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Gamma coherence

Overview

Gamma coherence is the alignment of population responses across pulses or gamma episodes. These examples compare two-cell timing references with Poisson-PING phase sweeps that measure the response of E-cells 1-5, plus a separate raster with a periodic green waveform as a timing reference.

Core ideas

Coherence is population timing alignment, not simply high firing rate. A pulse at a compatible gamma phase can reinforce a common response, while a mismatched pulse can land during inhibition or at a conflicting phase. Poisson PING makes this distinction clear because individual spikes vary while a phase-dependent population response can remain.

Essential model

For each sampled pulse phase $\varphi$, the Poisson-PING sweep functions simulate a population, count spikes from E-cells 1-5, and fit a line to the phase-versus-count response. The two sweep examples use different pulse periods; the green-reference example instead displays a Poisson-PING raster with its periodic waveform.

Code examples

All five examples live in one notebook, chapter38.ipynb. A shared model block defines the RTM/WB gating functions (m_e_inf, h_e_inf, tau_h_e, n_e_inf, tau_n_e, and their _i inhibitory-cell counterparts) and the synaptic-delay solver tau_d_q, reused by every example below.

  • simulate_two_cell/simulate_gamma_coherence_1/plot_gamma_coherence_1 plot two-cell inhibitory currents with E/I spike times and periodic timing markers.
  • simulate_gamma_coherence_2/plot_gamma_coherence_2 compare coupled inhibition with its mean-inhibition approximation (reusing simulate_two_cell).
  • simulate_poisson_ping/_poisson_ping_loop (numba-accelerated) build the Chapter 38 all-to-all Poisson-PING network, shared by all three POISSON_PING_3_* examples below.
  • simulate_poisson_ping_mismatched_pulses sweeps pulse phase for a 29 ms period (P_MISMATCHED_PULSES) via the shared simulate_poisson_ping_phase_sweep, plotting E-cell-1-5 spike counts with a linear fit.
  • simulate_poisson_ping_plus_green/plot_poisson_ping_plus_green display a Poisson-PING E/I raster with a green periodic timing waveform.
  • simulate_poisson_ping_plus_pulses sweeps pulse phase for a 31 ms period (P_PLUS_PULSES), reusing the same shared sweep helper.

What to look for

For the sweep plots, compare E-cell-1-5 spike counts across phase and inspect the fitted slope rather than reading them as rasters. Use the green waveform and raster only in its dedicated example to relate a population episode to the periodic timing reference.

Suggested order

  1. Run simulate_gamma_coherence_1/plot_gamma_coherence_1 and simulate_gamma_coherence_2/plot_gamma_coherence_2.
  2. Run simulate_poisson_ping_plus_green/plot_poisson_ping_plus_green to inspect its raster and waveform.
  3. Compare the two phase-versus-spike-count sweeps (simulate_poisson_ping_mismatched_pulses and simulate_poisson_ping_plus_pulses).

Prerequisites and related chapters

Chapter 23 introduces pulse timing, Chapter 30 PING, Chapter 32 Poisson PING, and Chapter 37 thresholding.

Running the examples

Open chapter38.ipynb in Jupyter, or via the Colab badge at the top of the notebook, and run all cells top to bottom. Poisson-PING output varies across runs unless a seed is fixed, so compare qualitative timing rather than exact spike identities.