In this talk, I will address some questions concerning singular limits in systems of PDEs arising from biology. More precisely, the analysis of diffusive enzyme reactions and plant-growth dynamics with autotoxicity will be presented. By proving and using certain results such as duality-, energy method and some bootstrap argument, we derive suitable a-priori estimates which allow to pass to the limit to obtain some cross diffusion systems. Moreover, by exploiting some projection method, we also derive the convergence rate of the singular limits.