{"title": "Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME)", "book": "Advances in Neural Information Processing Systems", "page_first": 790, "page_last": 798, "abstract": "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 \u201cbrute force\u201d approach is rather time-consuming and inefficient because the connectivity in neural circuits is sparse. Instead, we propose to measure a post-synaptic neuron\u2019s voltage while stimulating simultaneously multiple randomly chosen potentially pre-synaptic neurons. To extract the weights of individual synaptic connections 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. Multiple-neuron 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 post-synaptic neurons simultaneously, thus mapping their synaptic inputs in parallel, potentially reconstructing a complete neural circuit.", "full_text": " \n\n \n\nReconstruction of Sparse Circuits Using \nMulti-neuronal Excitation (RESCUME) \n\nTao Hu and Dmitri B. Chklovskii \n\nJanelia Farm Research Campus, HHMI \n19700 Helix Drive, Ashburn, VA 20147 \n\nhut, mitya@janelia.hhmi.org \n\nAbstract \n\nOne of the central problems in neuroscience is reconstructing synaptic \nconnectivity in neural circuits. Synapses onto a neuron can be probed by \nsequentially stimulating potentially pre-synaptic neurons while monitoring \nthe membrane voltage of the post-synaptic neuron. Reconstructing a large \nneural circuit using such a \u201cbrute force\u201d approach is rather time-consuming \nand inefficient because the connectivity in neural circuits is sparse. Instead, \nwe propose to measure a post-synaptic neuron\u2019s voltage while stimulating \nsequentially random subsets of multiple potentially pre-synaptic neurons. \nTo reconstruct these synaptic connections from the recorded voltage we \napply a decoding algorithm recently developed for compressive sensing. \nCompared to the brute force approach, our method promises significant \ntime savings that grow with the size of the circuit. We use computer \nsimulations to find optimal stimulation parameters and explore the \nfeasibility of our reconstruction method under realistic experimental \nconditions including noise and non-linear synaptic integration. Multi-\nneuronal stimulation allows reconstructing synaptic connectivity just from \nthe spiking activity of post-synaptic neurons, even when sub-threshold \nvoltage is unavailable. By using calcium indicators, voltage-sensitive dyes, \nor multi-electrode arrays one could monitor activity of multiple post-\nsynaptic neurons simultaneously, thus mapping their synaptic inputs in \nparallel, potentially reconstructing a complete neural circuit. \n\n \n\n1 \n\nI n t ro d u c t i o n \n\nUnderstanding information processing in neural circuits requires systematic characterization \nof synaptic connectivity [1, 2]. The most direct way to measure synapses between a pair of \nneurons is to stimulate potentially pre-synaptic neuron while recording intra-cellularly from \nthe potentially post-synaptic neuron [3-8]. This method can be scaled to reconstruct multiple \nsynaptic connections onto one neuron by combining intracellular recordings from the post-\nsynaptic neuron with photo-activation of pre-synaptic neurons using glutamate uncaging [9-\n13] or channelrhodopsin [14, 15], or with multi-electrode arrays [16, 17]. Neurons are \nsequentially stimulated to fire action potentials by scanning a laser beam (or electrode \nvoltage) over a brain slice, while synaptic weights are measured by recording post-synaptic \nvoltage. \n\nAlthough sequential excitation of single potentially pre-synaptic neurons could reveal \nconnectivity, such a \u201cbrute force\u201d approach is inefficient because the connectivity among \nneurons is sparse. Even among nearby neurons in the cerebral cortex, the probability of \nconnection is only about ten percent [3-8]. Connection probability decays rapidly with the \n\n \n\n1 \n\n\fdistance between neurons and falls below one percent on the scale of a cortical column [3, \n8]. Thus, most single-neuron stimulation trials would result in zero response making the \nbrute force approach slow, especially for larger circuits. \n\nAnother drawback of the brute force approach is that single-neuron stimulation cannot be \ncombined efficiently with methods allowing parallel recording of neural activity, such as \ncalcium imaging [18-22], voltage-sensitive dyes [23-25] or multi-electrode arrays [17, 26]. \nAs these techniques do not reliably measure sub-threshold potential but report only spiking \nactivity, they would reveal only the strongest connections that can drive a neuron to fire [27-\n30]. Therefore, such combination would reveal only a small fraction of the circuit. \n\nWe propose to circumvent the above limitations of the brute force approach by stimulating \nmultiple potentially pre-synaptic neurons simultaneously and reconstructing individual \nconnections by using a recently developed method called compressive sensing (CS) [31-35]. \nIn each trial, we stimulate F neurons randomly chosen out of N potentially pre-synaptic \nneurons and measure post-synaptic activity. Although each measurement yields only a \ncombined response to stimulated neurons, if synaptic inputs sum linearly in a post-synaptic \nneuron, one can reconstruct the weights of individual connections by using an optimization \nalgorithm. Moreover, if the synaptic connections are sparse, i.e. only K << N potentially \npre-synaptic neurons make synaptic connections onto a post-synaptic neuron, the required \nnumber of trials M ~ K log(N/K), which is much less than N [31-35]. \n\nThe proposed method can be used even if only spiking activity is available. Because multiple \nneurons are driven to fire simultaneously, if several of them synapse on the post-synaptic \nneuron, they can induce one or more spikes in that neuron. As quantized spike counts carry \nless information than analog sub-threshold voltage recordings, reconstruction requires a \nlarger number of trials. Yet, the method can be used to reconstruct a complete feedforward \ncircuit from spike recordings. \n\nReconstructing neural circuit with multi-neuronal excitation may be compared with mapping \nretinal ganglion cell receptive fields. Typically, photoreceptors are stimulated by white-noise \ncheckerboard stimulus and the receptive field is obtained by Reverse Correlation (RC) in \ncase of sub-threshold measurements or Spike-Triggered Average (STA) of the stimulus [36, \n37]. Although CS may use the same stimulation protocol, for a limited number of trials, the \nreconstruction quality is superior to RC or STA. \n\n \n2 \n\nM a p p i n g s y n a p t i c i n p u t s o n t o o n e n e u ro n \n\nWe start by formalizing the problem of mapping synaptic connections from a population of \nN potentially pre-synaptic neurons onto a single neuron, as exemplified by granule cells \nsynapsing onto a Purkinje cell (Figure 1a). Our experimental protocol can be illustrated \nusing linear algebra formalism, Figure 1b. We represent synaptic weights as components of a \ncolumn vector x, where zeros represent non-existing connections. Each row in the \nstimulation matrix A represents a trial, ones indicating neurons driven to spike once and \nzeros indicating non-spiking neurons. The number of rows in the stimulation matrix A is \nequal to the number of trials M. The column vector y represents M measurements of \nmembrane voltage obtained by an intra-cellular recording from the post-synaptic neuron: \n\ny = Ax. (1) \nIn order to recover individual synaptic weights, Eq. (1) must be solved for x. RC (or STA) \nsolution to this problem is x = (ATA)-1AT y, which minimizes (y-Ax)2 if M>N. In the case M>N is required. \n\nWe simulate circuit reconstruction from spike recordings in silico as follows. First, we draw \nsynaptic weights from an experimentally motivated distribution. Second, we generate a \n\n \n\n6 \n\n\frandom stimulation matrix and calculate the product Ax. Third, we linear half-wave rectify \nthis product and use the result as the instantaneous firing rate for the Poisson spike generator \n(Figure 6c). We used a rectifying threshold that results in 10% of spiking trials as typically \nobserved in experiments. Fourth, we reconstruct synaptic weights using STA and CS and \ncompare the results with the generated weights. We calculated mean error over 100 \nrealizations of the simulation protocol (Figure 6d). \n\nDue to the non-linear spike generating procedure, x can be recovered only up to a scaling \nfactor. We propose to calibrate x with a few brute-force measurements of synaptic weights. \nThus, in calculating the reconstruction error using l2 norm, we normalize both the generated \nand recovered synaptic weights. Such definition is equivalent to the angular error, which is \noften used to evaluate the performance of STA in mapping receptive field [37, 55]. \n\nWhy is CS superior to STA for a given number of trials (Figure 6d)? Note that spikeless \ntrials, which typically constitute a majority, also carry information about connectivity. While \nSTA discards these trials, CS takes them into account. In particular, CoSaMP starts with the \nSTA solution as zeroth iteration and improves on it by using the results of all trials and the \nsparseness prior. \n\n \n6 \n\nD i s c u s s i o n \n\nWe have demonstrated that sparse feedforward networks can be reconstructed by stimulating \nmultiple potentially pre-synaptic neurons simultaneously and monitoring either sub-\nthreshold or spiking response of potentially post-synaptic neurons. When sub-threshold \nvoltage is recorded, significantly fewer measurements are required than in the brute force \napproach. Although our method is sensitive to noise (with stimulation noise worse than \nsynapse noise), it is no less robust than the brute force approach or RC. \n\nThe proposed reconstruction method can also recover inputs onto a neuron from spike \ncounts, albeit with more trials than from sub-threshold potential measurements. This is \nparticularly useful when intra-cellular recordings are not feasible and only spiking can be \ndetected reliably, for example, when mapping synaptic inputs onto multiple neurons in \nparallel. For a given number of trials, our method yields smaller error than STA. \n\nThe proposed reconstruction method assumes linear summation of synaptic inputs (both \nexcitatory and inhibitory) and is sensitive to non-linearity of synaptic integration. Therefore, \nit is most useful for studying connections onto neurons, in which synaptic integration is \nclose to linear. On the other hand, multi-neuron stimulation is closer than single-neuron \nstimulation to the intrinsic activity in the live brain and can be used to study synaptic \nintegration under realistic conditions. \n\nIn contrast to circuit reconstruction using intrinsic neuronal activity [56, 57], our method \nrelies on extrinsic stimulation of neurons. Can our method use intrinsic neuronal activity \ninstead? 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(2007) Revealing network connectivity from response dynamics. Physical Review \nLetters 98(22):224101. \n\n \n\n9 \n\n\f", "award": [], "sourceid": 839, "authors": [{"given_name": "Tao", "family_name": "Hu", "institution": null}, {"given_name": "Anthony", "family_name": "Leonardo", "institution": null}, {"given_name": "Dmitri", "family_name": "Chklovskii", "institution": null}]}