Compressive sensing of neuronal connectivity maps from subsampled, cell-targeted optogenetic stimulation of a network model

Abstract

Mapping functional connectivity between neurons is an essential step towards probing the neural computations mediating behavior. The ability to consistently and robustly determine synaptic connectivity maps in large populations of interconnected neurons is a significant challenge in terms of yield, accuracy and experimental time. Here we developed a compressive sensing approach to reconstruct synaptic connectivity maps based on random two photon (2p) cell-targeted optogenetic stimulation and membrane voltage readout of many putative postsynaptic neurons. Using a biophysical network model of interconnected populations of excitatory and inhibitory neurons, we found that the mapping can be achieved with far fewer measurements than the standard pairwise sequential approach. We characterized the recall and precision probabilities as a function of network observability, sparsity, number of neurons stimulated per trial, off-target stimulation, synaptic reliability, propagation latency and network topology. We found that that network sparsity and synaptic reliability were primary determinants of the performance. In particular, in a network with 10% probability of neuronal connectivity, functional connections were recovered with >85% recall and >80% precision in half the trials that would be required for single cell stimulation. Our results suggest a rapid and efficient method to reconstruct functional connectivity of brain networks where sparsity is predominantly present.

High-throughputin vivosynaptic connectivity mapping of neuronal micro-circuits using two-photon holographic optogenetics and compressive sensing

“…In accordance with previous predictions 72, 74 , we observed that, under low connectivity rate (k ≤10%), higher F values, and therefore better coverage of the population, improved reconstruction performances (Fig. S10B-E).…”

“…To increase the throughput of connectivity mapping, we tested a parallel approach where we activated sub-groups of putative presynaptic neurons simultaneously and applied compressive sensing (CS) to reconstruct connectivity from the evoked postsynaptic response 72,74 . CS gives conditions under which a system of equations can be solved with fewer measurements than unknowns.…”

“…To design the protocol for patterned stimulation, we simulated a network of Izhikevich model neurons 91 with a user-defined connectivity rate k and a realistic distribution of synaptic weights and excitatory/inhibitory population, similar to 74 . We used N potential presynaptic cells and mimicked the multi-cell optical stimulation protocol by selecting M different patterns of F excitatory cells that are simultaneously stimulated, i.e.…”

“…This step can be avoided by integrating in the experimental protocol with optical readout of presynaptic activity using GCaMP imaging 58,69,71 or using voltage indicators. In the latter case, the evoked presynaptic response as well as precise spike times can be verified 104 to correct for any jitter in synaptic inputs, which is key for accurate reconstruction 74 .…”

“…Here, we present a novel experimental and computational strategy for in vivo high-throughput connectivity mapping where we combine optogenetics and temporally-focused 2D and 3D holographic light-multiplexing 48 to control the spiking activity of a single or multiple targets with single-cell resolution, millisecond resolution, and sub-millisecond precision. We also demonstrate that the speed and throughput of the method can be increased by combining 2P optogenetic multi-cell stimulation for presynaptic activation with compressive sensing (CS) 36,[72][73][74][75] -an approach that uses sparsity and incoherent sampling to find a solution to an underdetermined linear system 76,77 .…”