Trace Reconstruction Problems in Computational Biology

TL;DR

This paper surveys the theoretical and practical aspects of trace reconstruction in computational biology, focusing on its applications in immunogenomics and DNA data storage, and discusses new models and future research directions.

Contribution

It introduces new trace generation models, reviews existing theoretical results, and connects trace reconstruction to practical problems in biology and data storage.

Findings

Survey of theoretical results on trace reconstruction

Introduction of new models for biological trace generation

Discussion of practical challenges and future directions

Abstract

The problem of reconstructing a string from its error-prone copies, the trace reconstruction problem, was introduced by Vladimir Levenshtein two decades ago. While there has been considerable theoretical work on trace reconstruction, practical solutions have only recently started to emerge in the context of two rapidly developing research areas: immunogenomics and DNA data storage. In immunogenomics, traces correspond to mutated copies of genes, with mutations generated naturally by the adaptive immune system. In DNA data storage, traces correspond to noisy copies of DNA molecules that encode digital data, with errors being artifacts of the data retrieval process. In this paper, we introduce several new trace generation models and open questions relevant to trace reconstruction for immunogenomics and DNA data storage, survey theoretical results on trace reconstruction, and highlight their connections to computational biology. Throughout, we discuss the applicability and shortcomings of known solutions and suggest future research directions.