excitable bursting in the rat neurohypophysis · excitable bursting in the rat neurohypophysis...

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.

1

Hypothalamus

Pituitary

2

AVP/OT

Neurohypophysis(Posterior Pituitary)

PituitaryStalk

Supraoptic andParaventricular Nuclei

3

.

.

.

.

.

.

.

.

.

.

.

Dendrites

Soma Axon

Ca

pil

lary

Hypothalamus Pituitary

HormoneRelease

4

Somato-dendritic secretion of autocrine andparacrine messengers

.

.

.........

Ca

pil

lary

HormoneRelease

Dynorphin

Vasopressin

5

Autoregulatory somato-dendritic release

��

AVPDynorphin

�-receptor

DenseCore

Granule

Internalization

Binding

Unbinding

Dockingand

Release

��

�

V1-A receptor

�

6

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

9

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

10

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

11

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

12

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

13

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)

14

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

15

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)

17

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

18

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

20

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

22

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

23

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

26

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

27

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

28

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.

29

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

30

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

31

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.

32

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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