# Path Kinetics

Status: v0.2 reduced-order Complex I path kinetics

## Purpose

This layer turns extracted cofactor distances into hop-specific rate estimates. It is meant to make the simulation auditable: the protein/cofactor view, tunneling-window view, and Structure tab all use the same path-kinetics calculation.

## Path Merge

The default Complex I path is the human `5XTD` candidate path:

```text
FMN -> N3 -> N1b -> N4 -> N5 -> N6a -> N6b -> N2 -> Q
```

The human `5XTD` extraction currently lacks a computed `N2 -> Q` edge. The app fills only that missing edge from the comparative Q-bound bovine `8Q1U` path and marks it with an asterisk.

This merge is intentionally conservative:

- use `5XTD` when a human edge is computed
- use `8Q1U` only when the corresponding human edge is missing
- mark comparative edges and long edges visibly
- keep Fe-S assignment caveats visible

## Rate Estimate

For each edge with an extracted distance `R`, the app computes:

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

Current reduced-order settings:

```text
DeltaG = -0.10 eV
lambda = live hydration/dielectric-derived model value
environment scale = live geometry/hydration/supercomplex-derived model value
```

The implementation applies the environment term as:

```text
log10(k_ET)_display = log10(k_ET) + log10(environment scale)
```

The tunneling window also reports:

```text
relative coupling ~= exp(-beta R)
```

where `beta` is the live effective tunneling decay parameter.

## Bottleneck Rule

The bottleneck is the computed edge with the lowest `log10(k_ET)` under the current slider state.

The app also flags any edge above:

```text
14 A
```

as outside the usual productive single-hop window. This is a warning threshold, not a proof that no biological transfer can occur, because real proteins can involve alternate atom paths, water/protein mediation, conformational gating, and state-dependent geometry.

## Current Important Result

The comparative `8Q1U` `N2 -> Q` edge is:

```text
24.7 A
```

after redox-atom filtering. Under the current reduced-order Dutton calculation, this becomes the path bottleneck and is rendered as a long-edge warning.

Interpretation:

- This is useful as an instrument warning.
- It is not yet a publication-grade claim about the true mammalian Complex I terminal Q handoff.
- The next scientific upgrade is manual Q-site/conformation review and edge-specific redox energetics.

## Implementation

Core implementation:

```text
src/model/path-kinetics.js
```

Consumers:

```text
src/ui.js
src/render/canvas.js
```