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

Bi and Poo, 1998

prepost ttt

Spike time dependent plasticity (STDP)

STDP Curve

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

Nishiyama et. al. Nature, 2000 Bi and Poo J. Neurosci. 1998

Wittenberg and Wang, J. Neurosci 2006 Froemke and Dan, Nature 2006

Does the second LTD Window exist?Does the second LTD Window exist?