Free Energy Gap and Statistical Thermodynamic Fidelity of DNA Codes

Abstract

DNA nanotechnology often requires collections of oligonucleotides called "DNA free energy gap codes" that do not produce erroneous crosshybridizations in a competitive muliplexing environment. This paper addresses the question of how to design these codes to accomplish a desired amount of work within an acceptable error rate. Using a statistical thermodynamic and probabilistic model of DNA code fidelity and mathematical random coding theory methods, theoretical lower bounds on the size of DNA codes are given. More importantly, DNA code design parameters (e.g., strand number, strand length and sequence composition) needed to achieve experimental goals are identified.

A Two-Dimensional Deoxyribonucleic Acid (DNA) Matrix Based Biomolecular Computing and Memory Architecture

“…Figure 9 and ref. [10] show that error-free 50-mer codes of size 2 21 exist and that SynDCode can find them. In Figure 9, extrapolation of line e1 indicates that 50-mers are sufficient for a code of size 2 21 .…”

On critical relative distance of DNA codes for additive stem similarity

“…DNA nanotechnology often requires collections of DNA strands called free energy gap codes [7] that will correctly "self-assemble" into Watson-Crick duplexes and do not produce erroneous crosshybridizations. When these collections consist entirely of pairs of mutually reverse complementary DNA strands they are called DNA tag-antitag systems [4] and DNA codes [7]- [13].…”

“…When these collections consist entirely of pairs of mutually reverse complementary DNA strands they are called DNA tag-antitag systems [4] and DNA codes [7]- [13].…”

“…To calculate the additive stem w-similarity between two DNA sequences one should add up weights of all stems in the longest common Hamming subsequence between them (see, below Definition 1). Finally, our recent works [20]- [21] deal with non-additive stem w-similarity function, previously introduced in [7]. The given model also implies counting the weights of all formed stems between two DNA sequences with only difference that these stems are contained not in Hamming common subsequence but in subsequence in sense of Levenstein insertion-deletion metric.…”

“…The given model also implies counting the weights of all formed stems between two DNA sequences with only difference that these stems are contained not in Hamming common subsequence but in subsequence in sense of Levenstein insertion-deletion metric. To find more detailed discussion of applicability of proposed constructions for modeling DNA hybridization assays please refer to work [7].…”