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

2. 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.

3. 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

4. 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. 0.20.40.60.81 0 0.25 0.5 0.75 1 Ca (  M)  d  p  0.20.40.60.81 0 0.2 0.4 0.6 0.8 1 Ca (  M)  sec the rate function is: has the form *

5. 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

6. Ligand binding kinetics – sum of two exponentials with different time constants (Carmignoto and Vicini, 1992) Calcium Dynamics- first order ODE NR2A+NR2B 0.7 0.5 0.0 In these examples NMDA receptor kinetics- sum of two exponents

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

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

9. 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 ( )

10. Axon: output Action potentials | || | || | | | | | | || | | Neuron – cell body Dendrite: input Synapse Back propagating action potentials

11. 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

12. 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)

13. 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.

14. BPAP with wide tail (ms) Similar results: Karmarkar and Bunomano, 2002; Abarbanel et. al. 2003; Kitijima and Hara, 2000

15. Nishiyama et. al. Nature, 2000Bi and Poo J. Neurosci. 1998 Wittenberg and Wang, J. Neurosci 2006 Froemke and Dan, Nature 2006 Does the second LTD Window exist?