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

Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD Berton 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 Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.3/23

The Synapse

E.R. Kandel et al. Principles of Neural Science. 2000. M.B. Kennedy. Science 290 750–754 (2000). Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.4/23

Synaptic transmission

E.R. Kandel et al. Principles of Neural Science. New York: McGraw-Hill. 2000. Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.5/23

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). Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.6/23

AMPA receptor trafficking Exo/endocytosis τ ∼10-30min Lateral diffusion Brownian in ESM: ∼0.1µm2 /s Confined in PSD: ∼0.01µm2 /s PSD is confinement domain Spine neck impedance

PSD EXO END DEG

Immobilization by scaffolding AMPA receptor

Synthesis/degradation EXO

scaffolding protein

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). Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.7/23

Model – Spine geometry Cylinder Radius: r0 = 0.2µm Length: z0 = 1.0µm Body: ESM (AESM = 1.257µm2 ) Top: PSD (AP SD = 0.1257µm2 ) Bottom: dendrite junction

PSD r r0

z

z0 ESM

Diffusion is fast Time constant of diffusion: τ = A/D ∼ 10s Other time constants: τ ≥ 10min ⇒ uniform concentrations


Model – Trafficking P, Q: R: α, β : σ, k : h, Ω:

Free/Bound AMPAR concentration in PSD Free AMPAR concentration in ESM Binding/unbinding rate Exo/endocytosis PSD-ESM/ESM-dendrite hopping rate PSD

ESM

Q

Ω

h P

α

R

Ω

h σ

σ

k

DENDRITE

β

INTRACELLULAR Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.9/23

Model Equations – AMPAR in PSD hI dPI = −αI (L − QI − QII )PI + βI QI − (PI − RI ) dt AP SD dPII hII = −αII (L − QI − QII )PII + βII QII − (PII − RII ) dt AP SD σII + AP SD dQI = αI (L − QI − QII )PI − βI QI dt dQII = αII (L − QI − QII )PII − βII QII dt

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 hI ΩI σI dRI = (PI − RI ) − (RI − RI ) − kI RI + dt AESM AESM AESM dRII hII ΩII = (PII − RII ) − (RII − RII ) − kII RII dt AESM AESM

R = background AMPAR concentration in dendritic spine


Blocking exo/endocytosis 90

40 Total Bound GluR1/2 Free GluR1/2 Bound GluR2/3 Free GluR2/3

30

80 70 number of receptors in PSD

number of receptors in PSD

35

25

20

15

50 40 30

10

20

5

10

0

0 0

5

10

15 t [min]

20

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30

Total Bound GluR1/2 Free GluR1/2 Bound GluR2/3 Free GluR2/3

60

0

10

20

30 t [min]

40

50

60

C. Luscher et al. Neuron 24 649–658 (1999). Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.12/23

LTP trafficking

100 90


80 70

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

60 50 40 30 20 10 0

0

0.5

1

1.5

2

2.5 t [min]

3

3.5

4

4.5

5

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

100 90


80 70

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

60 50 40 30 20 10 0

0

5

10

15

20

25

t [hr]

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 trafficking During induction of LTD, AMPAR+GRIP → AMPAR+PICK µ

GRIP

h

ν

AMPAR α

PICK

h*

AMPAR β∗

β scaffolding protein

40


35

30

25

20

15

10

5

0

0

5

10

15 t [min]

20

25

30

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 LTD Induce LTD 3 times, then LTP

70

Total Bound GluR1/2 Free GluR1/2 Bound GluR2/3/GRIP Free GluR2/3/GRIP Bound GluR2/3/PICK Free GluR2/3/PICK Scaffolding


60

50

40

30

20

10

0

0

30

60

90

120

150

180

210

t [min]

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 blocking exo/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). Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.17/23

Conclusions 1. Significant fraction of PSD receptors are mobile Consistent with Groc et al., 2004; Ashby et al., 2006 Requires PSD-ESM barrier Required for exocytosis blockade time-course Required for LTD saturation 2. Significant diffusive impedance at spine neck Consistent with Ashby et al., 2006 Required for endocytosis blockade time-course Required for LTP time-course


Conclusions 3. Available scaffolding proteins are saturated with AMPAR under basal conditions Required for just about everything Hypothesis: “slot proteins” encode memory 4. Exocytosis of intracellular GluR1/2 during LTP must combine synaptic targeting Consistent with Schnell et al., 2002 Requires increased hopping, binding rate (e.g. stargazin) Requires additional scaffolding proteins Required for LTP time-course Biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD – p.19/23

Conclusions 5. Slow exchange of GluR1/2 with GluR2/3 after LTP requires maintenance of additional scaffolding proteins Required for exchange time-course 6. GRIP to PICK1 exchange must be accompanied by loss of scaffolding proteins Consistent with Colledge et al., 2003 Required for LTD time-course and saturation


Current work Multiple synapse model Single-synapse model distributed on dendritic cable Exo/endocytosis at soma (Adesnik et al., 2005) Homeostatic plasticity (Turrigiano et al., 1998) Heterosynaptic plasticity/competition (Royer and Paré, 2003) 350

45

300

40

250 35 Receptors in PSD

Receptor concentration

Total AMPAR in PSD Bound AMPAR in PSD

Dendritic AMPAR Free AMPAR in PSD Bound AMPAR in PSD

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25 100

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0 100

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400 500 600 700 Distance from soma [µm]

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15 100

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400 500 600 700 Distance from soma [µm]

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1000


Current work Effects of membrane curvature Curvature may affect receptor diffusion Estimate Ω Stochastic model Estimate variance in EPSP recordings


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