This study introduces a coupled flow-biology computational model based on scaling methods and dimensionless numbers. The aim is to illustrate the validity of this model for the investigation of vertical migration of colonies of the cyanobacterium Microcystis aeruginosa under turbulent flow conditions and affected by (light-induced) assimilation/respiration processes. This model connects the distinct time scales of turbulence (typically minutes for the integral time scale) and light-induced mass-density changes of cyanobacteria (diurnal). To compute the full Microcystis vertical migration cycles we combine Direct Numerical Simulations (DNS) of turbulence and this scaling approach. The Microcystis colonies are subjected to turbulence and DNS allows computation of their trajectories with a particle tracking algorithm. The latter is based on a simplified version of the Maxey-Riley equation describing the buoyancy and hydrodynamic forces on the colonies and requires knowledge of the smallest turbulent flow scales (down to the Kolmogorov scale, thus requiring DNS). The coupled flow-biology model proves to capture natural diurnal migration of Microcystis colonies. Under very low turbulence conditions Microcystis shows a quasi-periodic daily migration where the Stokes drag and the buoyancy force are predominant. Higher turbulence conditions override such periodicity, and mix the colonies thoroughly through the water column. Our analysis yields the buoyancy Stokes number Stb, which distinguishes the deterministic buoyancy dominated migration over the more chaotic random colony excursions due to turbulence.