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their dendrites in highly nonlinear ways. It is unknown how 
these dendritic nonlinearities in individual cells contribute 
to computations at the level of neural circuits. Here we show 
that dendritic nonlinearities are critical for the efficient 
integration of synaptic inputs in circuits performing analog 
computations with spiking neurons. We developed a theory that 
formalises how a neuron's dendritic nonlinearity that is 
optimal for integrating synaptic inputs depends on the 
statistics of its presynaptic activity patterns. Based on 
their in vivo preynaptic population statistics (firing rates, 
membrane potential fluctuations, and correlations due to 
ensemble dynamics), our theory accurately predicted the 
responses of two different types of cortical pyramidal cells 
to patterned stimulation by two-photon glutamate uncaging. 
These results reveal a new computational principle underlying 
dendritic integration in cortical neurons by suggesting a 
functional link between cellular and systems-level properties 
of cortical circuits.</abstractText>
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