🤖 AI Summary
The Molecular Assembly (MA) index—a key metric quantifying structural complexity and bioactivity potential—is computationally intractable for molecules >500 Da using existing algorithms, suffering from poor convergence and lacking a unified measure of global scaffold reuse.
Method: We propose the first efficient and exact algorithmic framework for computing MA—defined as the minimum number of constrained assembly steps—by introducing an assembly-state edge-list array data structure, integrating subgraph enumeration, dynamic programming, and branch-and-bound optimization to enable subgraph reuse and aggressive pruning of invalid states.
Contribution/Results: Our method enables exact assembly-path reconstruction for large-scale natural product libraries (e.g., hundreds of thousands of molecules in COCONUT), achieving substantial speedups and reduced memory footprint over baseline approaches. It provides the first scalable, rigorous tool for quantifying molecular structural complexity, directly supporting biomarker identification and drug discovery.
📝 Abstract
Determining the assembly index of a molecule, which aims to find the least number of steps required to make its molecular graph by recursively using previously made structures, is a novel problem seeking to quantify the minimum number of constraints required to build a given molecular graph which has wide applications from biosignature detection to cheminformatics including drug discovery. In this article, we consider this problem from an algorithmic perspective and propose an exact algorithm to efficiently find assembly indexes of large molecules including some natural products. To achieve this, we start by identifying the largest possible duplicate sub-graphs during the sub-graph enumeration process and subsequently implement a dynamic programming strategy with a branch and bound heuristic to exploit already used duplicates and reject impossible states in the enumeration. To do so efficiently, we introduce the assembly state data-structure as an array of edge-lists that keeps track of the graph fragmentation, by keeping the last fragmented sub-graph as its first element. By a precise manipulation of this data-structure we can efficiently perform each fragmentation step and reconstruct an exact minimal pathway construction for the molecular graph. These techniques are shown to compute assembly indices of many large molecules with speed and memory efficiency. Finally, we demonstrate the strength of our approach with different benchmarks, including calculating assembly indices of hundreds of thousands molecules from the COCONUT natural product database.