# pk-michaelis-menten

`station__pharmacokinetics__pk-michaelis-menten` · external (needs EXECUTION_BACKEND_URL configured) · domain `pharmacokinetics` · pv-relevance `pv-core`

Calculate Michaelis-Menten saturation kinetics. Rate = (Vmax × [S]) / (Km + [S]). When [S] >> Km: zero-order (capacity-limited). Models nonlinear elimination (ethanol, phenytoin).

> **Note:** This tool routes through an external execution backend. If `EXECUTION_BACKEND_URL` is unset on the server, calls return JSON-RPC error `-32603 "Tool execution backend not configured"`. Tools with `backend: native` execute in-process and are always callable.

## Agent metadata

- `idempotent`: unknown
- `read_only`: unknown
- `expected_latency_ms`: unknown (not yet contract-tested)
- `cost_tokens_estimate`: unknown

## Input schema

- `km` *number* (required) — Michaelis constant Km — concentration at half-Vmax (e.g. mg/L)
- `substrate_concentration` *number* (required) — Substrate (drug) concentration [S] (e.g. mg/L)
- `vmax` *number* (required) — Maximum metabolic velocity Vmax (e.g. mg/h)

## Example call

```json
POST /api/mcp
Content-Type: application/json

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/call",
  "params": {
    "name": "station__pharmacokinetics__pk-michaelis-menten",
    "arguments": {
      "km": 0,
      "substrate_concentration": 0,
      "vmax": 0
    }
  }
}
```

## Related

- [/tools](/tools) — all 3062 tools
- [/tools/pharmacokinetics__pk-michaelis-menten](/tools/pharmacokinetics__pk-michaelis-menten) — HTML page
- [/tools/pharmacokinetics__pk-michaelis-menten/json](/tools/pharmacokinetics__pk-michaelis-menten/json) — JSON form (agent-friendly)
- [/api/mcp](/api/mcp) — endpoint
- [/AGENTS.md](/AGENTS.md) — agent guide