ASAL-Inspired Agent-Based Framework for Glioblastoma

• The paper introduces an ASAL-inspired agent-based framework that integrates mitochondrial efficiency, ionic conductance, gap-junction coupling, and ROS dynamics to simulate multicellular bioelectric transitions.
• It employs coupled differential equations to model membrane potential, ATP dynamics, and ROS regulation, revealing a critical Meff threshold that marks the shift from healthy to tumor-like cellular states.
• Evolutionary strategies map genotype-phenotype resilience, demonstrating that mitochondrial leakiness below a Meff of 0.6 is sufficient to trigger bioelectric instability associated with glioblastoma.

An ASAL-inspired agent-based framework is a computational architecture designed to simulate multicellular bioelectric transitions, integrating mitochondrial efficiency, ionic conductance, gap-junction coupling, and reactive oxygen species (ROS) dynamics. Developed in the context of glioblastoma initiation, this framework leverages agent-based modeling to resolve cell-autonomous and tissue-scale electrophysiological signatures, especially those arising from metabolic dysfunction. "ASAL-inspired" refers to the inclusion of principles from active state-attractor landscapes, where agent behavior emerges from the dynamic coupling of bioelectrical and metabolic states. Central to this approach is the use of mitochondrial efficiency (Meff), a dimensionless scalar parameter that modulates oxidative phosphorylation-driven ATP production and, consequently, bioelectric stability.

1. Formal Definition and Implementation of Mitochondrial Efficiency

In the framework, mitochondrial efficiency is defined as follows:

$$\mathrm{Meff}(t) = \frac{J_{\mathrm{OX}(t)}}{J_{\mathrm{OX}^{\max}}}$$

where $J_{\mathrm{OX}^{\max}}$ is the maximal ATP production rate via oxidative phosphorylation under healthy, normoxic conditions, and $J_{\mathrm{OX}(t)}$ is the instantaneous rate in a given cell at time $t$ (Pawlak, 24 Nov 2025). Meff aggregates the effects of mitochondrial inner-membrane integrity, electron-transport-chain coupling, and substrate availability. In practice, oxygen tension is held constant; Meff acts as an abstract "leakiness" parameter directly scaling the oxidative ATP flux. When Meff < 1, glycolytic ATP production can partially compensate, but this reprogramming recapitulates the metabolic phenotype of the Warburg effect (Vazquez, 21 Mar 2024).

ATP dynamics in the framework are thus governed by:

$$\frac{d[\mathrm{ATP}]}{dt} = \mathrm{Meff} \cdot R_{OX} + (1-\mathrm{Meff}) \cdot R_{GLY} - \kappa_I \sum_\alpha |I_\alpha| - \frac{[\mathrm{ATP}] - [\mathrm{ATP}]_{base}}{\tau_{ATP}}$$

with parameters $R_{OX}$, $R_{GLY}$, $\kappa_I$, and $\tau_{ATP}$ as detailed in Table 1 below.

Parameter	Symbol	Value (healthy)	Units
Oxidative-ATP rate	$R_{OX}$	0.020	mM·ms⁻¹
Glycolytic rate	$R_{GLY}$	0.010	mM·ms⁻¹
ATP Km	$K_{M,ATP}$	0.6	mM
Pump max	$P_{max}$	1.0	μA·cm⁻²
ROS decay τ	$\tau_{ROS}$	10⁴	ms

2. Bioelectrical and Metabolic Feedbacks

Each agent (cell) solves coupled ordinary differential equations for:

• Membrane potential ($V$), modulated by a balance of Ohmic, voltage-gated, and pump currents.
• Intracellular ATP, via Meff-scaled metabolic flux and ATPase consumption.
• ROS, with dynamics driven by mitochondrial inefficiency ($k_{Meff}(1-\mathrm{Meff})$), intracellular $Ca^{2+}$, and linear decay.
• Intercellular coupling via gap-junctional conductance ($G_{gap}$), exponentially suppressed by local ROS:

$G_{gap}(ROS) = G_{gap}^{0} \exp(-k_{ROS} [ROS])$

Degradation of Meff by ROS is imposed:

$$\frac{d\,\mathrm{Meff}}{dt} = -k_{d} [ROS] - \frac{\mathrm{Meff} - \mathrm{Meff}_{init}}{\tau_{circ}}$$

This structure tightly couples energy transduction failures to electrophysiological instability, reflecting pathophysiological features of glioblastoma.

3. Critical Threshold and Bifurcation Analysis

The framework’s hallmark is the identification of a sharp bifurcation in bioelectric state as Meff is varied. Systematically sweeping Meff from 1.0 to 0.3, the fraction of depolarized cells ($\mathrm{DepolFrac}$) transitions steeply at:

$\mathrm{Meff}^* \approx 0.60$

Above this threshold ($\mathrm{Meff} > 0.6$), cells maintain hyperpolarized potentials ($V \approx -80$ mV), normal ATP ($\approx 1\,\mathrm{mM}$), and low ROS. Below it, the model predicts robust emergence of tumor-like attractors (depolarized $V \approx -30$ mV, ATP collapse $<0.1$ mM, high ROS). Jacobian-based local stability analysis confirms that one eigenvalue crosses zero at $\mathrm{Meff} \approx 0.6$, demarcating the loss of healthy bioelectric stability (Pawlak, 24 Nov 2025).

4. Evolutionary Optimization and Resilience Mapping

Evolutionary strategies (genetic algorithms, MAP-Elites) serve two purposes: to map genetic parameter resilience under fixed Meff (Stage B) and to track emergence of malignant attractors under evolving Meff (Stage C). Genotypes encode log-transformed conductances, initial Meff, pump kinetics, and gap-junction parameters. Fitness functions weigh depolarization fraction, deviation from healthy voltage, bioelectric entropy, and pattern scores tuned to GBM spatial signatures.

Key outcomes:

• Stage B: Hyperpolarization resists depolarization when Meff = 1, with high fitness for genotypes favoring high potassium leak and moderate pump strength.
• Stage C: Meff evolves down to 0.30; depolarized, ROS-dominated attractors dominate; "oncochannel" patterns emerge (↑$G_{Na_{VG}}$, ↓$G_{gap}$), quantifying the sufficiency of mitochondrial dysfunction for malignant transitions.

Fitness evolution (Stage C): Gen 0 → 9: $\overline{\mathrm{Meff}_{init}} = 0.39 \to 0.30$, $\overline{\mathrm{DepolFrac}} = 0.69 \to 0.97$, fitness 0.03 → 0.40.

5. Mechanistic and Biological Insights

The agent-based paradigm mechanistically links Meff deficit to cellular and tissue-level pathology:

• Meff↓ ⇒ oxidative ATP↓ ⇒ Na⁺/K⁺-ATPase failure ⇒ K⁺ leak dominance ⇒ membrane depolarization.
• Meff↓ ⇒ ROS↑ ⇒ gap-junction uncoupling ⇒ loss of voltage-buffering ⇒ spatial heterogeneity and depolarized clusters.
• ATP collapse ($[ATP] \to 10^{-2}$ mM in < 100 ms) and ROS surge (×10³) mirror the early bioenergetic crisis and oxidative-damage feedbacks observed in GBM.

These transitions recapitulate canonical oncogenic bioelectric phenomena, arguing that mitochondrial "leakiness" (Meff < 0.6) is both necessary and sufficient for bioelectric state shifts underpinning tumor initiation. The approach enables simultaneous exploration of genotype-phenotype landscapes and tissue-level biophysics.

6. Contextualization within Mitochondrial Efficiency Research

The ASAL framework formalizes Meff as a central control parameter, grounded in the biophysical metrics and energetic context established by Vazquez (Vazquez, 21 Mar 2024), molecular motor dissipation models (Matar et al., 30 Jun 2025), and evolutionary bioenergetics (Martin, 21 Mar 2025). Importantly,

• Vazquez’s proteomic-efficiency formalism links protein mass and occupied volume to ATP output, with empirical rates for glycolysis (88 mmol h⁻¹ g⁻¹) and OxPhos (52 mmol h⁻¹ g⁻¹), justifying the model’s treatment of glycolytic compensation under lowered Meff.
• Dissipative constraints in ATP synthase—internal friction, proton leak, and information-theoretic costs—impose upper bounds on achievable Meff, contextualizing agent-level Meff within global mitochondrial energetics (Matar et al., 30 Jun 2025).
• Bioenergetic resource allocation and evolutionary capacity for increased ATP throughput further clarify the system-level significance of Meff modulation (Martin, 21 Mar 2025).

7. Limitations and Prospective Extensions

The current ASAL-inspired framework approximates Meff phenomenologically, without explicit tracking of oxygen diffusion, NADH/NAD⁺ pools, or proton-motive force. ROS states are modeled as scalar fields, lacking chemical specificity (e.g., superoxide, hydrogen peroxide oxidation paths). The agent-based grid is 2D and omits vascularization or immune interaction. Prospective directions include:

• Coupling Meff to spatial gradients of oxygen via partial differential equations,
• Expanding ROS modeling to capture distinct redox chemistry,
• Integrating modules for mitochondrial biogenesis and autophagic turnover,
• Extending to 3D cellular architecture and microenvironmental feedback.

Such elaborations would enhance mapping between computational attractor landscapes and experimentally observed bioelectric and metabolic heterogeneity in oncogenesis.

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The ASAL-inspired agent-based framework robustly elucidates the interplay between mitochondrial efficiency and multicellular bioelectric transitions, offering a computational testbed for quantifying the mechanistic sufficiency of metabolic dysfunction in driving pathological state transitions (Pawlak, 24 Nov 2025).