Abstract
Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Highlights
Quantum biological studies have gained momentum, which can be judged by the number of recent publications related to this topic [1±21]
This case can be considered as a lower bound on quantum biological channel capacity
When the base error probability is larger than 10í2, the quantum biological channel capacity decreases dramatically, as shown in Figure 9, and in that regime the quantum coherence of biological systems cannot be preserved
Summary
Quantum biological studies have gained momentum, which can be judged by the number of recent publications related to this topic [1±21]. Yockey developed a discrete memoryless classical biological channel model, and explicitly derived the transitional probabilities among amino acids He represented the information transfer from DNA to protein as a communication problem and determined the corresponding classical biological channel capacity by maximizing the mutual information between. Even though the tautomeric forms occur with low probability (10í5±10í3), they introduce the occasional DNA storage and replication errors, which are responsible for mutations, aging and evolution. When the baseket |m2, representing one of codons (m), is transmitted over the quantum biological channel, it can be detected on the receiver (protein) side as baseket |n2 (n z m) due to the presence of genetic noise To completely characterize this quantum channel model it is essential to determine baseket transition probabilities. The Kraus operator Em,n is obtained as Em,n pm,n n m
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