Difficulties in applying the Scatchard model of ligand binding to proteins--proposal of new mathematical tools--application to salicylates

The vinblastine binding site adopts high- and low-affinity conformations during a transport cycle of P-glycoprotein

Conceptually one may envisage that substrate binding sites on the ABC transporter P-gp cycle between high- and low-affinity conformations in response to signals arising from nucleotide hydrolysis to effect active transport. A radioligand binding assay was used to characterize the interaction of [3H]vinblastine with P-gp and determine how drug binding site parameters are altered during a catalytic cycle of P-gp. In the absence of nucleotide, we show that [3H]vinblastine interacts with a single class of binding site with high affinity (K(d) = 80 +/- 18 nM). In the presence of the nonhydrolyzable ATP analogue AMP-PNP, the drug binding site was in a low-affinity conformation, manifest by a 9-fold increase in K(d) (K(d) = 731 +/- 20 nM). There was no alteration in the binding capacity, reflecting a complete shift in the high-affinity site to a low-affinity form. The posthydrolytic (Mg-ADP-V(i) bound) form of P-gp also exhibited low-affinity substrate binding (K(d) = 446 +/- 57 nM). Restoration of the high-affinity drug binding site conformation (K(d) = 131 +/- 32 nM) did not occur until release of phosphate from the posthydrolysis P-gp-Mg-ADP-P(i). complex. Our results suggest that alteration of the affinity of the vinblastine binding site involves only one nucleotide binding domain per transport cycle. The binding of ATP provides the signal to instigate this change, while release of phosphate post-ATP hydrolysis returns the transporter to its original state to complete the cycle.

The 1-exp function as an alternative model of non-linear saturable kinetics

Non-linear saturation kinetics can be described through a potency function, a trigonometric function, a logarithmic function, a hyperbolic function, or an exponential function. Saturable enzyme reaction kinetics can be alternatively formulated as a 1-exp function without the limitations of a steady-state assumption (d[C]/dt = 0, where C is the enzyme-substrate complex). The time-dependent substrate conversion (-d[S]/dt = V(max) [1-exp(-Ka [S])]) depends on the maximum velocity (V(max)), the association constant (Ka) and substrate concentration [S]. In contrast to the classical Michaelis-Menten equation, the 1-exp function has an explicit solution for the substrate concentration [S] in an integrated form. [S] = (1/Ka) ln[1-exp(Ka [S]o)) exp(- Ka V(max) t)] A deceleration term must be introduced to describe enzyme reaction kinetics realistically. The 1-exp function with deceleration term can also be expanded to describe the three inhibition types of enzyme reaction kinetics.

Binding sites of fluorescent probes on human serum albumin

Human serum albumin is known to have two major and selective drug binding sites, termed sites I and II. The fluorescent probes, dansylamide and dansylsarcosine selectively interact with sites I and II, respectively. However, the binding site of the fluorescent probe dansylglycine on human serum albumin is not clear from the literature. This study investigated whether dansylglycine interacts tightly with site I or II. Spectrofluorimetric titrations (quenching and complex) and circular dichroism measurements were performed to determine the binding characteristics of dansylglycine to human serum albumin. Modification in probe fluorescence was described by fluorescence titrations to be a result of competitive displacement by ligands. The pattern of displacement of this probe by several ligands whose primary binding sites are exactly known, enabled the identification of its specific binding site. The fluorescence of dansylglycine is only extensively changed when ligands of site II are added, suggesting that it strongly interacts with the benzodiazepine/indole binding site on human serum albumin.

Representation of affinity in the case of co-operativity in protein-ligand binding

We have already proposed a "Global Association Function" to represent the global affinity of proteins to a drug; it was first applied in the case of independent binding sites. In this paper, we show that this same function can also be used to assess interactions between sites by varying the number of interacting sites and their co-operativity level. The resulting curves in two application cases are given together with the corresponding Scatchard plot: i) in a system with one single class of identical and interacting sites, ii) in a system with two classes of sites in which either primary or secondary are interacting; unexpectedly, in this latter case we also observed that sometimes positive co-operativity occasionally resulted in a concave-up Scatchard plot which is unusually admitted. In addition, as described in one example, our function is assumption free; this might be an advantage over usual methods, such as discrete parameter methods, because they require additional and empirical hypotheses on their related binding model.

Stereoselective protein binding of ketoprofen: effect of albumin concentration and of the biological system

Equilibrium dialysis was used to study in vitro the enantioselective binding of R, S, and racemic ketoprofen at physiological pH and temperature in human serum albumin (HSA) (1, 20, and 40 g/liter) and in plasma. The binding of enantiomers in a racemic mixture was studied to see the effect of each isomer on the other's interaction with the protein. The free fractions were determined by high-performance liquid chromatography. The binding of ketoprofen enantiomers to albumin was enantioselective, depending on both drug and protein concentrations. Enantioselectivity was observed in plasma too but was the opposite of that in HSA at 40 g/liter. The percentage of each isomer unbound was higher in the racemic mixture than with the isomer alone. The displacement of probes specific for HSA sites I and II, studied by spectrofluorimetry, suggests that all three preparations of ketoprofen are bound mainly to site I and secondarily to site II.

Protein binding of indomethacin in human cerebrospinal fluid

The binding of the non-steroidal anti-inflammatory drug indomethacin to proteins in human cerebrospinal fluid (CSF), drawn during lumbar puncture from 10 patients affected by lumbosciatica, was measured by equilibrium dialysis and spectrofluorimetry. Similar binding studies on human serum albumin solutions (0.5 and 1 g/L) were performed using the same techniques. The mean binding percentage of indomethacin determined by equilibrium dialysis was 40%. The results obtained by both techniques allowed us to conclude that the binding of indomethacin in CSF was essentially due to albumin.

Freundlich and Langmuir isotherms as models for the adsorption of toxicants on activated charcoal

The Langmuir isotherm has been widely used to characterize the adsorption of solutes from aqueous solutions. Activated charcoal adsorption data obtained experimentally, using a wide range of adsorbate concentrations, fit the Langmuir isotherm poorly but evidence a good fit to the Freundlich isotherm. Statistical analysis reveals this to be also true of published data that was previously considered to adhere to the Langmuir isotherm. Over the range of possible adsorbate concentrations, the two isotherms predict rather different adsorption behavior. Of the two, the Freundlich isotherm is able to more fully account for observed antidotal effectiveness of activated charcoal in vivo. A method of graphical analysis is advanced that more readily distinguishes the relative goodness-of-fit of the two isotherms. This and the statistical paradigm employed to decide between the two competing hypotheses should allow the adsorption phenomena involving other adsorbents to be re-examined.

Association and transfer functions for analysis of drug binding to proteins

A global association function is proposed that characterizes the apparent overall equilibrium of drug protein binding. It is defined as a function of the total drug concentration and may be directly calculated from each experimental result. The binding transfer function represents the relative rates of change in the bound and free concentrations from the total concentration. Two applications are presented: one is an investigation of the effect of temperature on binding of salicylic acid to proteins in plasma; and the other is a comparison of the phenomenon in two different biological fluids (protein binding of sodium salicylate in plasma and in synovial fluid).

Specific and non-specific ligand binding to serum albumin

The applicability of a model of specific and non-specific binding sites for the binding of organic ligands to serum albumin was examined statistically. It is proposed in this model that there are a limited number of a single class of high affinity sites and an unlimited number of low affinity sites. Ligands bind to the former sites independently, as in the Scatchard model for a single class of binding sites, and to the latter sites in a partition-like manner, the amounts bound increasing linearly with the concentration of free ligands. In this study, data on the binding of warfarin to human serum albumin reported by Wilting et al. [J. Wilting et al., J. biol. Chem. 255, 3032 (1980)] and on the bindings of indomethacin and salicylic acid to human serum albumin reported by Hultmark et al. [D. Hultmark et al., Acta pharm. suecica 12, 259 (1975)] were used. These binding data were analyzed according to the model of specific and non-specific sites as well as the Scatchard model of two classes of binding sites. Statistical analyses showed that the model of specific and non-specific binding sites fitted the data for binding of all compounds very well, indicating the applicability of this model. An index of the upper limit of ligand concentrations necessary for accurate analysis of the binding data was also discussed.

Decrease of in vitro serum protein binding of salicylate in rheumatoid arthritis

Free and bound fractions of salicylates were separated by equilibrium dialysis and measured by spectrofluorimetry in 27 patients with rheumatoid arthritis and in 16 controls. The results showed that in patients with rheumatoid arthritis, the binding of salicylate to proteins decreased in an overproportional manner with the decrease of serum albumin concentrations. This phenomenon was linked with the severity of the inflammatory syndrome. The saturation binding capacity per unit of protein concentration was lower in the patients suffering from active forms of the condition, a finding which suggests that the changes observed are not due only to quantitative changes in the serum albumins. This study confirms the importance of determining free salicylate concentrations in the treatment of patients with inflammatory diseases.