complexity in the brain: emergent behavior from complex ... · intelligent behaviour. • neurons...

Complexity in the Brain: Emergent behavior from complex interactions within and between neurons

Stan Gielen

Content of presentation

• What is complex, intelligent behaviour ?– http://www.livesteaua.com/tags/robocup-videos/– http://www.robocup.nl/achievements.html

• The neural code: – Neuronal dynamics– Emergent behaviour of nonlinear interactions:

multi-stability and hysteresis• Distributed parallel processing

– The network connectivity is flexible by• Neuronal oscillations• Frequency modulation• Flexible task-dependent organisation

– What are the implicatons for control ?

Once upon a time in 1997 ….

IBM Deep Blue

Gary Kasparov

What is simple and what is difficult ?

Is chess more complex than playing soccer ?

http://www.livesteaua.com/tags/robocup-videos/http://www.robocup.nl/achievements.html

BrainComputing capacity : 10 petaflop

Storage capacity ~ 103 terabytes

Energy consumption ~ 30 Watt

1011 neurons

Time constant ~ 1 ms

Fujitsu K-Computer (nov 2011)Computing capacity : 10.5 petaflop*

Storage capacity ~ 10.5 terabyte

Energy consumption ~ 9.9 MW

88128 CPU-processors

Time constant ~1 ns

1 peta flop = 10^15 Floating Point Operations

The neural code

Currentcausing a magnetic field

Dipole,causing an electric field

EEG

MEG

Donders Centre for Cognitive Neuroimaging

~ 100.000 times weaker than earth magnetic field

You can get much further with a kind word and a gun, than with a kind word alone(Al Capone)

You can get much further with a kind word and a gun, than with a kind word alone(Al Capone)

You can get much further with experiment and theory, than with experiment alone(Computational NeuroScience group, Nijmegen)

Hodgkin-Huxley model

Fast variables• membrane potential V• activation rate for Na+ m

Slow variables• activation rate for K+ n• inactivation rate for Na+ h

-C dV/dt = gNam3h(V-Ena)+gKn4(V-EK)+gL(V-EL) + I

dm/dt = αm(1-m)-βmm

dh/dt = αh(1-h)-βhh

dn/dt = αn(1-n)-βnnddt

ddt

Neuron at rest

-70 mV

IVVW 3

3

)(1 aVb

W

W

V

-70 mV

IVVW 3

3

)(1 aVb

W

W

V

-70 mV +40 mV

Neurons are nonlinear oscillators

Fast variables• membrane potential V• activation rate for Na+ m

Slow variables• activation rate for K+ n• inactivation rate for Na+ h

-C dV/dt = gNam3h(V-Ena)+gKn4(V-EK)+gL(V-EL) + I

dm/dt = αm(1-m)-βmm

dh/dt = αh(1-h)-βhh

dn/dt = αn(1-n)-βnn

Multi-stability and parallel processing

Intra-cellular signaling

External input from other cells

nucleus

Ca2+

Calcium store

Cells reveal non-linear behavior

• Cell mitosis• Gene-expression and protein synthesis (e.g. pancreas) • Folding/unfolding of proteins (hormone secretion)

Discrete statesOnce started: complete it

Various stages of growth

Various stable states of cells

Membrane potentialCalcium oscillations

Caex

GCaLClex

GCl(Ca) ATPPMCA pump

Caer

ATP

SERCA pump

IP3R

Coupling : excitable membrane and intracellular calcium oscillations

Stability analysis

)( )( SocCaClCaleakKm

m IIIIIdTdVC

mmdtdm

mm )1()55( mVVhmGI CaCa

mmdtdh

hh )1(

dtBCadIIIJII

dtdCa

SERCACalk

CaERIPPMCA

Calk

Cahm

cyt ][)(3,

2

SERCACalk

CaERIP

ER IIIdt

dCa

)(3

2

wwdtdw

ww )1(

BCakCaBCaTkdtBCad

offcytBon 2][][))(( txf

dtxd

Poincaré map

)(~ tx

)()(~)( tytxtx

)( 1tx

)( 1 Ttx

)(~ tx

The map M : CnCn with

can be written in diagonal form with eigenvalues or Floquet multipliers with

Stability requires

)())(( TtxtxM

ses 2

s

0)( s1|| s

0))(~( txfdtxd

Multi-stability and hysteresis

Gielen et al., Phys Rev Lett 2009

Multi-stability and hysteresis

Conclusion

• In a network of cells with the same conditions everywhere, (clusters of) cells can be in different states (multi-stability) depending on the past (hysteresis).

• Multi-stability allows that subsets of neurons in a network can be in different states (parallel processing !)

• Hysteresis ensures that, once a process is started, it is completed, even if external input changes.

Liley model

1

)1(1)(

)()()(~

)(~

~,~

,)()(

)()()(

ˆ)(2

maxabs

max

,

l

ll

lklk

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llll

lklklllklklk

lklklk

lk

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lk

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eqlk

keqlk

klk

lkiel

klkkrk

kk

eSrSthS

tptthSNe

tIdtd

dtd

ehh

thhth

tIththhdtdh

Liley et al., Phys Rev E 2007

P4P3O2O1FzCzPz

1 s70 V

Brain rhythmsEyes closed

Alpha-rhythm (about 10 Hz)

Oscillatory activity in the brain at 40 – 80 Hz

Hardware of the brain and functional connectivity

How is the connectivity modulated to tune the brain for each particular task ?

• dynamic interactions

Canolty et al. Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies, PNAS 2010

Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies

Dynamic interactions between neurons

1. Plasticity by learning• time scale seconds, hours, days, ….

2. Spike timing dependent plasticity• Time scale milliseconds to second• bottom-up process

3. Modulation of excitability by other neurons• Time scale tenth of millisecond• Top-down process• Responsible for rhythmic oscillations

Human Brain Mapping 30:1791-1800 (2009)

Role of alpha-activity

Hypothesis : information is gated by inhibiting task-irrelevant regions.

Functional inhibition is reflected in oscillatory activity in the alpha band (8–13 Hz).

Human Brain Mapping 30:1791-1800 (2009)

Larger alpha-activity: more false alarms !

Alpha activity reflects a state of reduced perception

We can predict false alarms !

Hypothesis : information is gated by inhibiting task-irrelevant regions. Thefunctional inhibition is reflected in oscillatory activity in the alpha band (8–13 Hz).

Alpha-activity after rehearsal compared to that in “forgotten” condition

Inhibition is important in a word rehearsal taskHuygensgebouw


Inhibition is important in a word rehearsal task


Inhibition is important in a word rehearsal taskHuygensgebouw

Dorsal = “WHERE”

Ventral = “WHAT

Activity in posterior cortical areas (dorsal stream)

Identification Orientation

Selective inhibition of dorsal pathway for tasks requiring ventral stream

Alpha activity is a mechanism to inhibit particular brain areas

What modulates the alpha activity ?

Increase of Theta before a good response

OOHPS !

Theta activity from frontal cortex is anti-correlated with alpha posterior

alpha (10 Hz)

Theta (4-6 Hz)

Summary: where are we ?1. Nonlinear system theory is the key to understanding complex

intelligent behaviour.• Neurons and neuronal interactions are nonlinear systems with

complex and highly interesting emergent properties:More is different !




2. We understand the basic principles of• neuronal dynamics• dynamics of neuronal interactions• simple emergent properties




2. We understand the basic principles of• neuronal dynamics• dynamics of neuronal interactions• simple emergent properties

3. We see a glimpse of• the basic principles of the neuronal code (neuronal firing, neuronal

oscillations, neuronal ensembles, flexible distributed parallel processing)

• how intelligent behaviour is represented in the brain4. We have no clue as to how the network is modified for the job and how the

connections between neuronal regions are modulated to optimize the network architecture.

Challenges:

1.Understanding self-organization and changes in network architecture at various hierarchical levels by bottom-up and top-down processes2.Understanding the opportunities and limitations of the neural wetware (e.g. memory, decision making)

(see paper by Barabási)

What is required is a multi-disciplinary team of research groups to address complexity

Thank you for your attention !

Special thanks to my collaborators

Magteld Zeitler Martin Krupa Ingo Bojak

Functional Disconnection of Frontal Cortex and Visual Cortex in ADHD

index

middle

Communication by coherence (CTC) hypothesis

Synchronization of neuronal activity provides a label for cell assemblies

Canolty et al. Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies, PNAS 2010

Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies

Modulation of Gamma by Theta Rhythm

Short reaction time

Long reaction time

complexity in the brain: emergent behavior from complex ... · intelligent behaviour. • neurons...

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