We use a combination of in vitro whole cell recordings and computer simulations to characterize the cellular and synaptic properties that contribute to processing of auditory stimuli. Using a mouse thalamocortical slice preparation, we record the intrinsic membrane properties and synaptic properties of layer 3/4 regular-spiking (RS) pyramidal neurons and fast-spiking (FS) interneurons in primary auditory cortex (AI). We find that postsynaptic potentials (PSPs) evoked in FS cells are significantly larger and depress more than those evoked in RS cells after thalamic stimulation. We use these data to construct a simple computational model of the auditory thalamocortical circuit and find that the differences between FS and RS cells observed in vitro generate model behavior similar to that observed in vivo. We examine how feedforward inhibition and synaptic depression affect cortical responses to time-varying inputs that mimic sinusoidal amplitude-modulated tones. In the model, the balance of cortical inhibition and thalamic excitation evolves in a manner that depends on modulation frequency (MF) of the stimulus and determines cortical response tuning.