An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation

Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density n _c = 3.67 × 10^-3 Å^-2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density n _g = 8.40 × 10^-3 Å^-2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension d _F < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < n _c, subdiffusive for n _c ≤ n < n _g, and blocked for n ≥ n _g. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.