L1 ⚛ L1-302 ⊙ Testnet

Michaelis-Menten Enzyme Kinetics

Computational Chemistry · Enzymatic rate laws

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⬇ L1-302.md

# ⚛ 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._

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Read the attached Markdown (L1-302.md).
Regenerate L1-302.json so every field matches the Markdown.
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L2-302-001 Michaelis-Menten Enzyme Kinetics Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554114,
  "chain_hash": "0xa04d92a91515a657a029aa132c9699971aea9d4b4afb461933306e4794206fbf",
  "chain_tx_hash": "0xb5ca954ebc190f13eea0b58a1b59f8ffd7d93b2a25945c04c50a323a33325cd7",
  "domain": "Computational Chemistry",
  "hardness_fn": {
    "delta": 1,
    "kappa": 30,
    "metric": "Km_relative_error",
    "type": "epsilon_fn"
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "Km_relative_error",
    "regime": "Well-posed; linear in Lineweaver-Burk; Bayesian MCMC for Bayesian parameter estimation.",
    "secondary": "Vmax_relative_error"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "none",
    "difficulty_delta": 1,
    "domain": "Computational Chemistry",
    "integration_axis": "substrate_concentration",
    "noise_model": "gaussian",
    "primitives": [
      "E.enzyme_substrate",
      "O.composite_method",
      "O.rate_v"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "initial_rate_assay",
    "solution_space": "V_KM_parameter_pair",
    "sub_domain": "Enzymatic rate laws",
    "title": "Michaelis-Menten Enzyme Kinetics"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "michaelis_menten_forward"
    ],
    "allowed_omega_dimensions": [
      "S_range_mM",
      "N_data_points",
      "T_K",
      "pH"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "K_M rel error \u003c= 0.05",
      "forward_operator": "michaelis_menten_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_data_points": 20,
        "S_range_mM": [
          0.01,
          100
        ],
        "T_K": 298,
        "pH": 7.4
      },
      "problem_class": "michaelis_menten"
    },
    "epsilon_bounds": {
      "Km_relative_error": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "N_data_points": [
        5,
        10000
      ],
      "S_range_mM_max": [
        1,
        10000
      ],
      "S_range_mM_min": [
        0.001,
        1
      ],
      "T_K": [
        273,
        373
      ],
      "pH": [
        1,
        14
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Enzymatic rate laws",
  "title": "Michaelis-Menten Enzyme Kinetics"
}

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