Too much noise to sleep: Noise-induced transition from sleep to - - PowerPoint PPT Presentation

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Too much noise to sleep: state in a spiking network model Noise-induced transition from sleep to awake-like

Rodrigo F. O. Pena 1, 2 Antonio C. Roque 1 Michael A. Zaks 3

1Department of Physics, FFCLRP, University of São Paulo, Brazil 2Institute of Physics, Humboldt University of Berlin, Germany 3Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany

Second NeuroMat Workshop: New frontiers in neuromathematics

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Different brains states

Awake Sleep SWS or anesthesia

Shu et al., Nature 423:288-293, 2003 Cortical slice in vitro In vivo recordings

Weak correlations - asynchronous - irregular

Renart et al., Science 327, 587; 2010 Boustani et al., J Physiol (Paris) 101:99-109, 2007

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Izhikevich, IEEE Transactions on neural networks, 2003

A B C

RS IB

C

CH

D

FS

E F

LTS

Then

Isyn,i(t) = X

j✏P resyn

Gex/in

i/j

(t)(Eex/in − vi)

dGex/in

i/j

(t) dt = − Gex/in

i/j

(t) τex/in + gex/in X

tf

j

δ(t − tf

j )

Randomly connected 2 neurons Izhikevich’s formalism

10

˙ v = f(v) − u + I(t) ˙ u = a(bv − u) v(t) → c, u(t) → u(t) + d. v(t) = vpeak

(voltage) (recovery) Conductance-based synapses

Regular spiking Intrinsically bursting Chattering Fast spiking

Low-threshold spiking Low-threshold spiking

Ensemble of trajectories that leave to SSA

Rest

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

• If network correctly tuned, inhibitory conductance exceeds excitatory one: SSA;

Lifetime; network with LTS as inhibitory, 80%RS and 20%CH;

B C gex gin

Work published at Tomov, P., Pena, R. F., Zaks, M. A., & Roque, A. C. (2014). Sustained oscillations, irregular firing, and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types. Frontiers in computational neuroscience, 8.

Typical raster plot

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

• Activity is transiently self-sustained;
• Sensitive dependence of individual trajectories on initial conditions;
• Exponential distribution of lifetimes in the large ensemble of trajectories:

Lai, Y. C., & Tél, T., Transient chaos: complex dynamics on finite time scales, 2011

Attributes of transient chaos

Work published at Tomov, P., Pena, R. F., Zaks, M. A., & Roque, A. C. (2016). Mechanisms of self-sustained

• scillatory states in hierarchical modular networks with

mixtures of electrophysiological cell types. Frontiers in computational neuroscience, 10.

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Transient Chaos

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Neurons are stochastic

Lindner, B. (2016)

Spontaneous neurotransmitters release Channel noise unreliable synapses

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Neurons are stochastic: synaptic noise

Isyn(t) = Gex(t)(Eex − v) + Gin(t)(Ein − v) ˙ Gex/in(t) = −

Gex/in(t) τex/in

+ √ 2Dξ(t)

where we assume that the stochastic process ξ is Gaussian with hξ(t)i = 0 and hξ(t)ξ(s)i = δ(t s).

Point-conductance model described by Destexhe et. al., (2001).

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10

−5

10

1

10

2

10

3

10

4

10

5

10

6

Amplitude D Resilience time [ms] FS active FS silent LTS active LTS silent

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

awake sleep

Noise influences transitions awake->sleep sleep->awake

Experiments measuring amplitude and frequency of mEPSC in the cerebral cortex of mice and rats show that these are:
 
 lower after a few hours of sleep, higher after a few hours of wake, higher after sleep deprivation.

Rao et al., (2007), Liu et al., (2010)

−

10 10 10 Resilience time [ms]

2.5 3

−

Amplitude D

−

FS active FS silent LTS active LTS silent

sleep sleep awake awake

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

20 40 60 80 100 120 140 1 10 100 1000 PSD [1/s] 20 40 60 80 100 120 140 1 10 100 1000 PSD [1/s] 20 40 60 80 100 120 140 Frequency [Hz] 1 10 100 1000 PSD [1/s]

Young, Gerald A., et al. (1978): 89-91.

D=0.5x10

• 5

D=1.5x10

• 5

D=4.5x10

• 5

up

down awake

Power spectrum

Spectra agree with the literature;

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Up Down

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10

−5

5 10 15 20 25 30 35 40

D Averaged resilience time [ms]

(RS and FS) down (RS and LTS) down (RS and FS) up (RS and LTS) up

Down state is influenced by: Noise leveI Inhibition

−

(RS and FS) down (RS and LTS) down (RS and FS) up (RS and LTS) up

Experiments where inhibitory neurons are progressively blocked showed that inhibition influences up down transitions.

Sanchez-Vives, M. V, Journal of Neurophysiology (2010) Holcman, D. and Tsodyks, M. PLoS Comput Biol, (2006)

Evidences showing that noise regulates up down transitions.

Laboratório de Sistemas Neurais (SisNe) - rodrigo.pena@usp.br

Acknowledgement

Thanks for your attention