In the primary visual cortex (V1), single cell responses to simple visual stimuli (gratings) are usually dense but with a high trial-by-trial variability. In contrast, when exposed to full field natural scenes, the firing patterns of these neurons are sparse but highly reproducible over trials (Marre et al., 2005; Frégnac et al., 2006). It is still not understood how these two classes of stimuli can elicit these two distinct firing behaviours. A common model for simple-cell computation in layer 4 is the ``push-pull'' circuitry (Troyer et al. 1998). It accounts for the observed anti-phase behaviour between excitatory and inhibitory conductances in response to a drifting grating (Anderson et al., 2000; Monier et al., 2008), creating a wide temporal integration window during which excitation is integrated without the shunting or opponent effect of inhibition and allowed to elicit multiple spikes. This is in contrast to recent results from intracellular recordings in vivo during presentation of natural scenes (Baudot et al., 2013). Here the excitatory and inhibitory conductances were highly correlated, with inhibition lagging excitation only by few milliseconds (̃6 ms). This small lag creates a narrow temporal integration window such that only synchronized excitatory inputs can elicit a spike, similar to parallel observations in other cortical sensory areas (Wehr and Zador, 2003; Okun and Lampl, 2008). To investigate the cellular and network mechanisms underlying these two different correlation structures, we constructed a realistic model of the V1 network using spiking neurons with conductance based synapses. We calibrated our model to fit the irregular ongoing activity pattern as well as in vivo conductance measurements during drifting grating stimulation and then extracted predicted responses to natural scenes seen through eye-movements. Our simulations reproduced the above described experimental observation, together with anti-phase behaviour between excitation and inhibition during gratings and phase lagged activation during natural scenes. In conclusion, the same cortical network that shows dense and variable responses to gratings exhibits sparse and precise spiking to natural scenes. Work is under way to show to which extent this feature is specific for the feedforward vs recurrent nature of the modelled circuit.