Self Assembly Exploits Dimensional Reduction For Nucleation And Growth

Self-assembly is ubiquitous in biology and is often regulated to occur under specific conditions. A critical factor in nucleation and growth during self-assembly is the localization of monomers on membranes, as exploited in processes like endocytosis and viral budding. Membrane localization enhances monomer concentration by reducing the search space from three dimensions to two. This also alters pairwise binding probabilities due to the competition between entropic loss of confinement and enthalpic gain of binding. This enhancement, defined by the volume-to-area ratio, significantly boosts reaction rates. Our findings demonstrate that proteins can self-assemble in relatively dilute solutions by localizing to membranes, with key factors being the surface-area-to-volume ratio and membrane binding affinities. We quantify the change in critical nucleation size due to dimensional reduction for linear and nonlinear aggregates by determining shifts in chemical potentials near equilibrium. We further identify thermodynamic regimes where membrane confinement is most favorable, especially for systems where some components assemble entirely in solution while others partition between solution and membrane phases, such as in amyloid or DNA-binding proteins. This dual environment raises questions about how such systems "choose" between membrane-based and solution-based assembly pathways.