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Mathematical Models of Short-Term Synaptic plasticity

Neural Networks with Short-Term Synaptic Dynamics (Leiden, May 23 2008) Misha Tsodyks, Weizmann Institute. Mathematical Models of Short-Term Synaptic plasticity Computations in Neural Networks with Short-Term Synaptic Plasticity. Experiments: Henry Markram, Eli Nelken

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Mathematical Models of Short-Term Synaptic plasticity

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  1. Neural Networks with Short-Term Synaptic Dynamics(Leiden, May 23 2008)Misha Tsodyks, Weizmann Institute • Mathematical Models of Short-Term Synaptic plasticity • Computations in Neural Networks with Short-Term Synaptic Plasticity Experiments: Henry Markram, Eli Nelken Theory: Klaus Pawelzik, Alex Loebel

  2. Multineuron Recording

  3. Principles of Time-Dependency of Release Synaptic Facilitation Synaptic Depression Three Laws of Release Limited Synaptic Resources Release Dependent Depression Release Independent Facilitation AP onset Facilitation • Four Parameters of Release • Absolute strength • Probability of release • Depression time constant • Facilitation time constant Depression

  4. A Phenomenological Approach to Dynamic Synaptic Transmission • 4 Key Synaptic Parameters • Absolute strength • Probability of release • Depression time constant • Facilitation time constant

  5. Phenomenological model of synaptic depression (deterministic)

  6. . . . Stochastic transmission

  7. Binomial model of synaptic release Loebel et al, submitted

  8. The fitting process (deterministic model)

  9. Testing the Model experiment experiment model model

  10. Frequency-dependence of post-synaptic response

  11. Frequency-dependence of post-synaptic response

  12. Frequency-dependence of post-synaptic response

  13. Frequency-dependence of post-synaptic response Tsodyks et al, PNAS 1997

  14. The 1/f Law of Release

  15. Redistribution of Synaptic Efficacy

  16. RSE

  17. Shifting the Distribution of Release Probabilities

  18. Population signal Tsodyks et al, Neural Computation 1998

  19. Population signal

  20. Population signal ‘High-pass filtering’ of the input rate

  21. Steady-state signal

  22. Tsodyks et al PNAS 1997

  23. Synchronous change in pre-synaptic rates

  24. Synchronous change in pre-synaptic rates

  25. Synchronous change in pre-synaptic rates Abbott et al Science 1997

  26. Modeling synaptic facilitation (deterministic) Markram, Wang & Tsodyks PNAS 1998

  27. Facilitation

  28. Frequency-dependence of post-synaptic response

  29. Frequency-dependence of post-synaptic response

  30. Frequency-dependence of post-synaptic response

  31. Population signal Tsodyks et al 1998

  32. Steady-state signal

  33. A Small Circuit

  34. Recurrent networks with synaptic depression Tsodyks et al, J. Neurosci. 2000 Loebel & Tsodyks JCNS 2002 Loebel, Nelken & Tsodyks, Frontiers in Neurosci. 2007

  35. Simulation of Network Activity

  36. Simulation of Network Activity

  37. Origin of Population Spikes

  38. Network response to stimulation

  39. Experimental evidence for population spikes DeWeese & Zador 2006

  40. Simplified model (no inhibition, uniform connections, rate equations) i J J

  41. The rate model equations • There are two sets of equations representing the excitatory units firing rate, E , and their depression factor, R :

  42. Tone The tonic stimuli is represented by a constant shift of the {e}’s, that, when large enough, causes the network to spike and reach a new steady state

  43. DeWeese, …, Zador 2003

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