assembly-index

# Assembly Index Skill: Molecular Complexity Validation **Status**: ✅ Production Ready **Trit**: -1 (MINUS - validator/constraint) **Color**: #2626D8 (Blue) **Principle**: Complexity threshold → Life signature **Frame**: Assembly pathways with minimal step counting --- ## Overview **Assembly Index** measures molecular complexity by counting the minimum number of joining operations needed to construct a molecule from basic building blocks. Molecules with assembly index > 15 are biosignatures—too complex for random chemistry. 1. **Assembly pathway**: Shortest construction sequence 2. **Copy number threshold**: Abundance × complexity = life signal 3. **Molecular DAG**: Directed acyclic graph of substructures 4. **Mass spectrometry integration**: MA(m/z) measurement ## Core Formula ``` MA(molecule) = min |steps| to construct from primitives Life threshold: MA > 15 with copy_number > 1 ``` ```python def assembly_index(molecule: Molecule) -> int: """Compute minimum assembly steps via dynamic programming.""" substructures = enumerate_substructures(molecule) dag = build_assembly_dag(substructures) return shortest_path_length(dag, source="primitives", target=molecule) ``` ## Key Concepts ### 1. Assembly Pathway Enumeration ```python class AssemblyPathway: def __init__(self, molecule): self.mol = molecule self.fragments = self.decompose() def decompose(self) -> list[Fragment]: """Find all valid bond-breaking decompositions.""" return [split for split in self.mol.bonds if split.yields_valid_fragments()] def minimal_pathway(self) -> list[JoinOperation]: """DP over fragment DAG for minimum steps.""" memo = {} return self._dp_assemble(self.mol, memo) ``` ### 2. Copy Number Amplification ```python def is_biosignature(molecule, sample) -> bool: ma = assembly_index(molecule) copies = sample.count(molecule) # Life creates copies of complex molecules return ma > 15 and copies > 1 ``` ### 3. Tandem Mass Spectrometry Integration ```python def ma_from_ms2(spectrum: MS2Spectrum) -> float: """Estimate assembly index from fragmentation pattern.""" fragments = spectrum.peaks dag = reconstruct_assembly_dag(fragments) return dag.longest_path() ``` ## Commands ```bash # Compute assembly index just assembly-index molecule.sdf # Validate biosignature threshold just assembly-validate sample.ms2 # Compare assembly pathways just assembly-compare mol1.sdf mol2.sdf ``` ## Integration with GF(3) Triads ``` assembly-index (-1) ⊗ turing-chemputer (0) ⊗ crn-topology (+1) = 0 ✓ [Molecular Complexity] ``` ## Related Skills - **turing-chemputer** (0): Execute chemical synthesis programs - **crn-topology** (+1): Generate reaction network topologies - **kolmogorov-compression** (-1): Algorithmic complexity baseline --- **Skill Name**: assembly-index **Type**: Complexity Validator **Trit**: -1 (MINUS) **Color**: #2626D8 (Blue) ## ALife atlas Part of: `alife-commons`. Family: `complexity-measurement`. Canonical: `assembly-index`.