Model to rationalize and predict the formation of organic patterns originating from an enzyme-assisted self-assembly Liesegang-like process of peptides in a host hydrogel

Recently, we have investigated the enzyme-assisted self-assembly of precursor peptides diffusing in an enzyme-containing host gel, leading to various self-assembly profiles within the gel. At high enzyme concentrations, the reaction-diffusion self-assembly processes result in the formation of a continuous non-monotonous peptide self-assembly profile. At low enzyme concentrations, they result in the formation of individual self-assembled peptide microglobules and at intermediate enzyme concentrations both kinds of self-assembled structures coexist. Herein, we develop a Liesegang-type model that considers four major points: (i) the diffusion of the precursor peptides within the host gel, (ii) the diffusion of the enzymes in the gel, (iii) the enzymatic transformation of the precursor peptides into the self-assembling ones and (iv) the nucleation of these building blocks as the starting point of the self-assembly process. This process is treated stochastically. Our model predicts most of the experimentally observed features and in particular (i) the transition from a continuous to a microglobular pattern of self-assembled peptides through five types of patterns by decreasing the enzyme concentration in the host hydrogel. (ii) It also predicts that when the precursor peptide concentration decreases, the enzyme concentration at which the continuous/microglobules transition appears increases. (iii) Finally, it predicts that for peptides whose critical self-assembly concentration in solution decreases, the peptide concentration at which the continuous-to-microglobular transition decreases too. All these predictions are observed experimentally. A robust mathematical model that predicts the self-assembled peptide micropatterns with an enzyme-embedded host hydrogel is described. This model relies on many parameters and reproduces experimental observations.