# Model Spec

Status: v0.1 science instrument spine

## Standard

The simulation must be visually compelling, but it must not overstate the science. The goal is for a mitochondrial bioenergetics researcher, a protein electron-transfer biophysicist, and an aging/cancer metabolism researcher to recognize the model as disciplined, even where they may debate the hypothesis.

Core rule: if a visual element looks more certain than the evidence supports, the visual is wrong.

## Thesis

Mitochondrial electron flow is quantum-mechanical at the electron-transfer step: electrons move through redox cofactors by thermally assisted tunneling and hopping. The relevant biological control layer is not long-lived quantum coherence. It is environmental tuning: protein structure, redox potentials, donor-acceptor distances, hydration, dielectric screening, proton-coupled gating, membrane potential, cardiolipin-rich membrane organization, and supercomplex geometry.

Working hypothesis:

1. Young/regulated mitochondria protect productive quantum electron transfer by maintaining a tuned protein-membrane environment.
2. Aging progressively dysregulates that environment, increasing kinetic stalls, proton leak, ROS leak, and loss of ATP yield.
3. Cancer, in a broad and context-dependent sense, often rewires redox and bioenergetic control to sustain growth, survival, redox signaling, therapy resistance, and/or metastatic fitness.

This is a model of regulated quantum-enabled bioenergetics, not a claim that cancer or aging are caused by a single quantum switch.

## Evidence Classes

Supported foundation:

- Mitochondrial electron transport transfers electrons from NADH/FADH2-derived substrates through Complexes I-IV to oxygen.
- Complexes I, III, and IV pump protons across the inner mitochondrial membrane; Complex II does not.
- The proton motive force has electrical and chemical components.
- Biological electron transfer through proteins depends strongly on donor-acceptor distance, redox driving force, electronic coupling, and reorganization energy.
- ROS can arise when electrons leak to oxygen from redox centers or semiquinone states, especially in Complex I and Complex III.
- Aging is associated with mitochondrial bioenergetic decline, increased oxidative stress, altered cardiolipin/lipid environment, proton leak, and supercomplex destabilization in multiple contexts.
- Cancer metabolism is heterogeneous; mitochondria remain important in many cancers, and OXPHOS can support survival, resistance, and metastasis in subsets.

Model assumptions:

- The simulation compresses many individual cofactors into a tractable redox network.
- Parameter sliders alter effective rates, not atomistic structures.
- Tunneling protection means preservation of donor-acceptor coupling, geometry, hydration/dielectric support, and redox/proton gating.
- ROS probability is modeled as a competing leak branch whose probability increases with stalled carriers, high reduction pressure, excessive PMF, reverse electron transport conditions, or damaged coupling.

Hypothesis layer:

- Aging and cancer presets represent qualitative system-level tendencies, not universal states.
- The cancer preset is a generalized rewired/high-pressure condition, not a claim that all cancers have increased mitochondrial respiration.
- The model explores whether loss or rewiring of environmental tuning can explain different electron-flow signatures in aging and cancer-like states.

## Constants

| Symbol | Meaning | Value |
| --- | --- | ---: |
| F | Faraday constant | 96485 C mol^-1 |
| R | Gas constant | 8.314 J mol^-1 K^-1 |
| T | physiological temperature | 310.15 K |
| RT/F at 310.15 K | thermal voltage | 26.7 mV |
| 2.303RT/F at 310.15 K | pH-to-mV factor | 61.5 mV pH^-1 |

## Core Equations

Redox free energy:

```text
DeltaG = -n F DeltaE
```

For NADH to oxygen under biochemical standard-style values:

```text
E(NAD+/NADH) ~= -0.320 V
E(O2/H2O) ~= +0.820 V
DeltaE ~= 1.140 V
DeltaG ~= -2 * 96485 * 1.140 = -220 kJ mol^-1 NADH
```

Proton motive force:

```text
DeltaP = DeltaPsi - (2.303 R T / F) DeltaPH
```

The app displays PMF magnitude:

```text
PMF_magnitude ~= DeltaPsi_mV + 61.5 * DeltaPH_magnitude
```

Marcus electron transfer:

```text
k_ET = (2*pi/hbar) * |H_DA|^2
       * 1/sqrt(4*pi*lambda*kB*T)
       * exp[-(DeltaG + lambda)^2 / (4*lambda*kB*T)]
```

Electronic coupling distance dependence:

```text
H_DA = H0 * exp[-beta * R / 2]
```

Educational Dutton-style rate estimate used for relative rates:

```text
log10(k_ET) = 13 - 0.6*(R - 3.6) - 3.1*((DeltaG + lambda)^2 / lambda)
```

The Complex I path-kinetics layer applies this equation to each extracted redox-atom edge distance, marks the lowest-rate edge as the current bottleneck, and flags edges above 14 A as outside the usual productive single-hop window.

## Stoichiometry

Per 2 electrons:

| Entry path | Complex I | Complex III | Complex IV | Total pumped H+ |
| --- | ---: | ---: | ---: | ---: |
| NADH | 4 | 4 | 2 | 10 |
| FADH2/succinate via Complex II | 0 | 4 | 2 | 6 |

ATP synthase:

```text
mammalian c-ring ~= 8 H+ per 3 ATP through F_o
effective P/O ~= 2.5 ATP per NADH
effective P/O ~= 1.5 ATP per FADH2
```

## Visual Rules

- Complex I, II, III, IV, and V must be labeled correctly.
- Matrix, inner membrane, and intermembrane/crista lumen side must be separated correctly.
- Q moves within the inner membrane.
- Cytochrome c is on the intermembrane-side surface.
- Protons pump from matrix to intermembrane/crista lumen side.
- Protons return through ATP synthase to matrix.
- ROS leaks from plausible sites: Complex I FMN/Q and Complex III Qo.
- Electron transfer is shown as discrete probabilistic hops, not fluid electricity.

## No-Go Criteria

No-go if:

- Quantum is used as a generic glow effect.
- Cancer is presented as one metabolic state.
- Aging is presented as one linear decline.
- ROS is treated as only damage or only signal.
- ATP yield ignores proton leak and membrane potential.
- Equations appear in the UI but do not drive the simulation.