Classical and Quantum Error-Correction Coding in Genetics

Abstract

The subject of this chapter is the use of classical/quantum information theory and coding in genetics and evolution. The chapter starts with the description of using the concepts from both classical and quantum information theories to describe the evolution of biological channel capacity through generations. In order to do so, several classical and quantum biological channel models are employed including the Markovian classical and Markovian-like quantum model, hybrid quantum-classical model, multilevel symmetric channel model, and Kimura model-based Markovian process. In order to describe the reliable long-time storage of genetic information in DNA, the use of unequal error protection (UEP) coding is studied. Several classes of error-correction codes suitable for UEP on a cellular level are described including nested coding, multilevel coding (MLC), rateadaptive coding, and generalized LDPC coding. The use of concepts of constrained coding to describe the genetic information flow from DNA to proteins is also described as well as joint-constrained and error-correction coding. After that, the use of quantum error-correction concepts to deal with environmental errors including canonical quantum error-correction and stabilizer codes is briefly described. One particular class of stabilizer codes, known as topological codes, is then described that might be relevant to biological processes as they only involve the local qubits in encoding process. Another relevant class of codes, the subsystem codes, is then described. The key idea behind subsystem codes is to decompose the quantum code as the tensor product of two subsystems, exon subsystem A and intron subsystem B, and we are concerned with correcting errors only on the exon subsystem. Finally, we describe the use of nonbinary quantum stabilizer codes to deal with nucleobase substitution errors, both random and burst errors. We also briefly discuss the possible use of both classical and quantum error-correction concepts to improve tolerance to tumor and cancer introducing errors.

Improvement of Error Correction in Nonequilibrium Information Dynamics

“…Despite the stochastic nature of the underlying chemical processes, these information transfer processes require high accuracy. While kinetic proofreading is a well-known mechanism for error correction in biochemical reactions [ 6 ], the underlying mechanism for improving the performance of error corrections is still not fully understood, despite the existence of several classes of error-correction codes at the cellular level [ 7 ]. Our study reveals that the nonequilibrium effects resulting from dissipation cost to the environment are essential for improving the performance of error corrections, a finding with potential implications for investigating the universal mechanism by which information is transferred with high accuracy in biological systems.…”

“…1 ρ ρ can be regarded as the function U for the blocks of length N = 1, and q(y|x) is the transmission probability of the channel for the letters in the blocks. Thus, u is concave on the set of q(y|x), denoted by Q, and Q is a convex set, according to the proof in Equation (7). Then, the worst performance of a memoryless channel can happen with error probability 1 when q(y|x) = q(y|x ) for all x = x.…”

“…In biological systems, error correction is a crucial process that plays an essential role in maintaining the fidelity and accuracy of biological information transfer [ 5 , 6 , 7 ]. For example, in DNA replication, error correction mechanisms help to identify and correct errors that occur during the copying of DNA molecules, while in protein synthesis, error correction mechanisms ensure that the correct amino acids are incorporated into the growing polypeptide chain, minimizing the occurrence of misfolded or non-functional proteins.…”

Information Theory in Computational Biology: Where We Stand Today

“…Lastly, with recent advancements in quantum computations, Shannon’s classical information theory is paving the way for using quantum information theory with physics to further the understanding of biological systems. Active research is being pursued in many uses of quantum information theory, such as developing quantum biological channel models suitable for the study of quantum information transfer from DNA to proteins [ 208 ], quantum-mechanical modeling of spontaneous, induced, and adaptive mutations and their role in cancerous tumor developments [ 209 ] and using both classical and quantum error-correction coding in genetics and evolution [ 210 ]. We conjecture that information theory has a key role to play in many theoretical and application developments in these areas in the near future.…”

Progress in and Opportunities for Applying Information Theory to Computational Biology and Bioinformatics

“…Assessing human physiological and emotional states in more informative and accurate ways can be facilitated with Information Theory concepts, including mutual information [ 52 ]. Shannon’s classical Information Theory is being advanced toward the use of quantum Information Theory [ 37 ] for applications including studying quantum information transfer from DNA to proteins [ 53 ], quantum-mechanical modeling of mutations in cancer [ 54 ], and error-correction coding in genetics [ 55 ]. This editorial provides a brief overview of some key opportunities for advancing Computational Biology and Bioinformatics by applying Information Theory; a more comprehensive review of the progress and open challenges is available in [ 37 ].…”