Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms

We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches surface hopping method. The algorithm is asymptotically derived from the Schr\"odinger equation with rigorous approximation error analysis. The resulting algorithm can be viewed as a path integral stochastic representation of the semiclassical matrix Schr\"odinger equations. Our results provide mathematical understanding to and shed new light on the important class of surface hopping methods in theoretical and computational chemistry.Comment: 35 page

A machine learning approach to explore the spectra intensity pattern of peptides using tandem mass spectrometry data

Background: A better understanding of the mechanisms involved in gas-phase fragmentation of peptides is essential for the development of more reliable algorithms for high-throughput protein identification using mass spectrometry (MS). Current methodologies depend predominantly on the use of derived m/z values of fragment ions, and, the knowledge provided by the intensity information present in MS/MS spectra has not been fully exploited. Indeed spectrum intensity information is very rarely utilized in the algorithms currently in use for high-throughput protein identification. Results: In this work, a Bayesian neural network approach is employed to analyze ion intensity information present in 13878 different MS/MS spectra. The influence of a library of 35 features on peptide fragmentation is examined under different proton mobility conditions. Useful rules involved in peptide fragmentation are found and subsets of features which have significant influence on fragmentation pathway of peptides are characterised. An intensity model is built based on the selected features and the model can make an accurate prediction of the intensity patterns for given MS/MS spectra. The predictions include not only the mean values of spectra intensity but also the variances that can be used to tolerate noises and system biases within experimental MS/MS spectra. Conclusion: The intensity patterns of fragmentation spectra are informative and can be used to analyze the influence of various characteristics of fragmented peptides on their fragmentation pathway. The features with significant influence can be used in turn to predict spectra intensities. Such information can help develop more reliable algorithms for peptide and protein identification