RESUMO

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy-momentum tensor calculated from a post-Newtonian Maxwell-Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory.

RESUMO

The Donnan potential can be observed in many biological systems due to the presence of polyelectrolytes as proteins and nucleic acids. The aim of this work was to present a useful tool to describe the fixed and charge-regulated volume charge density profile through the use of a smoothing function and to obtain the electrostatic potential profile as well as the Donnan potential of this system by solving Poisson-Boltzmann (PB) equation. When we use the smoothing function, the Donnan potential arises automatically from the solution of only one Poisson-Boltzmann equation and it is not necessary to impose this potential for treating charged system in the presence of a membrane. The electrostatic behavior across the Bacillus brevis wall considering the dependence on the ionization of the cell wall functional groups as a function of the solution pH was analyzed. An important issue was to show that potentiometric titration data could be used together with the Poisson-Boltzmann equation to predict the electrostatic behavior (e.g., zeta potential) of the bacterial cell surface.

Assuntos

RESUMO

Four chemotypes of the rough lipopolysaccharides (LPS) membrane from Pseudomonas aeruginosa were investigated by a combined approach of explicit water molecular dynamics (MD) simulations and Poisson-Boltzmann continuum electrostatics with the goal to deliver the distribution of the electrostatic potential across the membrane. For the purpose of this investigation, a new tool for modeling the electrostatic potential profile along the axis normal to the membrane, MEMbrane POTential (MEMPOT), was developed and implemented in DelPhi. Applying MEMPOT on the snapshots obtained by MD simulations, two observations were made: (a) the average electrostatic potential has a complex profile but is mostly positive inside the membrane due to the presence of Ca(2+) ions, which overcompensate for the negative potential created by lipid phosphate groups; and (b) correct modeling of the electrostatic potential profile across the membrane requires taking into account the water phase, while neglecting it (vacuum calculations) results in dramatic changes including a reversal of the sign of the potential inside the membrane. Furthermore, using DelPhi to assign different dielectric constants for different regions of the LPS membranes, it was investigated whether a single frame structure before MD simulations with appropriate dielectric constants for the lipid tails, inner, and the external leaflet regions, can deliver the same average electrostatic potential distribution as obtained from the MD-generated ensemble of structures. Indeed, this can be attained by using smaller dielectric constant for the tail and inner leaflet regions (mostly hydrophobic) than for the external leaflet region (hydrophilic) and the optimal dielectric constant values are chemotype-specific.

Assuntos