman isotherm

We present a set of model-independent differential equations to analyze isothermal titration calorimetry (ITC) experiments. In contrast with previous approaches that begin with specific assumptions about the number of binding sites and the interactions among them (e.g., sequential, independent, cooperative), our derivation makes more general assumptions, such that a receptor with multiple sites for one type of ligand species (homotropic binding) can be studied with the same analytical expression. Our approach is based on the binding polynomial formalism, and the resulting analytical expressions can be extended to account for any number of binding sites and any type of binding interaction among them. We refer to the set of model-independent differential equations to study ITC experiments as a differential binding model (DBM). To demonstrate the flexibility of our DBM, we present the analytical expressions to study receptors with one or two binding sites. The DBM for a receptor with one site is equivalent to the Wiseman isotherm but with a more intuitive representation that depends on the binding polynomial and the dimensionless parameter c = K·MT, where K is the binding constant and MT the total receptor concentration. In addition, we show how to constrain the general DBM for a receptor with two sites to represent sequential, independent, or cooperative binding interactions between the sites. We use the sequential binding model to study the binding interaction between Gd(III) and citrate anions. In addition, we simulate calorimetry titrations of receptors with positive, negative, and noncooperative interactions between the two binding sites. Finally, we derive a DBM for titrations of receptors with n-independent binding sites.

Nonlinear least-squares fitting methods

This chapter provides an overview of the techniques involved in "fitting equations to experimental data" with a particular emphasis on the what can be learned with these techniques, what are the requirements of the experimental data for these techniques, and what are the underlying assumptions of these techniques. The layout of this chapter is to start with a set of experimental data, and then walk the reader through the analysis of this set of data. The rigorous mathematical methods are referenced but not presented in detail.

Investigation of the mechanism of binding between internalin B and heparin using surface plasmon resonance

Listeria monocytogenes, a food-borne pathogen that infects immunocompromised patients, enters and proliferates within mammalian cells by taking advantage of host cell machinery. While entry into macrophages and other phagocytic cells occurs constitutively, intracellular invasion of nonphagocytic cells, such as epithelial and endothelial cells, occurs through induced phagocytosis. Invasion of these nonphagocytic cell types is under the control of the secreted L. monocytogenes protein internalin B (InlB), which directly associates with and activates the receptor tyrosine kinase Met. Activation of Met by InlB has previously been shown to be potentiated by binding of glycosaminoglycans to the GW domains of this protein. We studied the interaction between heparin and full-length InlB as well as a truncated, functional form of InlB to understand the mode of interaction between these two molecules. InlB preferred long-chain (>or=dp14) heparin oligosaccharides, and the interaction with heparin fit a complicated binding model with a dissociation constant in the nanomolar range. While there are various explanations for this complicated binding model, one supported by our data involves binding and rebinding of InlB to multiple binding sites on heparin in a positive and weakly cooperative manner. This mode is consistent with enhancement of interaction of InlB with glycosaminoglycans for activation of Met.

Limitations in linearized analyses of binding equilibria: binding of TNP-ATP to the H4-H5 loop of Na/K-ATPase

Binding of TNP-ATP [2',3'- O-(2,4,6-trinitrophenyl)adenosine 5'-triphosphate, a fluorescent analogue of ATP] to the K605 protein was studied. This is an isolated N-domain in the cytoplasmic loop of the Na/K-ATPase alpha-subunit, lying between membrane-spanning segments 4 and 5 (sequence L(354)-I(604)). A titration equation is derived that explicitly makes it possible to relate the fluorescence of TNP-ATP and K605 solutions to total probe concentration in the sample. Using this, it is possible to obtain the value of the dissociation constant from the titration experiment without resorting to the Scatchard plot, which is far from optimal from the statistical point of view. Using the new formula with non-linear regression analysis, a value of the dissociation constant K(D) for TNP-ATP binding to the K605 protein of 3.03 +/- 0.28 microM at 22 degrees C was obtained. A series of fits to simulated data with added noise demonstrated clearly the advantage of non-linear regression using the new formula over the commonly employed linear regression using the Scatchard plot. The procedure presented is generally applicable to binding assays using changes in the fluorescence of ligands on binding.