Skip to content

chapter34.md

Latest commit

 

History

History
92 lines (74 loc) · 4.31 KB

chapter34.md

File metadata and controls

92 lines (74 loc) · 4.31 KB
Raw

Nested gamma-theta rhythms

Overview

These examples place gamma PING episodes inside a slower theta cycle. They first develop pre-O-LM and O-LM cell h- and A-current dynamics, then combine E, I, and O-LM populations under theta-modulated excitation or inhibition.

Core ideas

Theta modulation selects windows for gamma. The O-LM cell's h-current promotes slow post-inhibitory recovery, while its A-current can delay OLM spiking; together they shape O-LM inhibition and the timing of E-I activity. Nesting must be read from population rasters relative to the slower modulation, whether it arrives as a periodic boost to E-cell drive or a periodic pulse of external inhibition.

Essential model

The E-I-O-LM network keeps conductance currents $g,s,(E_{\rm rev}-v)$ and adds slow O-LM gates for h- and A-currents. A theta-periodic E drive or inhibitory conductance creates gamma packets at preferred theta phases.

Code examples

All eight examples live in one notebook, chapter34.ipynb. A shared block of pre-O-LM/O-LM gating functions (alpha_h/alpha_m/ alpha_n/beta_h/beta_m/beta_n, h_inf/m_inf/n_inf, tau_h/tau_m/tau_n, plus the h-current pair r_inf/tau_r and the A-current pair/quad a_inf/b_inf/tau_a/tau_b), the RTM/WB E-/I-cell gates (m_e_inf/h_e_inf/tau_h_e/n_e_inf/tau_n_e, m_i_inf/h_i_inf/tau_h_i/n_i_inf/tau_n_i), the synapse rise-time solver tau_peak_function/tau_d_q_function, and the population splay-state initializers rtm_init_population/wb_init_population/ olm_init_population are defined once and reused throughout the chapter:

  • plot_a_current_gates plots the O-LM cell's A-current gates and time constants (A-current).
  • simulate_eio_network/plot_eio_raster simulate a small E-I-O-LM population network (odeint-integrated, matching the original script's synaptic-term sign convention) and draw its three-population raster plus mean($v_E$)/mean($s_E$) traces (E-I-O-LM network, EIO_1).
  • simulate_olm_h_and_a_currents/plot_olm_h_and_a_currents integrate a single O-LM cell with both slow currents active (O-LM cell with h- and A-currents).
  • simulate_olm_h_current/plot_olm_h_current integrate the h-current -only comparison (O-LM cell with h-current).
  • simulate_ping_theta_drive/plot_ping_theta_raster apply a theta-modulated multiplicative boost to the E-cell drive (PING with theta-modulated drive), with the network stepper numba-accelerated.
  • simulate_ping_theta_inhibition (sharing plot_ping_theta_raster) applies a theta-periodic external inhibitory conductance pulse to the E cells instead (PING with theta-modulated inhibition).
  • simulate_pre_olm_voltage_trace/plot_pre_olm_voltage_trace show a single pre-O-LM cell's voltage trace under constant drive (pre-O-LM voltage trace).
  • plot_pre_olm_gates plots the pre-O-LM cell's steady-state gates and time constants (pre-O-LM gating variables).

Interactive sliders let you sweep the O-cell$\to$E-cell coupling strength g_hat_oe in the E-I-O-LM network, the A-/h-current strengths g_A/g_h in the two single-cell O-LM examples, the theta modulation depth alpha and external-inhibition strength g_ex in the two PING+theta examples, and the drive i_ext in the pre-O-LM voltage trace.

What to look for

Compare h-only with h-plus-A O-LM dynamics first. Then locate gamma raster packets relative to theta and compare drive-selected with inhibition-selected windows. Use the E-I-O-LM network's raster to separate E, I, and O-LM roles.

Suggested order

  1. Run the pre-O-LM gating/voltage-trace examples and the A-current plot.
  2. Compare the two O-LM-current examples (h-only vs. h-plus-A).
  3. Run the E-I-O-LM network, then the theta-drive and theta-inhibition PING examples.

Prerequisites and related chapters

Chapter 9 introduces slow conductances, Chapter 20 chemical synapses, and Chapters 30-33 PING, ING, weak PING, and beta timing.

Running the examples

Open chapter34.ipynb in Jupyter, or via the Colab badge at the top of the notebook, and run all cells top to bottom. The E-I-O-LM network (simulate_eio_network) integrates a 115-dimensional system with scipy.integrate.odeint and is the slowest cell in the chapter, taking a few minutes; the theta-modulated PING network cells are numba-accelerated and much faster.