Biophysical model of AMPA receptor trafﬁcking and its ...

Biophysical model of AMPA receptortrafficking and its regulation during

LTP/LTDBerton A. Earnshaw and Paul C. Bressloff

Department of Mathematics, University of Utah

Salt Lake City, Utah 84112

Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.1/23

The brain: unparalled parallel computer

1011 neurons

∼ 10 − 10, 000

synapses/neuron

network is plastic

regulates behavior

can learn and remember!


Mathematical Neuroscience at Utah

Cognition↑

Systems↑

Cortical Areas↑

Small Networks↑

Neurons↑

Dendrites↑

Synapses


The Synapse

E.R. Kandel et al. Principles of Neural Science. 2000.M.B. Kennedy. Science 290 750–754 (2000).


Synaptic transmission

E.R. Kandel et al. Principles of Neural Science. New York: McGraw-Hill. 2000.


LTP/LTD: Long-term potentiation/depression

T.V.P. Bliss and G.L. Collingridge. Nature 361 31–39 (1993).S.M. Dudek and M.F. Bear. PNAS 89 4363–4367 (1992).


AMPA receptor traffickingExo/endocytosis τ ∼10-30min

Lateral diffusionBrownian in ESM: ∼0.1µm2/sConfined in PSD: ∼0.01µm2/sPSD is confinement domainSpine neck impedance

Immobilization by scaffolding

Synthesis/degradation

M.D. Ehlers. Neuron 28 511–525 (2000).M. Passafaro et al. Nat. Neurosci. 4 917–926 (2001).

C. Tardin et al. EMBO J. 22 4656–4665 (2003).L. Groc et al. Nat. Neurosci. 7 695–696 (2004).

M.C. Ashby et al. J. Neurosci. 26 7046–7055 (2006).

DEG

END

EXO

EXO

PSD

AMPA receptor

scaffolding protein


Model – Spine geometryCylinder

Radius: r0 = 0.2µmLength: z0 = 1.0µmBody: ESM (AESM = 1.257µm2)Top: PSD (APSD = 0.1257µm2)Bottom: dendrite junction

Diffusion is fastTime constant of diffusion:τ = A/D ∼ 10sOther time constants: τ ≥ 10min⇒ uniform concentrations

ESM

r0

z0

PSD

r

z


Model – TraffickingP,Q: Free/Bound AMPAR concentration in PSD

R: Free AMPAR concentration in ESMα, β: Binding/unbinding rateσ, k: Exo/endocytosish,Ω: PSD-ESM/ESM-dendrite hopping rate

PSD ESM

α

β

kσ

P RQ

h

h

Ω

Ω

INTRACELLULAR

DE

ND

RIT

E

σ


Model Equations – AMPAR in PSD

dPI

dt= −αI(L − QI − QII)PI + βIQI −

hI

APSD

(PI − RI)

dPII

dt= −αII(L − QI − QII)PII + βIIQII −

hII

APSD

(PII − RII)

+σII

APSD

dQI

dt= αI(L − QI − QII)PI − βIQI

dQII

dt= αII(L − QI − QII)PII − βIIQII

Subscripts: I = GluR1/2, II = GluR2/3

L = scaffolding protein concentration (e.g. PSD-95)Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.10/23

Model Equations – AMPAR in ESM

dRI

dt=

hI

AESM

(PI − RI) −ΩI

AESM

(RI − RI) − kIRI +σI

AESM

dRII

dt=

hII

AESM

(PII − RII) −ΩII

AESM

(RII − RII) − kIIRII

R = background AMPAR concentration in dendritic spine


Blocking exo/endocytosis

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

t [min]

nu

mb

er o

f re

cep

tors

in P

SD

TotalBound GluR1/2Free GluR1/2Bound GluR2/3Free GluR2/3

C. Luscher et al. Neuron 24 649–658 (1999).

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

90

t [min]

nu

mb

er o

f re

cep

tors

in P

SD

TotalBound GluR1/2Free GluR1/2Bound GluR2/3Free GluR2/3


LTP trafficking

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

90

100

t [min]

nu

mb

er o

f re

cep

tors

in P

SD Total

Bound GluR1/2Free GluR1/2Bound GluR2/3Free GluR2/3Scaffolding

D.H. O’Connor et al. PNAS 102 9679–9684 (2005).Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.13/23

Exchange of GluR1/2 with GluR2/3

0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

t [hr]

nu

mb

er o

f re

cep

tors

in P

SD

TotalBound GluR1/2Free GluR1/2Bound GluR2/3Free GluR2/3Scaffolding

S.G. McCormack et al. Neuron 50 75–88 (2006).Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.14/23

LTD traffickingDuring induction of LTD, AMPAR+GRIP → AMPAR+PICK

α β β∗

GRIP PICKµ

ν

scaffoldingprotein

AMPAR AMPAR

h*h

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

t [min]

nu

mb

er o

f re

cep

tors

in P

SD

S.M. Dudek and M.F. Bear. PNAS 89 4363–4367 (1992).Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.15/23

Saturation of LTDInduce LTD 3 times, then LTP

0 30 60 90 120 150 180 2100

10

20

30

40

50

60

70

t [min]

nu

mb

er o

f re

cep

tors

in P

SD

TotalBound GluR1/2Free GluR1/2Bound GluR2/3/GRIPFree GluR2/3/GRIPBound GluR2/3/PICKFree GluR2/3/PICKScaffolding

S.M. Dudek and M.F. Bear. J. Neurosci. 13 2910–2918 (1993).Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.16/23

Review – Experiments reproduced

1. Basal AMPAR numbers (Cottrell et al., 2000)

2. Changes in synaptic strength after blockingexo/endocytosis (Luscher et al., 1999)

3. Changes in synaptic strength during LTP expression(O’Connor et al., 2005)

4. Slow exchange of GluR1/2 with GluR2/3 after LTP(McCormack et al., 2006)

5. Changes in synaptic strength during LTD expression,stimulation frequency dependence (Dudek and Bear,1992)

6. Saturation of LTD (Dudek and Bear, 1993).


Conclusions

1. Significant fraction of PSD receptors are mobileConsistent with Groc et al., 2004; Ashby et al., 2006Requires PSD-ESM barrierRequired for exocytosis blockade time-courseRequired for LTD saturation

2. Significant diffusive impedance at spine neckConsistent with Ashby et al., 2006Required for endocytosis blockade time-courseRequired for LTP time-course


Conclusions

3. Available scaffolding proteins are saturated withAMPAR under basal conditions

Required for just about everythingHypothesis: “slot proteins” encode memory

4. Exocytosis of intracellular GluR1/2 during LTP mustcombine synaptic targeting

Consistent with Schnell et al., 2002Requires increased hopping, binding rate (e.g.stargazin)Requires additional scaffolding proteinsRequired for LTP time-course


Conclusions

5. Slow exchange of GluR1/2 with GluR2/3 after LTPrequires maintenance of additional scaffoldingproteins

Required for exchange time-course

6. GRIP to PICK1 exchange must be accompanied by lossof scaffolding proteins

Consistent with Colledge et al., 2003Required for LTD time-course and saturation


Current workMultiple synapse model

Single-synapse model distributed on dendritic cableExo/endocytosis at soma (Adesnik et al., 2005)Homeostatic plasticity (Turrigiano et al., 1998)Heterosynaptic plasticity/competition (Royer andParé, 2003)

100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

Distance from soma [µm]

Rec

epto

r co

nce

ntr

atio

n

Dendritic AMPARFree AMPAR in PSDBound AMPAR in PSD

100 200 300 400 500 600 700 800 900 100015

20

25

30

35

40

45

Distance from soma [µm]

Rec

epto

rs in

PS

D

Total AMPAR in PSDBound AMPAR in PSD


Current work

Effects of membrane curvatureCurvature may affect receptor diffusionEstimate Ω

Stochastic modelEstimate variance in EPSP recordings


The end


Biophysical model of AMPA receptor trafﬁcking and its ...

Documents

Transcript of Biophysical model of AMPA receptor trafﬁcking and its ...