A Calcium dependent model of synaptic plasticity (CaDp) Describe various induction protocols.
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Transcript of A Calcium dependent model of synaptic plasticity (CaDp) Describe various induction protocols.
Can a single model, based on a limited set of assumptions, account for the various induction protocols?
Approach: Find a minimal set of assumptions that can qualitatively account for the various forms of induction.
Assumption 1: The calcium control hypothesis.
The idea that calcium levels control the sign and magnitude of synaptic plasticity has been around for a while (Lisman, 1989; Bear et. al., 1987; Artola et. al. 1990)
ΔΔWW
LTDCa
LTPθd θp
I. A Unified theory of NMDA Receptor-Dependent synaptic plasticity
)]([ ii Ca
dt
dW
ΩΩ function function
)( )]([)]([ iiii WCaCa
dt
dW
Where and
*This equation can be derived from a lower level biophysical formulation. (Castellani et. al. 2001, Shouval et. al. 2002)
The calcium control hypothesis, is a generalization of this equation.
0.2 0.4 0.6 0.8 10
0.25
0.5
0.75
1
Ca ( M)
d p
0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Ca ( M)
sec -1
the rate function is: has the form
*
Assumption 2: NMDA receptors are the primary source of calcium influx to spines during synaptic plasticity (Sabatini et. al 2002).
• Voltage dependence of NMDAR (Jahr and Stevens, 1990)
Standard assumptions
Fra
ctio
n o
fop
en N
MD
AR
ICa
• Ligand binding kinetics – sum of two exponentials with different time constants (Carmignoto and Vicini, 1992)
• Calcium Dynamics- first order ODE
CaiCa
i ICadt
Cad ][
1][
msCa 5020
NR2A+NR2B
0.7
0.5
0.0
In these examples
NMDA receptor kinetics- sum of two exponents
Pairing Induced Plasticity Voltage clamping postsynaptic neuron while stimulating presynapticaly at 1 Hz.
Examples LTP/LTD curve
WW
prepost ttt
For the calcium control hypothesis to account for STDP it is necessary that:
• For (post-pre) the calcium influx is
higher than at baseline ( )
• For ( pre-post) the calcium influx is
higher than at ( )
0t
0t0t
pd Ca ][
pCa ][
Axon: output
Action potentials
| || | || |
| | |
| | || | |
Neuron – cell body
Dendrite: input
Synapse
Back propagating action potentials
Assume a narrow spike (Width 3ms)
Problems:• No difference between baseline and post-pre
• Only a small elevation in Ca for pre-post
Back spike – assume width 3ms
Assumption 3:The Back Spike has a slow component (long tail).
narrow spike (3ms)
spike with long tail (width 25 ms)
An example of a BPAP recorded by C. Colbert from a hippocampal dendrite (slice, from 180 gm Sprague Dawley rat at 31o C , 150µM from soma)
Back Spike with long tail (tail width 25ms)
Problems solved •Ca level in post-pre larger than at baseline.
• Larger elevation of Ca in pre-post condition.
BPAP with wide tail
(ms)
Similar results: Karmarkar and Bunomano, 2002; Abarbanel et. al. 2003;Kitijima and Hara, 2000