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[…] Imaging data were analyzed using the open-source Thunder library described in ). Thunder uses the Apache Spark cluster computing platform for manipulating and analyzing large-scale image and time series data. All analyses described here were performed on a local cluster, but can be reproduced identically on cloud compute, and sample data is made available on Amazon S3 (see below).Using Thunder, light-sheet data were first registered by cross-correlation to a reference volume, and each voxel’s time series was converted to ΔF/F. We then developed a regression analysis to capture the extent to which neuronal responses were predicted by directionally specific behavior. First, two one-dimensional parameters were derived from the fictive swim signals: one capturing the instantaneous amplitude of swimming (strictly positive), and another capturing the instantaneous direction (positive for right, negative for left). We noted that, across many experiments, these two parameters tended to fall within the same region of a two-dimensional space (after normalizing amplitude to have a maximum of 1) (). To compute neuronal tuning within this space, we expanded the instantaneous value of the two signals into a nonlinear basis; intuitively, this corresponds to dividing the two-dimensional space into several small wedges each corresponding to a range of directions and amplitudes. We used a polar basis, separably and evenly tiling amplitude (three bins) and angle (four bins). Each basis had a flat top and raised cosine transition region, with 50% overlap; see and for the parameterization of this basis (), which is more commonly used to tile the two-dimensional Fourier domain. With this basis, we represented instantaneous behavior with 12 predictor time series, each 1 x T, where T is the duration of an experiment. These predictors were each convolved with an impulse kernel k intended to reflect typical calcium dynamics; the kernel had a linear rise of 1 s and a linear decay of 5 s; variations of the kernel both in shape (e.g. exponential decay) and timing (0.5 s rise and 2 s decay) yielded qualitatively similar maps. Along with a constant offset term, this yielded a 13 x T predictor matrix X. We then used ordinary least squares regression to infer the best fitting coefficients b:b=(XXT)−1XTrwhere r is the T x 1 fluorescence time course of either a single voxel or a neuron. The 12 coefficients (ignoring the constant) describe tuning with the two-dimensional behavioral space (e.g. polar wedge plots in ), and R2 from the regression captures prediction accuracy. Computing a weighted angular mean yields a single laterality index, used to determine hue in computational maps (, ). Note that a bilinear model () could have been used to estimate behavioral tuning and temporal kernel simultaneously, but preliminary analyses showed that tuning was largely invariant to the shape of the temporal kernel.An example data set (one of the same data sets used to generate maps in ) is available on Amazon S3 at s3://neuro.datasets/ahrens.lab/spontaneous.turning/2/, including both neural data and behavioral regressors. And an example analysis in the form of a Jupyter notebook are included as Supplementary Files (spontaneous-turning.html, spontaneous-turning.ipynb); the notebook shows how to load data from that URI and generate a map for one of the data sets shown in . [...] To register light-sheet data to the confocal data in the Z-Brain (), we used the Computational Morphometry toolkit (CMTK, https://www.nitrc.org/projects/cmtk/). To solve this cross-modal registration problem, we used two different strategies for the two types of transgenes (nuclear and cytoplasmic GCaMP). For Tg(elavl3:GCaMP6f/s) registrations, we used a single Tg(elavl3:GCaMP6f;elavl3:H2B-mKate2) fish to create a bridging reference brain from the light-sheet data to the Z-Brain. This fish was imaged on the light-sheet microscope live, then imaged again by confocal microscopy live, fixed in 4% PFA and stained with tERK, and then finally the transgene signals and tERK stain were imaged by confocal microscopy. We then used CMTK to calculate the morphing transformations through each of these steps using the Tg(elavl3:H2B-mKate2) to align the light sheet → live confocal → fixed confocal data, and then the tERK stain to align the to Z-Brain reference brain. To register the three Tg(elavl3:GCaMP6f) and one Tg(elavl3:GCaMP6s) fish in this study, each fish is aligned to the light-sheet volume of the bridging brain using the Tg(elavl3:GCaMP6f) signal, and then the 4 transformation steps (1 fish specific, 3 common to all fish) are concatenated and applied using CMTK’s ‘reformatx’ tool.For Tg(elavl3:H2B-GCaMP6f), the anatomical volume of the 11 fish imaged in this study were all registered to a single template Tg(elavl3:H2B-GCaMP6f) fish. These 12 volumes were averaged, and then this mean-volume registered to the Tg(elavl3:H2B-RFP) () Z-Brain volume, which is the average of 10 fish. The two transformation steps for each fish are then concatenated and applied using ‘reformatx.’ To confirm the accuracy of alignment, we compared the positioning of reticulospinal cells imaged live on the light-sheet microscope to the same label in the Z-Brain, which revealed good overlap (), thus validating the accuracy of our alignment in this area.To analyze the anatomical features of the Tg(elavl3:H2B-GCaMP6f) derived functional volumes, we used the Z-BrainViewer and the ‘ZBrainAnalysisOfMAP-Maps’ function () to compare the positioning of features with regions and cell type labels in the Z-Brain atlas (supplementary Data: SupplementaryData_ZBrainAnalysisOfNucMaps.xls). [...] Tg(alpha-tubulin:C3PA-GFP);Tg(elavl3:H2B-GCaMP6f) or Tg(alpha-tubulin:C3PA-GFP);Tg(elavl3:jRCaMP1a) fish at 6dpf were embedded in 2% agarose in a 35-mm petri dish. For some experiments, the reticulospinal neurons were retrogradely labeled with 20% alexa-680-dextran according to published protocols (). The fish were imaged under a two-photon microscope at 930 nm (1050 nm for jRCaMP1a) in the anterior hindbrain at the level of rhombomeres 2–3. The ARTR was functionally identified by using a correlational measure to construct a correlation map as described above. Individual cells of either the medial or lateral cluster were selected on one side of the brain in a plane containing sections of all four clusters. We modified the neurite tracing protocol developed by () to trace projections from a subset of ARTR neurons. Cells were selected using custom written software and PA-GFP was activated using a protocol for iterative activation: ten 250 ms pulses of 780 nm pulsed infrared laser light were administered over a course of 16 cycles spaced 15 min apart for 4 hr. Selective activation was confirmed after each cycle by switching to 930 nm and imaging the selected plane for increased fluorescence. At the end of 4 hr, fish were transferred to an incubator and kept in the dark for another hour to allow additional time for GFP transport along the neurites. Subsequently, the fish were imaged on a Zeiss 710 confocal microscope using a 20x or 40x objective. The confocal stacks were then analyzed using the Simple Neurite Tracer plugin in FIJI (ImageJ). […]

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