how excitatory and inhibitory synaptic conductances ...

HOW EXCITATORY AND INHIBITORY SYNAPTIC CONDUCTANCES SHAPE CORTICAL SLOW-WAVE OSCILLATIONS

M. RUDOLPH1 , N. C. ROY2 , Q. Z OU1 , V. F. D ESCALZO 3 , R. R EIG3 , M. S ANCHEZ -V IVES 3 , D. C ONTRERAS 2 & A. D ESTEXHE1 1

Unité de Neurosciences Intégratives et Computationnelles CNRS, Gif-sur-Yvette, France 2

3

Dept. Neurosci., University of Pennsylvania, Philadelphia, USA

Inst. Neurosci., Universidad Miguel Hernandez-CSIC, Alicante, Spain

Ladislav Tauc Conference 2003 in Neurobiology Gif-sur-Yvette, FRANCE, December 4-5, 2003

Abstract We combined stochastic neuronal models with intracellular recordings in rat barrel cortex in vivo in order to characterize the time course of excitatory and inhibitory synaptic conductances during the depolarized (up) and hyperpolarized (down) states which characterize slow-wave oscillations. Surprisingly, in this preparation we observed that up and down states are characterized by a similar input conductance. Applying a method to estimate synaptic conductances from subthreshold membrane potential fluctuations (see companion poster) revealed that the transition to up states is associated with a concomitant increase in the mean excitatory and decrease in the mean inhibitory conductance, while the variances of both conductances increase and show highfrequency fluctuations. These results were integrated into detailed biophysical models of cortical pyramidal neurons to deduce plausible time-dependent patterns of (random) synaptic bombardment that reproduce these conductance estimations, as well as the typical evolution of firing and subthreshold activity during the up state. This combination of computational and intracellular experiments predicts a level of tonic inhibition in the down state, and that a drop in this inhibition triggers the up state. These results suggest a dominant role for inhibition in orchestrating neocortical slow waves.

Supported by CNRS and Human Frontier Science Program.

Introduction It has been hypothesized [1] that rapid eye movement (REM) sleep plays an important role in the consolidation of recent memory traces. During REM sleep, the repetition of the activation pattern of specific neuronal populations received during wakefulness [2, 3], provides the basis for plastic changes at synaptic terminals to take place. However, recent studies also suggest a role of slow-wave sleep in the consolidation of memory [4, 5]. The hypothesis is that specific changes in synaptic weights are established during activated states, i.e. during wakefulness, while the regular and synchronized activation of synapses in the cortex during slowwave sleep periods could further potentiate or depress synaptic efficacies. This way, synaptic efficacy changes established during activated states will be promoted and/or stabilized into a permanent form. This hypothesis can be tested by evaluating the role of global slow oscillations in the cortical network [6, 7]. Here, as a prerequisite, we characterize the temporal changes in the network activity, based on intracellular recordings in vivo and in vitro. We approached this issue in the context of stochastic calculus [8] by explicitly solving the stochastic passive membrane equation subject to multiplicative Ornstein-Uhlenbeck noise terms [9]. The latter provide an effective model for the excitatory and inhibitory synaptic conductances due to the ongoing activity in the cortical network. This approach provides a novel method for characterizing synaptic noise, its mean and variance, based on intracellular recordings obtained under current stimuli (current clamp), aiming at the extraction of information about the underlying network activity.

METHODS Models of cortical neurons Stochastic models Effective models of subthreshold in vivo neuronal dynamics were constructed using the stochastic passive membrane equation subject to two independent colored Ornstein-Uhlenbeck [10] multiplicative synaptic noise processes describing inhibitory and excitatory conductances g e t and gi t [11]: aCm

dV t dt

dg e i t dt

a gL V t

gi t V t

Ee

2σ2 e i

g e i t g e i 0 ξ e i t τ e i τ e i

ge t V t

1

EL

Ei Iext (1)

Here, V t denotes the membrane potential, Iext a stimulating current, Cm the specific membrane capacity, a the membrane area, gL and EL are the leak conductance and reversal potential, Ee and Ei the reversal potentials for ge t and gi t , respectively. ξ e i denote Gaussian white noise processes with zero mean and unit standard deviation for excitation and inhibition, respectively. The stochastic conductances ge t and gi t are characterized by their means g e i 0 (static conductances), standard deviations σ e i and time constants τ e i .

Computational models The conductance measurements were incorporated in a three-compartment pyramidal neuron model [12]. AMPA-and GABAA -mediated synaptic inputs were simulated with a different density in perisomatic (only GABAergic synapses) and dendritic regions (high density of AMPA synapses, lower density of GABAergic synapses), according to morphological measurements [13]. Synaptic inputs were simulated according to kinetic models driven by Poisson processes (see details in [14]). The total synaptic conductances, as well as their variances, were estimated by voltage-clamping the soma at the reversal of either AMPA or GABAA inputs (0 and -75 mV, respectively). The total conductance was controlled by the release frequency at each synapse, while the conductance variance was controlled by changing the correlation between different synapses. These values were adjusted to match the values estimated from intracellular recordings in vivo.

METHODS Experimental protocols and conductance estimation Intracellular recordings in vivo Surgery and Preparation. In vivo experiments were conducted in accordance with the ethical guidelines of the NIH and with the approval of the Univ. Pennsylvania IACUC. Adult male Sprague-Dawley rats (350-450 g) were anesthetized with urethane (1.5 g/kg i.p.). Buprenorphine (0.03 mg/kg s.c.) was administered to provide additional analgesia. Animals were paralyzed with gallamine triethiodide and artificially ventilated. End-tidal CO2 (3.5-3.7%) and heart rate were continuously monitored. Body temperature was maintained at 37 o C via servocontrolled heating blanket and rectal thermometer. The depth of anesthesia was maintained by supplemental doses of the same anesthetic in order to keep a constant high-amplitude, lowfrequency EEG as recorded from a bipolar electrode lowered into the cortex. For intracellular recordings, the animal was placed in a stereotaxic apparatus and a craniotomy was made to expose the surface of the barrel cortex (1.0-3.0 mm posterior to bregma, 4.0-7.0 mm lateral to the midline). The dura was resected over the recording area, and mineral oil was applied to prevent desiccation. The stability of recordings was improved by drainage of the cisterna magna, hip suspension, and filling of the holes made for recording with a solution of 4% agar. Electrophysiological Recordings. Intracellular recordings were performed with glass micropipettes pulled on a P-97 Brown-Flaming puller. Pipettes were filled with 3M potassium acetate and had DC resistances of 80-90 MΩ. The intracellular recording pipette was lowered into the brain within 1 mm of the EEG electrode. Pipettes were oriented normal to the cortical surface, and the vertical depth was read on the scale of the micromanipulator. A high impedance amplifier (bandpass of 0-5 kHz) with active bridge circuitry was used to record and inject current into the cells. Data were digitized at 10 kHz.

Characterization of synaptic conductance noise See companion poster: M. Rudolph, M. Badoual, Z. Piwkowska, T. Bal, J.G. Pelletier, D. Par´ e, A. Destexhe A novel method for estimating synaptic conductances and their variances from intracellular recordings.

METHODS Two-current clamp protocol for estimating the time evolution of excitatory and inhibitory synaptic conductances Iext 2

Iext 1

intracellular recordings

Vm amplitude distributions ρ(V)

ρ(V)

ρ(V)

V

V

V1 σV1

V

g e0 g i0 σe σi

synaptic noise parameters

estimation of synaptic noise parameters

V

ρ(V)

ρ(V)

ρ(V)

V

V

V2 σV2

g e0 g i0

σe σi time

Intracellular recordings obtained at two different clamped currents (e.g. for repeated stimuli or aligned slow-wave oscillations) are analyzed in corresponding time windows (top) with respect to their membrane potential probability distributions (middle). From these, the mean and variance of the membrane potential can be deduced for each time window. This allows to calculate the mean and variance of excitatory and inhibitory conductances at corresponding times (bottom) by using equation (??), thus providing a characterization of the time course of network activity during stimuli or specific cortical activity states.

SLOW-WAVE OSCILLATIONS IN VIVO Intracellular and population activity during slow-wave sleep Local EEG

Intracellular recording

200 µm

Local EEG

1 mV

Intracellular

20 mV

-80 mV 1s

Local EEG

1 mV

Intracellular

20 mV

-100 mV

Intracellular and population activity during slow-wave sleep at two different constant current levels (Iext1 0 014 nA, top traces; Iext2 0 652 nA, bottom traces).

SLOW-WAVE OSCILLATIONS IN VIVO Intracellular activity during slow-wave oscillations Slow wave start

Slow wave end Local EEG

1 mV

Firing rate 0.2

Subthreshold membrane potential -100 mV 10 mV 200 ms

300 ms 0.5

0 ms

0.4

ρ(V)

-300 ms ρ(V)

0.2

0.4

0.1

-300 ms ρ(V)

0.3

0.5

-120

0.2

0.4

-110

-100

0.1

0.3

0.5 0.4

-90

V (mV)

0.3

0.5

0.2

0.4

0.1

0.3

0.5

0.2

0.4

0.1

-120

-110

-100

-90

V (mV)

0.3 -120

0.2

-110

-100

0.1 -120

ρ(V)

ρ(V)

0.3

0.5

300 ms

Membrane potential distributions 0 ms

ρ(V)

-90

V (mV)

-120

0.2

-110

-100

-90

V (mV)

0.1 -110

-100

-90

V (mV)

-120

-110

-100

-90

V (mV)

Characterization of intracellular activity during slow-wave oscillations. The population activity (top; Local EEG) is used to align individual intracellular recordings (blue dashed) corresponding to the start (left) and end (right) of the up-states characterizing slow-wave oscillations. During the up-state of slow-wave oscillations, cells discharge at higher rate (middle; Firing rate). The membrane potential is markedly depolarized and displays high amplitude fluctuations (middle; Subthreshold membrane potential). A characterization of the subthreshold membrane potential time course describing intracellular activity during slow waves is obtained by calculating the membrane potential probability distributions for small time windows as a function of time relative to the alignment (bottom; Membrane potential distributions).

SLOW-WAVE OSCILLATIONS IN VIVO Estimation of the mean and variance of excitatory and inhibitory synaptic conductances during slow waves Slow wave start

Slow wave end

Local EEG (mV)

1 0.5 0 -0.5 -1

V (mV)

-70 -80 -90 -100 -110

σV (mV)

Population activity

12 10 8 6 4 2

Intracellular activity

Iext 1 Iext 2

g0 (nS)

Synaptic conductance estimates 5 0

g e0 g i0

-5 -10

σ g (nS)

20

σe σi

15 10 5 -300

-100

100

Time (ms)

300

-300

-100

100

300

Time (ms)

Gaussian approximations of the membrane potential distributions yield the mean V and standard deviation σV (middle) as function of time during slow-wave oscillations. Corresponding values for V and σV at two different currents (Iext1 0 014 nA, Iext2 0 652 nA) yield the mean ge0 , gi0 and standard deviation σe , σi of excitatory and inhibitory conductances (bottom).

SLOW-WAVE OSCILLATIONS IN VIVO Pooled data for the time course of synaptic conductances during slow-wave oscillations SW start n018_000

SW end

SW start n029_000

σ g (nS)

σ g (nS)

g 0 (nS)

5 0 -5 -10 -15

g 0 (nS)

5 0 -5 -10 -15 15 10 5 -300 -100

100

300

-300 -100

Time (ms)

100

10 5

300

-300 -100

100

300

-300 -100

Time (ms)

SW end

100

300

Time (ms)

SW start n030_001

SW end

σ g (nS)

g 0 (nS)

5 0 -5 -10 -15

g 0 (nS)

5 0 -5 -10 -15

σ g (nS)

15

Time (ms)

SW start n018_003

15 10 5 -300 -100

100

300

-300 -100

Time (ms) SW start n032_000

100

15 10 5

300

-300 -100

100

Time (ms)

Time (ms)

SW end

SW start

300

-300 -100

100

300

Time (ms) n028_001 SW end

σ g (nS)

g 0 (nS)

5 0 -5 -10 -15

g 0 (nS)

5 0 -5 -10 -15

σ g (nS)

SW end

15 10 5 -300 -100

100

Time (ms)

300

-300 -100

100

Time (ms)

300

15 10 5 -300 -100

100

300

-300 -100

Time (ms)

100

Time (ms)

g e0 g i0

300

σe σi

Time course of synaptic conductances during slow waves for different cells. The start of the up-state is accompanied by a decrease in the mean inhibitory (red) and increase in mean excitatory (blue) conductance, whereas the end of the up-state shows the opposite temporal pattern. The standard deviation of both excitatory (light blue) and inhibitory (orange) conductances increases during the start, and decrease during the end of the up-state. In addition, a change in the temporal pattern of the standard deviation of synaptic conductances can be observed.

CHARACTERIZATION OF SLOW WAVES Simplified model of the conductance time course during slow-wave oscillations

Amplitude Time ∞

Max slope

Amplitude Amplitude Time -∞

Onset Time of max slope

σg

g0

Slow-wave start

Slow-wave end

g e0 g i0

Time

Time

Time

Time

σe σi

In a minimal model, the time course of the mean and standard deviation of excitatory and inhibitory synaptic conductances characterizing the start and end of the up-state during a slowwave oscillation can be described by sigmoidal functions (bottom). The latter are characterized by their amplitude, the maximum slope, the time of the maximum slope and the onset (top).

CHARACTERIZATION OF SLOW WAVES Amplitude changes of synaptic conductances during slow waves

inhibitory conductance


10 5 0 -5

SW end SW start

-10 -10

-5

0

5

10 5 0 -5 -10

10

-10

excitatory conductance

Max slope (nS/ms)

0.4 0.2 0 -0.2 -0.4 -400 -200

0

-5

200 400


0

5

10




g0

σg

Amplitude (nS)

g0

σg

0.4 0.2 0 -0.2 -0.4 -400 -200

0

200 400


Amplitude (top) and maximum slope (bottom) for the mean and standard deviation of synaptic conductances during the start (green) and end (blue) of the up-state in a slow-wave oscillation. During the start, the mean excitatory conductance increases (positive slope) whereas the mean inhibitory conductance decreases (negative slope). The opposite pattern is observed during the end of the up-state. The standard deviation of both excitatory and inhibitory conductances increases at up-state onset (positive slope in both cases), and decreases at its end (negative slope in both cases).

CHARACTERIZATION OF SLOW WAVES Temporal aspects of conductance changes during slow waves

150 100

SW end SW start

50 0 -50 -100 -150 -100

0

σg

150 100 50 0 -50 -100 -150 -100

100

0

100



g0

σg

Onset (ms) inhibitory conductance


Time of max slope (ms) inhibitory conductance


g0

300 200 100 0 -100 -200 -300 -200

0

200


300 200 100 0 -100 -200 -300 -200

0

200


Time of the maximum slope (top) and the onset (bottom) for the mean (left) and standard deviation (right) of synaptic conductances during the start (green) and end (blue) of the upstate in a slow-wave oscillation. During the start, the time of the maximum slope of the mean excitatory conductance slightly precedes that of inhibition, whereas at the end of the up-state the onset shows a precedence of the excitatory mean. No temporal preference are observed for the standard deviations of excitatory and inhibitory synaptic conductances.

MODELS OF SLOW-WAVE OSCILLATIONS Simplified computational model of slow waves based on in vivo recordings Incorporating the in vivo measurements of the mean (ge0, gi0) and standard deviation (σe, σi) of synaptic conductances in a three-compartment pyramidal neuron model [12] led to slow waves with characteristics consistent with intracellular recordings in vivo.

20 mV -60 mV 1s

Down-state

ρ(V)

Up-state

ρ(V)

0.8

σV = 5.32 mV

0.16

σV = 0.25 mV

0.6

0.12

0.4

0.08

0.2

0.04 -80

-70

-60

-50

-40

Membrane potential (mV)

-80

-70

-60

-50

-40

Membrane potential (mV)

Computational model of slow waves based on intracellular measurements in vivo. The release rates and correlation at excitatory and inhibitory synapses were adjusted to match the values estimated from the experimental recordings. The parameters were, for the down-state: 14.45 nS leak, leak reversal of -90 mV, no excitation, release rate for GABAA of 1 Hz (correlation coefficient = 0). For the up states, GABAA rates dropped to 0.4 Hz (leading to a conductance decrease of 8 nS), with a correlation coefficient of 0.2 (σi 2 nS), while AMPA released at a rate of 0.4 Hz (equivalent to a total conductance of 4 nS) and had a correlation coefficient of 0.5 (σe 0.5 nS). The figure shows a voltage trace simulating a few seconds of slow waves (top) as well as the Vm distribution obtained for the up-states and down-states (bottom).

Conclusions Using a novel method for estimating the effective synaptic conductances based on intracellular recordings at different constant current injections, we characterized the temporal pattern of the mean and variance of excitatory and inhibitory synaptic conductances in single cortical cells during slow-wave oscillations in vivo. This analysis shows that: (1) The up-state observed during a slow-wave oscillations in vivo is triggered by an increase in the mean excitatory conductance and a decrease in the mean inhibitory conductance. The termination of the up-state shows the opposite temporal pattern. (2) The variance of both excitatory and inhibitory synaptic conductances increases during the start and decreases at the end of the up-state during a slow-wave oscillation. A change in the temporal pattern of variance changes is observed, with large fluctuations with periods around 50 ms. (3) The time of the maximum slope of changes in the conductance mean shows a slight precedence for excitation at the beginning of the up-state in a slowwave oscillation. Up-states terminate with a slight precedence of the decrease in the excitatory mean observed in the onset. No temproal precedence is observed in the variance of synaptic conductance changes. (4) Simplified computational model descibing the time course of conductance during a slow-wave oscillation by step functions or sigmoidal changes yield slow waves with characteristics consistent with in vivo recordings. The goal of this combination of computational and intracellular experiments is to characterize the spatiotemporal patterns of synaptic bombardment in single cortical cells during slow-wave oscillations, a premise for understanding the possible physiological role of slow waves in consolidation of memory.

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