Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs.NIH Office of the Director (Grant 5T32EB019940-03)National Institute on Deafness and Other Communication Disorders (Grant R01-DC009183)National Institute of Neurological Disorders and Stroke (Grant U19-NS104648)National Institute of Mental Health (Grant R25 MH062204

Differentially Timed Extracellular Signals Synchronize Pacemaker Neuron Clocks

<div><p>Synchronized neuronal activity is vital for complex processes like behavior. Circadian pacemaker neurons offer an unusual opportunity to study synchrony as their molecular clocks oscillate in phase over an extended timeframe (24 h). To identify where, when, and how synchronizing signals are perceived, we first studied the minimal clock neural circuit in <i>Drosophila</i> larvae, manipulating either the four master pacemaker neurons (LN_vs) or two dorsal clock neurons (DN₁s). Unexpectedly, we found that the PDF Receptor (PdfR) is required in both LN_vs and DN₁s to maintain synchronized LN_v clocks. We also found that glutamate is a second synchronizing signal that is released from DN₁s and perceived in LN_vs via the metabotropic glutamate receptor (mGluRA). Because simultaneously reducing <i>Pdfr</i> and <i>mGluRA</i> expression in LN_vs severely dampened Timeless clock protein oscillations, we conclude that the master pacemaker LN_vs require extracellular signals to function normally. These two synchronizing signals are released at opposite times of day and drive cAMP oscillations in LN_vs. Finally we found that PdfR and mGluRA also help synchronize Timeless oscillations in adult s-LN_vs. We propose that differentially timed signals that drive cAMP oscillations and synchronize pacemaker neurons in circadian neural circuits will be conserved across species.</p></div

LN_v and non-LN_v clock neurons maintain LN_v synchrony.

<p>All experimental lines and <i>Pdf></i>+control larvae in RNAi experiments include <i>UAS-Dcr-2</i>, but this is omitted from written genotypes for simplicity. Desynchrony data were calculated from 3–4 independent experiments, each consisting of at least three but usually five or more brains. Total number of LN_v clusters analyzed are in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959.s010" target="_blank">Table S1</a>. ** <i>p</i><0.01; *** <i>p</i><0.001. (A) Representative images of LN_vs in control larvae (<i>+</i>/<i>UAS-Pdfr^RNAi</i>) or in larvae with reduced <i>Pdfr</i> levels in LN_vs (<i>Pdf>Pdfr^RNAi</i>) or all clock neurons except LN_vs (<i>tim-Gal4; Pdf-Gal80</i>><i>Pdfr^RNAi</i>) immunostained for PDF (green), TIM (red), and PDP1 (blue) at CT3 on day 3 in DD. The lower panels for each genotype are the same images with the green channel (PDF) removed and replaced by a dashed white line outlining LN_vs. (B) Box plots showing the ST DEV in TIM expression as in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio-1001959-g001" target="_blank">Figure 1</a>. Statistical comparisons by ANOVA with Tukey's post hoc test show both <i>Pdf>Pdfr^RNAi</i> (F_2,49 = 12.33, <i>p</i><0.0001) and <i>tim-Gal4; Pdf-Gal80</i>><i>Pdfr^RNAi</i> (F_2,51 = 8.158, <i>p</i> = 0.0008) significantly increase the ST DEV of TIM levels compared to parental controls, reflecting increased desynchrony. (C) Representative images of larval LN_vs stained for PDF (green), TIM (red), and PDP1 (blue) at CT3 on day 3 in DD. From left to right, Control <i>DN₁>+</i>, and +/<i>UAS-Dti</i> LN_v clusters, and a representative desynchronized <i>DN₁>Dti</i> LN_v cluster. The green channel (PDF) has been removed from the lower panel and replaced by a dashed white outline of LN_vs. (D) Box plots showing quantification of desynchrony through measurement of ST DEV in TIM expression in larval LN_vs in control or DN₁ ablated larvae at ZT3, CT3, and CT9. <i>DN₁>Dti</i> increases ST DEV at CT 3 compared to both parental controls (ANOVA with Tukey's post hoc test, F_2,49 = 10.5, <i>p</i><0.0001). There was no significant difference between <i>DN₁>Dti</i> and controls at ZT3 (Student's <i>t</i> test, <i>p</i> = 0.35) or CT9 (Student's <i>t</i> test, <i>p</i> = 0.31).</p

Model for regulation of cAMP levels and the molecular clock in clock neurons.

<p>Black arrows and text show established pathways; grey arrows and text reflect pathways inferred but not yet demonstrated. Left panel: In LN_vs, PDF signals via PDFR and Gα/AC3 to boost intracellular cAMP <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959-Mertens1" target="_blank">[18]</a>–<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959-Duvall1" target="_blank">[21]</a>. In this study, we show that glutamate (glu) signals received via mGluRA reduce cAMP levels, likely by inhibiting AC3. Differentially timed release of PDF and glutamate signals results in cAMP rhythms. PKA responds to cAMP to increase stability of the PER/TIM dimer via PER <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959-Li1" target="_blank">[46]</a> and likely also via TIM (data here and inferred from non-LN_vs <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959-Seluzicki1" target="_blank">[45]</a>). Right panel: In non-LN_v clock neurons, PDF signals via PDFR through Gα and unknown Adenyl cyclase(s) (AC) to boost intracellular cAMP. By analogy with what we show here for LN_vs, we propose that an inhibitory signal released at a different time of day from PDF inhibits AC activity to generate a cAMP rhythm in non-LN_vs. PKA responds to cAMP to increase stability of the PER/TIM dimer through TIM <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959-Seluzicki1" target="_blank">[45]</a> and likely also PER (by analogy with LN_vs <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959-Li1" target="_blank">[46]</a>).</p

mGluRA and PdfR regulate intracellular cAMP.

<p>Statistical comparisons are by ANOVA with Tukey's post hoc test. Error bars show SEM. Whiskers represent 95% confidence. * <i>p</i><0.05; ** <i>p</i><0.01; *** <i>p</i><0.001; **** <i>p</i><0.0001. (A) Larvae were dissected and analyzed on day 2 in DD. CFP and YFP levels were measured in the projections of <i>Pdf>Epac1-camps</i> LN_vs. The ratio of CFP/YFP reflects the basal level of cAMP. The CFP/YFP ratio oscillates in control (<i>Pdf>Epac1-camps</i>) LN_v projections, peaking at CT24 (ANOVA F_3,62 = 2.933, <i>p</i> = 0.04). There is no significant oscillation in <i>Pdf>Epac1-camps</i>+<i>mGluRA^RNAi</i> (F_3,59 = 0.815, <i>p</i> = 0.49) or <i>Pdf>Epac1-camps</i>+<i>Pdfr^RNAi</i> (F_3,47 = 1.068, <i>p</i> = 0.37). The CFP/YFP ratio is significantly increased at CT12 in <i>Pdf>Epac1-camps</i>+<i>mGluRA^RNAi</i> compared to control LN_vs (F_2,38 = 5.021, <i>p</i> = 0.0017) but not in <i>Pdf>Epac1-camps</i>+<i>Pdfr^RNAi</i>, consistent with glutamate signals inhibiting cAMP at CT12. (B) Averaged Epac-1-camps CFP/YFP ratio responses to bath application of 100 nM PDF or vehicle (arrow). The wild-type (<i>Pdf>Epac1-camps</i>) response to 100 nM PDF is shown in blue, and the wild-type response to vehicle is shown in black. Knockdown of <i>GluCl</i> (<i>Pdf>Epac1-camps</i>+<i>GluCl^RNAi</i>, green) had no significant effect on the response to PDF, but knockdown of <i>mGluRA</i> (<i>Epac1-camps</i>+<i>mGluRA^RNAi</i>, magenta) significantly increased the cAMP response of LN_vs to PDF. Vehicle traces represent 10 LN_v cell bodies from five brains (10, 5), wild-type PDF (10, 5), <i>Pdf>GluCl^RNAi</i> PDF (20, 9), and <i>Pdf>mGluRA^RNAi</i> PDF (27, 12). (C) Comparison of mean maximum Epac-1-camps CFP/YFP ratio changes between 0 and 240 s [dashed line in (B)] [genotypes and sample sizes as in (B)]. Application of 100 nM PDF significantly increased cAMP in LN_vs of <i>Pdf>Epac1-camps</i> flies compared to vehicle (<i>p</i><0.0001 by unpaired <i>t</i> tests). PDF responses of <i>Pdf>Epac1-camps</i>+<i>GluCl^RNAi</i> LN_vs were not significantly different from wild-type LN_vs (<i>p</i> = 0.6217). PDF responses of <i>Pdf>Epac1-camps</i>+<i>mGluRA^RNAi</i> LN_vs were significantly higher than wild-type (<i>p</i> = 0.024) and <i>Pdf>Epac1-camps</i>+<i>GluCl^RNAi</i> (<i>p</i> = 0.0193) LN_vs. (D) Model: We propose that LN_vs signal to each other via PDF around dawn. This signal is received by PdfR, which acts via Gαs/AC3 to increase intracellular cAMP. DN₁s release glutamate around dusk. This signal is received by mGluRA in LN_vs, which acts via Gαi to inhibit AC3 and reduce intracellular cAMP. Daily regulation of cAMP by external signals promotes robust TIM oscillations and LN_v synchrony.</p

A DN₁ glutamate signal mediated via mGluRA synchronizes LN molecular oscillations.

<p>All experimental lines and <i>Pdf>+</i>control larvae in RNAi experiments include <i>UAS-Dcr-2</i>, but this is omitted from written genotypes for simplicity. Desynchrony data were calculated from 2–5 independent experiments, each consisting of at least four brains. Total numbers of LN_v clusters analyzed are in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959.s010" target="_blank">Table S1</a>. * <i>p</i><0.05; *** <i>p</i><0.001. (A and B) Representative images of larval LN_vs stained for PDF (green), TIM (red), and PDP1 (blue) at CT3 on day 3 in DD. Genotypes in (A) are control(<i>+/UAS-Gad1</i>) and <i>DN₁>Gad1</i> experimental larvae. Genotypes in (B) are control (<i>Pdf>+</i>) and experimental larvae in which <i>GluCl</i> (<i>Pdf>GluCl^RNAi</i>) or <i>mGluRA</i> (<i>Pdf>mGluRA^RNAi</i>) levels are reduced in LN_vs, and <i>mGluRA^112b/+</i> heterozygous control or <i>mGluRA^112b</i> mutant LN_vs. (C) Histograms showing percentage of synchronized (green) or desynchronized (red) LN_v clusters for TIM (left panel) or PDP1 (right panel) at CT3. Top: 14% of control (<i>+/UAS-Gad1</i>) LN_v clusters are desynchronized compared to 71% of <i>DN₁>Gad1</i> LN_v clusters by TIM staining, and 21% of control (<i>+/UAS-Gad1</i>) LN_v clusters have detectable PDP1 expression compared to 64% in <i>DN₁>Gad1</i> brains. Middle: ∼20% of <i>Pdf>GluCl^RNAi</i> or +/<i>UAS-mGluRA^RNAi</i> larval brains have desynchronized TIM levels compared to 62% of <i>Pdf>mGluRA^RNAi</i> brains. Less than 20% of <i>Pdf>GluCl^RNAi</i> or <i>+/UAS-mGluRA^RNAi</i> larval brains have detectable PDP1 expression, compared to 71% of <i>Pdf>mGluRA^RNAi</i> brains. Bottom: 50% of <i>mGluRA^112b</i> mutant LN_vs show desynchronized TIM expression, compared to 8% of <i>mGluRA^112b/</i>+ controls. For PDP1, 29% of LN_v clusters are desynchronized in <i>mGluRA^112b</i> mutants, compared to 4% of <i>mGluRA^112b/</i>+ controls. In addition, 3/24 <i>mGluRA^112b</i> mutants had all four LN_vs expressing PDP1 compared to 0/25 control LN_v clusters. (D) Box plots showing quantification of desynchrony by measuring ST DEV in TIM levels within a cluster in larval LN_vs in control, <i>DN₁>Gad1</i>, <i>Pdf>GluCl^RNAi</i>, and <i>Pdf>mGluRA^RNAi</i> larvae at CT3 on day 3 in DD. <i>DN₁>Gad1</i> (Student's <i>t</i> test, <i>p</i> = 0.0004) and <i>Pdf>mGluRA^RNAi</i> (ANOVA with Tukey's post hoc test, F_2,50 = 5.597, <i>p</i> = 0.0064) significantly increase the ST DEV in TIM levels, reflecting increased LN_v desynchrony, whereas <i>Pdf>GluCl^RNAi</i> does not (ANOVA with Tukey's post hoc test, F_2,39 = 0.93, <i>p</i> = 0.40).</p

Synchronized TIM and PDP1 oscillations in LN_vs depend on PDF signaling.

<p>Larval LN_vs were immunostained using TIM, PDP1, and PDF antibodies at CT 9, 15, 21, and 3 on days 2–3 in DD after 4 days prior entrainment to 12∶12 LD cycles. Desynchrony data were calculated from 3–5 independent experiments, each with at least three brains. Error bars represent SEM. For total number of LN_v clusters analyzed, see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959.s010" target="_blank">Table S1</a>. * <i>p</i><0.05; ** <i>p</i><0.01; *** <i>p</i><0.001; **** <i>p</i><0.0001. (A) Representative images of <i>y w</i> (Control, top panels), <i>Pdf⁰¹</i> mutants (middle), and <i>Pdfr^han</i> mutants (bottom) stained for PDF or GFP (green), TIM (red), and PDP1 (blue). The lower panels for each genotype are the same images with the green channel removed and replaced by a dashed white line outlining the LN_vs. <i>Pdf⁰¹</i> LN_vs were identified via anti-GFP antibody staining of a UAS-GFP transgene driven by <i>Pdf-Gal4</i>, and PDP1 was not included in this experiment. (B) TIM immunostaining was quantified in Control (blue), <i>Pdfr^han</i> (red), and <i>Pdf⁰¹</i> (green) LN_vs on days 2 and 3 in DD. TIM oscillates in <i>Pdfr^han</i> (ANOVA F_3,37 = 13.68, <i>p</i><0.0001) and <i>Pdf⁰¹</i> (ANOVA F_3,56 = 16.80, <i>p</i><0.0001) mutants. However, there is significantly more TIM at CT3 on day 3 in <i>Pdfr^han</i> and <i>Pdf⁰¹</i> mutant LN_vs than in control LN_vs (Student's <i>t</i> test, both <i>p</i><0.0001). At CT15, TIM levels are significantly reduced in <i>Pdf⁰¹</i> mutants compared to <i>Pdfr^han</i> or control LN_vs (Student's <i>t</i> test, both <i>p</i><0.0003). (C) PDP1 immunostaining was quantified in LN_vs of Control (blue) and <i>Pdfr^han</i> mutant (red) larval brains on days 2 and 3 in DD. PDP1 oscillates in <i>Pdfr^han</i> LN_vs (ANOVA, F_3,37 = 46.22, <i>p</i><0.0001). PDP1 levels were significantly higher at CT3 on day 3 in <i>Pdfr^han</i> mutant LN_vs than in control LN_vs (Student's <i>t</i> test, <i>p</i><0.01). (D and E) Histograms show the percentage of LN_v clusters in which TIM (D) or PDP1 (E) was detected in either none or all four LN_vs (“synchronized,” green bars) or in one, two, or three LN_vs (“desynchronized,” red bars). (F and G) To further quantify desynchrony, the standard deviation (ST DEV) in TIM (F) or PDP1 (G) levels within a cluster of control, <i>Pdf⁰¹</i>, and <i>Pdfr^han</i> mutant LN_vs is shown as a box plot. Statistical comparisons by ANOVA with Tukey's post hoc test reveal significant increases in ST DEV in TIM in <i>Pdf⁰¹</i> (F_3,55 = 26.71, <i>p</i><0.0001) and <i>Pdfr^han</i> (F_3,53 = 12.13, <i>p</i><0.0001) mutant LN_vs compared to control LN_vs at CT3 but not CT9. The ST DEV in PDP1 in <i>Pdfr^han</i> mutant LN_vs was also significantly elevated at CT3 but not CT9 (F_3,52 = 5.03, <i>p</i> = 0.004). The box shows the 25th–75th percentile, and whiskers represent the 95% confidence interval.</p

PdfR and mGluRA promote high-amplitude TIM oscillations and larval behavioral rhythms.

<p>All experimental lines and <i>Pdf>+</i>control larvae also include <i>UAS-Dcr-2</i> for RNAi experiments, but this is omitted from written genotypes for simplicity. Desynchrony data were calculated from 2–4 independent experiments, each consisting of at least five brains. Total number of LN_v clusters analyzed are in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001959#pbio.1001959.s010" target="_blank">Table S1</a>. Error bars represent SEM. (A) Representative images of larval LN_vs at CT 9, 15, 21, and 3 on days 2–3 in DD for control (<i>+/UAS-mGluRA^RNAI</i>; +/<i>UAS-Pdfr^RNAi</i>) or <i>Pdf>mGluRA^RNAi+Pdfr^RNAi</i> larval LN_vs immunostained for TIM (red), PDP1 (blue), and PDF (green). PDF staining is removed from lower panels, with LN_vs indicated by a white line. (B) Histogram showing the number of synchronized (green) or desynchronized (red) LN_v clusters in control (<i>+/UAS-mGluRA^RNAI</i>; +/<i>UAS-Pdfr^RNAi</i>) or <i>Pdf>mGluRA^RNAi+Pdfr^RNAi</i> larval brains, determined by TIM staining at CT3. (C) Average TIM levels of control (blue) and <i>Pdf>mGluRA^RNAi+Pdfr^RNAi</i> (green) LN_vs. TIM oscillations are dampened in <i>Pdf>mGluRA^RNAi+Pdfr^RNAi</i> larval LN_vs (two-way ANOVA significant Genotype effect, F_1,102 = 119.53, <i>p</i><0.0001, and Genotype×Time interaction, F_3,102 = 100.11, <i>p</i><0.0001). (D) Larval light avoidance was measured by counting the number of larvae on the dark side of a Petri dish after 15 min. Light avoidance was assayed on day 2 (CT12, 18, 24) or day 3 (CT6) of DD after prior LD entrainment. Control (<i>Pdf>+</i>) larvae (grey) and <i>Pdf>Pdfr^RNAi</i> larvae (blue) show similarly phased light avoidance rhythms, peaking at dawn (two-way ANOVA, no Genotype×Time interaction, F_3,22 = 0.31, <i>p</i> = 0.82). <i>Pdf>mGluRA^RNAi+Pdfr^RNAi</i> larvae lose light avoidance rhythms (ANOVA F = 0.13, <i>p</i> = 0.94).</p

PdfR and mGluRA are required in LN_vs for normal evening activity and timing of sleep onset.

<p>All experimental lines and <i>Pdf>+</i>control larvae also include <i>UAS-Dcr-2</i> for RNAi experiments, but this is omitted from written genotypes for simplicity. Error bars show SEM. *** <i>p</i><0.001. (A) Locomotor activity was recorded for 3–4 days in LD cycles, followed by 10 days in DD (shaded area of actograms). Representative actograms are shown for <i>Pdf>+</i> control flies and for <i>Pdf>GluCl^RNAi</i> and <i>Pdf>Pdfr^RNAi+mGluRA^RNAi</i> experimental flies. (B) Graphs show average locomotor activity over the first 5 days in DD. Each panel shows two control genotypes: <i>Pdf>+</i> (blue, <i>n</i> = 19) and <i>+/UAS-mGluRA^RNAI</i>; +/<i>UAS-Pdfr^RNAi</i> (green, <i>n</i> = 26). Experimental genotypes are shown in red. Top left: <i>Pdf>GluCl^RNAi</i> (<i>n</i> = 37). Top right: <i>Pdf>mGluRA^RNAi</i> (<i>n</i> = 54). Bottom left: <i>Pdf>Pdfr^RNAi</i> (<i>n</i> = 33). Bottom right: <i>Pdf>Pdfr^RNAi+mGluRA^RNAi</i> (<i>n</i> = 37). Activity between ∼CT6 and 18 is elevated in <i>Pdf>mGluRA^RNAi</i>, <i>Pdf>Pdfr^RNAi</i>, and <i>Pdf>Pdfr^RNAi+mGluRA^RNAi</i> flies compared to controls or <i>Pdf>GluCl^RNAi</i>. (C) Histogram shows the average sleep latency on the first day in DD. <i>Pdf>Pdfr^RNAi+mGluRA^RNAi</i> flies show significantly increased sleep latency compared to <i>Pdf>+</i>, <i>+/UAS-mGluRA^RNAI</i>; +/<i>UAS-Pdfr^RNAi</i>, and <i>Pdf>GluCl^RNAi</i> controls (ANOVA F = 6.83, <i>p</i> = 0.0003).</p