Goldman equation | EPFL Graph Search

The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the reversal potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E. Goldman of Columbia University, and the Medicine Nobel laureates Alan Lloyd Hodgkin and Bernard Katz. Equation for monovalent ions The GHK voltage equation for M monovalent positive ionic species and A negative: :E_{m} = \frac{RT}{F} \ln{ \left( \frac{ \sum_{i}^{n} P_{M^{+}{i}}[M^{+}{i}]\mathrm{out} + \sum{j}^{m} P_{A^{-}{j}}[A^{-}{j}]\mathrm{in}}{ \sum{i}^{n} P_{M^{+}{i}}[M^{+}{i}]\mathrm{in} + \sum{j}^{m} P_{A^{-}{j}}[A^{-}{j}]_\mathrm{out}} \right) } This results in the following if we consider a membrane separating two \mathrm{K}{x}\mathrm{Na}{1-x}\mathrm{Cl}-solutions: :E_{m, \mathrm{K}_{x}\mathrm{\text{N

Direct Visualization of Single Ions in the Stern Layer of Calcite

Jean-François Molinari, Maria Ricci, Peter Spijker, Francesco Stellacci, Kislon Voitchovsky

Calcite is among the most abundant minerals on earth and plays a central role in many environmental and geochemical processes. Here we used amplitude modulation atomic force microscopy (AFM) operated in a particular regime to visualize single ions close to the (10 (1) over bar4) surface of calcite in solution. The results were acquired at equilibrium, in aqueous solution containing different concentrations of NaCl, RbCl, and CaCl2. The AFM images provide a direct and atomic-level picture of the different cations adsorbed preferentially at certain locations of the calcite water interface. Highly ordered water layers at the calcite surface prevent the hydrated ions from directly interacting with calcite due to the energy penalty incurred by the necessary restructuring of the ions' solvation shells. Controlled removal of the adsorbed ions from the interface by the AFM tip provides indications about the stability of the adsorption site. The AFM results show the familiar "row pairing" of the carbonate oxygen atoms, with the adsorbed monovalent cations located adjacent to the most prominent oxygen atoms. The location of adsorbed cations near the surface appears better defined for monovalent ions than for Ca2+, consistent with the idea that Ca2+ ions remain further away from the surface of calcite due to their larger hydration shell. The precise distance between the different hydrated ions and the surface of calcite is quantified using MD simulation. The preferential adsorption sites found by MD as well as the ion residence times close to the surface support the AFM findings, with Na+ ions dwelling substantially longer and closer to the calcite surface than Ca2+. The results also bring new insights into the problem of the Stern and electrostatic double layer at the surface of calcite, showing that parameters such as the thickness of the Stern layer can be highly ion dependent.

American Chemical Society2013

Formation and study of single metal ion–phospholipid complexes in biphasic electrospray ionization mass spectrometry

Daniel Filipe Dos Santos Alves Jana, Hubert Girault, Manuel Alejandro Méndez Agudelo, Michel Prudent

Single metal ion-phospholipid complexes are observed in biphasic electrospray ionization mass spectrometry (BESI-MS) using a dual-channel microsprayer. Such a microsprayer makes it possible to put into contact two immiscible liquids within the Taylor cone. Thus, L-alpha-dipalmitoyl phosphatidylcholine (DPPC) dissolved in 1,2-dichloroethane (DCE) reacts with aqueous metal cations (M = Na+, K+, Ca2+, Cu2+, La3+) yielding the formation of M-DPPCn complexes. The number of phospholipid molecules ranges from 1 to 4 for monovalent ions, to 8 for divalent and to more than 10 for trivalent ions respectively. The large number of ligands observed involves the formation of solvent free single ion-phospholipid complexes.

Royal Society of Chemistry2010

Direct Visualization of Single Ions in the Stern Layer of Calcite

Jean-François Molinari, Maria Ricci, Peter Spijker, Francesco Stellacci, Kislon Voitchovsky

American Chemical Society2013