- Neurons in one barrel in layer 4 (L4) in the mouse vibrissa somatosensory cortex are innervated mostly by neurons from the VPM nucleus and by other neurons within the same barrel. During quiet wakefulness or whisking in air, thalamic inputs vary slowly in time, and excitatory neurons rarely fire. A barrel in L4 contains a modest amount of neurons; the synaptic conductances are not very strong and connections are not sparse. Are the dynamical properties of the L4 circuit similar to those expected from fluctuation-dominated, balanced networks observed for large, strongly coupled and sparse cortical circuits? To resolve this question, we analyze a network of 150 inhibitory parvalbumin-expressing fast-spiking inhibitory interneurons innervated by the VPM thalamus with random connectivity, without or with 1600 low-firing excitatory neurons. Above threshold, the population-average firing rate of inhibitory cortical neurons increases linearly with the thalamic firing rate. The coefficient of variation CV is somewhat less than 1. Moderate levels of synchrony are induced by converging VPM inputs and by inhibitory interaction among neurons. The strengths of excitatory and inhibitory currents during whisking are about three times larger than threshold. We identify values of numbers of presynaptic neurons, synaptic delays between inhibitory neurons, and electrical coupling within the experimentally plausible ranges for which spike synchrony levels are low. Heterogeneity in in-degrees increases the width of the firing rate distribution to the experimentally observed value. We conclude that an L4 circuit in the low-synchrony regime exhibits qualitative dynamical properties similar to those of balanced networks.