The role of the casimir effect as a physical model for the organization of lipid membranes

Abstract

Biological membranes are essential structures for life. In recent decades, it has been proposed that quantum phenomena, such as the Casimir effect, could play an additional role in the organization of these systems at the nanoscale. This work aims to evaluate the feasibility of this hypothesis by understanding the Casimir effect as a possible physical contribution to the behavior of lipid membranes. To this end, the canonical quantization of the electromagnetic field was first developed, establishing the necessary theoretical framework for calculating the vacuum energy. Subsequently, the Casimir force was derived for two geometric configurations: parallel flat plates and concentric spheres, using regularization and renormalization techniques to address the inherent discrepancies in the calculation. Finally, the physical plausibility of applying these results to the biological context was analyzed by comparing the magnitude and distance dependence of the Casimir force with other known membrane interactions. The results show that, while both geometries produce consistent expressions, the resulting behavior is monotonous, lacking equilibrium points or energy minima that would explain why the membrane stabilizes at its characteristic thickness. It is concluded that the planarparallel plate representation is sufficient as a first approximation, given that curvature correction is negligible at the cellular scale, and that the Casimir effect constitutes a geometrically plausible, albeit still exploratory, model to complement the physical understanding of lipid membrane organization.