The microbial part of the pelagic food web is believed to be a highly dynamic and tightly coupled network in which system behavior emerges from organism properties and interactions. A central goal in microbial ecology is a quantitative understanding of these interactions. A key aspect of these linkages is again the efficiency of food acquisition in the different groups of planktonic organisms. Here we estimate osmotrophic nutrient affinity for inorganic nitrogen and phagotrophic prey clearance values, using a parsimonious model of the microbial food web and modern Bayesian Markov chain Monte Carlo (MCMC) methods. The model is fitted to experimental data from five mesocosms filled with northern Baltic seawater containing an N-limited summer community and perturbed with different nutrient additions. The MCMC method successfully found one common set of parameters that not only gave a good fit to perturbation responses in all five mesocosms, but also was in reasonable agreement, both with values derived theoretically from first principles and allometric relationships, and with affinity values for phosphate in the experimental literature. Key properties of the structure and functioning of the microbial plankton food web can thus be derived and understood from fundamental physical-chemical laws governing affinity for nutrient uptake by osmotrophs, and size-selective grazing by key functional groups of phagotrophs.