Trace Reconstruction Problems in Computational Biology

Tree trace reconstruction using subtraces

Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, Rácz, and Rashtchian [10] used combinatorial methods to show that $\exp({\mathrm{O}} (k \log_{k} n))$ samples suffice to reconstruct a complete k-ary tree with n nodes with high probability. We provide an alternative proof of this result, which allows us to generalize it to a broader class of tree topologies and deletion models. In our proofs we introduce the notion of a subtrace, which enables us to connect with and generalize recent mean-based complex analytic algorithms for string trace reconstruction.

Robust data storage in DNA by de Bruijn graph-based de novo strand assembly

DNA data storage is a rapidly developing technology with great potential due to its high density, long-term durability, and low maintenance cost. The major technical challenges include various errors, such as strand breaks, rearrangements, and indels that frequently arise during DNA synthesis, amplification, sequencing, and preservation. In this study, a de novo strand assembly algorithm (DBGPS) is developed using de Bruijn graph and greedy path search to meet these challenges. DBGPS shows substantial advantages in handling DNA breaks, rearrangements, and indels. The robustness of DBGPS is demonstrated by accelerated aging, multiple independent data retrievals, deep error-prone PCR, and large-scale simulations. Remarkably, 6.8 MB of data is accurately recovered from a severely corrupted sample that has been treated at 70 °C for 70 days. With DBGPS, we are able to achieve a logical density of 1.30 bits/cycle and a physical density of 295 PB/g.

DNA data storage is a rapidly developing technology with great potential due to its high density, long-term durability, and low maintenance cost. Here the authors present a strand assembly algorithm (DBGPS) using de Bruijn graph and greedy path search.