Donnan Potential across the Outer Membrane of Gram-Negative Bacteria and Its Effect on the Permeability of Antibiotics

The cell envelope structure of Gram-negative bacteria is unique, composed of two lipid bilayer membranes and an aqueous periplasmic space sandwiched in between. The outer membrane constitutes an extra barrier to limit the exchange of molecules between the cells and the exterior environment. Donnan potential is a membrane potential across the outer membrane, resulted from the selective permeability of the membrane, which plays a pivotal role in the permeability of many antibiotics. In this review, we discussed factors that affect the intensity of the Donnan potential, including the osmotic strength and pH of the external media, the osmoregulated periplasmic glucans trapped in the periplasmic space, and the displacement of cell surface charges. The focus of our discussion is the impact of Donnan potential on the cellular permeability of selected antibiotics including fluoroquinolones, tetracyclines, β-lactams, and trimethoprim.

A Numerical Method for Electrical Potential on Membranes with Fixed Charge

The potential developed on a membrane with fixed charge plays crucial roles in many biological and engineering systems. The classic Teorell-Meyer-Siever (TMS) theory gives an analytical expression of the membrane potential only for limited cases of simple solutions. A numerical method that can be applied to the general cases was developed in this study. With a boundary updating scheme, a numerical solution to the Nernst-Planck-Poisson equations was obtained rigorously without the commonly used simplifications and assumptions in previous studies. The features of the membrane potentials with different fixed charges were investigated with this numerical method under various conditions. The validity of this numerical method was verified by identical values of Donnan potential obtained with well-established analytical methods. The suitability and applicability of analytical TMS model were assessed by comparison to the numerical method.

Theory of Inhomogeneous Rod-like Coulomb Fluids

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson–Boltzmann and Maier–Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity to a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic–isotropic wetting phase with a Donnan potential difference.

Ion Pairing and Dielectric Decrement in Glycosaminoglycan Brushes

Molecular dynamics simulations of hyaluronic acid and heparin brushes are presented that show important effects of ion-pairing, water dielectric decrease, and co-ion exclusion. Results show equilibria with electroneutrality attained through screening and pairing of brush anionic charges by cations. Most surprising is the reversal of the Donnan potential that would be expected based on electrostatic Boltzmann partitioning alone. Water dielectric decrement within the brush domain is also associated with Born hydration-driven cation exclusion from the brush. We observe that the primary partition energy attracting cations to attain brush electroneutrality is the ion-pairing or salt-bridge energy associated with cation-sulfate and cation-carboxylate solvent-separated and contact ion pairs. Potassium and sodium pairing to glycosaminoglycan carboxylates and sulfates consistently show similar abundance of contact-pairing and solvent-separated pairing. In these crowded macromolecular brushes, ion-pairing, Born-hydration, and electrostatic potential energies all contribute to attain electroneutrality and should therefore contribute in mean-field models to accurately represent brush electrostatics.

Ion Pairing and Dielectric Decrement in Glycosaminoglycan Brushes

Molecular dynamics simulations of hyaluronic acid and heparin brushes are presented that show important effects of ion-pairing, water dielectric decrease, and co-ion exclusion. Results show equilibria with electroneutrality attained through screening and pairing of brush anionic charges by cations. Most surprising is the reversal of the Donnan potential that would be expected based on electrostatic Boltzmann partitioning alone. Water dielectric decrement within the brush domain is also associated with Born hydration-driven cation exclusion from the brush. We observe that the primary partition energy attracting cations to attain brush electroneutrality is the ion-pairing or salt-bridge energy associated with cation-sulfate and cation-carboxylate solvent-separated and contact ion pairs. Potassium and sodium pairing to glycosaminoglycan carboxylates and sulfates consistently show similar abundance of contact-pairing and solvent-separated pairing. In these crowded macromolecular brushes, ion-pairing, Born-hydration, and electrostatic potential energies all contribute to attain electroneutrality and should therefore contribute in mean-field models to accurately represent brush electrostatics.

Ion Pairing and Dielectric Decrement in Glycosaminoglycan Brushes

Molecular dynamics simulations of hyaluronic acid and heparin brushes are presented that show important effects of ion-pairing, water dielectric decrease, and co-ion exclusion. Results show equilibria with electroneutrality attained through screening and pairing of brush anionic charges by cations. Most surprising is the reversal of the Donnan potential that would be expected based on electrostatic Boltzmann partitioning alone. Water dielectric decrement within the brush domain is also associated with Born hydration-driven cation exclusion from the brush. We observe that the primary partition energy attracting cations to attain brush electroneutrality is the ion-pairing or salt-bridge energy associated with cation-sulfate and cation-carboxylate solvent-separated and contact ion pairs. Potassium and sodium pairing to glycosaminoglycan carboxylates and sulfates consistently show similar abundance of contact-pairing and solvent-separated pairing. In these crowded macromolecular brushes, ion-pairing, Born-hydration, and electrostatic potential energies all contribute to attain electroneutrality and should therefore contribute in mean-field models to accurately represent brush electrostatics.

Theory of Inhomogeneous Calamitic Coulomb Fluids

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a calamitic counterion-only system in proximity of a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic-isotropic wetting phase with a Donnan potential difference.