“can we predict synchrony and asynchrony in networks coupled by multiple dendritic gap...
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““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!