We integrate cell micropatterning technology with dynamic clamp electrophysiology to realize a hybrid neuronal network of biological and computational neurons for investigating the effect of neuronal firing properties on the network function. A simple convergent neuronal network unit, consisting of three neurons connected in a two-input one-output architecture, is considered. We first show computationally that the output of the convergent unit changes from a logical AND gate-like state to an OR gate-like state with a minor perturbation in synaptic weight which is physiologically plausible. Then, using a hybrid network of a primary rat hippocampal neuron and model neurons, we demonstrate that this functional tuning can be physically embedded. The nonlinearity of neuronal activation underlies the ability to abruptly switch between the two output states, which is also verified by conductance modulation experiments. Our work demonstrates that dynamic clamp technology extends the constructive approach using cell micropatterning for investigating the cellular mechanisms of signal processing within well-defined neuronal networks.