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Towards Mass Spectrum Analysis with ASP

Nils Küchenmeister, Alex Ivliev, Markus Krötzsch

TL;DR

The paper addresses the combinatorial challenge of inferring molecular structures from partial mass spectrometry data by introducing Genmol, an ASP-based prototype that uses canonical tree and graph representations to achieve strong symmetry-breaking during grounding. By grounding symmetry-breaking constraints early and leveraging ASP's declarative power, Genmol dramatically reduces redundant solutions and scales better than naive approaches, approaching the performance of commercial tools in many cases. The approach is validated on a large, real-world dataset, showing substantial reductions in solution counts for cyclic graphs and near-complete symmetry-breaking for acyclic graphs, with a practical, extensible framework for further refinement. The work also provides a broader methodological contribution by detailing canonical representations and their ASP realizations, offering transferable insights for other undirected graph-generation problems.

Abstract

We present a new use of Answer Set Programming (ASP) to discover the molecular structure of chemical samples based on the relative abundance of elements and structural fragments, as measured in mass spectrometry. To constrain the exponential search space for this combinatorial problem, we develop canonical representations of molecular structures and an ASP implemen- tation that uses these definitions. We evaluate the correctness of our implementation over a large set of known molecular structures, and we compare its quality and performance to other ASP symmetry-breaking methods and to a commercial tool from analytical chemistry. Under consideration in Theory and Practice of Logic Programming (TPLP).

Towards Mass Spectrum Analysis with ASP

TL;DR

The paper addresses the combinatorial challenge of inferring molecular structures from partial mass spectrometry data by introducing Genmol, an ASP-based prototype that uses canonical tree and graph representations to achieve strong symmetry-breaking during grounding. By grounding symmetry-breaking constraints early and leveraging ASP's declarative power, Genmol dramatically reduces redundant solutions and scales better than naive approaches, approaching the performance of commercial tools in many cases. The approach is validated on a large, real-world dataset, showing substantial reductions in solution counts for cyclic graphs and near-complete symmetry-breaking for acyclic graphs, with a practical, extensible framework for further refinement. The work also provides a broader methodological contribution by detailing canonical representations and their ASP realizations, offering transferable insights for other undirected graph-generation problems.

Abstract

We present a new use of Answer Set Programming (ASP) to discover the molecular structure of chemical samples based on the relative abundance of elements and structural fragments, as measured in mass spectrometry. To constrain the exponential search space for this combinatorial problem, we develop canonical representations of molecular structures and an ASP implemen- tation that uses these definitions. We evaluate the correctness of our implementation over a large set of known molecular structures, and we compare its quality and performance to other ASP symmetry-breaking methods and to a commercial tool from analytical chemistry. Under consideration in Theory and Practice of Logic Programming (TPLP).

Paper Structure

This paper contains 8 sections, 1 theorem, 1 equation, 7 figures.

Table of Contents

  1. Introduction
  2. Analysis of Mass Spectra with Genmol
  3. Problem Definition: Enumeration of Molecules
  4. Canonical tree representations of molecular graphs
  5. Canonical Molecular Trees
  6. Canonical Molecular Graphs
  7. ASP Implementation
  8. Answer Set Programming

Key Result

proposition 1

The relation $\prec$ of Definition def_tree_order is a strict total order on molecular trees.

Figures (7)

  • Figure 1: User interface of Genmol
  • Figure 2: Hydrogen-suppressed molecular graph of adenine ($\mathit{C}_5\mathit{H}_5\mathit{N}_5$) and corresponding spanning tree with cycle edges (dotted); superscripts indicate correspondence of vertices
  • Figure 3: Canonical molecular tree of threonine ($\mathit{C}_4\mathit{H}_9\mathit{N}\mathit{O}_3$); central vertex is circled
  • Figure 4: Molecular trees of glycine ($\mathit{C}_2\mathit{H}_5\mathit{N}\mathit{O}_2$); central vertices are circled
  • Figure 5: Tree representation of adenine and molecular tree with replaced cycle edges
  • ...and 2 more figures

Theorems & Definitions (15)

  • definition 1
  • definition 2
  • example 1
  • definition 3
  • definition 4
  • example 2
  • proposition 1
  • proof
  • definition 5
  • example 3
  • ...and 5 more