excitable bursting in the rat neurohypophysis · excitable bursting in the rat neurohypophysis...
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Excitable Bursting in the Rat Neurohypophysis
Peter RoperMathematical Research Branch,
NIDDK, National Institutes of Health,
Bethesda, MD
March 4, 2005
The hormone vasopressin (AVP) regulates:
• blood osmolality (blood concentration)
• blood pressure
• kidney function
• liver function
Secretion increases during dehydration – mediated by a net depolarizationof the cell.
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Hypothalamus
Pituitary
2
AVP/OT
Neurohypophysis(Posterior Pituitary)
PituitaryStalk
Supraoptic andParaventricular Nuclei
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.
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Dendrites
Soma Axon
Ca
pil
lary
Hypothalamus Pituitary
HormoneRelease
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Somato-dendritic secretion of autocrine andparacrine messengers
.
.
.........
Ca
pil
lary
HormoneRelease
Dynorphin
Vasopressin
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Autoregulatory somato-dendritic release
��
AVPDynorphin
�-receptor
DenseCore
Granule
Internalization
Binding
Unbinding
Dockingand
Release
��
�
V1-A receptor
�
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Basal firing is slow-irregular
• Poisson distributed spike train
• Spikes evoked by random synaptic input
• Firing rate ≤ 1.5Hz
0 0.4 0.8 1.2
40mV
-57mV
Time (s)
MembranePotential (mV)
• Each spike triggers secretion of AVP into the blood 7
Dehydration alters the firing pattern
0 0.4 0.8 1.2
40mV
-67mV
Time (seconds)
MembranePotential (mV)
Slow Irregular
(<1.5Hz)
-65mV
0 20 40 60 80
Time (seconds)
40mV
Fast Continuous
(>3Hz)
-63mV
0 20 40 60 80
40mV
Time (seconds)
Phasic(>3Hz)
Increasing Stress
Transient Response
• AVP cells switch to a phasic pattern
• under extreme stress, AVP cells further switch to fast-continuous
• single, non-repeating bursts can be evoked in slow-irregular AVP cells8
Ionic CurrentsTrans-membrane currents mediated by voltage and/or calcium sensitive ionchannels
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Mathematical ModelHodgkin-Huxley type system with a simple calcium dynamics
− CdV
dt=
Spiking Currents︷ ︸︸ ︷INa + ICa + IA + IK + IC
+Reset Currents︷︸︸︷
Ileak +Synaptic Input︷︸︸︷
Isyn
d[Ca2+]idt
= αICa(t)− γ([Ca2+]i − [Ca2+]rest
)I
Na
IK
Soma
ICa
IA
Ic
Na/Ca
K
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The DAPEach evoked spike is followed by a transient depolarization (DAP)
0 1.5 3 64.5
-65mV
5mV
Time (s)
DAP
which depends on calcium
0
10
20
30
-50 -49 -48 -47
Calcium(nM from rest)
DAP decay (mV)
-54
-50
-46
-42
0 2 4 6
Time (s)
0
0.25
0.5
0.75
1
0 2 4 6
Calcium(normalized)
Time (s)
V (mV)
�=1.851
�f=0.165
�s=1.683
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Modelling the DAP
Ileak = IK,leak + INa,leak
We model (Li and Hatton, 1997) the DAP by a transient (V - and)Ca2+ -dependent modulation of a persistent potassium current: IK,leak
IK,leak = (1−R) GK,leak (V − EK)
0.5
1
200 300 400
R
200 300 400
Increasing
CalciumIK,leak = 0IK,leak = max
100
0.5
1R
[Ca ]2+
i[Ca ]2+
i
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Comparing DAP’s from experiment and model
Time (seconds)
0 2 4 6
Time (seconds)
-62.6mV
0 2 4 6
10mV
MembranePotential
Membraneotential
88nM
0 2 4 6
10nM
CalciumConcentration
10mV
-65mV
0 2 4 6
10nM
CalciumConcentration
MembranePotential
Membraneotential
113nM
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Multiple DAP’s summate to a plateau that is above spike threshold:
-65mV
40mV
Evoked Spikes
Summed DAPPlateau Potential
40mV
Time (ms) Time (ms)
AppliedCurrent
0 100 200 300 400 5000 100 200 300 400 500
-65mV
and such plateaus sustain phasic bursts
0 4 8 12 16
20mV
Plateau
Rest
Time (s)
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0
5µm
�F/F
50%
25 mm
0 5 10 15 20
Time(s)
40mV
384
95
[Ca ]
(nM)
2+
i
Cell 00302B
-52mV
Calcium
• Reaches a plateau early in the burst
• Remains elevated until burst terminates
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Question: HOW does burst terminate?
.
.
.........
Cap
illa
ry
HormoneRelease
Dynorphin
Vasopressin
• AVP cells secrete an opioid – dynorphin – from their dendrites
• Dynorphin inhibits AVP cell activity
• Propose that effects of dynorphin increase during active phaseand clear during silent phase 16
Dynorphin agonists (U50-3):
• Inhibit the DAP
• Prevent bursting (Brown et al., 1999)
Dynorphin antagonists (BNI):
• Prolong durst duration (Brown, 1999)
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HOW does dynorphin act?
• We propose that dynorphin shifts the half-activation of R to higherCa2+ concentrations
200 300 400 200 300 400
IncreasingD
[Ca ]2+
i
500
[Ca ]2+
i
0.5
1
R
0.5
1
R
• Thus raising the plateau threshold while leaving [Ca2+]i unchanged
• Eventually plateau can no longer support spiking and cell falls silent –burst terminates
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Increasing
DDecreasing Both
and D
Increasing
Post-BurstDAP
(Slow depolarization)(Burst terminates)
Decreasing
[Ca ]2+
i
[Ca ]2+
i
[Ca ]2+
i
( )
[Ca ]2+
i
R
[Ca ]2+
i
R
[Ca ]2+
i
R
[Ca ]2+
i
R
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Dynamics of dynorphin and the κ-receptor
• D is augmented by ∆ when the cell fires the ith spike (say at time Ti)
• D decays exponentially between spikes
ddt
D = ∆δ(t− Ti)−1τD
D ∆ = constant
Upregulation of the κ-receptorPropose that ∆ increases as a function of D
ddt
D = ∆δ(t− Ti)−1τD
D ∆(D) = ∆0 + εD
Time
D
Active Silent
• Interpretation: dynorphin upregulates κ-receptor density
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Comparisons between real and model bursts
350
110
[Ca ]
(nM)
2+
i
10s
0
50%
F/F
-52mV
40mV
2384
95
10s
Somatic
[Ca ] (nM)2+
i
-65mV
40mV
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If cell depolarized far enough...
...phasic activity
40mV
40mV
0 100 200
-50mV
-50mV
0 40 80 120 160
Model
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Analysis: the Fast/Slow reduction
To analyze the phasic model – first split into fast and slow components
• fast: the spiking currents – INa, ICa, IK, IA, Ic
• slow : the plateau oscillation – [Ca2+]i and D
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Spiking currents (Ispike) pass through saddle-node bifurcationas plateau amplitude increased:
-60
-40
-20
0
20
40
V (mV)
-1 -0.5 0 0.5 1
R
PD
SN
HB
Rthresh
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Dissociation of SLOW from FAST nontrivial:
...the two subsystems are not autonomous
Instead write SLOW as a firing rate model and decouple subsystems withthis ansatz
d
dtC = ν(R)∆Ca −
1τCa
(C − Cr)
d
dtD = ν(R)∆D − D
τD
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Empirically ν can be fit to
ν ={
0 R ≤ Rthresh
Γ (R−Rthresh)γR > Rthresh
0
5
10
15
0 0.25 0.5 0.75 1
�
Firing Frequency (Hz)
Plateau Amplitude(Fraction of Maximum)
R
Iapp=0.5 Iapp=0
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and Rthresh is a linear function of Iosm
0
0.1
0.2
0.3
0.4
0 0.4 0.8 1.2
Rthresh
Iapp
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Nullclines
0
2
4
6
100 150 200 250 300 350
0
10
20
100 200 300 400 500
I =app 0.0
Iapp= 5.5
Ci= 0
. D = 0
.
Ci= 0
.
D = 0
.
0
5
10
15
100 200 300 400
Iapp= 3.0
Ci= 0
. D = 0
.
(i) (ii)
(iii)
Ci (nM)
D
Ci (nM)Ci (nM)
DD
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Sub-threshold behaviour
Excitable Bursting – Iapp = 0
• Stable fixed point at D = 0 and [Ca2+]i = [Ca2+]rest.
• System is excitable – single oscillations can be evoked by moving thesystem above threshold (∆Ca2+ > 30nM).
200
300
400
500
600
0 10 20 30 40 50 60
Time (sec)
0
2
4
6
8
Ci
D
0
2
4
6
100 150 200 250 300 350
Ci= 0
.
D = 0
.
Ci(nM)
D
• Single oscillations are equivalent to evoked bursts in the full model.
• Threshold is close to the calcium influx due to 3 spikes.
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Super-threshold behaviourIf the applied current (Iapp) is increased above threshold, then the fixedpoint loses stability and the system starts to oscillate – phasic activity.
200
400
600
800
0 20 40 60 80
0
5
10
15
20
Time (sec)
Ci
D
0
5
10
15
100 200 300 400
Ci= 0
. D = 0
.
Ci(nM)
D
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Firing transitions
• stable steady state V phasic oscillation:slow irregular V phasic V saddle-node bifurcation
• phasic oscillation V stable steady state:phasic V fast continuous V Hopf Bifurcation
100
200
300
400
Ci
0 2 4 6
Iapp
SNIC
HB
oscillatory burstingsubthreshold/excitable bursting
fast-continuous
firing
Ithresh
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Conclusions
We have constructed the first qualitative and quantitative model of theelectrical activity of vasopressin MNC’s
We propose that phasic activity must be driven by an auto-regulatorymechanism, and that dynorphin/κ-opioid receptor secretion is a likelycandidate for this mechanism.
Our model reproduces:
• single spikes, basal firing and the fine structure of bursts
• the sequence of firing patterns observed during physiological stress
• (the transient discharge that occurs during sudden stress)
We have also shown that the cells have both excitable and phasic burstingmodes: possibly explaining the difference between in vivo and in vitrorecordings.
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Collaborators
Theory
Arthur ShermanJohn Naradzay (UBC)
Experimental – University of Tennessee, Memphis
Bill ArmstrongJoseph Callaway (calcium imaging)Ryoichi Teruyama (electrophysiology)Talent Shevchenko (electrophysiology)Chunyan Li (electrophysiology)
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