Statistical Characterization of a 1D Random Potential Problem - with applications in score statistics of MS-based peptide sequencing

TL;DR

This paper provides a comprehensive thermodynamic analysis of a 1D random potential model and extends the transfer matrix method to improve peptide sequencing in proteomics.

Contribution

It introduces a complete solution for the 1D hopping model's density of states and generalizes the transfer matrix technique for peptide sequencing applications.

Findings

Density of states fully determines thermodynamic behavior.

Transfer matrix method can be applied to peptide sequencing.

Enhanced statistical significance assessment in proteomics.

Abstract

We provide a complete thermodynamic solution of a 1D hopping model in the presence of a random potential by obtaining the density of states. Since the partition function is related to the density of states by a Laplace transform, the density of states determines completely the thermodynamic behavior of the system. We have also shown that the transfer matrix technique, or the so-called dynamic programming, used to obtain the density of states in the 1D hopping model may be generalized to tackle a long-standing problem in statistical significance assessment for one of the most important proteomic tasks - peptide sequencing using tandem mass spectrometry data.