A Calcium dependent model of synaptic plasticity (CaDp) Describe various induction protocols.

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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) ΔWΔWΔWΔW LTD Ca LTPθdθd θpθp I. A Unified theory of NMDA Receptor-Dependent synaptic plasticity Ω function

Whereand *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 Ca (  M)  d  p  Ca (  M)  sec 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 Fraction of open NMDAR I Ca

Ligand binding kinetics – sum of two exponentials with different time constants (Carmignoto and Vicini, 1992) Calcium Dynamics- first order ODE NR2A+NR2B In these examples NMDA receptor kinetics- sum of two exponents

Pairing Induced Plasticity Voltage clamping postsynaptic neuron while stimulating presynapticaly at 1 Hz. ExamplesLTP/LTD curve W W

Bi and Poo, 1998 Spike time dependent plasticity (STDP) STDP Curve

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 ( )

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 31 o C, 150 µ M 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, 2000Bi and Poo J. Neurosci Wittenberg and Wang, J. Neurosci 2006 Froemke and Dan, Nature 2006 Does the second LTD Window exist?