A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces

Understanding the interaction of estrogenic ligands with estrogen receptors: a survey of the functional and binding kinetic studies

The investigation of estrogen actions and their interaction characteristics with estrogen receptors (ERs) to induce unique functional features inside cells have allowed us to understand better the regulation of many vital physiological and cellular processes in humans. The biological effects of estrogenic ligands or compounds are mediated via estrogen receptors that act as the ligand-activated transcription factors. Therefore, the study on ligand-ER interaction properties and mechanism of ligand-ER complexes binding to specific estrogen response elements located in the promoters of target genes are very critical to realize the complicated biological process regulated by the endogenous estrogens. Several reviews have provided comprehensive and updated information on the influence of estrogen receptors in health and disease. However, the mechanism of estrogen-ERs binding and affinity aspects at molecular level is relatively under-investigated. This review thus aims to shed light on the significance of the binding kinetics of ligand-ER interactions because the information provide great assistance to define how a ligand or a drug can communicate with physiology to produce a desired therapeutic response. In addition, the most frequently used methodologies for the binding kinetic study are highlighted over the last decade.

Protein surface roughness accounts for binding free energy of Plasmepsin II-ligand complexes

The calculation of absolute binding affinities for protein-inhibitor complexes remains as one of the main challenges in computational structure-based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high-resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x-ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave-one-out cross-validation showed that our model reproduced accurately the absolute binding free energies for our training set (R²  = 0.76; <|error|> =0.55 kcal/mol; SD_error  = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.

Effect of a highly concentrated lipopeptide extract of Bacillus subtilis on fungal and bacterial cells

Lipopeptides produced by Bacillus subtilis are known for their high antifungal activity. The aim of this paper is to show that at high concentration they can damage the surface ultra-structure of bacterial cells. A lipopeptide extract containing iturin and surfactin (5 mg mL(-1)) was prepared after isolation from B. subtilis (strain OG) by solid phase extraction. Analysis by atomic force microscope (AFM) showed that upon evaporation, lipopeptides form large aggregates (0.1-0.2 microm(2)) on the substrates silicon and mica. When the same solution is incubated with fungi and bacteria and the system is allowed to evaporate, dramatic changes are observed on the cells. AFM micrographs show disintegration of the hyphae of Phomopsis phaseoli and the cell walls of Xanthomonas campestris and X. axonopodis. Collapses to fungal and bacterial cells may be a result of formation of pores triggered by micelles and lamellar structures, which are formed above the critical micelar concentration of lipopeptides. As observed for P. phaseoli, the process involves binding, solubilization, and formation of novel structures in which cell wall components are solubilized within lipopeptide vesicles. This is the first report presenting evidences that vesicles of uncharged and negatively charged lipopeptides can alter the morphology of gram-negative bacteria.

Michaelis-Menten kinetics under spatially constrained conditions: application to mibefradil pharmacokinetics

Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten (MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.

Continuous measurements of a binding reaction using a capacitive biosensor

A capacitive biosensor with polyclonal antibodies raised against human serum albumin (HSA) immobilized on a gold transducer has been developed for continuous measurement of HSA in the muM-range. A mathematical model has been refined to describe integral HSA-binding curves assuming that (i) binding is essentially irreversible under the conditions used, (ii) the signal is scaled as the number of non-occupied binding sites and (iii) the rate of disappearance of available binding sites is scaled as the number of available binding sites and analyte concentration in solution. Deconvolution of the curves using the mathematical model indicates clearly that it is possible to retrieve concentration profiles (isocratic, linearly or exponentially increasing gradients) of the analyte in the continuous sample flow from the normalized integral binding (NIB) curves. The data presented constitutes the theoretical background and the first step towards the development of an analytical system allowing on-line detection of the concentration profile of the analyte from NIB-curves. Since the system can be used for extended time periods between regeneration steps, a low frequency of regeneration steps can be expected.

A survey of the year 2002 commercial optical biosensor literature

We have compiled 819 articles published in the year 2002 that involved commercial optical biosensor technology. The literature demonstrates that the technology's application continues to increase as biosensors are contributing to diverse scientific fields and are used to examine interactions ranging in size from small molecules to whole cells. Also, the variety of available commercial biosensor platforms is increasing and the expertise of users is improving. In this review, we use the literature to focus on the basic types of biosensor experiments, including kinetics, equilibrium analysis, solution competition, active concentration determination and screening. In addition, using examples of particularly well-performed analyses, we illustrate the high information content available in the primary response data and emphasize the impact of including figures in publications to support the results of biosensor analyses.

Binding and dissociation kinetics using fractals: an analysis of electrostatic effects and randomly coupled and oriented coupled receptors on biosensor surfaces

A fractal analysis is used to analyze the influence of: (a) electrostatic interactions on binding and dissociation rate coefficients for antibodies HH8, HH10, and HH26 in solution to hen egg-white lysozyme (HEL) immobilized on a sensor chip surface [Biophys. J. 83 (2002) 2946]; and (b) the binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip surface [Methods 20 (2000) 310]. Single- and dual-fractal models were employed to fit the data. Values of the binding and the dissociation rate coefficient(s) and the fractal dimensions were obtained from a regression analysis provided by Corel Quattro Pro 8.0 (Corel Corporation Limited, Ottawa, Canada. 1997). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. It is of interest to compare the results obtained by the fractal analysis with that of the original analysis [Biophys. J. 83 (2002) 2946]. For example, as one goes from the binding of 21 nM HH10/HEL to the binding of 640 nM HH10/HEL(K97A), Sinha et al. [Biophys. J. 83 (2002) 29461 indicate that the enhancement of diffusional encounter rates may be due to 'electrostatic steering' (a long-range interaction). Our analysis indicates that there is an increase in the value of the fractal dimension, Df1 by a factor of 1.12 from a value of 2.133-2.385. This increase in the degree of heterogeneity on the surface leads to an increase in the binding rate coefficient, k1 by a factor of 1.59 from 12.92 to 20.57. The fractal analysis of binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip [Methods 20 (2000) 310] surface are consistent with the degree of heterogeneity present on the sensor chip surface for the random and the oriented case. As expected, the random case will exhibit a higher degree of heterogeneity than the oriented case, leading to subsequently a higher binding rate coefficient.