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

Nonlinear Poisson-Boltzmann solutions for charged parallel plates: When opposite charges repel

I present an exact solution of the Poisson-Boltzmann equation for two parallel plates and discuss the solution properties. I discuss in more detail plates with opposite charges: In this case, there are two critical separations, Lc,1 < Lc,2. For separations less than Lc,1, the force between plates is repulsive. It switches to attractive at Lc,1, but with the electric potential having the same sign on both plates. For L > Lc,2, the force remains attractive, and the potential at the plates has the same sign as the charge on each plate. I also describe charge regulation, determined by pKa, and provide formulas for both the critical distance where oppositely charged plates repel and their charging process. The implications of these results for the nanoparticle assembly, as driven by electrostatic interactions, are also discussed.

The role of phospholipids in drug delivery formulations - Recent advances presented at the Researcher's Day 2023 Conference of the Phospholipid Research Center Heidelberg

This Focus on Meetings contribution summarizes recent advances in the research on phospholipids and their applications for drug delivery and analytical purposes that have been presented at the hybrid Researcher's Day 2023 Conference of the Phospholipid Research Center (PRC), held on July 3-5, 2023, in Bad Dürkheim, Germany. The PRC is a non-profit organization focused on expanding and sharing scientific and technological knowledge of phospholipids in pharmaceutical and other applications. This is accomplished by, e.g., funding doctoral and postdoctoral research projects. The progress made with these projects is presented at the Researcher's Day Conference every two years. Four main topics were presented and discussed in various lectures: (1) formulation of phospholipid-based nanocarriers, (2) therapeutic applications of phospholipids and phospholipid-based nanocarriers, (3) phospholipids as excipients in oral, dermal, and parenteral dosage forms, and (4) interactions of phospholipids and phospholipid-based vesicles in biological environment and their use as analytical platforms.

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

How Cell-Penetrating Peptides Behave Differently from Pore-Forming Peptides: Structure and Stability of Induced Transmembrane Pores

Peptide-induced transmembrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell-penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions, and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore-forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small-angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that although AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

How cell penetrating peptides behave differently from pore forming peptides: structure and stability of induced transmembrane pores

Peptide induced trans-membrane pore formation is commonplace in biology. Examples of transmembrane pores include pores formed by antimicrobial peptides (AMPs) and cell penetrating peptides (CPPs) in bacterial membranes and eukaryotic membranes, respectively. In general, however, transmembrane pore formation depends on peptide sequences, lipid compositions and intensive thermodynamic variables and is difficult to observe directly under realistic solution conditions, with structures that are challenging to measure directly. In contrast, the structure and phase behavior of peptide-lipid systems are relatively straightforward to map out experimentally for a broad range of conditions. Cubic phases are often observed in systems involving pore forming peptides; however, it is not clear how the structural tendency to induce negative Gaussian curvature (NGC) in such phases is quantitatively related to the geometry of biological pores. Here, we leverage the theory of anisotropic inclusions and devise a facile method to estimate transmembrane pore sizes from geometric parameters of cubic phases measured from small angle X-ray scattering (SAXS) and show that such estimates compare well with known pore sizes. Moreover, our model suggests that whereas AMPs can induce stable transmembrane pores for membranes with a broad range of conditions, pores formed by CPPs are highly labile, consistent with atomistic simulations.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

Lipid nanoparticles with ionizable lipids: Statistical aspects

Lipid nanoparticles (LNPs) with size ∼100 nm are now used for fabrication of a new generation of drugs and antiviral vaccines. To optimize their function or, more specifically, interaction with cell membranes, their composition often includes ionizable lipids which are neutral or cationic (after association with H^{+}). Physically, such LNPs represent an interesting example of mesoscopic nanosystems with complex and far from understood properties. Experimentally, they can be studied at cell-membrane mimics. Herein, I analyze theoretically three related aspects. (i) I describe how the extent of protonation of ionizable lipids located at the surface of LNPs depends on the H^{+} concentration by using the phenomenological Langmuir-Stern and Poisson-Boltzmann models with continuum distribution of charges and the dipole model with discrete charges. In these frameworks, the H^{+} adsorption isotherms are predicted to be close to Langmuirian provided the fraction of ionizable lipids is smaller than 0.5. (ii) I scrutinize the interaction between charged LNPs and their interaction with a supported lipid bilayer (SLB) by using the phenomenological theory and lattice-gas model. The long-term association or attachment is predicted provided the charges are opposite. The models make it possible to estimate the size of the contact region (provided a LNP is not deformed) and the number of lipid-lipid bonds in this region. (iii) I briefly discuss denaturation of a LNP during interaction with the SLB and argue that it may occur via a few stepwise transitions.