Diffuse Double Layer Theory for Electrolytes of Unsymmetrical Valence Types

Grahame, David C.

doi:10.1063/1.1699109

Cited by 250 publications

(98 citation statements)

References 4 publications

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“…4B) by Ca 2þ (solid red line in Fig. 4B) in Ca 2þ -loaded buffer indicated by the MC simulation is fully consistent not only with the GIXF results but also with the analytical continuum description of ion distributions near charged surfaces according to Gouy-Chapman theory (21,22). Another important conclusion that we can draw from the continuum description and MC simulations is that the net charge across the interface is completely compensated on sufficiently long length scales † .…”

Section: Resultssupporting

confidence: 63%

Quantitative determination of ion distributions in bacterial lipopolysaccharide membranes by grazing-incidence X-ray fluorescence

Schneck

Schubert²,

Konovalov³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

116

134

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A model of the outer membrane of Gram-negative bacteria was created by the deposition of a monolayer of purified rough mutant lipopolysaccharides at an air/water interface. The density profiles of monovalent (K þ ) and divalent (Ca 2þ ) cations normal to the lipopolysaccharides (LPS) monolayers were investigated using grazingincidence X-ray fluorescence. In the absence of Ca 2þ , a K þ concentration peak was found in the negatively charged LPS headgroup region. With the addition of CaCl 2 , Ca 2þ ions almost completely displaced K þ ions from the headgroup region. By integrating the experimentally reconstructed excess ion density profiles, we obtained an accurate measurement of the effective charge density of LPS monolayers. The experimental findings were compared to the results of Monte Carlo simulations based on a coarse-grained minimal model of LPS molecules and showed excellent agreement.monolayer | Monte Carlo simulation | electrostatics | biological interface B iological surfaces expose a variety of charged macromolecules that interact with various sorts of ions under physiological conditions. However, despite the crucial role of charged macromolecules in modulating the interaction between cells and their surrounding environments, the quantitative understanding of electrostatics at such soft, complex interfaces still remains a general scientific challenge. For example, the outer membrane surface of Gram-negative bacteria is mainly composed of lipopolysaccharides (LPSs) (1), whose negatively charged saccharide head groups stabilize the structural integrity of bacteria and protect bacteria against their environment. Several in vivo studies (2, 3) demonstrated that bacteria increase their resistance against cationic antimicrobial peptides (e.g., protamine) in the presence of divalent cations (Ca 2þ , Mg 2þ ). Therefore, for the development of peptide-based antibiotics (4), it is important to understand the molecular mode of action of antimicrobial peptides.A number of theoretical models for the interactions of LPS molecules with divalent cations (5-7), suggested that the ions would bind to the charged 2-keto-3-deoxyoctonoic acid (KDO) groups (the "inner core") thereby stabilizing the membrane. Recently, we measured grazing-incidence X-ray scattering from a monolayer of rough mutant LPS from Salmonella enterica sv. Minnesota at an air/water interface and demonstrated the Ca 2þ -induced increase in the electron density near the inner core (8). These observations were supported by the results of Monte Carlo (MC) simulations of a coarse-grained model (8). A further challenge would be to extend such a strategy to wild-type LPSs that possess polydisperse, specific O-polysaccharide chains (O-side chains). Pink et al. (9) carried out MC simulations of a minimal model of the more complex, wild-type LPSs from Pseudomonas aeruginosa (PAO1) and concluded that divalent cations would induce a collapse of the negatively charged O-sidechains toward the membrane surface. Because it is difficult in practice to deposit LPSs wit...

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Section: Resultssupporting

confidence: 63%

Quantitative determination of ion distributions in bacterial lipopolysaccharide membranes by grazing-incidence X-ray fluorescence

Schneck

Schubert²,

Konovalov³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

116

134

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“…Based on the theoretical physicochemical analyses given by McLaughlin et al (1971) and other investigators earlier (Gouy, 1909;Chapman, 1913;Grahame, 1947Grahame, , 1953Overbeek, 1952;Chandier, Hodgkin & Meves, 1965;Gilbert & Ehrenstein, 1969), there are certain specific experimental predictions one could make if screening (and not specific binding) was the mechanism by which external calcium affected the threshold potential for 118 AXONAL SURFACE POTENTIAL: EFFECT OF CATIONS 119 spike initiation. The most obvious prediction is that if calcium is substituted by an identical concentration of some other divalent cation, the effect on threshold potential will be the same since the binding energy of a particular cation is no longer relevant.…”

mentioning

confidence: 99%

Possible screening of surface charges on crayfish axons by polyvalent metal ions

D'Arrigo¹

1973

The Journal of Physiology

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SUMMARY1. The effect of different polyvalent metal ions in the external solution upon the threshold membrane potential for spike initiation in crayfish axons has been studied by means of intracellular micro-electrodes. The metal ions tested included six divalent cations (Ca2+, Mg2+, Sr2+, Ba2+, Co2+, and Ni2+) and three trivalent cations (La +, Y3+ and Eu3+).2. Identical extracellular concentrations of different cations with the same valence had essentially the same effect on threshold membrane potential. However, a very low concentration of trivalent cations (about 225 /SM) was found to be equivalent to a much higher divalent cation concentration (13.5 mM) as measured by their effects on threshold potential.3. Upon a tenfold increase in concentration, the threshold potential for spike initiation was shifted in a positive direction by 30-6 mV with divalent cations and by 208 mV with trivalent cations.4. It is shown that a hypothesis involving screening of negative charges at the axonal membrane surface, based on Gouy-Chapman theory, predicts these various experimental results rather closely.5. It is concluded that a high negative charge density, sufficient to render a screening mechanism possible, exists at the surface of crayfish axons in the region of the sodium 'gates'. 6. The density of surface charges is calculated to be approximately le-/43 A2. This calculation is discussed in connexion with the possible molecular identity of the sodium 'gates' in crayfish axons and other excitable systems.

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“…[8], [15], [16], p. 474). En conséquence, le phénomène d'adsorption au contact du substrat est modélisé, pour une classe très générale de formulations de la densité surfacique de charges σ, par la condition mêlée de Fourier-Robin non linéaire (cf.…”

Section: Le Cadre Généralunclassified

Sur le système de Nernst-Planck-Poisson-Boltzmann résultant de l’homogénéisation par convergence à double échelle

Gagneux¹,

Millet²

2014

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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Diffuse Double Layer Theory for Electrolytes of Unsymmetrical Valence Types

Abstract: Equations are derived for the variation of potential with distance and for the components of charge and capacity in the diffuse double layer at a plane interface for electrolytes of the 1:2 and 2:1 valence types. Some additional relations are also deduced for other valence types.

Cited by 250 publications

References 4 publications

Quantitative determination of ion distributions in bacterial lipopolysaccharide membranes by grazing-incidence X-ray fluorescence

Quantitative determination of ion distributions in bacterial lipopolysaccharide membranes by grazing-incidence X-ray fluorescence

Possible screening of surface charges on crayfish axons by polyvalent metal ions

Sur le système de Nernst-Planck-Poisson-Boltzmann résultant de l’homogénéisation par convergence à double échelle

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