A Mathematical Analysis Using Fractals for Binding Interactions of Nuclear Estrogen Receptors Occurring on Biosensor Surfaces

Ramakrishnan, Anand; Sadana, Ajit

doi:10.1006/abio.2002.5581

Cited by 16 publications

(5 citation statements)

References 20 publications

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“…Fractal studies also conWrm these observations. A fractal dimension greater than two is normally associated with volume (Christofoletti 1999; Ramakrishnan and Sadana 2002). Analysis performed with the Gwyddion 2.5 software produced a fractal dimension of 2.30 for Xcc cells before the addition of lipopeptides.…”

Section: Evect Of Lipopeptides On Gram-negative Bacterial Cellsmentioning

confidence: 99%

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

et al. 2008

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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.

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Section: Evect Of Lipopeptides On Gram-negative Bacterial Cellsmentioning

confidence: 99%

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

et al. 2008

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“…Concerning that, it has been mainly used for identification of functional sites in proteins . The use of FD for the study of protein‐ligand interactions and the estimation of binding strength has been described in few works . Our work focuses on this less explored aspect of FD.…”

Section: Discussion and Summarymentioning

confidence: 99%

“…In the protein‐ligand interaction context, Todoroff et al demonstrated that surface roughness correlates with ligand binding potential. Furthermore, mathematical approaches using fractal concepts for modeling the binding and dissociation interactions between ligands and nuclear estrogen receptors occurring on surface plasmon resonance biosensor chip surfaces have been previously described . These results highlighted FD like a valuable tool for the description of molecular interaction sites and protein‐ligand interaction.…”

Section: Introductionmentioning

confidence: 97%

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

Valdés‐Tresanco

Valdés-Tresanco

Valiente

et al. 2017

J of Molecular Recognition

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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. Leaveone-out cross-validation showed that our model reproduced accurately the absolute binding free energies for our training set (R 2 = 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. Most rapid methods for estimation of binding free energies, such as, so-called empirical or knowledge-based (statistical) scoring functions, have been proposed. These methods are based on very simple energy functions 4-6 or on the frequency of occurrence of different atom-atom contact pairs in complexes of known structure. 7,8 The simplicity of the energy function along with the lack of conformational sampling and explicit water treatment makes these approaches very fast, but usually at the cost of accuracy. 9 Thus, further development of fast and accurate methods to complement the already existing ones is still needed.

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“…In general, many cellular reactions take place under dimensionally restricted conditions, e.g., two-dimensional (2D) membranes, quasi-one-dimensional tubes or other disordered media. This type of reaction has been found to exhibit noninteger kinetic orders in in vitro experimental studies (Sadana, 2001;Ramakrishnan and Sadana, 2002) and in simulation (Koo and Kopelman, 1991), rather than the usual integer kinetic order derived from mass-action kinetics. These noninteger kinetic orders are related to the fractal dimension of the space in which the reaction occurs; therefore, the nonconventional kinetics have been referred to as ''fractal kinetics'' (Kopelman, 1988).…”

Section: Introductionmentioning

confidence: 95%

Michaelis-Menten Kinetics under Spatially Constrained Conditions: Application to Mibefradil Pharmacokinetics

Kosmidis

Karalis

Argyrakis

et al. 2004

Biophysical Journal

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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.

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A Mathematical Analysis Using Fractals for Binding Interactions of Nuclear Estrogen Receptors Occurring on Biosensor Surfaces

Cited by 16 publications

References 20 publications

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

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

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

Michaelis-Menten Kinetics under Spatially Constrained Conditions: Application to Mibefradil Pharmacokinetics

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