Coupling of Charge Regulation and Geometry in Soft Ionizable Molecular Assemblies

The size, shape, and charge of structures, such as proteins and amphiphile assemblies, respond in an interconnected manner to solution ionic conditions. We analyze assemblies of an amphiphile (C16K2), with two ionizable amino acids [lysine (K)] coupled to a 16-carbon alkyl tail, via small-angle X-ray scattering (SAXS), nonlinear Poisson-Boltzmann theory (nl-PB), and hybrid Monte Carlo-molecular dynamics (MC-MD) simulations. SAXS revealed structural transitions from spherical micelles to cylindrical micelles to bilayers with increasing pH. By combining SAXS-determined structural information and nl-PB, we derived the molecular degree of ionization as a function of pH. The back-calculated titration curves matched the experimental data over an extended pH range, without adjustable parameters. Similarly, the SAXS data on the evolution of spherical micelle structure with ionic strength were combined with nl-PB and MC-MD to derive the bare and effective charges. MC-MD, which considered finite ion sizes, showed that bare and effective charges saturate quickly with increasing salt concentration. Furthermore, the calculated effective charges closely matched results from Zeta-potential measurements. The presented approach has advantages over customary methods for charge regulation, such as the Henderson-Hasselbalch (HH) or Hill models, where molecular ionization/deionization in assemblies is described by effective pKs that are distinct from the pK for isolated molecules. However, these models lack a physical explanation for these pK shifts. By contrast, our approach of combining structural details with an electrostatic model and simulations provides a more intuitive understanding of structure-charge coupling and a framework for understanding charge regulation in many synthetic and biological systems.