Technical Summary: MC-BRIDGE

Problem Statement

Molecular communication (MC) for organoid-facing readouts requires a framework that connects extracellular chemical transport, receptor binding kinetics, and Organic Electrochemical Transistor (OECT) transduction to final detection metrics. Existing models often isolate components or lack a unified end-to-end framework that accounts for the coupling of geometry, noise covariance, calibration, and receptor memory. Specifically, there is a need for a modular simulation environment that can rigorously evaluate OECT-based MC receiver designs, distinguishing between physical layer effects (diffusion, binding) and receiver processing effects (noise, calibration, decision logic) while handling multichannel correlated noise and inter-symbol interference (ISI).

Methodology

The paper introduces MC-BRIDGE (Molecular Communication Bioelectronic Receiver-chain Integrated Design and Guided Evaluation), a modular simulation framework. The methodology is structured around a replaceable module chain that maps a transmitted symbol sequence through the following stages:

1. Release: Finite rectangular bursts or stochastic Poisson emission of molecules (e.g., Dopamine, Serotonin).
2. Transport & ISI: Modeled via 3D effective extracellular Green's functions, accounting for diffusion, tortuosity, clearance, and finite-area observation (averaging over a square gate rather than a point).
3. Binding: Implementation of both deterministic Langmuir kinetics and stochastic birth–death occupancy models (Gillespie SSA) for receptor sites.
4. Transduction: A quasi-static OECT model converting bound sites to current via transconductance and volumetric capacitance.
5. Noise & Referencing: Synthesis of multichannel colored noise (thermal, flicker, drift) on an independent electrical time grid. This includes matched-control referencing (subtracting a control channel signal) to mitigate common-mode noise.
6. Detection: Charge-domain integration over a decision window, followed by MoSK, CSK, or Hybrid decision logic using calibrated thresholds.

Verification Protocol:
The framework employs a rigorous verification protocol combining analytical solutions, independent numerical references (Brownian motion simulations, Gillespie SSA), and convergence tests. Key verification steps include:

• Comparing analytical transport with Brownian simulations.
• Validating stochastic binding against exact-transition methods.
• Ensuring consistency between finite-area quadrature and point-observer limits.
• Using disjoint seed sets for calibration, adaptive search, and held-out evaluation to prevent overfitting and ensure unbiased performance estimation.

Key Contributions

1. Modular Framework: A unified architecture linking release, transport, binding, OECT transduction, and detection through explicit input/output interfaces that preserve physical and statistical meaning.
2. Consistent Electrical/Statistical Treatment: Generation of full-sequence multichannel colored noise on an electrical grid independent of the molecular step, utilizing general positive-semidefinite correlation matrices and a common one-sided power spectral density (PSD) convention.
3. Verification and Transfer Evidence:
   • Validation of finite-area observation versus center-point models.
   • Comparison of lumped binding versus nodewise binding.
   • Analysis of calibration transfer across operating points (varying molecule budget, distance, and control gain).
   • Sensitivity analysis of ISI and memory depth.
4. Held-Out Budget Bound: A methodology using independent "held-out" records with seeds disjoint from search and calibration to establish a tested-grid upper bound on the minimum molecule budget meeting a Symbol Error Rate (SER) target.

Results

Using a reference tri-channel scenario (Dopamine-selective, Serotonin-selective, and Hydrogel-matched Control channels) targeting brain organoid interfaces:

• Finite-Area Effect: Replacing a center-point observer with a finite-area (200 µm square gate) observer retains only 27.5% of the center-point decision-charge magnitude at nominal separation, significantly altering the signal scale.
• Control Referencing: The benefit of control referencing (CTRL) is conditional on covariance. When selective–CTRL correlation is favorable, CTRL reduces SER (e.g., from 0.017 to 0.005 at specific budgets). However, at zero correlation, CTRL can degrade performance.
• Calibration Transfer: Fixed nominal thresholds fail under operating point mismatch (SER rising to 0.609). Scheduled refresh and per-point recalibration significantly mitigate this, though per-point recalibration remains the optimistic benchmark.
• Memory and ISI: Retaining receptor memory (propagating occupancy across symbols) without ISI mitigation leads to high SER (e.g., 0.686 with $H_{ISI}=3$). Occupancy reset (no-ISI) benchmarks are necessary to isolate receiver processing performance.
• Budget Bound: For the passive-field, no-ISI, per-point calibrated scenario, the adaptive search and held-out evaluation support a minimum molecule budget bound of approximately 300,848 molecules/symbol (0.50 amol) to meet an SER target of $10^{-2}$.

Significance and Claims

The paper claims that MC-BRIDGE provides a necessary computational method for the controlled, reproducible comparison of OECT-MC receiver hypotheses. Its significance lies in:

• Decoupling Effects: It separates the impacts of geometry, covariance, calibration, and memory on receiver conclusions, which are often conflated in single end-to-end curves.
• Reusability: The modular interface allows candidate designs to be compared using the same OECT charge statistic while retaining intermediate physical states.
• Rigorous Evaluation: By enforcing disjoint seed sets for calibration and evaluation, and using block-bootstrap intervals for error estimation, the framework provides statistically robust bounds on performance metrics like SER and mutual information.

The authors emphasize that the reported bounds are conditional on the specific assumptions of the passive-observer model, occupancy reset, and per-point calibration. They note that predicting device performance in real-world scenarios requires mass-conserving reactive transport models and measurements of actual device parameters, which are beyond the scope of this simulation framework.