Modelling the
model systems
Gareth Leng
Once upon a time, neurons were thought to
communicate by transmitters that excited or
inhibited other neurons.
These signals were regulated
by action potentials that evoked
transmitter release at synapses,
with short lasting effects.
Information processing consisted of sophisticated
spatio-temporal patterns of activation.
GABA, glutamate, ACh and the catecholamines
Peptides in the brain…..
Oxytocin, vasopressin, cholecystokinin, opioids, tachykinins,
GHRH, LHRH, TRH, CRF, somatostatin, NPY, orexins, substance P, apelin, CART,
AgRP, PACAP, galanin, VIP, urocortin, PrRP, neurotensin, neuromedins,
ANP, BNP, angiotensin, BDNF, ghrelin, MCH, a-MSH…. >100 so far
Vasopressin Cells
Supraoptic nucleus
Neural lobe
Spike activity
Firing rate
30
Spikes/s
0
1 min
Phasic firing is efficient for vasopressin
secretion
Secretion maximal at ~13 Hz
(Dutton & Dyball 1977)
… increases with burst duration
up to ~20 s (Shaw et al. 1984)
… fatigues at longer burst
durations, reversed by silences
Bicknell et al. (1984)
In the neural lobe…
9,000 oxytocin cells
and
9000 vasopressin cells
project there.
9,000 vasopressin cells
1,840 endings
436 swellings
Jean Nordmann (1976)
John Morris (1976)
9,000 vasopressin cells
Jean Nordmann (1976)
John Morris (1976)
1,840 endings
2240 vesicles
436 swellings
1.48 x 1010 vesicles
258 vesicles
Jean Nordmann (1976)
John Morris (1976)
1.48 x 1010 vesicles
Each vesicle
contains 85,000
molecules of
vasopressin
How much vasopressin is released
per second?
Plasma vasopressin concentration (pg/ml )
basal conscious
dehydrated, conscious
basal anaesthesia
max stimulated
1
10
85
220
Total in circulation at basal levels (in 60 ml) = 60 pg.
Half-life ~2 min.
Needs secretion rate of 0.35 pg/s
Daily basal secretion is ~ 30 ng
(content is enough for ~ 6 days of modest dehydration)
How many vesicles per spike?
basal anaesthesia
4 spikes/s
max stimulated
10 spikes/s
23 vesicles/cell/s
~5 vesicles/cell/spike
58 vesicles/cell/s
6 vesicles/cell/spike
2000 release sites
so at any one site it takes
about 400 spikes to release
one vesicle, on average
• Peptide vesicles are
found in synapses….
• But not many
Confocal images of dendrites of GnRH neurons
Most peptide is in
dendrites.
Dendrites are
>85% of the
cell volume
Campbell, R. E. et al. Endocrinology 2005;146:1163-1169
Intermittent, stereotyped bursts
Intra-mammary
pressure
1 min
0.5 s
Oxytocin cells
Suckling
40
CCK
Firing rate
(spike/s)
0
0
5
10
15
Time (min)
Vasopressin cells
40
0
0
10
20
Time (min)
30
20
Oxytocin facilitates reflex milk-ejection
• Oxytocin itself
facilitates bursting
• Apparently a positivefeedback system
• But why does only
suckling evoke bursts
?– other ways of
activating the cells
don’t do this
Oxytocin
(3 ng i.c.v.)
1 min
Oxytocin
Hypertonic saline infusions raise the firing rate of
oxytocin neurones linearly
16
10
12
CCK
8
Firing rate (Hz)
5
4
0
0
0
0
25
50
75
Time (min)
100
300
125
NaCl infused (mg)
The bursting looks as though it might
result from positive-feedback – but
increasing the mean activity of oxytocin
cells paradoxically reduces bursting
activity
Suckling
Spikes/s
40
CCK
20
0
5 min
Suckling has small, mixed effects on background activity, it
tends to inhibit active cells and activate silent cells. Bursts
occur every 3-10 min and are approximately synchronised
amongst all oxytocin cells.
There is no synchrony in the background activity, but near
bursts there is a weak cross-correlation between some pairs of
cells, and increased irregularity of firing
Confusingly, directly inhibiting oxytocin
cells can trigger bursts (only happens
during suckling)
80
Frequency
(spikes/s)
GABA applied to SON
40
0
0
Time (s)
600
Moos, J. Physiol., 1995
Suckling is necessary for bursting….
Irritatingly, sometimes a single burst will
occur after the suckling stimulus has been
removed
Suckling stimulus
20
Spikes/s
10
0
Strangely, although most oxytocin cells burst then
fall silent, some fall silent without bursting
10mm Hg
In vivo
Spikes/s
8
0
0
25
50
Time (s)
75
100
The spike-response model
• EPSP and IPSPs are represented as exponentially decaying pulses
• These are generated randomly
• When the simulated membrane potential crosses a “spike threshold” a
spike is generated.
• After each spike, the cell is transiently hyperpolarised /depolarised
Spikes
20mV
EPSP
2s
Mean membrane
potential –75mV
Mean membrane
potential –68mV
Spontaneous spiking in oxytocin cells is governed by a random
(Poisson) process subject to a post-spike refractoriness
1
Incidence
0
0
200
400
Interspike interval (ms)
0.02
Hazard
0
0
100
Time since spike (ms)
200
Hyperpolarising
afterpotential
(HAP, 20 ms)
Post-spike potentials
Hyperpolarising
afterpotential
(HAP, 20 ms)
after-hyperpolarisation
(AHP, ~2 s)
Model parameters
•
•
•
•
Spike threshold (mV),
Resting potential
EPSP and IPSP height (mV), half-life (ms), rates (/s)
HAP, described by exponentially decaying change in
spike threshold
0.03
oxytocin cell + model fit
0
0
100
200
300
Interspike interval (ms)
400
500
A single model will fit the interspike interval distributions of
oxytocin cells at different firing rates following infusion of
hypertonic saline
800
600
Spikes/ bin
400
200
0
0
100
200
Interspike interval (ms)
Leng et al. (2001) J. Neurosci 21:6967-77
300
But does this help?
0.04
0.03
Within bursts
Frequency
Within bursts, the inter-spike
intervals are consistently shorter
than almost all intervals seen in
other conditions
0.02
Between bursts
0.01
0
0
0.1
0.2
0.3
Interspike interval (s)
0.4
0.5
Oxytocin is made in the supraoptic nucleus.
These cells send their axons to the pituitary
gland, where oxytocin is released into the blood
The Supraoptic
Nucleus
Oxytocin facilitates reflex milk-ejection
• dendro-dendritic
interactions
Oxytocin
(3 ng i.c.v.)
1 min
• dependent on
oxytocin release
• apparently a
positive-feedback
system
Oxytocin
Microdialysis
To measure local
oxytocin
SON
Optic
Chiasm
40
Hypertonic
saline
Oxytocin
pg/30min
500
Plasma
SON
ip HS
250
0
0
30 min
SON
Optic
Chiasm
4
Oxytocin
pg/30min
2
0
10Hz
50Hz
Neural stalk stimulation (spike activity)
evokes oxytocin release into blood, but not
release from dendrites.
SON
Optic
Chiasm
**
4
Oxytocin
pg/30min
TG
2
0
10Hz
50Hz
50Hz
Thapsigargin primes dendritic oxytocin release
(Ludwig et al Nature 2002)
Axons
Inputs
Peptide
Dendrites
Dendritic release not
activated by electrical Peptides trigger
activity
release independently
of electrical activity and…
…prime dendritic
stores
Priming
Nature (2002) 418.
J. Neurosci. (2003) 23.
Dendritic release
coupled to
electrical activity
Oxytocin cells, coupled via dendrites
Dendritic bundles
~3000 oxytocin cells
~2 dendrites per cell
Each dendrite is part of a bundle
of 3-5 dendrites
Each cell connected to ~8 others
OT cells
Initial network had just 15 cells; current
network has 384 cells
Dendro-dendritic connections
Sparse and random
EMERGENT BEHAVIOUR
Behaviour in a complex non-linear system that arises
“spontaneously” above a critical level of complexity
Bursting in the model
60
40
Frequency (sp/s)
20
0
60
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
40
20
0
60
40
20
0
Time (min)
Soma
Suckling input
bundle
V (mV)
r
×
r
THAP, TAHP
TOT (+)
synaptic input
EC (-)
0
-40
THAP (mV)
15
10
5
0
TOT (mV)
40
TAHP (mV)
-80
20
0
0
-10
-20
245
250
Time (s)
255
260
0.04
0.03
Frequency
Within bursts
0.02
Between bursts
0.01
0
0
0.1
0.04
0.2
0.3
Interspike interval (s)
0.4
0.5
Frequency
0.03
Within bursts
0.02
Between bursts
0.01
0
0
0.1
0.2
0.3
Interspike interval (s)
0.4
0.5
Milk-ejection bursts; experiment and model
100
100
Frequency (sp/s)
80
Frequency
(spikes/s)
60
40
20
0
0
20
40
0
60
100
10
20
30
40
50
Spike number
60
Frequency (sp/s)
100
spikes/s
0
0
10
1
0
20
40
Time (s)
60
0
1
2
3
Tim e (s )
4
5
Increasing the excitatory input rate in the model …
results in the termination of bursting
Frequency (sp/s)
40% increase in excitatory input
Model
60
40
20
0
400
Frequency (spikes/s)
40
In vivo
Glutamate
G lu
ta m a te
600
800
1000
1200
T im e (s )
1400
1600
1800
Hypertonic saline
20
0
0
1000 Time (s)
2000
3000
Moos, J. Physiol., 1995
Model
Frequency (sp/s)
Enhancing inhibitory activity promotes bursting
GABA
60
40
20
0
0
100
200
300
400
500
600
700
800
Time (s)
This paradoxical effect of triggering milk-ejection bursts was also described in vivo
In vivo
Frequency (sp/s)
80
GABA
40
0
0
Time (s)
600
Moos, J. Physiol., 1995
Suckling is necessary for bursting….
but a single burst can occur after the pups are removed
Suckling stimulus
60
40
20
0
Spikes/s
Model
60
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
40
20
0
60
40
20
0
In vivo
Spikes/s
Time (min)
20
10
0
Suppressing afferent excitation by OT silences OT cells
In vivo
10mm Hg
Model
40
Spikes/s
20
Spikes/s
8
0
10
0
Spikes/s
25
50
Time (s)
75
100
5
0
2
4
6
Time (min)
8
10
no burst activity preceding milk ejection but typical “post burst” silence
post- burst silence is not simply a consequence of activity-dependent AHP
Activity becomes more irregular
and more cross-correlated approaching bursts
Average ifr
Average cross-correlation
0.020
0.91
0.018
0.90
0.016
0.89
0.014
0.88
0.012
0.010
0.87
0.86
-100
0.008
-80
-60
-40
-20
Time from burst (s)
0
20
-100
-80
-60
-40
-20
0
20
Time from burst (s)
: consequence of the progressive strengthening of the interactions
between neighbouring cells in the network topology
Mean of 136 bursts, 48 cell network, 8 dendrites per bundle
Random connectivity is essential...
Modifying the mean number of dendrites per bundle affects bursting
8 dendrites/bundle
3 dendrites/bundle
60
40
Frequency (sp/s)
20
0
60
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
40
20
0
60
40
20
0
Time (min)
A minimum of 8 random connections are needed
to ensure that OT cells are all interconnected
Random connectivity is essential...
350
350
350
350
300
300
300
300
250
250
250
250
200
200
200
200
150
150
150
150
100
100
100
100
50
5050
50
00 00
160
210
135
135
162
215 164140
140
166
220
168
170
225
145
145
172
230
174150
176
150235
Time
Time(s)
(s)
(s)
Time
(s)
Time
Synchronous activation of release within the brain will
lead to a “tidal wave” of oxytocin through the forebrain
• Peptide release from a given nerve ending is very rare
• The peptide released at a single event is much more than needed for
synaptically localised action
• Peptides are very long lasting
• Peptides can “bind neurones together” into co-ordinated activity
• This can lead to co-ordinated peptide release that can spread to
distant targets
• Peptides affect the functional wiring of neuronal circuits
• They re-programme the brain.
In the brain….
• The hypothalamus has 9000
oxytocin cells and ~12 ng
oxytocin – in ~11,000 vesicles
per cell.
• 1 vesicle released/cell every
1000s = ~0.001 pg/s.
• If the half-life is 30s, and the
distribution volume of ECF is
1µl (i.e. ~the whole
hypothalamus)….
• This will sustain an average
concentration of >50 pg/ml
(throughout the hypothalamus).
• Effective concentrations in the
periphery are ~ 10 pg/ml
Before
During labour, oxytocin can
trigger maternal behaviour
After
Oxytocin may have a role in
bonding between sexual partners
Prairie Vole
Sociable
Biparental
Monogamous
Montane Vole
Antisocial
Minimally Parental
Promiscuous