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Conductance-Based Synapses and Hypercolumn Models in Visual Cortex Networks

This lecture delves into the intricacies of conductance-based synapses and their role within the visual cortical hypercolumn model. It highlights the dynamics of synaptic filtering, the significance of presynaptic spike trains, and the balance conditions governing membrane potential across neural circuits. By employing mean field theory, the lecture explores effective single-neuron dynamics in high-conductance states and discusses how these principles apply to modeling responses in the primary visual cortex. References include key works from Lerchner, Ahmadi, and Hertz, providing a comprehensive framework for understanding these neural mechanisms.

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Conductance-Based Synapses and Hypercolumn Models in Visual Cortex Networks

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  1. Lecture 11: Networks II:conductance-based synapses, visual cortical hypercolumn model References: Hertz, Lerchner, Ahmadi, q-bio.NC/0402023 [Erice lectures] Lerchner, Ahmadi, Hertz, q-bio.NC/0402026 (Neurocomputing, 2004) [conductance-based synapses] Lerchner, Sterner, Hertz, Ahmadi, q-bio.NC/0403037 [orientation hypercolumn model]

  2. Conductance-based synapses In previous model:

  3. Conductance-based synapses In previous model: But a synapse is a channel with a (neurotransmitter-gated) conductance:

  4. Conductance-based synapses In previous model: But a synapse is a channel with a (neurotransmitter-gated) conductance:

  5. Conductance-based synapses In previous model: But a synapse is a channel with a (neurotransmitter-gated) conductance: where is the synaptically-filtered presynaptic spike train

  6. Conductance-based synapses In previous model: But a synapse is a channel with a (neurotransmitter-gated) conductance: where is the synaptically-filtered presynaptic spike train kernel:

  7. Conductance-based synapses In previous model: But a synapse is a channel with a (neurotransmitter-gated) conductance: where is the synaptically-filtered presynaptic spike train kernel:

  8. Conductance-based synapses In previous model: But a synapse is a channel with a (neurotransmitter-gated) conductance: where is the synaptically-filtered presynaptic spike train kernel:

  9. Model

  10. Model

  11. Model

  12. Mean field theory Effective single-neuron problem with synaptic input current

  13. Mean field theory Effective single-neuron problem with synaptic input current

  14. Mean field theory Effective single-neuron problem with synaptic input current with

  15. Mean field theory Effective single-neuron problem with synaptic input current with where = correlation function of synaptically-filtered presynaptic spike trains

  16. Balance condition Total mean current = 0:

  17. Balance condition Total mean current = 0:

  18. Balance condition Total mean current = 0: Mean membrane potential just below q:

  19. Balance condition Total mean current = 0: Mean membrane potential just below q: define

  20. Balance condition Total mean current = 0: Mean membrane potential just below q: define

  21. Balance condition Total mean current = 0: Mean membrane potential just below q: define Solve for rb as in current-based case:

  22. Balance condition Total mean current = 0: Mean membrane potential just below q: define Solve for rb as in current-based case:

  23. Balance condition Total mean current = 0: Mean membrane potential just below q: define Solve for rb as in current-based case: =>

  24. High-conductance-state

  25. High-conductance-state

  26. High-conductance-state Va “chases” Vsa(t) at rate gtot(t)

  27. High-conductance-state Va “chases” Vsa(t) at rate gtot(t)

  28. High-conductance-state Va “chases” Vsa(t) at rate gtot(t)

  29. High-conductance-state Va “chases” Vsa(t) at rate gtot(t) Effective membrane time constant ~ 1 ms

  30. Membrane potential and spiking dynamics for large gtot

  31. Fluctuations Measure membrane potential from :

  32. Fluctuations Measure membrane potential from :

  33. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations:

  34. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations:

  35. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations:

  36. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations: Use balance equation in

  37. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations: Use balance equation in =>

  38. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations: Use balance equation in => or

  39. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations: Use balance equation in => or with

  40. Fluctuations Measure membrane potential from : Conductances: mean + fluctuations: Use balance equation in => or with

  41. Effective current-based model High connectivity:

  42. Effective current-based model High connectivity:

  43. Effective current-based model High connectivity:

  44. Effective current-based model High connectivity:

  45. Effective current-based model High connectivity:

  46. Effective current-based model High connectivity: Like current-based model with

  47. Effective current-based model High connectivity: Like current-based model with (but effective membrane time constant depends on presynaptic rates)

  48. Firing irregularity depends on reset level and ts

  49. Modeling primary visual cortex

  50. Modeling primary visual cortex Background: • Neurons in primary visual cortex (area V1) respond strongly to oriented • stimuli (bars, gratings)

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