The Coupling of Charge Regulation and Geometry in Soft Ionizable Molecular Assemblies

The size, shape, and charge of soft assembled nano-structures, like those in biology, respond in an interconnected manner to solution ionic conditions. Customarily, the charge regulation of ionizable groups is described through a pK_a (ion dissociation constant), deduced from Henderson-Hasselbalch or Hill model fits to titration data. However, such models do not account for the size and shape of assemblies and lack a physical explanation for apparent pK_a shifts. This leaves a gap in the intuitive understanding of the charge regulation process. To tackle this problem, we combined X-ray scattering, molecular dynamics simulations and Poisson-Boltzmann theory to predict the degree of ionization in charged assemblies. We analyzed the self-assembly and charge regulation of the peptide amphiphile C₁₆K₂: a two ionizable amino acid [Lysine (K)] head group coupled to a 16-carbon length tail. Experiments and simulations revealed assembly shape and size transitions as a function of pH and salt concentration. An electrostatic model then allowed extraction of the shape and size-dependent degree of ionization. Overall, our study elucidates key principles in analyzing the coupling of electrostatics and nano-scale details of soft nano-structures which play a crucial role in biological systems.