Single-cell PIC mechanism and pool spasticity¶

The cell-level basis for the pool-level phenotypes in 01_sci_iemg_mechanistic.py. Up-regulating the motoneuron dendritic Ca PIC (gamma) and somatic Na PIC (gnapbar_napp), rather than sculpting the drive.

Note: this didactic example uses a deliberately strong gamma=0.2 -> 1.5 stress test to make the bistability obvious; it is illustrative and is NOT the manuscript SCI parameterization (which is gamma=0.5 -> 1.3, nap_factor=1 -> 5, used in 01_sci_iemg_mechanistic.py).

Top: a single type-S motoneuron under the same dendritic ramp, control vs SCI, showing amplification and self-sustained firing (recruit/derecruit hysteresis).
Bottom: a motor pool in which the same brief low-MVC command yields a self-sustained involuntary discharge (a spasm) only when the PIC is up-regulated.

Reuses the shared helpers in _pic_protocols.py. NERLab model throughout.

# sphinx_gallery_thumbnail_number = -1

Import Libraries¶

import sys
from pathlib import Path

import seaborn as sns
from matplotlib import pyplot as plt

from myogen import set_random_seed

sys.path.insert(0, str(Path(__file__).resolve().parent))
import _pic_protocols as pic  # noqa: E402

plt.style.use("fivethirtyeight")
plt.rcParams["path.simplify"] = False  # draw every sample on dense EMG traces

Setup¶

Fix the seed and create a results directory next to this script (the gallery runs each subsection in its own directory, so we use a __file__-relative path rather than a bare ./results).

set_random_seed(42)
NAP_CEILING = 0.00215
N_MU = 60

try:
    save_path = Path(__file__).parent / "results"
except NameError:
    save_path = Path.cwd() / "results"
save_path.mkdir(exist_ok=True, parents=True)

Single-Cell Mechanism: Control vs SCI Dendritic Ramp¶

A slow triangular dendritic current ramp is applied to one type-S motoneuron. Under control (gamma=0.2) recruitment and derecruitment are roughly symmetric; under SCI (gamma=1.5, somatic NaP x5, capped at the verified-safe NAP_CEILING) the cell self-sustains, so it derecruits at a much lower current than it recruited (positive hysteresis).

ctrl_cell = pic.ramp_hysteresis(gamma=0.2, nap_factor=1.0, imax_nA=12.0)
sci_cell = pic.ramp_hysteresis(gamma=1.5, nap_factor=5.0, imax_nA=12.0,
                               nap_ceiling=NAP_CEILING)
print(f"single-cell: ctrl I_on={ctrl_cell['i_on']:.2f}/I_off={ctrl_cell['i_off']:.2f} "
      f"| SCI I_on={sci_cell['i_on']:.2f}/I_off={sci_cell['i_off']:.2f}")

Motor-Pool Spasm: Self-Sustained Discharge After Command Offset¶

The same brief low-MVC voluntary command drives an SCI pool. With the up-regulated PIC the discharge persists past the command offset (a spasm); the tail/command-on RMS ratio quantifies the residual involuntary activity.

command, t_off_s, total_s = pic.brief_command_drive(total_s=10.0)
muscle, _ = pic.build_muscle(N_MU)
iemg_sim = pic.make_iemg_simulator(muscle, N_MU)
sci_pool = pic.run_pool(command, n_mu=N_MU, gamma=1.5, nap_factor=5.0,
                        nap_ceiling=NAP_CEILING, total_s=total_s)
sci_emg = pic.synthesize_iemg(sci_pool, N_MU, iemg_sim=iemg_sim,
                              snr_dB=None, t_off_s=t_off_s)
print(f"pool: spikes after command offset = {pic.spikes_after(sci_pool, t_off_s)} "
      f"| tail/on RMS = {sci_emg['tail_ratio']:.3f}")

Figure¶

Top row: single-cell membrane potential (control vs SCI). Bottom row: the SCI motor-pool iEMG, with the command offset marked in red; the discharge persists beyond it.

fig, axes = plt.subplots(2, 1, figsize=(10, 6))
axes[0].plot(ctrl_cell["t"] / 1000.0, ctrl_cell["v"], lw=0.3, color="tab:blue",
             label="control (gamma=0.2)")
axes[0].plot(sci_cell["t"] / 1000.0, sci_cell["v"], lw=0.3, color="k",
             label="SCI (gamma=1.5, NaP x5)")
axes[0].set_title("Single MN — same dendritic ramp: SCI shows self-sustained firing")
axes[0].set_ylabel("Vm (mV)")
axes[0].legend(loc="upper right", fontsize=7)
axes[1].plot(sci_emg["times"], sci_emg["iemg"], lw=0.2, color="k")
axes[1].axvline(t_off_s, color="tab:red", lw=0.8, ls="--")
axes[1].set_title("Motor pool iEMG (SCI) — spasm persists past command offset (red)")
axes[1].set_xlabel("time (s)")
axes[1].set_ylabel("iEMG (a.u.)")
for ax in axes:
    sns.despine(ax=ax, trim=True, offset=2)
fig.tight_layout()
fig.savefig(save_path / "pic_spasticity.svg")
fig.savefig(save_path / "pic_spasticity.pdf")
plt.show()

Total running time of the script: ( 0 minutes 0.000 seconds)

Download Python source code: 02_simulate_pic_spasticity.py

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