Glutamate excitotoxicity in retinal ganglion cells

Glutamate is the primary excitatory neurotransmitter in the retina, mediating synaptic transmission from bipolar cells to RGCs [1,10]. Under physiological conditions, glutamate release is tightly regulated, and RGCs respond appropriately to visual stimuli through activation of ionotropic glutamate receptors, including -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-D-aspartate (NMDA) receptors [11]. However, pathological conditions such as ischemia, elevated intraocular pressure, or metabolic stress can trigger excessive glutamate release and impaired reuptake, leading to sustained receptor activation [2,3].

NMDA receptors play a central role in excitotoxicity due to their high permeability to calcium ions (Ca²⁺) [10,12]. Unlike AMPA receptors, which primarily conduct sodium and potassium, NMDA receptors allow substantial Ca²⁺ influx upon activation [13]. While physiological Ca²⁺ signaling is essential for synaptic plasticity and normal cellular function, excessive Ca²⁺ accumulation activates destructive enzymatic cascades, including calpains, phospholipases, and endonucleases, ultimately leading to cell death [10,14]. This calcium-mediated excitotoxicity has been implicated in numerous neurodegenerative conditions, making NMDA receptor modulation an attractive therapeutic target [10,15].

Magnesium as an endogenous NMDA receptor modulator

A unique property of NMDA receptors is their voltage-dependent block by extracellular magnesium ions (Mg²⁺) [16,17]. At resting membrane potentials, Mg²⁺ ions occupy the receptor channel pore, preventing ion flux despite glutamate binding. Membrane depolarization relieves this block, allowing current flow through the receptor [18]. Recent cryo-electron microscopy (cryo-EM) structural studies have identified three distinct Mg²⁺-binding sites on NMDA receptors, revealing that Mg²⁺ exerts multifaceted regulatory effects beyond simple pore block, including allosteric modulation through the N-terminal domain [19]. This voltage-dependent gating mechanism underlies the role of NMDA receptors as coincidence detectors, requiring both presynaptic glutamate release and postsynaptic depolarization for activation [11,20].

The Mg²⁺ block of NMDA receptors has attracted considerable interest as a potential neuroprotective mechanism [10,21]. Elevated extracellular Mg²⁺ enhances the voltage-dependent block, reducing Ca²⁺ influx through NMDA receptors even during pathological glutamate exposure [18]. Importantly, because the block is voltage-dependent rather than absolute, Mg²⁺ supplementation may provide neuroprotection while partially preserving NMDA receptor function, potentially avoiding the adverse effects associated with complete receptor antagonism [10,12].

Clinical and experimental evidence supports the neuroprotective potential of Mg²⁺. In stroke models, Mg²⁺ administration reduced infarct volume and improved functional outcomes [22]. The Field Administration of Stroke Therapy–Magnesium (FAST-MAG) trial demonstrated the feasibility of prehospital Mg²⁺ therapy in acute stroke patients, though the trial showed no significant overall functional benefit; post-hoc analyses suggested possible efficacy in specific stroke subtypes [23]. In the visual system, Mg²⁺ supplementation has shown promise in animal models of glaucoma and retinal ischemia [3,10]. However, clinical translation has been hampered by incomplete understanding of the optimal Mg²⁺ concentrations and timing required for effective neuroprotection without compromising neural function.

The therapeutic window challenge

A critical challenge in Mg²⁺-based neuroprotection is identifying the therapeutic window—the range of concentrations that provide meaningful protection against excitotoxicity while preserving normal synaptic transmission [10]. Too little Mg²⁺ fails to adequately block NMDA receptors during pathological activation, while excessive Mg²⁺ may impair physiological signaling. Physiological extracellular Mg²⁺ concentration in cerebrospinal fluid is approximately 0.8–1.0 mM [24], and therapeutic strategies typically aim for mild hypermagnesemia (1.5–2.5 mM) to enhance neuroprotection [22].

Complicating this picture is the frequency-dependence of NMDA receptor contribution to synaptic transmission. At low stimulation frequencies, AMPA receptors dominate fast synaptic transmission, and NMDA receptor block has minimal functional impact [11]. However, at high frequencies characteristic of excitotoxic conditions, NMDA receptors contribute significantly to temporal summation and sustained depolarization [25]. This frequency-dependence suggests that the therapeutic window may vary with the level of synaptic activity, a hypothesis that has not been systematically investigated.

Additionally, the timing of Mg²⁺ intervention relative to excitotoxic insult onset may critically influence efficacy. Calcium accumulation begins rapidly upon excessive NMDA receptor activation, and delayed intervention may fail to prevent irreversible damage [14]. Understanding the temporal constraints on Mg²⁺ neuroprotection is essential for clinical translation, particularly in acute conditions such as retinal ischemia where treatment delays are common.

Computational modeling of RGC neuroprotection

Computational modeling provides a powerful approach to systematically investigate the complex parameter space of Mg²⁺ neuroprotection [26]. Conductance-based models incorporating Hodgkin-Huxley-type dynamics [27] can capture the voltage-dependent interactions between intrinsic conductances, synaptic receptors, and Mg²⁺ block with high temporal resolution. Such models enable exploration of conditions that would be difficult or impossible to study experimentally, including systematic variation of Mg²⁺ concentration, stimulation frequency, and intervention timing.

Previous computational studies have examined various aspects of RGC physiology, including intrinsic firing properties [28], responses to electrical stimulation [29], and synaptic integration [30]. Computational approaches have also proven valuable for understanding NMDA and AMPA receptor dynamics in the context of synaptic plasticity and pathological conditions [12,31]. However, comprehensive modeling of Mg²⁺-mediated neuroprotection in RGCs, particularly addressing the frequency-dependence of therapeutic windows and temporal constraints on intervention, has not been reported.

Aims and overview of the present study

In this study, we developed a biophysically detailed computational model of an RGC to investigate the neuroprotective effects of extracellular Mg²⁺ during glutamatergic excitotoxicity. Our model incorporates voltage-gated sodium, potassium, and calcium conductances; AMPA and NMDA receptor-mediated synaptic currents; the voltage-dependent Mg²⁺ block of NMDA receptors following the Jahr-Stevens formulation [18]; and intracellular calcium dynamics.

We systematically varied extracellular Mg²⁺ concentration (0.2–2.5 mM) and glutamatergic stimulation frequency (10–100 Hz) to address three key questions: (1) What are the frequency-dependent therapeutic windows for Mg²⁺ neuroprotection? (2) How does the trade-off between neuroprotection and function preservation vary with activity level? (3) What are the temporal constraints on Mg²⁺ intervention during excitotoxic stress?

Our results reveal a narrow but clinically relevant therapeutic window at excitotoxic frequencies, identify a spike loss plateau phenomenon that creates an optimal zone for neuroprotection, and demonstrate that Mg²⁺ protection efficacy declines steeply with intervention delay.

Computational model

We developed a single-compartment conductance-based model of an RGC to investigate the neuroprotective effects of Mg²⁺ during glutamatergic excitotoxicity. The model incorporates Hodgkin-Huxley-type intrinsic conductances [27], glutamatergic synaptic inputs via AMPA and NMDA receptors, and intracellular calcium dynamics. The model architecture was informed by previous computational studies of RGC electrophysiology [28,29].

Rationale for single-compartment approach

The single-compartment approach was chosen based on the relatively compact dendritic morphology of RGCs, where the soma is electrotonically close to synaptic input sites, making somatic recordings representative of integrated synaptic responses [28]. Unlike pyramidal neurons with extensive dendritic arbors (1000+ m), RGC dendritic trees typically span 100–300 m, with relatively uniform electrotonic properties. This approach enables systematic exploration of the fundamental Mg²⁺ concentration–function trade-off while maintaining computational tractability and interpretability. The implications of dendritic compartmentalization are addressed in the Discussion.

Membrane dynamics

The membrane potential V evolves according to:

(1)

where is the membrane capacitance [32]. The ionic currents include voltage-gated sodium (I_Na), delayed rectifier potassium (I_Kdr), A-type potassium (I_KA), L-type calcium (I_CaL), calcium-activated potassium (I_KCa), and leak (I_L) conductances.

Intrinsic conductances

Voltage-gated currents followed standard Hodgkin-Huxley formalism [27]:

(2)

(3)

(4)

(5)

(6)

The A-type potassium current kinetics were based on Connor and Stevens [33], while L-type calcium channel properties followed Fox et al. [34]. The calcium-activated potassium current was modeled as:

(7)

with M [35].

Conductance values were: g_Na = 120 mS/cm², g_Kdr = 36 mS/cm², g_KA = 8 mS/cm², g_CaL = 0.3 mS/cm², g_KCa = 0.3 mS/cm², and mS/cm². Reversal potentials were: E_Na = +50 mV, mV, E_Ca = +120 mV, mV, and resting potential mV, consistent with experimental measurements in mammalian RGCs [36,37]. Complete parameter values including synaptic kinetics are provided in Tables 1,2 and S2 Table.

Download:

• PNG
  larger image
• TIFF
  original image

Table 1. Model parameters: Intrinsic properties. Membrane properties, reversal potentials, and ionic conductances. Complete parameters with full references are provided in S2 Table.

https://doi.org/10.1371/journal.pone.0348068.t001

Download:

• PNG
  larger image
• TIFF
  original image

Table 2. Model parameters: Synaptic and Ca²⁺ dynamics. Synaptic conductances, receptor kinetics, Mg²⁺ block parameters, calcium dynamics, and stimulation protocol. Primary references: Hodgkin & Huxley 1952 [27]; Jahr & Stevens 1990 [18]; Patneau & Mayer 1990 [39]; Destexhe et al. 1994 [38]. The calcium scaling factors k_Ca,NMDA and k_Ca,CaL were fitted to experimental data (see Methods); full sourcing for all parameters is provided in S2 Table.

https://doi.org/10.1371/journal.pone.0348068.t002

Synaptic conductances

Glutamatergic input activated both AMPA and NMDA receptor-mediated currents [11]:

(8)

(9)

where E_exc = 0 mV, g_AMPA = 0.25 mS/cm², and g_NMDA = 1.2 mS/cm².

Synaptic gating variables s followed first-order kinetics with glutamate-dependent activation [31,38]:

(10)

where EC₅₀ (half-maximal effective concentration) values were EC_50,AMPA = 0.5 mM and M [39], with decay time constants ms [40] and ms [41]. Rise time constants were ms and ms.

Voltage-dependent Mg²⁺ block of NMDA receptors

The voltage-dependent Mg²⁺ block of NMDA receptors was modeled following Jahr and Stevens [18]:

(11)

where mM^-1 and mV^-1. This function captures the relief of Mg²⁺ block at depolarized potentials, a hallmark property of NMDA receptors that underlies their role as coincidence detectors [16,17].

Intracellular calcium dynamics

Intracellular calcium concentration evolved according to a single-compartment model [42]:

(12)

where f_Ca = 0.15 represents the fractional calcium current through NMDA receptors [13], k_Ca,NMDA = 0.012 and k_Ca,CaL = 0.003 are dimensionless scaling factors (fitted to produce peak Ca²⁺ transients in the 0.5–5 M range during excitotoxic stimulation, consistent with experimental measurements in cultured neurons [42,43]; these factors implicitly absorb the conversion from current density [A/cm²] to concentration [M] given the single-compartment geometry), M [44], and ms reflects combined buffering and extrusion [42].

Glutamatergic stimulation

Glutamate release was simulated as brief (2 ms) pulses of 1 mM concentration, approximating synaptic cleft concentrations during vesicular release [45]. Stimulation frequencies of 10, 30, 60, 80, 90, and 100 Hz were tested, representing physiological to excitotoxic stimulation levels. Note on frequency interpretation: The 80 + Hz stimulation frequencies serve as modeling proxies for the sustained receptor activation that occurs during pathological glutamate accumulation (e.g., during ischemia), rather than representing directly measured physiological firing rates. This approach enables systematic parameter exploration while capturing the essential feature of excitotoxicity: prolonged, intense glutamatergic stimulation exceeding normal physiological ranges. Each simulation ran for 3000 ms total. Pulsatile glutamatergic input was applied from t = 0 ms; however, to minimize initialization artifacts, we excluded the first 500 ms from all analyses and computed spike counts and peak Ca²⁺ over the steady-state window t = 500–3000 ms (i.e., T_stim = 2.5 s at 80 Hz N_pulses = 200).

Dose-response analysis

Extracellular Mg²⁺ concentration was varied from 0.2 to 2.5 mM. This range spans from severely deficient to moderately elevated levels relative to the physiological concentration of approximately 0.8–1.0 mM in cerebrospinal fluid [24]. High-resolution sampling (0.1 mM steps) was performed in the critical therapeutic region (1.0–2.5 mM) to precisely identify optimal concentrations.

Intervention timing protocol

To assess the temporal window for neuroprotection, we simulated an excitotoxic stress protocol (80 Hz stimulation from t = 0.5 s to t = 4.5 s, total 4 s stress duration) with Mg²⁺ supplementation (from 0.2 mM to 1.8 mM) applied at varying delays: pre-treatment, at stress onset (+0 s), and delayed by +0.1, + 0.2, + 0.3, + 0.4, + 0.5, + 0.75, + 1, + 2, and +3 s relative to stress onset. Simulations were run to 6 s to capture post-stress dynamics; peak calcium metrics were evaluated during the defined stress window. This protocol models clinical scenarios where Mg²⁺ therapy might be initiated at different times relative to ischemic onset [22].

Spike detection

Action potentials were detected using a threshold crossing method (V > −20 mV). Spike probability was calculated as the ratio of detected spikes to expected stimulus pulses during the steady-state period. Spike loss was defined as %.

Calcium metrics

Peak intracellular calcium, , was defined as the maximum reached during the analysis window (500–3000 ms for dose-response analysis; 500–4500 ms for intervention timing analysis, corresponding to the 0.5–4.5 s stress window). This metric captures the maximum calcium load experienced by the cell, which determines excitotoxic vulnerability.

Therapeutic criteria

Two criteria defined the therapeutic window, reflecting the dual goals of neuroprotection and function preservation [10]: (1) Neuroprotection: Peak M (model toxicity threshold). This threshold is supported by experimental evidence that sustained Ca²⁺ elevations above this level are associated with excitotoxic injury [14,43], and is consistent with thresholds used in established computational models of excitotoxicity [42]. Sensitivity analysis was performed across the range of 0.6–1.4 M; the therapeutic window was robust for thresholds between 1.0–1.3 M, and no window exists below 1.0 M (S2 Fig). (2) Function preservation: Spike reduction ≤20% relative to baseline (0.2 mM Mg²⁺). This threshold was chosen based on clinical observations that visual function remains largely preserved with modest RGC loss, while deficits become detectable when loss exceeds ∼30% [5]. The framework allows adjustment of this criterion based on specific clinical priorities. The optimal therapeutic range was defined as Mg²⁺ concentrations satisfying both criteria simultaneously.

Protection efficacy

For intervention timing analysis, protection efficacy was calculated as:

(13)

Numerical methods

All simulations were performed in MATLAB R2023b (MathWorks, Natick, MA) using the forward Euler method with a time step of dt = 0.02 ms. Numerical accuracy was verified by comparing the forward Euler method against a fourth-order Runge-Kutta (RK4) solver, demonstrating <0.2% difference in peak calcium values under identical conditions (S3 Fig). Convergence analysis with decreasing step sizes confirmed that dt = 0.02 ms provides sufficient accuracy while maintaining computational efficiency. All simulations are deterministic; repeated runs under identical parameters yield bit-identical results.

Model behavior and Mg²⁺-dependent NMDA block

The RGC model exhibited physiologically realistic spiking behavior in response to glutamatergic stimulation (Fig 1), consistent with experimental recordings from mammalian RGCs [36,37]. The neuroprotection mechanism (Fig 1A) involves glutamate activation of both AMPA and NMDA receptors, with Mg²⁺ selectively blocking NMDA receptors to reduce calcium influx while preserving AMPA-mediated fast transmission. At low extracellular Mg²⁺ (0.2 mM), the neuron reliably followed input stimuli across all tested frequencies, with strong NMDA receptor activation driving substantial calcium influx. The voltage-dependent Mg²⁺ block function (Fig 1B) demonstrated that at resting potential (−65 mV), NMDA conductance was reduced to approximately 3%, 6%, and 24% of maximum at Mg²⁺ concentrations of 2.0, 1.0, and 0.2 mM, respectively, in agreement with experimental measurements [16,18]. Representative voltage traces (Fig 1C) demonstrate maintained spiking across Mg²⁺ concentrations at 80 Hz, though with reduced reliability at higher concentrations.

Download:

• PNG
  larger image
• TIFF
  original image

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 M 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.

https://doi.org/10.1371/journal.pone.0348068.g001

Increasing extracellular Mg²⁺ progressively reduced intracellular calcium accumulation (Fig 1D, F). At 80 Hz stimulation, peak calcium decreased from 4.59 M at 0.2 mM Mg²⁺ to 0.84 M at 2.0 mM Mg²⁺, representing an 82% reduction (Fig 1F). Notably, spike probability remained near 1.0 at frequencies up to 60 Hz regardless of Mg²⁺ concentration, indicating that AMPA receptor-mediated currents plus intrinsic conductances were sufficient to maintain transmission reliability at these frequencies (Fig 1E).

Frequency-dependent effects of Mg²⁺ on spike output

Dose-response analysis revealed a striking frequency-dependent effect of Mg²⁺ on spike output (Fig 2A). At physiological frequencies (10–60 Hz), spike reduction remained at 0% across all Mg²⁺ concentrations tested, demonstrating that NMDA receptor block did not compromise synaptic transmission under normal conditions. In contrast, at excitotoxic frequencies (80 Hz), Mg²⁺ concentrations ≥1.0 mM progressively reduced spike output, with reduction reaching 10% at 1.0 mM and plateauing at 20% for concentrations between 1.4–2.0 mM. It is important to distinguish two related ranges: the spike loss plateau extends across 1.4–2.0 mM, while the optimal therapeutic window—where calcium additionally falls below the 1.0 M toxicity threshold—is the narrower subset of 1.6–2.0 mM. The 80 Hz frequency represents a critical boundary: at 60 Hz and below, therapeutic windows remain relatively wide (≥1.1 mM), while at frequencies above 80 Hz (90, 100 Hz; Fig 2), no Mg²⁺ concentration simultaneously satisfies both neuroprotection and function criteria—the window closes entirely.

Download:

• PNG
  larger image
• TIFF
  original image

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.

https://doi.org/10.1371/journal.pone.0348068.g002

This spike loss plateau represents a critical finding: within the 1.4–2.0 mM range, spike reduction remained constant at 20% while calcium reduction continued to improve (Fig 2B). This dissociation between spike output and calcium dynamics reflects the distinct roles of AMPA and NMDA receptors: AMPA receptors drive fast spiking while NMDA receptors, with their slower kinetics ( ms), provide temporal summation and calcium entry [41].

Identification of therapeutic windows

The trade-off between neuroprotection and function preservation defined frequency-dependent therapeutic windows (Fig 3). At 80 Hz, plotting calcium reduction against spike reduction revealed an optimal zone where both criteria were satisfied (Fig 3A). Concentrations below 1.6 mM failed to reduce calcium below the toxicity threshold, while concentrations above 2.0 mM exceeded the 20% spike loss limit.

Download:

• PNG
  larger image
• TIFF
  original image

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 M 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).

https://doi.org/10.1371/journal.pone.0348068.g003

High-resolution analysis (0.1 mM steps) precisely identified the optimal range at 80 Hz as 1.6–2.0 mM (S1 Fig, S1 Table). Within this range, all concentrations achieved peak calcium below 1.0 M (ranging from 0.97 M at 1.6 mM to 0.84 M at 2.0 mM) while maintaining spike loss at exactly 20% (160 of 200 expected spikes). This narrow therapeutic window corresponds to mild hypermagnesemia, a clinically achievable target [24]. Sensitivity analysis confirmed robustness across the tested threshold range, with the therapeutic window maintained for Ca²⁺ toxicity thresholds between 1.0–1.3 M (S2 Fig).

The therapeutic window width decreased with increasing stimulation frequency (Fig 3B): 10 Hz: 0.5–2.5 mM (width: 2.0 mM); 30 Hz: 1.0–2.5 mM (width: 1.5 mM); 60 Hz: 1.4–2.5 mM (width: 1.1 mM); 80 Hz: 1.6–2.0 mM (width: 0.4 mM); 90 Hz and 100 Hz: no therapeutic window exists (spike loss exceeds 20% at all neuroprotective concentrations). This narrowing reflects the increasing reliance on NMDA receptor-mediated currents for maintaining spike output at high frequencies [25].

Temporal constraints on Mg²⁺ intervention

The intervention timing protocol demonstrated that Mg²⁺ protection efficacy is highly sensitive to intervention delay (Fig 4). Pre-treatment and intervention at stress onset (+0 s) both achieved 100% protection efficacy, maintaining peak calcium near 1.0 M. However, protection declined steeply with delay: ≥50% protection required intervention within 0.2 s (efficacy at +0.1 s: 82%; at +0.2 s: 50%), while by +0.5 s delay efficacy dropped to approximately 11%, and delays of ≥1 s provided negligible protection (≤3%; Fig 4B).

Download:

• PNG
  larger image
• TIFF
  original image

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.

https://doi.org/10.1371/journal.pone.0348068.g004

The calcium dynamics underlying this temporal sensitivity are evident in Fig 4A. Without Mg²⁺ supplementation, calcium rose rapidly during stress, reaching toxic levels within the first second. Delayed interventions failed to prevent this initial calcium surge, and although Mg²⁺ application eventually reduced the rate of calcium accumulation, peak levels had already exceeded the toxicity threshold. These findings parallel clinical observations that early intervention is critical for neuroprotective efficacy in stroke and other ischemic conditions [22,23].

Because excitotoxic drive begins abruptly in our protocol, the seconds-scale intervention window reflects the rapid early rise of rather than a fundamental biological constraint. We therefore re-expressed timing sensitivity in terms of normalized Ca²⁺ progress—the fraction of untreated peak accumulation reached at the moment of intervention (Fig 5A). Under this state-based representation, ≥50% protection requires intervention before ∼35% of the untreated Ca²⁺ peak is reached, regardless of the absolute time required. The derivation of progress values from the no-Mg²⁺ Ca²⁺ trace is shown in Fig 5B, which illustrates the steep rise characteristic of the abrupt-onset protocol used in simulations.

Download:

• PNG
  larger image
• TIFF
  original image

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 , where 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 treatment occurs—rather than a strict seconds-scale clinical deadline.

https://doi.org/10.1371/journal.pone.0348068.g005

Mechanistic basis of Mg²⁺ neuroprotection

Detailed analysis of synaptic currents confirmed the mechanistic cascade underlying Mg²⁺ neuroprotection (Fig 6). Comparison of low (0.2 mM) versus therapeutic (1.8 mM) Mg²⁺ at 80 Hz revealed that elevated Mg²⁺ substantially reduced NMDA current amplitude (Fig 6B), with peak NMDA current amplitude decreasing by approximately 85% (integrated charge Q_NMDA reduced by 77%; Fig 6D). Despite the strong NMDA block, AMPA current magnitude changed only modestly (∼15%) due to the indirectly altered voltage trajectory (Fig 6C), confirming that the Mg²⁺ block acts selectively on NMDA receptors without directly suppressing AMPA-mediated transmission. This reduction in NMDA current directly translated to reduced calcium influx (Fig 6E), with peak calcium remaining below the 1.0 M threshold throughout stimulation at 1.8 mM Mg²⁺, compared to exceeding 4 M at 0.2 mM Mg²⁺.

Download:

• PNG
  larger image
• TIFF
  original image

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 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 , showing a 77% reduction at 1.8 mM. E: Intracellular calcium accumulation and peak within the displayed 250 ms window (4.17 0.83 M; 80% reduction); note that the full-protocol peak at 0.2 mM Mg²⁺ over the complete 2500 ms analysis window is 4.59 M, 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.

https://doi.org/10.1371/journal.pone.0348068.g006

Importantly, despite the dramatic reduction in NMDA current, spike generation was only modestly affected (Fig 6A). Both conditions produced regular spiking, though with slightly reduced amplitude and reliability at elevated Mg²⁺. This preservation of function reflects the role of AMPA receptors and intrinsic conductances in maintaining spike generation [11]. The mechanistic cascade is summarized schematically (Fig 6F): increased [Mg²⁺]_ext enhanced NMDA block reduced I_NMDA decreased Ca²⁺ influx neuroprotection.

Summary of principal findings

Our simulations demonstrate that extracellular Mg²⁺ provides frequency-dependent neuroprotection through voltage-dependent NMDA receptor block. At physiological stimulation frequencies (10–60 Hz), elevated Mg²⁺ substantially reduced intracellular calcium accumulation (50–85%, across the 1.0–2.5 mM range) without compromising spike output, indicating that AMPA receptor-mediated transmission alone is sufficient to maintain synaptic function under normal conditions.

However, at the modeled excitotoxic boundary (80 Hz), a narrow therapeutic window of 1.6–2.0 mM emerged, where both neuroprotection (peak Ca²⁺ below 1.0 M) and function preservation (spike loss ≤20%) criteria were satisfied simultaneously. This finding is clinically relevant, as concentrations in this range represent mild hypermagnesemia that is achievable through therapeutic intervention [22,24].

The spike loss plateau phenomenon observed at 80 Hz represents a particularly important finding. Within the 1.4–2.0 mM range, spike reduction remained constant at 20% while calcium accumulation continued to decrease. However, it is the narrower 1.6–2.0 mM subset—where calcium additionally falls below the 1.0 M toxicity threshold—that constitutes the true therapeutic window, creating an “optimal zone” for simultaneous neuroprotection and function preservation. This dissociation reflects the distinct biophysical roles of AMPA and NMDA receptors [11,41].

Comparison with previous computational studies

Our modeling approach extends previous computational investigations of glutamatergic synaptic transmission and NMDA receptor dynamics. The synaptic kinetics and NMDA receptor formulations employed in our model are consistent with established frameworks [31,38]. The voltage-dependent Mg²⁺ block formulation follows the Jahr-Stevens model [18], which has been extensively validated against experimental data [11,25].

Previous computational work on opioid-induced synaptic plasticity has demonstrated that modifications to NMDA receptor function can profoundly influence calcium dynamics and downstream signaling cascades [12,31]. Interestingly, computational studies of cocaine’s effects on neuronal excitability have shown that drugs affecting potassium conductances can dramatically alter action potential generation [46]. While our model focuses on Mg²⁺ modulation of NMDA receptors, both studies highlight how relatively modest changes in ionic conductances can produce qualitatively different firing patterns.

Mechanistic insights into Mg²⁺ neuroprotection

The mechanistic cascade underlying Mg²⁺ neuroprotection in our model is consistent with the established physiology of NMDA receptor-mediated excitotoxicity [14,16,17]. Recent cryo-EM structural studies have provided unprecedented insights into the molecular basis of Mg²⁺ action on NMDA receptors, identifying three distinct binding sites [19]. The approximately 85% reduction in NMDA current amplitude observed at therapeutic Mg²⁺ concentrations directly translates to reduced calcium loading.

A critical insight from our model is that the voltage-dependence of the Mg²⁺ block creates a natural activity-dependent filter. This mechanism differs fundamentally from competitive NMDA receptor antagonists, which reduce receptor function in a voltage-independent manner [15]. The voltage-dependent nature of Mg²⁺ block may explain why Mg²⁺ supplementation has shown promise in neuroprotection without adverse cognitive effects [22].

Biological interpretation of intervention timing

The steep decline in protection with intervention delay (≥50% protection requires ≤0.2 s; ∼11% by 0.5 s in our protocol) should not be interpreted as a literal clinical deadline. Rather, it reflects the importance of relative timing within the excitotoxic process. In our idealized protocol, stress begins abruptly at full intensity; clinical conditions such as retinal ischemia or glaucoma involve gradual glutamate accumulation over minutes to hours. The same principle holds: earlier intervention, before the cell has accumulated substantial Ca²⁺ load, yields greater protection—but the absolute timescale is set by the rate of Ca²⁺ accumulation in the specific pathological context, not by the seconds-scale protocol used here.

More directly, our results provide strong support for prophylactic Mg²⁺ supplementation in at-risk scenarios (e.g., patients undergoing ocular surgery, those with acute angle-closure glaucoma attacks, or retinal vascular occlusion), where treatment can be initiated before or concurrent with excitotoxic stress onset. The 100% protection efficacy observed with pre-treatment underscores this preventive strategy. For slowly progressive conditions such as glaucoma, the timing results suggest that neuroprotective intervention early in the disease course—before cumulative calcium-mediated damage becomes extensive—offers the greatest potential benefit.

Our quantitative reanalysis (Fig 5) provides a rigorous framework for this interpretation. By re-expressing timing in terms of normalized Ca²⁺ progress—the fraction of untreated peak accumulation at intervention—we demonstrate that protection efficacy is determined by the state of the cell (Ca²⁺ load) rather than absolute clock time. The critical state-based threshold for ≥50% protection corresponds to ∼35% Ca²⁺ progress. In biological settings where excitotoxicity develops more gradually than in our abrupt-onset simulations, the same Ca²⁺-state threshold would correspond to longer absolute intervention windows. This state-based interpretation reconciles our seconds-scale simulation results with the clinical reality that neuroprotective interventions in stroke show diminishing returns with treatment delay [22,23], while avoiding the implication of an unrealistic seconds-scale clinical deadline.

Validation against experimental and clinical data

Our predicted optimal Mg²⁺ range (1.6–2.0 mM) corresponds to mild hypermagnesemia that is readily achievable clinically. Normal serum Mg²⁺ is 0.7–1.0 mM, while therapeutic hypermagnesemia protocols (e.g., for eclampsia or neuroprotection trials) routinely achieve 2.0–3.5 mM [22]. The FAST-MAG trial demonstrated that serum levels of 2.5–3.0 mM can be achieved within 2 hours of prehospital administration [23].

Several experimental findings align with our predictions. Studies of retinal ischemia have reported reduced RGC loss with Mg²⁺ supplementation at concentrations within our therapeutic range [3]. Conversely, the Intravenous Magnesium Efficacy in Stroke (IMAGES) trial found no benefit from Mg²⁺ in stroke when administered late (median 7 hours post-onset) [47], consistent with our finding that delayed intervention provides negligible protection. This framework may help explain mixed clinical results: efficacy depends critically on both concentration (within the narrow therapeutic window) and timing (early intervention).

Translational considerations for Mg²⁺ concentrations

Retinal extracellular Mg²⁺ is regulated by the blood-retinal barrier, with concentrations typically 10–15% below serum levels (similar to cerebrospinal fluid). Achieving our therapeutic range of 1.6–2.0 mM in retinal tissue would therefore require serum levels of approximately 1.8–2.3 mM—within the range routinely achieved in clinical hypermagnesemia protocols [22,23]. Local delivery routes such as intravitreal injection could potentially achieve therapeutic retinal concentrations with lower systemic exposure, though pharmacokinetic studies specific to retinal Mg²⁺ distribution would be needed to optimize such approaches.

Understanding mixed clinical results

Several clinical trials of Mg²⁺ neuroprotection have yielded disappointing results, which our computational framework may help contextualize. The IMAGES trial found no benefit from intravenous Mg²⁺ in stroke, but treatment was initiated late (median 7 hours post-symptom onset) and achieved serum levels (1.5–1.8 mM) at the lower end of our therapeutic range [47]. Our model predicts negligible protection with delayed intervention (≥1 s in model time) and suggests that concentrations below 1.6 mM may provide insufficient NMDA block at excitotoxic frequencies.

Similarly, the FAST-MAG trial, despite achieving higher serum Mg²⁺ levels with early prehospital administration, showed no overall benefit—though subgroup analyses hinted at efficacy in specific stroke subtypes [23]. Our findings suggest that population heterogeneity in excitotoxic severity (analogous to different stimulation frequencies) could produce variable responses, as the therapeutic window narrows dramatically at higher stress levels. This hypothesis remains to be tested experimentally.

These considerations highlight the potential value of computational modeling: by identifying critical dependencies on concentration and timing, such frameworks may help guide trial design toward parameter regimes with higher probability of success.

Implications for RGC neuroprotection

Glaucoma, affecting over 70 million people worldwide, is characterized by progressive RGC loss [4,5]. Recent studies have identified caspase-mediated pathways as promising therapeutic targets [6], and emerging evidence supports synergistic neuroprotective approaches [9]. Additionally, neurotrophic factor delivery through gene therapy vectors has shown remarkable promise [48]. Our findings suggest that Mg²⁺ supplementation in the range of 1.6–2.0 mM could provide meaningful neuroprotection and may act synergistically with these emerging strategies.

Model limitations and future directions

We acknowledge several limitations inherent to our computational approach. Our RGC model uses a single-compartment approach that cannot capture dendritic Ca²⁺ microdomains [49]. Dendritic compartmentalization of NMDA receptors could create localized Ca²⁺ microdomains with peak concentrations significantly exceeding our soma-averaged estimates. This spatial heterogeneity has two implications: (1) local Ca²⁺ might reach toxic levels more rapidly, potentially increasing timing sensitivity beyond our predictions, and (2) spatial isolation could provide compartmentalized protection, possibly enabling efficacy at lower bulk Mg²⁺ concentrations. Our single-compartment estimates should therefore be considered conservative, representing an upper bound on the required therapeutic concentration. Future multi-compartment models incorporating realistic RGC dendritic morphology and NMDA receptor distributions would help quantify these spatial effects.

Glutamate input was modeled as periodic pulses; real excitotoxic environments involve irregular patterns. The model omits glial glutamate clearance and network-level interactions [31]. The criteria defining our therapeutic window are physiologically motivated but simplified [14]. The steep decline in protection with delay (≥50% protection requires ≤0.2 s) arises from our specific abrupt-onset protocol; clinical ischemia develops more gradually, and the equivalent timescale would be correspondingly longer. The Mg²⁺ concentrations cannot be directly equated to clinical dosing [24]. Finally, these predictions require experimental validation.

Despite these limitations, the model provides a mechanistically grounded framework, identifies testable predictions, and establishes a computational platform that can be extended as experimental data become available.