scholarly journals Integral Representation of Electrostatic Interactions inside a Lipid Membrane

Molecules ◽  
2020 ◽  
Vol 25 (17) ◽  
pp. 3824
Author(s):  
Guilherme Volpe Bossa ◽  
Sylvio May
Keyword(s):  
Electrostatic Interactions ◽  
Lipid Membrane ◽  
Single Point ◽  
Integral Representations ◽  
Low Dielectric ◽  
Salt Ions ◽  
Dipole Interactions ◽  
Linear Limit ◽  
Poisson Boltzmann ◽  
Mobile Ions

Interactions between charges and dipoles inside a lipid membrane are partially screened. The screening arises both from the polarization of water and from the structure of the electric double layer formed by the salt ions outside the membrane. Assuming that the membrane can be represented as a dielectric slab of low dielectric constant sandwiched by an aqueous solution containing mobile ions, a theoretical model is developed to quantify the strength of electrostatic interactions inside a lipid membrane that is valid in the linear limit of Poisson-Boltzmann theory. We determine the electrostatic potential produced by a single point charge that resides inside the slab and from that calculate charge-charge and dipole-dipole interactions as a function of separation. Our approach yields integral representations for these interactions that can easily be evaluated numerically for any choice of parameters and be further simplified in limiting cases.

scholarly journals Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 129
Author(s):  
Guilherme Volpe Bossa ◽  
Sylvio May
Keyword(s):  
Free Energy ◽  
Double Layer ◽  
Electric Double Layer ◽  
Low Dielectric Constant ◽  
Surface Charges ◽  
Dielectric Interface ◽  
Charge Densities ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
The Continuum

Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

scholarly journals Basic Residue Clusters in Intrinsically Disordered Regions of Peripheral Membrane Proteins: Modulating 2D Diffusion on Cell Membranes

Physchem ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 152-162
Author(s):  
Miquel Pons
Keyword(s):  
Membrane Proteins ◽  
Electrostatic Interactions ◽  
Lipid Membrane ◽  
Conformational Ensemble ◽  
Basic Residue ◽  
Intrinsically Disordered ◽  
Intrinsically Disordered Regions ◽  
Peripheral Membrane Proteins ◽  
Charged Residues ◽  
Disordered Regions

A large number of peripheral membrane proteins transiently interact with lipids through a combination of weak interactions. Among them, electrostatic interactions of clusters of positively charged amino acid residues with negatively charged lipids play an important role. Clusters of charged residues are often found in intrinsically disordered protein regions, which are highly abundant in the vicinity of the membrane forming what has been called the disordered boundary of the cell. Beyond contributing to the stability of the lipid-bound state, the pattern of charged residues may encode specific interactions or properties that form the basis of cell signaling. The element of this code may include, among others, the recognition, clustering, and selective release of phosphatidyl inositides, lipid-mediated protein-protein interactions changing the residence time of the peripheral membrane proteins or driving their approximation to integral membrane proteins. Boundary effects include reduction of dimensionality, protein reorientation, biassing of the conformational ensemble of disordered regions or enhanced 2D diffusion in the peri-membrane region enabled by the fuzzy character of the electrostatic interactions with an extended lipid membrane.

scholarly journals Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

2020 ◽  
pp. 2042006
Author(s):  
Jiahui Chen ◽  
Jingzhen Hu ◽  
Yongjia Xu ◽  
Robert Krasny ◽  
Weihua Geng
Keyword(s):  
Boltzmann Distribution ◽  
Dielectric Medium ◽  
Boundary Integral ◽  
Acid Dissociation ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
Computing Procedure ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Electrostatic Calculations

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

Interaction between like-charged surfaces mediated by uniformly charged counter-nanoparticles

2019 ◽  
Vol 33 (10) ◽  
pp. 1950092 ◽  
Author(s):  
Simone Spada ◽  
Stefano Maset ◽  
Klemen Bohinc
Keyword(s):  
Interfacial Layer ◽  
Electrostatic Interactions ◽  
Water Solution ◽  
Finite Size ◽  
Model Parameters ◽  
Spherical Nanoparticles ◽  
Lagrange Equations ◽  
Spatial Profile ◽  
Charged Surfaces ◽  
Mobile Ions

An electric interfacial layer appears when the mobile ions or nanoparticles of an electrolyte solution interact with an extended, charged surface. The distribution of ions or nanoparticles is driven by electrostatic interactions and entropy. We consider continuously charged spherical nanoparticles of finite size. At thermodynamic equilibrium, the spatial profile of the concentration is obtained by deriving the appropriate Euler–Lagrange equations. We discuss how various model parameters of the nanoparticles influence structural properties of the electric interfacial layer. We calculate the pressure between two like-charged surfaces embedded in a water solution of continuously charged spherical nanoparticles.

Direct Osmotic Pressure Measurements in Articular Cartilage Demonstrate Nonideal and Concentration-Dependent Phenomena

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Brandon K. Zimmerman ◽  
Robert J. Nims ◽  
Alex Chen ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Osmotic Pressure ◽  
Electrostatic Interactions ◽  
Swelling Pressure ◽  
Confined Compression ◽  
Human Cartilage ◽  
Poisson Boltzmann ◽  
Triphasic Theory

Abstract The osmotic pressure in articular cartilage serves an important mechanical function in healthy tissue. Its magnitude is thought to play a role in advancing osteoarthritis. The aims of this study were to: (1) isolate and quantify the magnitude of cartilage swelling pressure in situ; and (2) identify the effect of salt concentration on material parameters. Confined compression stress-relaxation testing was performed on 18 immature bovine and six mature human cartilage samples in solutions of varying osmolarities. Direct measurements of osmotic pressure revealed nonideal and concentration-dependent osmotic behavior, with magnitudes approximately 1/3 those predicted by ideal Donnan law. A modified Donnan constitutive behavior was able to capture the aggregate behavior of all samples with a single adjustable parameter. Results of curve-fitting transient stress-relaxation data with triphasic theory in febio demonstrated concentration-dependent material properties. The aggregate modulus HA increased threefold as the external concentration decreased from hypertonic 2 M to hypotonic 0.001 M NaCl (bovine: HA=0.420±0.109 MPa to 1.266±0.438 MPa; human: HA=0.499±0.208 MPa to 1.597±0.455 MPa), within a triphasic theory inclusive of osmotic effects. This study provides a novel and simple analytical model for cartilage osmotic pressure which may be used in computational simulations, validated with direct in situ measurements. A key finding is the simultaneous existence of Donnan osmotic and Poisson–Boltzmann electrostatic interactions within cartilage.

scholarly journals Potential of Kale and Lettuce Residues as Natural Adsorbents of the Carcinogen Aflatoxin B1 in a Dynamic Gastrointestinal Tract-Simulated Model

Toxins ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 771
Author(s):  
Alma Vázquez-Durán ◽  
María de Jesús Nava-Ramírez ◽  
Daniel Hernández-Patlán ◽  
Bruno Solís-Cruz ◽  
Víctor Hernández-Gómez ◽  
...  
Keyword(s):  
Hydrogen Bonding ◽  
Gastrointestinal Tract ◽  
Aflatoxin B1 ◽  
Electrostatic Interactions ◽  
Hydrophobic Interactions ◽  
Maximum Adsorption Capacity ◽  
Promising Alternative ◽  
Simulated Model ◽  
Dipole Interactions ◽  
Natural Adsorbents

Adsorption of the carcinogen aflatoxin B1 (AFB1) onto agro-waste-based materials is a promising alternative over conventional inorganic binders. In the current study, two unmodified adsorbents were eco-friendly prepared from kale and lettuce agro-wastes. A dynamic gastrointestinal tract-simulated model was utilized to evaluate the removal efficiency of the sorptive materials (0.5%, w/w) when added to an AFB1-contaminated diet (100 µg AFB1/kg). Different characterization methodologies were employed to understand the interaction mechanisms between the AFB1 molecule and the biosorbents. Based on adsorption results, the biosorbent prepared from kale was the best; its maximum adsorption capacity was 93.6%, which was significantly higher than that of the lettuce biosorbent (83.7%). Characterization results indicate that different mechanisms may act simultaneously during adsorption. Non-electrostatic (hydrophobic interactions, dipole-dipole interactions, and hydrogen bonding) and electrostatic interactions (ionic attractions) together with the formation of AFB1-chlorophyll complexes appear to be the major influencing factors driving AFB1 biosorption.

DelEnsembleElec: Computing Ensemble-Averaged Electrostatics Using DelPhi

2013 ◽  
Vol 13 (1) ◽  
pp. 256-268 ◽  
Author(s):  
Lane W. Votapka ◽  
Luke Czapla ◽  
Maxim Zhenirovskyy ◽  
Rommie E. Amaro
Keyword(s):  
Molecular Dynamics ◽  
Influenza Virus ◽  
Boltzmann Equation ◽  
General Theory ◽  
Electrostatic Interactions ◽  
Biological Interest ◽  
Single Structure ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electrostatic Calculations

AbstractA new VMD plugin that interfaces with DelPhi to provide ensemble-averaged electrostatic calculations using the Poisson-Boltzmann equation is presented. The general theory and context of this approach are discussed, and examples of the plugin interface and calculations are presented. This new tool is applied to systems of current biological interest, obtaining the ensemble-averaged electrostatic properties of the two major influenza virus glycoproteins, hemagglutinin and neuraminidase, from explicitly solvated all-atom molecular dynamics trajectories. The differences between the ensemble-averaged electrostatics and those obtained from a single structure are examined in detail for these examples, revealing how the plugin can be a powerful tool in facilitating the modeling of electrostatic interactions in biological systems.

scholarly journals Multiple native-like conformations trapped via self-association-induced hydrophobic collapse of the 33-residue β-sheet domain from platelet factor 4

1995 ◽  
Vol 306 (2) ◽  
pp. 407-419 ◽  
Author(s):  
E Ilyina ◽  
K H Mayo
Keyword(s):  
Electrostatic Interactions ◽  
Nuclear Overhauser Effect ◽  
Alpha Helix ◽  
Platelet Factor 4 ◽  
Random Coil ◽  
Beta Sheet ◽  
Platelet Factor ◽  
Hydrophobic Collapse ◽  
Low Dielectric ◽  
Self Association

Native platelet factor 4 (PF4) (70 residues) has a hydrophobic three-stranded anti-parallel beta-sheet domain on to which is folded an amphipathic C-terminal alpha-helix and an aperiodic N-terminal domain. The 33-amino acid beta-sheet domain from PF4 (residues 23-55) has been synthesized and studied by c.d. and n.m.r. At 10 degrees C and low concentration, peptide 23-55 appears to exist in aqueous solution in a random-coil distribution of highly flexible conformational states. Some preferred conformation, however, is observed, particularly within a relatively stable chain reversal from Leu-45 to Arg-49. As the peptide concentration and/or temperature is increased, a new conformational state(s) appears and intensifies as slowly exchanging (600 MHz 1H-n.m.r. chemical-shift time scale) random-coil resonances disappear. Hill plots of the concentration-dependence indicated mostly tetramer formation as found in native PF4. Although apparent resonance linewidths in aggregate state(s) are of the order of 100 Hz, sequence-specific assignments for most resonances could be made. N.m.r./nuclear Overhauser effect structural analysis indicates the formation of multiple native-like anti-parallel beta-sheet conformations, kinetically trapped via subunit-association-induced hydrophobic collapse and stabilized by low-dielectric electrostatic interactions among/between Gly-28 and Lys-50 in opposing subunits. Results are discussed in terms of protein folding.

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