Adsorption-Coupled Diffusion of Gold Nanoclusters within a Large-Pore Protein Crystal Scaffold

Large-pore protein crystals (LPCs) are ordered biologically derived nanoporous materials exhibiting pore diameters greater than 8 nm. These substantial pores distinguish LPCs from typical nanoporous scaffolds, enabling engineered LPC materials to readily uptake, immobilize, and release macromolecular guests. In this study, macromolecular transport within an LPC environment was experimentally and computationally investigated by studying adsorption-coupled diffusion of Au₂₅(glutathione)₁₈ nanoclusters within a cross-linked LPC scaffold via time-lapse confocal microscopy, bulk equilibrium adsorption, and hindered diffusion simulation. Equilibrium adsorption data is congruent with a Langmuir adsorption model, exhibiting strong binding behavior between nanoclusters and the scaffold. The standard Gibbs free energy of binding is equivalent to -37.2 kJ/mol, and the maximum binding capacity of 1.25 × 10³ mg/g corresponds to approximately 29 nanoclusters per LPC unit cell. The hindered diffusion model showed good agreement with experimental data, revealing a pore diffusion coefficient of 3.7 × 10^-7 cm²/s under low nanocluster concentration. Furthermore, the model was sufficient to determine adsorption and desorption kinetic values for k_a and k_d equal to 13 cm³/mol·s and 1.7 × 10^-7 s^-1, respectively. At higher nanocluster concentrations, the simulated pore diffusion coefficient could be reduced by 3 orders of magnitude to 3.4 × 10^-10 cm²/s due to the effects of pore occlusion. This study demonstrates a strategy to analyze adsorption-coupled diffusion data to better understand complex transport of fluorescent macromolecules into LPCs. This approach fits the observable fluorescence data to the key molecular details and will benefit downstream efforts to engineer LPC-based nanoporous materials.