Positive Feedback and Synchronized Bursts in Neuronal Cultures

陳志強

C. K. Chan

Institute of Physics, Academia Sinica

National Central University, Taiwan

中央研究院 物理研究所

KIAS 2015

Collaborators P. Y. Lai, Central Univ.

Y. T. Huang, Central Univ.

C. T. Huang,

Academia Sinica

C. C. Chen,

Academia Sinica

Moore’s Law

https://humanswlord.files.wordpress.com/2014/01/moores-law-graph-gif.png

Neuromorphic Computation IBM: True North Chip (2014)

1 million programmable neurons and 256 million programmable synapses.

5.4 billion transistors at 28nm, < 70 mw, size of a stamp

http://www.research.ibm.com/articles/brain-chip.shtml

Living Networks

• Connections

- small world, scale free, random …

- 2D, 3D

- feed forward, recurrent …

• Synaptic Dynamics

- facilitation

- depression

Dynamics of Neural Cultures: Synchronized Bursting

Multi-Electrode Array

http://www.multichannelsystems.com/

Synchronized Burst (SB) of a neuronal network • Neuronal network : excitable network

• Brain, slice, dissociated neuronal network

• SB : synchronization + neuron burst

5 s

40 mV

Wagenaar, PRE 73, 1539 (2006)

(discrete repeated firings)

firing rate

raster plot

Cultures play rich synchronized burst (SB) dynamics

Daniel A. Wagenaar , BMC Neuroscience2006, 7:11

firing rate change with days

Dissociated neuronal cultured network is a good material to study SB

High density culture recorded by MEA

Basic Questions

• What are the basic dynamics of these living neuronal network?

• Can memories be written and read back from them?

• Can these networks perform useful functions?

SB has hidden information?

Gordon the Robot (2008) https://www.youtube.com/watch?v=1-0eZytv6Qk

Why we are not seeing more of Gordon?

Outline

• Properties of Synchronized Bursts

• Mean field model of firing rate with synaptic plasticity (TM model)

• Extended TM model (TMX)

• Implications of TMX model

• Summary

Neuronal cultures and MEA Wistar rat E17 cortical cells

Density : 2500 cells/mm2 ; Area : 5 mm2

Coating : 0.1 % PEI

Medium : DMEM + 5%FBS + 5%HS

Incubator : 37 ℃ and 5% CO2

3 – 5 neurons / electrode

200 μm 40 μm

MEA60 system (MEA1060-Inv-BC + Qwane ITO-200 chip)

Sampling rate : 20K Hz Chip : 60 electrodes (8×8)

Diameter : 40 μm Spacing : 200 μm

13 DIV 9 DIV

Synchronized burst firing histogram (SBFH)

Co

un

ts /

5 m

s

spike detection

0 s 90 s

Raster plot of a SB

τIBI

elec

tro

des

Firing rate histogram

τB

Characteristic Patterns

Reverberation Is Enhanced by Decreasing Magnesium Ions

Increasing NMDAR Conductance

Reverberation Is Suppressed by Increasing Glutamate

Increasing System Noise

Reverberation Is Enhanced by Increasing Bicuculline

Decreasing Inhibition Connections

Summary

DIV ↑ noise ↑ (Glu ↑)

Conductance

↑ (Mg↓)

Inhibition ↓ (BIC ↑)

Firing rate ↑ ↑ ↑ ↑

Bursting rate ↑ ↑ ↑ ―

Burst duration

↓ ↓ ↑ ↑

reverberation ↓ ↓ ↑ ↑

Demo of positive feedback in the Panther CGS765 tube VCA

https://www.youtube.com/watch?v=S6_AF28BrQM

Mean field description

E(t)

Network

E’(t)

synchronized burst

similar activity

rate model

mean-field model

Positive Feedback

If E’(t) > E(t)

Recurrent connection

Short term synaptic facilitation

ISRN Neurology, Sumiko Mochida,Volume 2011 (2011), Article ID 919043, 7 pages

[Ca2

+ ]

Resting Ca2+

~ 100 nM

Residual Ca2+

~ 1 μM

1st action potential 2nd action potential

(a)

(b)

Ca2+

1st action potential Residual Ca2+ 2nd action potential Resting Ca2+

Short term synaptic depression

Blitz, Dawn M. et al. Nat. Rev. Neurosci. (5), 2004

Tsodyks-Markram (TM) model I

𝑑𝑥

𝑑𝑡=

1−𝑥

𝜏𝐷− 𝑢𝑥𝐸

𝑑𝑢

𝑑𝑡=

𝑈−𝑢

𝜏𝑓+ 𝑈(1 − 𝑢)𝐸

Firing rate

Depression

Facilitation

𝑑𝐸

𝑑𝑡=

1

𝜏[−𝐸 + 𝑏 𝑙𝑛 1 + 𝑒

𝐽𝑢𝑥𝐸−𝐼0𝑏 ]

Cortes, Jesus M., et al. PNAS 110.41 (2013): 16610-16615.

Tsodyks-Markram (TM) model II

High firing Steady state

Oscillatory steady state

Low firing steady state

(will not stop!)

I0 = -1

I0 = -1.3

I0 = -2

TMX model

𝑑𝑥

𝑑𝑡=

𝜒0−𝑥

𝜏𝐷− 𝑢𝑥𝐸

𝑑𝑢

𝑑𝑡=

𝑈−𝑢

𝜏𝑓+ 𝑈(1 − 𝑢)𝐸

𝑑𝜒0

𝑑𝑡=

𝑋0−𝜒0

𝜏𝑥− 𝛽𝐸 𝜏𝑥 : recovery time constant of 𝜒0 (20 s)

β : slow depletion rate (0.01)

𝑥 : fraction of available resources

𝑢 : release probability

𝜒0 : baseline of 𝑥

𝑈 : baseline of 𝑢 (0.3)

𝜏𝐷 : recovery time constant of 𝑥 (0.15 s)

𝜏𝐹 : recovery time constant of 𝑢 (1.5 s)

𝐽 : strength of recurrent connections

𝑏 : neuronal gain function (1.5)

𝐸 : firing rate

𝐼0 : inhibition current (-1.3)

𝑋0 : maximum available resources slow

depletion

firing rate

available resource

release probability

𝜏 : recovery time constant of 𝑥 (20 s)

𝑑𝐸

𝑑𝑡=

1

𝜏[−𝐸 + 𝑏 𝑙𝑛 1 + 𝑒

𝐽𝑢𝑥𝐸−𝐼0𝑏 ]

Simulated SBFH at different DIV

J = 5.8, 𝜏𝐷 = 0.15 s and U = 0.3.

J = 4.8, 𝜏𝐷 = 0.2 s and U = 0.28.

J = 6.8, 𝜏𝐷 = 0.1 s and U = 0.32

χ0 is the main factor to terminate the SB

X0 : Maximum available resources

SB initiates by a big enough positive feedback

𝑑𝐸

𝑑𝑡=

1

𝜏[−𝐸 + 𝑏 𝑙𝑛 1 + 𝑒

𝐽𝑢𝑥𝐸−𝐼0𝑏 ]

How does SB generate?

Faster recovery controls the firing patterns

E(H

z)

E(H

z)

𝑑𝑥

𝑑𝑡=

𝜒0−𝑥

𝜏𝐷− 𝑢𝑥𝐸

𝑑𝑢

𝑑𝑡=

𝑈−𝑢

𝜏𝑓+ 𝑈(1 − 𝑢)𝐸

How do reverberations generate?

χ0 is the main factor to terminate the SB

𝑑𝜒0

𝑑𝑡=

𝑋0−𝜒0

𝜏𝑥− 𝛽𝐸

How does SB terminate?

Physical Origin of slow recovery

Role of Astrocytes?

Astrocyte modulates neuronal activity by various gliotransmitters

KERRI SMITH, NATURE(468), Nov. 2010

Glial mechanism for Slow recycling

Blitz, Dawn M. et al. Nat. Rev. Neurosci. (5), 2004

Ratio of Glia to Neurons More glia higher intelligence ?

Exp Neurol. 1985 Apr;88(1):198-204.

Human astrocytes are larger and more complex than those of infra primate mammals, suggesting that their role in neural processing has expanded with evolution. To assess the cell-autonomous and species selective properties of human glia, we engrafted human glial progenitor cells (GPCs) into neonatal immuno deficient mice. Upon maturation, the recipient brains exhibited large numbers and high proportions of both human glial progenitors and astrocytes. The engrafted human glia were gap-junction coupled to host astroglia, yet retained the size and pleomorphism of hominid astroglia, and propagated Ca2+ signals 3-fold faster than their hosts. Long-term potentiation (LTP) was sharply enhanced in the human glial chimeric mice, as was their learning, as assessed by Barnes maze navigation, object-location memory, and both contextual and tone fear conditioning. Mice allografted with murine GPCs showed no enhancement of either LTP or learning. These findings indicate that human glia differentially enhance both activity-dependent plasticity and learning in mice

Cell Stem Cell 12, 342–353, March 7, 2013 ª2013 Elsevier Inc.

Implications

• SB might be a sign of too much feedback (connections) similar to some types of epilepsy

• Slow recycling mechanism might be carried out by astrocytes

• Training protocol should be done in a low active neural network. • Decrease number of glia

• 3D cultures

• Control network topology

• Need glia in True North?