Magnesium neuroprotection in retinal ganglion cells: A computational study of frequency-dependent therapeutic windows and intervention timing

Fig 1. RGC model overview and Mg2+-dependent dynamics. A: Schematic of the neuroprotection mechanism: glutamate activates AMPA and NMDA receptors; Mg2+ blocks NMDA receptors, reducing calcium influx. B: Voltage-dependent Mg2+ block of NMDA receptors at three concentrations (0.2, 1.0, 2.0 mM), following the Jahr-Stevens formulation. C: Representative voltage traces at 80 Hz stimulation showing spiking at three Mg2+ concentrations. D: Intracellular calcium dynamics at 80 Hz; dashed red line indicates the 1.0 μM toxicity threshold. E: Spike probability across frequencies for all Mg2+ concentrations; dashed line at 0.8 indicates 20% spike loss. F: Peak intracellular calcium at 80 Hz for each Mg2+ concentration; red line indicates toxicity threshold. The shaded green region indicates concentrations within the therapeutic window.

Fig 2. Dose-response analysis across stimulation frequencies. A: Spike loss relative to 0.2 mM baseline as a function of Mg2+ concentration. Note that only excitotoxic frequencies (≥80 Hz) produce spike loss, with a plateau at 20% for 1.4–2.0 mM. At 90–100 Hz, spike loss exceeds 20% across all concentrations, closing the therapeutic window. B: Calcium reduction as a function of Mg2+ concentration, showing monotonic improvement at all frequencies.

Fig 3. Frequency-dependent therapeutic windows. A: Trade-off space at 80 Hz plotting calcium reduction against spike loss. Green points indicate optimal concentrations satisfying both criteria (calcium < 1.0 μM and spike loss ≤ 20%). The green shaded region indicates the therapeutic window (1.6–2.0 mM, labeled “OPTIMAL”). B: Therapeutic window width decreases with increasing stimulation frequency, from 2.0 mM at 10 Hz to 0.4 mM at 80 Hz. At frequencies >80 Hz, no window exists (“None” label).

Fig 4. Intervention timing determines protection efficacy. A: Calcium dynamics during 80 Hz stress (0.5–4.5 s) with Mg2+ supplementation at different delays. Pre-treatment and +0 s intervention maintain calcium near the toxicity threshold, while delayed interventions fail to prevent calcium overload. B: Protection efficacy as a function of intervention timing. Pre-treatment and immediate intervention achieve 100% protection; efficacy drops to 11% at +0.5 s delay and approaches zero for delays ≥ 1 s. The critical window for ≥50% protection is ≤0.2 s (indicated by shaded region); this reflects the rapid Ca2+ rise under our abrupt-onset protocol rather than a literal clinical deadline.

Fig 5. Protection efficacy depends on Ca2+ progress, not absolute time. A: Protection efficacy replotted against normalized Ca2+ accumulation at the moment of Mg2+ application. Efficacy at each delay is computed using Eq. 13: the fraction of peak calcium reduction achieved relative to the pre-treated condition (100% = pre-treatment performance; 0% = no intervention). Ca2+ progress is defined as ([Ca2+](t)−[Ca2+]rest)/([Ca2+]peaknoMg−[Ca2+]rest), where [Ca2+]peaknoMg is the peak from the untreated trace—a treatment-independent reference for excitotoxic phase. The critical state-based threshold for ≥50% protection (∼35% Ca2+ progress; dashed green line) is derived from the + 0.2 s condition, the last delay yielding ≥50% protection. B: Derivation of progress values from the no-Mg2+ Ca2+ trace. The steep rise reflects the abrupt-onset protocol used in simulations. Because Ca2+ accumulation in vivo is typically slower than in this protocol (acute ischemia: minutes–hours; chronic glaucoma: early disease stage), the same state-based threshold maps to correspondingly longer clock times. The model thus predicts relative phase sensitivity—intervention efficacy depends on when during the Ca2+ rise…

Fig 6. Mechanistic basis of Mg2+ neuroprotection. A: Membrane potential at 80 Hz comparing low (0.2 mM, red) and therapeutic (1.8 mM, blue) Mg2+. B: Voltage-dependent Mg2+ factor B(V) (fraction unblocked; lower values indicate stronger block), with mean ⟨B⟩ decreasing from 0.35 (0.2 mM) to 0.12 (1.8 mM). C: AMPA current (no direct Mg2+ block; the ∼15% change reflects the altered V(t) trajectory indirectly). D: NMDA current and integrated charge QNMDA=∫|INMDA|dt, showing a 77% reduction at 1.8 mM. E: Intracellular calcium accumulation and peak [Ca2+]i within the displayed 250 ms window (4.17 → 0.83 μM; 80% reduction); note that the full-protocol peak at 0.2 mM Mg2+ over the complete 2500 ms analysis window is 4.59 μM, as reported in the Results. Dashed line indicates the toxicity threshold. F: Quantitative summary of the neuroprotection cascade linking Mg2+ elevation to reduced NMDA-driven Ca2+ load.