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UHRMS Formula Assignment: Diophantine-Based Recalibration Yields Lorentzian Mass Error Distribution as the Limiting
Neda Safaridehkohneh1, Albrecht Ott1
1Department of Physics, Center for Biophysics, Saarland University, Saarbrücken 66123, Germany.
Journal of the American Society for Mass Spectrometry
|December 26, 2025
Summary
This study introduces a Diophantine method for molecular formula assignment in ultrahigh-resolution mass spectrometry (UHRMS). The novel approach improves spectral interpretation accuracy for complex samples by statistically analyzing mass errors.
Area of Science:
- Analytical Chemistry
- Spectrometry
- Computational Chemistry
Background:
- Ultrahigh-resolution mass spectrometry (UHRMS) is crucial for analyzing complex molecular mixtures.
- Fourier transform techniques (FTICR-MS, FT-Orbitrap-MS) offer high resolution but pose interpretation challenges.
- Nontargeted analysis of complex samples often results in difficult spectral interpretation.
Purpose of the Study:
- To introduce a novel Diophantine method for accurate molecular formula assignment in UHRMS.
- To address challenges in spectral interpretation for complex samples.
- To enhance the statistical consistency and accuracy of molecular formula determination.
Main Methods:
- Development and application of a Diophantine method for molecular formula assignment.
- Statistical analysis of random mass error using Gaussian distribution.
- Distinguishing systematic calibration errors from random mass errors.
- Quantification of random mass error as Lorentzian distribution.
Main Results:
- The Diophantine method enables statistically consistent molecular formula assignment.
- Systematic errors from suboptimal calibration can be effectively distinguished from random errors.
- The method quantifies random mass error, consistent with Fourier transform-based instruments.
- Molecular formula assignments approach the theoretical limit of achievable accuracy.
Conclusions:
- The Diophantine method offers a robust approach to molecular formula assignment in UHRMS.
- This method significantly improves spectral interpretation accuracy for complex samples.
- The technique is self-consistent and pushes the boundaries of mass spectrometry accuracy.
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