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Synaptic basis of a sub-second representation of time in a neural circuit model

Barri, A., Wiechert, M. T., Jazayeri, M., DiGregorio, D. A.·2022·Nature Communications
DOI 10.1038/s41467-022-35395-yPMC PMC9780315
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Abstract

Temporal sequences of neural activity are essential for driving well-timed behaviors, but the underlying cellular and circuit mechanisms remain elusive. We leveraged the well-defined architecture of the cerebellum, a brain region known to support temporally precise actions, to explore theoretically whether the experimentally observed diversity of short-term synaptic plasticity (STP) at the input layer could generate neural dynamics sufficient for sub-second temporal learning. A cerebellar circuit model equipped with dynamic synapses produced a diverse set of transient granule cell firing patterns that provided a temporal basis set for learning precisely timed pauses in Purkinje cell activity during simulated delay eyelid conditioning and Bayesian interval estimation. The learning performance across time intervals was influenced by the temporal bandwidth of the temporal basis, which was determined by the input layer synaptic properties. The ubiquity of STP throughout the brain positions it as a general, tunable cellular mechanism for sculpting neural dynamics and fine-tuning behavior.

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Fig. 1 Cerebellar cortex model with short-term synaptic plasticity within the input layer (CCMSTP). a1 Synaptic model scheme showing the principal parameters. a2-6 Properties of the five model synapse types matching experimental groups from ref. 30. Left: Schemes show differences in presynaptic parameters; the postsynaptic side is identical for all groups. Right: average synaptic weights in response to repetitive 100 Hz stimulation as in ref. 39. Insets: First five responses with paired-pulse ratio (PPR) roughly mimic results from ref. 30. Color code for synapse groups is the same as in ref. 30. b Scheme of CCMSTP. MFs are classified according to the groups in (a). Percentages indicate relative frequency of MF groups. Insets: firing rate distributions for different MF groups. c Simulation of CCMSTP with randomly drawn JE weights. First panel: 5 sample MFs. Every second, MF activity is re-drawn from distributions in (b). Second panel: Normalized weights of 10 example MF-GC synapses. Third panel: activity of 10 sample GCs. Last panel: PC activity with different shades of gray indicating different E/I ratios onto the PC. d Same as c but without STP transient dynamics. Low amplitude GC and PC firing rate transients result from 10 ms GC integration time constant. e Example simulation in which correlated (black symbols) and uncorrelated (red symbols) MF patterns were presented to the network in alternation. The correlation coefficient for sequential patterns was ≈0.85. Firing rates are color-coded. f1 Steady-state subtracted GC responses from simulation in (e) for uncorrelated (left) and correlated MF pattern switches (right). f2 Same as (f1) but for PC. g Normalized standard deviation of PC transient amplitudes for switches between MF patterns of differing levels of correlation.
Fig. 1 Cerebellar cortex model with short-term synaptic plasticity within the input layer (CCMSTP). a1 Synaptic model scheme showing the principal parameters. a2-6 Properties of the five model synapse types matching experimental groups from ref. 30. Left: Schemes show differences in presynaptic parameters; the postsynaptic side is identical for all groups. Right: average synaptic weights in response to repetitive 100 Hz stimulation as in ref. 39. Insets: First five responses with paired-pulse ratio (PPR) roughly mimic results from ref. 30. Color code for synapse groups is the same as in ref. 30. b Scheme of CCMSTP. MFs are classified according to the groups in (a). Percentages indicate relative frequency of MF groups. Insets: firing rate distributions for different MF groups. c Simulation of CCMSTP with randomly drawn JE weights. First panel: 5 sample MFs. Every second, MF activity is re-drawn from distributions in (b). Second panel: Normalized weights of 10 example MF-GC synapses. Third panel: activity of 10 sample GCs. Last panel: PC activity with different shades of gray indicating different E/I ratios onto the PC. d Same as c but without STP transient dynamics. Low amplitude GC and PC firing rate transients result from 10 ms GC integration time constant. e Example simulation in which correlated (black symbols) and uncorrelated (red symbols) MF patterns were presented to the network in alternation. The correlation coefficient for sequential patterns was ≈0.85. Firing rates are color-coded. f1 Steady-state subtracted GC responses from simulation in (e) for uncorrelated (left) and correlated MF pattern switches (right). f2 Same as (f1) but for PC. g Normalized standard deviation of PC transient amplitudes for switches between MF patterns of differing levels of correlation.CC BY · PubMed Central
Fig. 2 Simulating Purkinje cell pauses during eyelid conditioning. a Scheme of eyelid conditioning. CS: conditioned stimulus (red). US: unconditioned stimulus (violet). After experiencing CS and US pairings at a fixed temporal interval over many trials, the animal learns to close its eyelid just before the US is delivered (green). A pause in PC activity (blue) precedes the eyelid closure (target time, gray dashed line). b The CS is modeled as an instantaneous change in MF firing rate. Top: plot of firing rates of 100 MFs, sorted according to synaptic types (MF groups). MF firing rates are color-coded and drawn according to the distributions shown in Fig. 1b. Bottom: two sample MF rates per synaptic group. Colors as in Fig.1. c Model GC responses to the CS. Top: 1000 GCs sorted according to average firing rate after CS onset. Firing rates are color-coded. Bottom: steady-state subtracted and individually normalized GC transient responses. d Pdf of the distribution of GC activity decay times to 10% of the transient peak. e Example of delay eyelid conditioning over the course of 4000 learning steps for a 200 ms delay. Dashed line represents the target time used in the supervised learning procedure. Without STP-induced GC transients, no PC pause could be learned (pink line). f Simulated PC responses after 4000 learning trials for each target time (colored dashed lines).
Fig. 2 Simulating Purkinje cell pauses during eyelid conditioning. a Scheme of eyelid conditioning. CS: conditioned stimulus (red). US: unconditioned stimulus (violet). After experiencing CS and US pairings at a fixed temporal interval over many trials, the animal learns to close its eyelid just before the US is delivered (green). A pause in PC activity (blue) precedes the eyelid closure (target time, gray dashed line). b The CS is modeled as an instantaneous change in MF firing rate. Top: plot of firing rates of 100 MFs, sorted according to synaptic types (MF groups). MF firing rates are color-coded and drawn according to the distributions shown in Fig. 1b. Bottom: two sample MF rates per synaptic group. Colors as in Fig.1. c Model GC responses to the CS. Top: 1000 GCs sorted according to average firing rate after CS onset. Firing rates are color-coded. Bottom: steady-state subtracted and individually normalized GC transient responses. d Pdf of the distribution of GC activity decay times to 10% of the transient peak. e Example of delay eyelid conditioning over the course of 4000 learning steps for a 200 ms delay. Dashed line represents the target time used in the supervised learning procedure. Without STP-induced GC transients, no PC pause could be learned (pink line). f Simulated PC responses after 4000 learning trials for each target time (colored dashed lines).CC BY · PubMed Central
Fig. 3 MF-GC synaptic time constants and their relative weights determine the time course of GC responses. a Scheme of GC inputs in the simplified synaptic model. Each GC receives exactly two distinct high release probability driver (red) and low release probability supporter MFs (blue). b Schemes of the reduced synaptic model of high pv (red) and low pv synapses (blue). c Left: scheme of single pool response with the time constant τsyn (blue line) to a firing rate switch during CS presentation (black solid line). The dashed black line separates the transient (At) from the steady-state amplitude (As). Right: equations determining the synaptic time constant and synaptic input. d Slow vesicle pool time constant (τsyn) versus presynaptic MF firing rate. Different shades of gray indicate different release probabilities. e Driver synapse transient amplitude (At) versus relative firing rate change for a baseline firing rate of 80 Hz (m−mpre/mpre, mpre= 80 Hz). A negative At corresponds to a transient decrease in firing rate. Same color code as in (d). f Sample fast GC. Left: driver and supporter MF firing rates drawn from thresholded normal distributions (Nthr(200 Hz, 15 Hz) and Nthr(25 Hz, 15 Hz), respectively) and the corresponding synaptic responses. For clarity, only the τsyn of the respective slow pool is indicated. Upper right panel: GC threshold (dashed line), total synaptic input (black line), total driver input (red line), and total supporter input (blue line). The transient response is dominated by the driver input (red). Lower right panel: resulting GC firing rate response. g Like (f) but for a sample slow GC. The transient response is dominated by the supporter input (blue).
Fig. 3 MF-GC synaptic time constants and their relative weights determine the time course of GC responses. a Scheme of GC inputs in the simplified synaptic model. Each GC receives exactly two distinct high release probability driver (red) and low release probability supporter MFs (blue). b Schemes of the reduced synaptic model of high pv (red) and low pv synapses (blue). c Left: scheme of single pool response with the time constant τsyn (blue line) to a firing rate switch during CS presentation (black solid line). The dashed black line separates the transient (At) from the steady-state amplitude (As). Right: equations determining the synaptic time constant and synaptic input. d Slow vesicle pool time constant (τsyn) versus presynaptic MF firing rate. Different shades of gray indicate different release probabilities. e Driver synapse transient amplitude (At) versus relative firing rate change for a baseline firing rate of 80 Hz (m−mpre/mpre, mpre= 80 Hz). A negative At corresponds to a transient decrease in firing rate. Same color code as in (d). f Sample fast GC. Left: driver and supporter MF firing rates drawn from thresholded normal distributions (Nthr(200 Hz, 15 Hz) and Nthr(25 Hz, 15 Hz), respectively) and the corresponding synaptic responses. For clarity, only the τsyn of the respective slow pool is indicated. Upper right panel: GC threshold (dashed line), total synaptic input (black line), total driver input (red line), and total supporter input (blue line). The transient response is dominated by the driver input (red). Lower right panel: resulting GC firing rate response. g Like (f) but for a sample slow GC. The transient response is dominated by the supporter input (blue).CC BY · PubMed Central
Fig. 4 Learning performance depends on MF firing rate distributions. a First panel: Driver and supporter MF firing rate pdfs (μD = 200 Hz, μS = 25 Hz, σD = σS = 15 Hz). Second panel: Resulting joint At and τsyn distribution, featuring four partially overlapping clusters, corresponding to the slow and fast pools for driver and supporter synapses, and marginal distributions. The color code of the joint distribution scales logarithmically. Colors of marginal distributions indicate driver (red) and supporter (blue) components. Third panel: Normalized GC transient responses to CS. Inset: pdf of the distribution of decay times to 10% of the transient peak. Fourth panel: learned PC pauses, averaged over n = 20 simulations with different realizations of MF patterns and MF-GC connectivity. Dashed lines mark CS-US intervals (color code is the same as in Fig. 2e). Fifth panel: Error for each CS-US interval is calculated based on PC response amplitude, full-width at half-maximum and temporal deviation (Fig. S2a) and averaged over n = 20 realizations of MF patterns and MF-GC connectivity. Black lines indicate the distribution ranges; gray boxes indicate the 25th to 75th percentile range and black-white circles the medians. b Same as a, but with μS = 70 Hz. Inset: black line is the pdf for simulation with μS = 70 Hz and gray line is the pdf from (a) for comparison. Fifth panel: change in error relative to the average error in (a). c Same as (a), but with μD = 100 Hz and σD = 50 Hz. d Same as (a), but without driver inputs.
Fig. 4 Learning performance depends on MF firing rate distributions. a First panel: Driver and supporter MF firing rate pdfs (μD = 200 Hz, μS = 25 Hz, σD = σS = 15 Hz). Second panel: Resulting joint At and τsyn distribution, featuring four partially overlapping clusters, corresponding to the slow and fast pools for driver and supporter synapses, and marginal distributions. The color code of the joint distribution scales logarithmically. Colors of marginal distributions indicate driver (red) and supporter (blue) components. Third panel: Normalized GC transient responses to CS. Inset: pdf of the distribution of decay times to 10% of the transient peak. Fourth panel: learned PC pauses, averaged over n = 20 simulations with different realizations of MF patterns and MF-GC connectivity. Dashed lines mark CS-US intervals (color code is the same as in Fig. 2e). Fifth panel: Error for each CS-US interval is calculated based on PC response amplitude, full-width at half-maximum and temporal deviation (Fig. S2a) and averaged over n = 20 realizations of MF patterns and MF-GC connectivity. Black lines indicate the distribution ranges; gray boxes indicate the 25th to 75th percentile range and black-white circles the medians. b Same as a, but with μS = 70 Hz. Inset: black line is the pdf for simulation with μS = 70 Hz and gray line is the pdf from (a) for comparison. Fifth panel: change in error relative to the average error in (a). c Same as (a), but with μD = 100 Hz and σD = 50 Hz. d Same as (a), but without driver inputs.CC BY · PubMed Central
Fig. 5 Correlating release probability and MF firing rates improves learning performance. a Top: distribution of MF firing rates (m) used to drive the network, divided into low (supporter, green) and high (driver, yellow) rates. Bottom: Distribution of synaptic release probabilities (pv), divided into low (light gray) and high (dark gray) probabilities. b Top: pv versus m for 500 sample synapses for a network with a strong negative rank correlation between the m category (supporter or driver) and the pv category (high or low). Bottom: same as top, but for strongly positive correlated m and pv. c Learned PC pauses for low (left) and high (right) correlations. CS-US intervals are color-coded as in Fig. 2f. Each curve is the average of n = 20 simulations with different realizations of MF patterns and MF-GC connectivity. d–f Same as (a–c), but for distributions divided into five groups. g Left: MF rates and release probabilities for five synapse types where the average group firing rate is as in (d), but the firing rate variance progressively decreases with the average rate. Right: resulting PC eyelid response learning for high correlations. h Same as (g) but with zero-rate MFs added to the lowest rate distribution. Dashed lines indicate the case when the count of lowest rates and release probabilities is doubled.
Fig. 5 Correlating release probability and MF firing rates improves learning performance. a Top: distribution of MF firing rates (m) used to drive the network, divided into low (supporter, green) and high (driver, yellow) rates. Bottom: Distribution of synaptic release probabilities (pv), divided into low (light gray) and high (dark gray) probabilities. b Top: pv versus m for 500 sample synapses for a network with a strong negative rank correlation between the m category (supporter or driver) and the pv category (high or low). Bottom: same as top, but for strongly positive correlated m and pv. c Learned PC pauses for low (left) and high (right) correlations. CS-US intervals are color-coded as in Fig. 2f. Each curve is the average of n = 20 simulations with different realizations of MF patterns and MF-GC connectivity. d–f Same as (a–c), but for distributions divided into five groups. g Left: MF rates and release probabilities for five synapse types where the average group firing rate is as in (d), but the firing rate variance progressively decreases with the average rate. Right: resulting PC eyelid response learning for high correlations. h Same as (g) but with zero-rate MFs added to the lowest rate distribution. Dashed lines indicate the case when the count of lowest rates and release probabilities is doubled.CC BY · PubMed Central
Fig. 6 STP-generated temporal basis enables the computation of Bayesian time-interval estimates. a Full width at half maximum (cyan) and normalized amplitudes (magenta) of learned PC pauses versus delay interval from the experimentally constrained CCMSTP (see Fig. 2). Solid lines are linear fits. b Scheme of CCMSTP with added dentate nucleus cell. c Scheme of Bayesian integration. The sample interval ts (red dashed line, here drawn from a uniform distribution, upper left) is subject to a noisy measurement yielding a measured interval tm (lower left). CCMSTP implements Bayesian integration yielding an estimated interval te (right). d PC responses after 12,000 learning trials, averaged over n = 20 simulations with different realizations of MF patterns and MF-GC connectivity. Shaded area indicates standard deviation. Different colors represent learning of different uniform sample interval distributions. e Same as (d), but for DN cell activity. f Rescaled DN cell activity for different learned interval distributions (colored) and fitted theoretical Bayesian least squares (BLS) estimator (solid black line), with wweber = 0.12 resulting from fit. g Squared deviation of rescaled DN activity from the BLS estimator for all tested intervals. h–k Same as (d–g), but for the reduced model. The reduced model firing rate parameters were μD = 200 Hz, μS = 20 Hz, σD=10Hz and σS = 15 Hz and resulted in DN activity consistent with a Bayesian least squares model with wweber = 0.09.
Fig. 6 STP-generated temporal basis enables the computation of Bayesian time-interval estimates. a Full width at half maximum (cyan) and normalized amplitudes (magenta) of learned PC pauses versus delay interval from the experimentally constrained CCMSTP (see Fig. 2). Solid lines are linear fits. b Scheme of CCMSTP with added dentate nucleus cell. c Scheme of Bayesian integration. The sample interval ts (red dashed line, here drawn from a uniform distribution, upper left) is subject to a noisy measurement yielding a measured interval tm (lower left). CCMSTP implements Bayesian integration yielding an estimated interval te (right). d PC responses after 12,000 learning trials, averaged over n = 20 simulations with different realizations of MF patterns and MF-GC connectivity. Shaded area indicates standard deviation. Different colors represent learning of different uniform sample interval distributions. e Same as (d), but for DN cell activity. f Rescaled DN cell activity for different learned interval distributions (colored) and fitted theoretical Bayesian least squares (BLS) estimator (solid black line), with wweber = 0.12 resulting from fit. g Squared deviation of rescaled DN activity from the BLS estimator for all tested intervals. h–k Same as (d–g), but for the reduced model. The reduced model firing rate parameters were μD = 200 Hz, μS = 20 Hz, σD=10Hz and σS = 15 Hz and resulted in DN activity consistent with a Bayesian least squares model with wweber = 0.09.CC BY · PubMed Central

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Metadata

Authors
Barri, A., Wiechert, M. T., Jazayeri, M., & DiGregorio, D. A.
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2022-12-22
Volume
13
Issue
1
ISSN
2041-1723
DOI
10.1038/s41467-022-35395-y
PMC
PMC9780315
Cited by
43
References
9
Language
en
Licence
Funders
  • Agence Nationale de la Recherche (ANR-19-CE16-0019, ANR-21 -CE16 0036 01)
  • Fondation pour la Recherche Médicale (Team Award)

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