Applications of synthetic biology require robust and scalable biological processing structures. Primitive processing structures such as logic gates, oscillators and a simple flip-flop have already been implemented in prokaryotic and eukaryotic cells. In our research we focused primarily on designing robust and reliable master-slave variant of a flip-flop cell. The latter changes its value only on the raising or falling edge of the clock signal and therefore allows efficient synchronization of separate building blocks of the biological circuit. A model of such cell has consequently been used when designing more complex biological system, where the functional logic has been distributed along a population of cells, which communicate through quorum sensing. The basis of our research is a deterministic reaction-diffusion system comprised of first order non-linear differential equations. Simulations of this model have been performed using second order Runge-Kutta and Finite difference numerical methods. In order to explore the viable kinetic parameter space we have utilized the genetic algorithms as a search technique. The resulting parameter value combinations indicate that a potential implementation inside a microbial consortium is possible. Distribution of functional logic between cell populations therefore allows implementing more complex structures.