McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

Cationic antimicrobial peptides are promising sources for novel therapeutic agents against multi-drug-resistant bacteria. HHC-36 (KRWWKWWRR) is a simple but effective antimicrobial peptide with similar or superior activity compared with several conventional antibiotics. In this biophysical study, unique conformational properties of this peptide and some of its analogs as well as its interaction with lipid membranes are investigated in detail. Circular dichroism (CD) and molecular dynamics modeling studies of HHC-36 in different environments reveal a dynamic amphipathic structure composed of competing turn conformations with free energies lower than that of the unfolded state, implying a strong influence of tryptophan interactions in formation of the turns. CD spectra and gel electrophoresis also show strong evidence of self-association of this peptide in aqueous milieu and interaction with both neutrally and negatively charged lipid membrane systems. Isothermal titration calorimetry and acrylamide fluorescence quenching experiments emphasize the preference of HHC-36 for negatively charged vesicles. In addition, dye leakage experiments suggest that this peptide functions through a surface-associated mechanism with weak lytic activity against bacterial model membranes.

Carbon nanotubes (CNTs) have potential benefits in medicine, e.g. as drug delivery vehicles. However, CNTs and related nanoparticles might be significantly toxic. Although it is well established that cells ingest CNTs, we still have a limited understanding of the interactions at a molecular level between CNTs and cell membranes. Rational CNT derivatizations may allow targeting specific receptors as well as better penetrating cells, while pristine CNTs have shown strong antibacterial activity. In many cases, mechanistic details of such experimental results remain unknown. Consequently, recent computational and theoretical studies have tried to model possible internalization mechanisms of functionalized nanoparticles into cells. Here, we report coarse-grained molecular dynamics simulations of pristine CNTs in interaction with a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer. Both single-and multi-wall CNTs, of different lengths (from 2 to 10 nm) and diameters (from 1.5 to 5 nm), are investigated. We characterize the insertion mechanism of pristine CNTs into the cell membrane model. Strong perturbations of the membrane are observed, as assessed by important phase transitions in the lipid bilayer. Based on our simulations of pristine CNTs, we finally suggest a mechanism for their antibacterial activity. The overall results shed light on the action of CNTs in cellular environment, which will contribute to guide both prevention of health risks and development of therapeutic applications.

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