Two-dimensional rigid colloid aggregation models may be applied to protein layers when no large conformational change is involved. Yet, following adsorption, several proteins undergo a conformational transition that may be involved in aggregative structures. Our focus here is how a conformational change might influence surface clustering in a diffusion-aggregation model. We propose a model including diffusion, aggregation, and unfolding of proteins that are randomly adsorbed onto a surface. Our model allows simulating the case where protein-protein interaction favors unfolding and the case where this interaction prevents it. We study the effect of a simple disk-to-rod unidirectional unfolding and investigate the morphology of the resulting clusters in the diffusion- and reaction-limited regimes. A rich variety of structures is produced, with fractal dimension differing from that in universal diffusive aggregation models. Increasing unfolding probability shifts the system from the neighbor-induced to the neighbor-prevented unfolding regime. The intermediate structures that arise from our model could be helpful in understanding the assembly of different observed protein structures.