The motility of microorganisms in liquid media is an important issue in active matter, and it is not yet fully understood. Previous theoretical approaches dealing with the microscopic description of microbial movement have modeled the propelling force exerted by the organism as a gaussian white noise term in the equation of motion. We present experimental results for ciliates of the genus "Colpidium", which do not agree with the white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion
