# ⚛  L1 Principle — Michaelis-Menten Enzyme Kinetics

**ID:** `L1-302` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Enzymatic rate laws*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** V KM parameter pair
> **📡 Carrier:** none · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 1 · **⛓ Block:** 41554114

---

## 🧠 1. Introduction

**Michaelis-Menten Enzyme Kinetics** is a **nonlinear inverse problem** whose unknown lives in **V KM parameter pair** space, within the **Enzymatic rate laws** sub-domain of **Computational Chemistry**.

Measurements consist of none via a **initial rate assay** sensing mechanism.

The forward operator applies, in order: E · enzyme substrate operator; O · composite method operator; O · rate v operator.

Observations are corrupted by additive Gaussian noise. Well-posed; linear in Lineweaver-Burk; Bayesian MCMC for Bayesian parameter estimation.

## ⚙ 2. Forward Model

Physical chain: **x** → E · enzyme substrate → O · composite method → O · rate v → **y** (detector).

```
y = `O.rate_v` `O.composite_method` `E.enzyme_substrate` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.enzyme_substrate` | E · enzyme substrate operator |
| `O.composite_method` | O · composite method operator |
| `O.rate_v` | O · rate v operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Enzymatic rate laws |
| Carrier | none |
| Problem class | nonlinear_inverse |
| Solution space | V_KM_parameter_pair |
| Noise model | gaussian |
| Integration axis | substrate_concentration |
| Difficulty delta | 1 |
| L dag | 2.5 |

## 📡 4. Measurement Model

Well-posed; linear in Lineweaver-Burk; Bayesian MCMC for Bayesian parameter estimation.

| Metric | Value |
|---|---|
| Metric | Km_relative_error |
| Secondary | Vmax_relative_error |

## 📏 5. Operating Range (Ω)

**Center problem class:** `michaelis_menten` · **Forward operator:** `michaelis_menten_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Ph | — | 7.4 |
| T k | — | 298 |
| S range mm | mm | 0.01 – 100 |
| N data points | — | 20 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Ph | — | 1 – 14 |
| T k | — | 273 – 373 |
| N data points | — | 5 – 10000 |
| S range mm max | — | 1 – 10000 |
| S range mm min | — | 0.001 – 1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** K_M rel error <= 0.05

| Metric | Range |
|---|---|
| Km relative error | 0.01 – 0.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **Km_relative_error**, with κ = `30` and δ = `1`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xa04d92a91515a657a029aa132c9699971aea9d4b4afb461933306e4794206fbf`
- **Chain tx hash:** `0xb5ca954ebc190f13eea0b58a1b59f8ffd7d93b2a25945c04c50a323a33325cd7`
- **Chain block:** `41554114`

---

## File Mapping

This bundle consists of: `L1-302.md`, `L1-302.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-302.md` | Source of truth — edit this | Human or LLM |
| `L1-302.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-302`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._