The self-assembly of model peptides has been studied using Brownian dynamics (BD) computer simulations. In particular, a bead-spring coarse-grained model (a model in which a set of molecules is represented by a single bead and the bonding interactions by simple spring forces) has been designed to mimic small proteins called ‘silaffins’ observed to favour the formation of amorphous silica nanospheres in vitro and involved in the biomineralisation of certain diatoms cell walls. The coarse-grained model used in the simulations keeps the primary characteristics of the silaffins, these being a 15 amino acid hydrophilic backbone and two modified lysine residues near the ends of the backbone each carrying a hydrophobic polyamine chain. In the simulations, the model peptides self-assemble to form micelles, networks of strands, or discontinuous structures depending on the peptide concentration and the system temperature. The simulation results show that over a broad range of peptide volume fractions (0.05-25%) the characteristic structural lengthscales fall in the range 12-45 nm. This suggests that the self-assembled structures observed may act as either nucleation points or scaffolds for the deposition of 10-100 nm silica-peptide composite building blocks from which diatom skeletons and synthetic nanospheres are made. A systematic coarse-grained computer-simulation study of the role of putrescine homologues H₂N-(CN₂)n-NH₂ on silica morphogenesis is presented. Brownian dynamics simulations of model putrescine are performed highlighting the importance of aggregation on the degree of silica deposition. The results suggest that over a broad range of solute concentration (15-50 mM) the characteristic lengthscales of the observed self-assembled structures correlate with structural properties of the silicas observed in vitro.