Areas of the brain involved in various forms of memory exhibit patterns of neural activity quite unlike those in canonical computational models. We show how to use well-founded Bayesian probabilistic autoassociative recall to derive biologically reasonable neuronal dynamics in recurrently coupled models, together with appropriate values for parameters such as the membrane time constant and inhibition. We explicitly treat two cases. One arises from a standard Hebbian learning rule, and involves activity patterns that are coded by graded firing rates. The other arises from a spike timing dependent learning rule, and involves patterns coded by the phase of spike times relative to a coherent local field potential oscillation. Our model offers a new and more complete understanding of how neural dynamics may support autoassociation.