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Springer eBooks

Quantum Information Theory and Quantum Mechanics-Based Biological Modeling and Biological Channel Capacity Calculation

Ivan B. Djordjević

Published Oct 5, 2015• 1 citation
Publisher
DOI
10.1007/978-3-319-22816-7_4

Related papers

Quantum Biological Information Theory

Ivan B. Djordjević

Springer eBooks•Oct 5, 2015•28 citations

Quantum Biological Channel Modeling and Capacity Calculation

Ivan B. Djordjević

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.

Life•Dec 10, 2012•12 citations

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

Ivan B. Djordjević

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.

Life•Aug 24, 2015•5 citations

Quantum Information in Biological Systems

Shantilal Gangadas Goradia

Bulletin of the American Physical Society•Mar 3, 2015•0 citations

Quantum Information Biology

Masanari Asano, Irina Basieva, Andrei Yu. Khrennikov +3 more

•Jan 1, 2016•0 citations

Quantum Entanglement and Information Theory in Radical Pair Navigation

Chandan Sheikder, Zhang Weimin, Chen Xiaopeng +3 more

This repository contains the computational framework, simulation code, and raw data used in the manuscript "Quantum Entanglement and Information Theory in Radical Pair Navigation." We built the simulation framework using Python and the Quantum Toolbox in Python (QuTiP v4.7). The code models the open quantum system dynamics of the FAD•−/Trp•+ radical pair mechanism (RPM) implicated in avian magnetoreception. The repository includes scripts to compute the following: Spin Hamiltonian Dynamics: Construction of the two-electron spin Hamiltonian, incorporating Zeeman interactions and the dominant hyperfine couplings for both the FAD•− and Trp•+ radicals. Open System Evolution: Integration of the Lindblad master equation to track the time evolution of the singlet and triplet state populations under biological decoherence channels (spin relaxation, environmental dephasing, and radical recombination). Quantum Fisher Information (QFI): Calculation of the symmetric logarithmic derivative and QFI to determine the fundamental angular sensitivity limits of the radical pair compass. Information Theory: Computation of the Shannon mutual information and channel capacity between the Earth's magnetic field orientation and the molecular signaling states.

•May 6, 2026•0 citations
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.
Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.
This repository contains the computational framework, simulation code, and raw data used in the manuscript "Quantum Entanglement and Information Theory in Radical Pair Navigation." We built the simulation framework using Python and the Quantum Toolbox in Python (QuTiP v4.7). The code models the open quantum system dynamics of the FAD•−/Trp•+ radical pair mechanism (RPM) implicated in avian magnetoreception. The repository includes scripts to compute the following: Spin Hamiltonian Dynamics: Construction of the two-electron spin Hamiltonian, incorporating Zeeman interactions and the dominant hyperfine couplings for both the FAD•− and Trp•+ radicals. Open System Evolution: Integration of the Lindblad master equation to track the time evolution of the singlet and triplet state populations under biological decoherence channels (spin relaxation, environmental dephasing, and radical recombination). Quantum Fisher Information (QFI): Calculation of the symmetric logarithmic derivative and QFI to determine the fundamental angular sensitivity limits of the radical pair compass. Information Theory: Computation of the Shannon mutual information and channel capacity between the Earth's magnetic field orientation and the molecular signaling states.