  One of the central problems in neuroscience is reconstructing synaptic
connectivity in neural circuits. Synapses onto a neuron can be probed by
sequentially stimulating potentially pre-synaptic neurons while monitoring the
membrane voltage of the post-synaptic neuron. Reconstructing a large neural
circuit using such a "brute force" approach is rather time-consuming and
inefficient because the connectivity in neural circuits is sparse. Instead, we
propose to measure a post-synaptic neuron's voltage while stimulating
sequentially random subsets of multiple potentially pre-synaptic neurons. To
reconstruct these synaptic connections from the recorded voltage we apply a
decoding algorithm recently developed for compressive sensing. Compared to the
brute force approach, our method promises significant time savings that grow
with the size of the circuit. We use computer simulations to find optimal
stimulation parameters and explore the feasibility of our reconstruction method
under realistic experimental conditions including noise and non-linear synaptic
integration. Multineuronal stimulation allows reconstructing synaptic
connectivity just from the spiking activity of post-synaptic neurons, even when
sub-threshold voltage is unavailable. By using calcium indicators,
voltage-sensitive dyes, or multi-electrode arrays one could monitor activity of
multiple postsynaptic neurons simultaneously, thus mapping their synaptic
inputs in parallel, potentially reconstructing a complete neural circuit.
