Resonant synchronization of heterogeneous inhibitory networks

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Cerebellar oscillations: Anesthetized rats Transgenic animals Recurrent model Review of literature: γ Network resonance Life simulations Resonance frequency Conclusion Resonant synchronization of heterogeneous inhibitory networks E. De Schutter with: Reinoud Maex (modeling) Antonia Volny-Luraghi (experiments) Hugo Cornelis and Mike Wijnants (software and equipment) Theoretical Neurobiology, University of Antwerp, Belgium http://www.bbf.uia.ac.be

Oscillations in normal animals: anesthetized rat Purkinje cell simple spike responses to tactile input: sometimes oscillator Happens rarely (~5% of recordings), always 1 Hz. Jl9hast1 Nose punctate 3 113 Hz Counts/bin 2 1 -.5.5.1.15.2.25 Time (sec) Jl9gcst8 contra punctate brush 3 119 Hz Counts/bin 2 1 -.5.5.1.15.2.25 Time (sec)

Cerebellum can generate high frequency oscillations Cortex: 6 Hz QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Cerebellum: 18 Hz Surface recordings from cat brain (chloroform + ether anesthesia) Adrian J. Physiol. 1935

Oscillations in transgenic animals: Transgenic mice show fast frequency oscillations in cerebellum: recordings in awake transgenic mice lacking calcium binding proteins local field potentials (LFP) show spindle-shaped periods of fast oscillation (167.8 ± 36. H LFP oscillation frequency is fairly constant, amplitude is highly variable. LFP oscillations reduced by blocking GABA inhibition or gap junctions. LFP oscillations are synchronized along parallel fiber axis, but not along sagittal axis. QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Cheron et al. J. Neurosci. 24

Oscillations in transgenic animals: model Recurrent inhibition between molecular layer neurons: Model with 1 spiking inhibitory neurons: Purkinje cells and ML interneurons. Heterogeneous: neurons differ in excitability, synaptic weights randomized. All neurons: 6 voltage gated channels, no spike afterhyperpolarization, no cellular resonanc Feedforward excitation: randomly activated parallel fibers with 16 synapses on dendrite Nearest neighbor inhibitory coupling: recurrent inhibition. + gap junctions (interneurons on Introduces a resonant frequency in 15-25 Hz range. High inhibitory neuron firing rates are required: neurons must fire in resonance window.

Oscillations in transgenic animals: model Recurrent inhibition between molecular layer neurons: Spindles are produced continuously and with high power. Explains effects of blocking GABA A inhibition (= blocks recurrent inhibition). Strong enhancement by gap junctions between interneurons. Oscillations unveil physiological phenomenon of resonance. 1 ms Power spectrum: QuickTime and a TIFF (LZW) decompressor are needed to see this picture. recurrent inhibition recurrent inhibition + gap junctions no recurrent inhibition oscillations not synchronized in sagittal axis: oscillations synchronized along parallel fiber beam Firing Frequency (Hz) 2 ms

Cerebellar oscillations : conclusions Fast oscillations of Purkinje cell simple spike firing: stimulus evoked in anesthetized rats in ~5% of recordings. transgenic animal: spontaneous fast oscillations synchronized along parallel fiber axis. LFPO amplitudes vary over time (spindles). blockade of inhibition or gap junctions decreases LFPOs. Model of fast cerebellar oscillations: recurrent inhibitory network of Purkinje cells (recurrent collaterals) + ML interneurons or recurrent inhibitory network of ML interneurons driving Purkinje cells.

Cerebellar oscillations : conclusions Fast oscillations of Purkinje cell simple spike firing: stimulus evoked in anesthetized rats in ~5% of recordings. transgenic animal: spontaneous fast oscillations synchronized along parallel fiber axis. LFPO amplitudes vary over time (spindles). blockade of inhibition or gap junctions decreases LFPOs. Model of fast cerebellar oscillations: recurrent inhibitory network of Purkinje cells (recurrent collaterals) + ML interneurons or recurrent inhibitory network of ML interneurons driving Purkinje cells. discovery of resonant frequency.

Cerebellar oscillations : conclusions Fast oscillations of Purkinje cell simple spike firing: stimulus evoked in anesthetized rats in ~5% of recordings. transgenic animal: spontaneous fast oscillations synchronized along parallel fiber axis. LFPO amplitudes vary over time (spindles). blockade of inhibition or gap junctions decreases LFPOs. Model of fast cerebellar oscillations: recurrent inhibitory network of Purkinje cells (recurrent collaterals) + ML interneurons or recurrent inhibitory network of ML interneurons driving Purkinje cells. discovery of resonant frequency. What causes the resonance? What determines the resonance frequency?

Literature: oscillations caused by synchronized firing Both excitatory and inhibitory neuron populations participate: QuickTime and a TIFF (LZW) decompressor are needed to see this picture. 4 Hz oscillation in cortex Singer & Gray Ann. Rev. Neurosci 1995 Jefferys et. al. TINS 1996

Literature: oscillations caused by synchronized firing Multiple population mechanisms may be responsible for 4 Hz oscillation QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Freeman Keller Wilson and Bower Traub, Jefferys, Jefferys et al. TINS 1996

Kainate evokes gamma frequency oscillation in hippocampu Control 1 Pyramidal neuron Interneuron Power (1-9 V 2 /Hz) 8 Kainate IPSPs Power (1-9 V 2 /Hz) 8 peak at γ Buhl et al. 2 mv 1 1 1 Frequency (Hz)

How can recurrent inhibition synchronize? With slow inhibition (small α) only synchronous firing is stable: Pair of reciprocal inhibitory integrate and fire neurons coupled with α function g syn = g syn α 2 e αt phase stable unstable 1.5 1 4. 3. Alpha QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture..5 2. 1.5 1..5.5 1 1.5 2 2.5 3 3.5 Time (ms) α focus on shape of synaptic current Van Vreeswijk, Abbott & Ermentrout J. Comput. Neurosci. 1994 (similar results:ernst, Pawelzik & Geisel Phys. Rev. Lett. 1995)

How can recurrent inhibition synchronize? The decay time constant of inhibition sets oscillation frequency: Experimental manipulation of decay of GABA A currents with pentobarbital Voltage clamp inhibitory currents in interneurons No barbital: 44 Hz 2 µm barbital: 22 Hz QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Hippocampal slice with AMPA/NMDA receptors blocked Computer simulation (128 inhibitory interneurons) QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Whittington, Traub & Jefferys Nature 1995

How can recurrent inhibition synchronize? Wang & Buzsáki confirm dependence of oscillation frequency on τ syn : The synchronization is dependent on firing frequency of neurons: Network of recurrently coupled inhibitory neurons without axonal delays. Conductance based models activated by current injection. QuickTime and a TIFF (LZW) decompressor are needed to see this picture. QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Wang & Buzsáki J. Neurosci. 1996

How can recurrent inhibition synchronize? The decay time constant of inhibition sets oscillation frequency? Problem: decay time constant is much shorter! Whittington measured compound inhibitory currents but Traub simulated this as single synapse QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Bartos, Vida, & Jonas PNAS 22

How can recurrent inhibition synchronize? Is the frequency range of recurrent inhibitory networks limited? Gap junctions between pyramidal neuron axons essential for fast oscillations (not blocked by bicuculline in hippocampus). QuickTime and a TIFF (LZW) decompressor are needed to see this picture. QuickTime and a TIFF (LZW) decompressor are needed to see this picture. Traub & Bibbig J. Neurosci. 2 QuickTime and a TIFF (LZW) decompressor are needed to see this picture. autocorrelation e cross corellation e - i

Mechanisms of oscillation with recurrent inhibition Recurrent inhibition with a delay introduces a resonant frequency: GENESIS simulations #1

Mechanisms of oscillation with recurrent inhibition Recurrent inhibition with a delay introduces a resonant frequency: Delay (axonal + synaptic) is essential. delay = 1 ms delay = ms LFP or EEG 1 ms 1 ms raster plot Maex and De Schutter J. Neuroscience 23: 153-1514 (23)

Mechanisms of oscillation with recurrent inhibition Recurrent inhibition with a delay introduces a resonant frequency: Delay (axonal + synaptic) is essential (van Vreeswijck et al., 1994; Ernst et al., 1995). delay = 1 ms delay = ms LFP or EEG 1 ms 1 ms raster plot GENESIS simulations #2 Maex and De Schutter J. Neuroscience 23: 153-1514 (23)

Mechanisms of oscillation with recurrent inhibition Recurrent inhibition with a delay introduces a resonant frequency: Delay (axonal + synaptic) is essential (van Vreeswijck et al., 1994; Ernst et al., 1995). Neurons must fire (181 ± 1 Hz) close to frequency of oscillation (187 Hz) = resonance. delay = 1 ms delay = ms LFP or EEG 1 ms 1 ms raster plot LFP power for varying spiking frequencies 12 8 4 resonance 12 8 4 1 1 1 neuron firing frequency 1 1 1 neuron firing frequency

Mechanisms of oscillation with recurrent inhibition Synaptic delay sets the resonant frequency (1D network): Synaptic delay (= axonal delay + latency of synaptic transmission) has strongest effect. Predicted resonance frequency: f=1/(4d) (nearest neighbor inhibition). Synaptic weights set the power. Synaptic current decay time constant has much weaker effects ( Wittington et al., 1995; 15 12 9 Traub et al., 1996; Wang and Buzsáki, 1996). Changing synaptic weight Changing synaptic decay Changing synaptic delay weight.5 weight 1. weight 2. weight 4. 15 1 decay.25 decay.5 decay 1. decay 2. decay 4. 15 1 delay.25 delay.5 delay 1. delay 2. delay 4. 6 3 5 5 1 1 1 neuron spiking frequency (Hz) 1 1 1 neuron spiking frequency (Hz) 1 1 1 neuron spiking frequency (Hz

Mechanisms of oscillation with recurrent inhibition Synaptic delay sets the resonant frequency (1D network): f=1/(4d) Similar relation in networks with slowly firing neurons (Brunel and Wang, 23). Synaptic current decay has weak effect, but for each delay there is an optimal decay. predicted resonance frequency: 1/4d 1 1 Resonance peak 1 1 1 1 neuron spiking frequency (Hz) τ =.75 τ = 1.5 τ = 3. synaptic current deca τ = 6. τ = 12.

75 Mechanisms of oscillation with recurrent inhibition Improved resonance with long range connections (1D network): Resonance is now determined by mean delay of inhibition for each radius r: gamma oscillation possible for r > 6 with realistic short synaptic decay time constants. Power as r. Peak width as r. 5 25 delay = 1 ms radius 1 radius 2 radius 4 radius 8 1 1 1 1 1 1 neuron spiking frequency (Hz) predicted frequency: 1/4d 1 1 1 neuron spiking frequency (Hz) r = 16 r = 8 r = 4 r = 2 47 Hz 7 Hz 125 Hz 172 Hz

Mechanisms of oscillation with recurrent inhibition Resonance in 2D networks: Same relationship between mean delay and resonance provided the connection probability between two neurons, or the connection weight, tapers off with distanc Oscillations at frequencies close to f R are generated over broad range of firing rates A 15 Ca b Da b 1 3 f (Hz) 5 ISI (ms) 3 f (Hz) 5 ISI (ms) 5 c c 1 1 1 Frequency (Hz) B 1 1 D C d.2 d.2 1 1 1 1 Mean firing rate (Hz) Time (s) Maex and De Schutter J. Neuroscience 23: 153-1514 (23).1 8.4 Time (s) 8.6

Mechanisms of oscillation with recurrent inhibition Resonance in networks with sparse, asymmetrical connections: A non-topographic network with a mean number of five synapses per neuron produces at resonance a power close to that of the fully connected network. A 4 B 4 2 2 1 5 Ca 1 1 1 Number of synapses per neuron 1 1 1 Frequency (Hz) 5 synapses fully connected (1) Da Maex and De Schutter J. Neuroscience 23: 153-1514 (23)

Mechanisms of oscillation with recurrent inhibition Modulating effects: Gap junctions increase oscillation power without changing resonance frequency. Noise and heterogeneity decrease oscillation power. The resonance phenomenon is very robust provided synaptic delays are present ( Wang and Buzsáki, 1996 which did not have delays). 3 2 1 Gap junctions Current injection 1 1 1 Frequency (Hz) Maex and De Schutter J. Neuroscience 23: 153-1514 (23)

Mechanisms of oscillation with recurrent inhibition Reason for f = 1 / (4d) relation: Firing of postsynaptic neuron is highest in time window [-d, d]: otherwise IPSP will coincide with expected spike. The sine wave best covering this 2d time window has a 4d period. f=1/(4d) is well known property of physical systems (e.g. acoustic resonance). 1 8 δ 1 δ 2 1.5 1 spike neuron 1 δ 2 6 4 d = 1 ms.5 -.5 window synchronous spike neuron 2 = 2d optimal window inhibition neuron 2 = 2d 1 2 3 4 5 6 7 2 2 4 6 8 1 δ 1 (ms) -1-1.5 optimal oscillation frequency = 1/(4d)

Resonant oscillations : conclusions Fast oscillations of Purkinje cell simple spike firing: stimulus evoked in anesthetized rats in ~5% of recordings. transgenic animal: spontaneous fast oscillations synchronized along parallel fiber axis. LFPO amplitudes vary over time (spindles). blockade of inhibition or gap junctions decreases LFPOs. Model of fast cerebellar oscillations: recurrent inhibitory network of Purkinje cells (recurrent collaterals) + ML interneurons or recurrent inhibitory network of ML interneurons driving Purkinje cells. discovery of resonant frequency. Resonant oscillation through recurrent inhibition: axons are importan neurons fire at rates close to the oscillation frequency. synaptic delay is necessary: f=1/(4d) axonal arborization may determine resonance resonance enhanced by long range connections. may be further enhanced/modulated by intrinsic cellular resonant properties. this resonance mechanism may operate in normal cerebellum but also during gamma oscillations in cortex and hippocampus.

Resonant synchronization with recurrent inhibition Axonal + synaptic delays between interneurons set resonant frequency: Multiple classes of inhibitory interneurons with typical axonal arbors: Each class has its own resonant frequency based on mean axonal delay (connectivity). Selection by excitatory drive of class with right resonance sets overall network frequency. Not selected inhibitory neurons do not synchronize and provide background inhibition. I 12 Hz I I E 8 Hz I 4 Hz I I

Resonant oscillations : conclusions Fast oscillations of Purkinje cell simple spike firing: stimulus evoked in anesthetized rats in ~5% of recordings. transgenic animal: spontaneous fast oscillations synchronized along parallel fiber axis. LFPO amplitudes vary over time (spindles). blockade of inhibition or gap junctions decreases LFPOs. Model of fast cerebellar oscillations: recurrent inhibitory network of Purkinje cells (recurrent collaterals) + ML interneurons or recurrent inhibitory network of ML interneurons driving Purkinje cells. discovery of resonant frequency. Resonant oscillation through recurrent inhibition: axons are important neurons fire at rates close to the oscillation frequency. synaptic delay is necessary: f=1/(4d) axonal arborization may determine resonance resonance enhanced by long range connections. may be further enhanced/modulated by intrinsic cellular resonant properties. this resonance mechanism may operate in normal cerebellum but also during gamma oscillations in cortex and hippocampus. also applies to I 1 E 1 I 2 E 2 I 1 instead of I 1 I 2 I 1 networks.

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