1. Toward a Biophysical Model of Spike-Time Dependent Plasticity
A Monte Carlo model of Ca2+ dynamics in dendritic spines.
Kevin Franks
The Salk Institute

2. Biochemistry of LTP/LTD?
High Ca2+ through NMDARs induces LTP via CaMKII
Low Ca2+ through NMDARs induces LTD via calcineurin
Role for VDCCs in LTD, maybe for LTP?

3. About MCell Allows: Monte Carlo simulator of microphysiology
3D random walk diffusion
Stochastic biochemical kinetic state transitions
3D representation of surfaces of arbitrary complexity

4. Spine Model

5. Ca2+ Sources NMDARs ~20 NMDARs at synapse
VDCCs
~20 NMDARs at synapse
~ 5 VDCCs anywhere on the spine surface

6. Voltage-gating in MCell

7. Ca2+ Sinks Low density of surface pumps High density of ER pumps
Spine apparatus
Pumps
Low density of surface pumps
High density of ER pumps

8. Ca2+ Buffers ~100 mM Ca2+-binding proteins throughout the spine
~ 20 mM CaM at PSD
s  20
optional addition of fluorescent indicators
CBPs

9. Simulating fluorescent Ca2+ transients

10. Sub- & superlinear Ca2+ fluorescence
Action potential
EPSP
Action potential + EPSP
(linear sum)
EPSP + Action potential
(linear sum)
Action potential  EPSP
(50 ms apart)
EPSP  Action potential
(50 ms apart)
See Koester & Sakmann (1998)
What about [Ca2+]i?

11. DF/F  [Ca2+]i

12. An intuitive model (?)

13. LTP-inducing protocol
EPSP 10 ms before AP

14. LTD-inducing protocol
EPSP 10 ms after AP

15. Biochemistry of LTP/LTD?
High Ca2+ through NMDARs can induce LTP via CaMKII
Low Ca2+ through NMDARs can induce LTD via calcineurin 

16. Ineffectual protocol
EPSP 90 ms before AP

17. Problems with the simple model:

18. Dendritic Spines A Biochemist’s View From: Sheng and Lee
Nature Neurosci, 2000

19. APs don’t induce Ca2+ gradients in spines...

20. …but EPSPs do induce Ca2+ gradients

21. Differential distribution of CaM

22. Conclusions
We are able to accurately model intracellular Ca2+ dynamics at high spatial and temporal resolution.
Large and moderate Ca2+ currents are not sufficient to explain the selective induction of LTP and LTD, respectively, with STDP.
We suggest that differential induction decisions are made in highly organized subdomains of the spine.

23. Acknowledgements
Thanks to:
Terrence Sejnowski
Thomas Bartol

24. Ca2+/Calmodulin Complex
Calmodulin is a molecular differentiator:
Responds to rapid increases in [Ca2+]
Ca2+
Ca2+
Ca2+
Ca2+
6x106
9.5x106
8x106
4.3x107 B0 B1 B2 B3
B4* 40 40
600
600
(Stable)
(Unstable)
(Stable)

25. Courtesy of Richard Weinberg

26. Fluorescent Ca2+ transients allow determination of endogenous buffering capacity
Ks  20 means 1/20 of the Ca2+ ions remain free, or, 95% of Ca2+ entering the spine is buffered
[sensor] KD
B =
([Ca2+]rest + KD)([Ca2+]peak+KD)