““Can we predict synchrony and Can we predict synchrony and asynchrony in networks coupled by asynchrony in networks coupled by multiple dendritic gap junctions?”multiple dendritic gap junctions?”

Frances K. SkinnerFrances K. Skinner

Toronto Western Research InstituteToronto Western Research Institute

University Health Network and University Health Network and

University of TorontoUniversity of Toronto

New York UniversityNew York University

April 13, 2008April 13, 2008

From Scholarpedia:Mathematical Biology article of

Frank Hoppensteadt

• “highly interdisciplinary nature” • “barriers to collaborations between mathematicians and biologists” • “a shift from mathematical analysis to computer simulation due mostly

to improvements in computer power and accessibility.. With the shift being made possible to include more information in models and still derive useful insights from them.”

Especially in neuroscience with all the details being uncovered, increasingly sophisticated techniques etc. these comments are very timely. With increasing specialization and interdisciplinarity and potential moving apart of mathematical and biological sciences (or separation of viewpoints) we organized a Theoretical Neuroscience Minisymposium at 2006 Society for Neuroscience meeting, one of the aims being to help counteract this.

Interneuron Heterogeneity

Domain-specific innervation of hippocampal interneurons

Different types of interneurons containing calcium-binding proteins and neuropeptides

purple –laminaewhere axonal arbortypically extendsturquoise indicatesthat other interneuronsrather than principalcells are targets

apical

basal

McBain and Fisahn NRN 2001

• General challenge – how to best consider various neurobiological details.

• Specific challenge – understanding the contribution of electrical coupling in different contexts.

• Outline of Talk: background, discussion of some of our previous work, and then get to question posed for this talk.

““Can we predict synchrony and Can we predict synchrony and asynchrony in networks coupled by asynchrony in networks coupled by multiple dendritic gap junctions?”multiple dendritic gap junctions?”

Frances K. SkinnerFrances K. Skinner

Toronto Western Research InstituteToronto Western Research Institute

University Health Network and University Health Network and

University of TorontoUniversity of Toronto

New York UniversityNew York University

April 13, 2008April 13, 2008

Acknowledgements

Tariq Zahid

Fernanda Saraga, Leo Ng

NSERC of Canada

Computing support – RIS of UHN

The hippocampus (part of medial temporal lobe) is an intensely studied region of the brain because:

• It is associated with memory and learning (i.e., LTP, LTD), epileptic seizures, and neurogenesis.

• It exhibits a wide range of population rhythmic activity patterns (<1 to >200 Hz) that are associated with various behavioural states.

• It is amenable to experiment, retaining its synaptic circuitry and thus population activities in the slice.

EEG activities of mouse hippocampus

Sharp wave-ripples

Electrode location Theta-Gamma SPW-ripples

Gillis et al., J. Neurosci. Meth. (2005)

Spontaneous Rhythmic Field Potentials (SRFPs)(Liang Zhang’s lab; Wu et al. J Physiol 2002, J Neurophysiol 2005)

Blockade of field rhythms and pyramidal IPSPs by GABA-A receptor antagonist

rhythmic activities also dependent on electrical coupling (gap junctions)

Background

Electrical coupling (i.e., gap junctions) is present in much of the mammalian brain (e.g., inferior olive, striatum, neocortex, hippocampus, retina, thalamus).

In particular, gap junctions occur between inhibitory cells, often of the same type,and can be located at sites quite distant (> 200 μm) from the soma.

Interneurons represent 10-20%

of the neuronal population but may provide the precise temporal structure

necessary for ensembles of

neurons to perform specific functions.

- Buzsáki and Chrobak, 1995

Interneuron Heterogeneity

Domain-specific innervation of hippocampal interneurons

Different types of interneurons containing calcium-binding proteins and neuropeptides

purple –laminaewhere axonal arbortypically extendsturquoise indicatesthat other interneuronsrather than principalcells are targets

apical

basal

McBain and Fisahn NRN 2001

Background

From Fukuda & Kosaka, J Neurosci 2000

Gap junctions located farfrom cell bodies, atnon-proximal sites

(basket cells in hippocampus)

Gap junctions can bemodulated

Inhibitory cells have active dendrites, spikes can begenerated in dendrites

Dendrodendritic Gap Junctions

Fukuda & Kosaka, J Neurosci 2000

Model (Hippocampal Basket Cell)

50 mV

100 ms

Saraga et al., J Neurophysiol 2006

Morphology from Gulyas et al.(1999)

372-compartmentmodel developed

in NEURON

Passive dendrites

WB used for kinetic model basis, Martina and Jonas (1997), Martina et al (1998)used as conductance value basis and spike characteristics and electrophysiological

responses from Morin et al. (1996) and van Hooft et al. (2000).

Anatomical distance to soma (m)Ele

ctro

ton

ic d

ista

nce

to

so

ma

(L

)

Vin

Anatomical distance from soma (m)

Ele

ctro

ton

ic d

ista

nce

fro

m s

om

a (

L) Vout

s d d

Vin =0.25

Vout=0.14

“Reduced” 3-compartment model

based on matching electrotonic length from soma (Vout)

100 300500 0

0.04

0.12

0.4

1.2

0 100300 500

PRCs calculated usingXPPAUT (Ermentrout, 2002)

0.5%

1.5%

10%

1%

50 mV

10 ms

s d d d ds

Voltage along dendrite

(Distal) phase response curves (PRCs)

Using the reduced model geometry

Phase

Ph

ase

Sh

ift

Predicted Network Dynamics75

50

25

0

28

26

24

23

20

18

16

14

0.1 1 10 100

% Active

Intr

insi

c F

requ

ency

(H

z)

% P

hase

Lag

LOW MEDIUM HIGH

Phase lags determined frominteraction functions calculatedusing XPPAUT (Ermentrout, 2002)

Weakly coupled oscillatortheory used to define threedifferent dynamic regions-LOW, MEDIUM, HIGHthat refer to PRCs with

particular characteristics(e.g., negative PRCs

for MEDIUM)

Results %

Pha

se L

ag

g gap

Simulations confirm theoretical predictions

% Active

0.1 1 10 100

75

50

25

0

% Active

Intr

insi

c F

requ

enc

y (H

z)

% P

hase

Lag

LOW MED HIGH

•“Weak coupling” is about 10 pS (comparing predicted and simulated)• Compare full and reduced model phase lag values to“define” synchronous and asynchronous• Synchronous is 10% or less phase lag, asynchronous otherwise

Cell 1: 15% basal attenuation, 2% apical attenuationCell 2: 8% basal attenuation, 8% apical attenuationCell 3: 6% basal attenuation, 14% apical attenuation

CELL 3

basal

apical

apical

basal

Cell 1, apical coupling(multistability)

Beyond weak coupling

Beyond weak coupling

Beyond weak coupling

Discussion and Conclusions• PRC skewness quantifications can be used to predict whether

synchronous or asynchronous modes occur in electrically coupled basket cells.

• Averaged PRCs can be used to predict modes for coupling at multiple sites.

• Predictions cannot be made under all circumstances and multistability can occur.

• Different apical and basal attenuation (due to different channel densities) allow more ‘robust’ asynchrony to occur with coupling on the more attenuated dendritic side.

• Network couplings that produce asynchrony (as compared to synchrony) with weak coupling encompass more dynamic richness (i.e., range of possible phase lags) with gap junction conductance changes.

• Thus, gap junction coupling may be able to tune networks in and out of synchronous activities if asynchrony with weak coupling is predicted.

the end

• Thank you!