Quantum Biological Information Theory

Quantum Biological Information Theory

Ivan B. Djordjevic Quantum Biological Information Theory

Ivan B. Djordjevic Department of Electrical and Computer Engineering University of Arizona Tucson, AZ, USA ISBN 978-3-319-22815-0 ISBN 978-3-319-22816-7 (ebook) DOI 10.1007/978-3-319-22816-7 Library of Congress Control Number: 2015947789 Springer Cham Heidelberg New York Dordrecht London Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)

to Milena

Preface 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 a few. It has become evident that certain organisms can harness some of the quantummechanical features for a biological advantage over competitors. On the other hand, the standard DNA template-replication paradigm is not able to explain neither the long-term storage of the genetic information nor the evolution of genetic material through generations. Classical/quantum information theory provides the limits, known as channel capacity, beyond biological errors that cannot be corrected for. Any correction mechanism in communication systems has the limits on error correction capability. The DNA pol proofreading and DNA repair mechanisms are weak error correction concepts, far away from biological channel capacity, and as such are unable to explain the faithful preservation of the genetic information through the ages. The concepts from unequal error protection must be used to explain the faithful preservations of important genes through generations. However, this genetic stability is not absolute, regardless of genetic error correction mechanism. On the other hand, the imperfect stability in genetic material is also responsible for evolution. Without evolution, life will be in the same form as it initially appeared. There were also 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 classical information theory. However, given that many biological processes in organisms are quantum mechanics dependent, classical information theory is insufficient to provide proper answers to many open problems today. Moreover, given that Shannon (classical) entropy is just the special case of von Neumann (quantum) entropy, it appears that only quantum information theory efforts are relevant. The key idea in this book is to describe various biological processes as communication processes, be they of classical, quantum, or hybrid nature. By using this approach, we describe the information flow from DNA to protein as the quantum communication channel problem. In this model, DNA replication, DNA to mrna transcription, and mrna to protein translations are considered as imperfect vii

viii Preface processes subject to biological errors. We employ this model to describe both faithful preservation of genetic information and the evolution of genetic information from generation to generation. We then establish the connection between operator sum representation, used to model quantum biological channels, and quantum master equation (QME), widely used in quantum biology to describe various processes listed above, in particular photosynthesis, magnetoreception, and photoreception, and demonstrate that QME is just the Markovian approximation of the operator sum representation. This indicates that the quantum channel model description given by operator sum representation and the QME description are equivalent to each other (under the Markovian approximation) and can be interchangeably used to simplify the description of quantum biological process. The particular use of representation is dictated by the biological problem at hand. Therefore, our approach essentially integrates quantum information theory (QIT) and currently existing quantum biology (QB) approaches, and as such it can be called the quantum biological information theory. The book Quantum Biological Information Theory is a self-contained, tutorialbased introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors, as well as their effects. For additional details on the book, an interested reader is referred to the introduction chapter and contents. The unique features of the book include: It integrates quantum information and quantum biology concepts. The book does not require the prior knowledge of quantum mechanics. The book does not require any prerequisite material except basic concepts of vector algebra at undergraduate level. The book does not require prior knowledge in genetics or cell biology. This book offers in-depth discussion of the quantum biological channel modeling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models on tumor and cancer development, quantum modeling of bird navigation compass, quantum aspects of photosynthesis, and quantum biological error correction. The successful reader of the book will be well prepared for further study in this area and will be qualified to perform independent research. Finally, the author would like to thank Charles Glaser, Jeffrey Taub, and Nicole Lowary of Springer US for their tremendous effort in organizing the logistics of the book including editing and promotion, which is indispensible to make this book happen. Tucson, AZ Ivan B. Djordjevic

Contents 1 Introduction... 1 1.1 Quantum Biology Perspective... 1 1.2 Quantum Information Theory and Biology... 7 1.3 Organization of the Book... 13 1.4 Concluding Remarks................................. 15 References............................................. 16 2 Quantum Information Theory Fundamentals... 21 2.1 State Vectors, Operators, Projection Operators, and Density Operators................................ 21 2.1.1 State Vectors and Operators.... 22 2.1.2 Projection Operators.... 23 2.1.3 Photon, Spin-½ Systems, and Hadamard Gate.......... 24 2.1.4 Density Operators.............................. 26 2.2 Measurements, Uncertainty Relations, and Dynamics of a Quantum System... 29 2.2.1 Measurements................................. 29 2.2.2 Uncertainty Principle............................ 32 2.2.3 Time-Evolution Schr odinger Equation............... 33 2.3 Quantum Information Processing (QIP) Fundamentals.... 36 2.3.1 Superposition Principle, Quantum Parallelism, Quantum Gates, and QIP Basics.................... 37 2.3.2 No-Cloning Theorem and Distinguishing the Quantum States............................. 42 2.3.3 Quantum Entanglement.......................... 44 2.3.4 Operator Sum Representation........... 46 2.3.5 Decoherence Effects, Depolarization, and Amplitude Damping Channel Models............. 48 2.4 Classical (Shannon) and Quantum (von Neumann) Entropies... 52 ix

x Contents 2.5 Holevo Information, Accessible Information, and Holevo Bound..... 53 2.6 Schumacher s Noiseless Quantum Coding Theorem and Holevo Schumacher Westmoreland Theorem... 54 2.6.1 Schumacher s Noiseless Quantum Coding Theorem and Quantum Compression................ 54 2.6.2 Holevo Schumacher Westmoreland Theorem and Channel Coding............................ 59 2.7 Quantum Error-Correction Concepts... 64 2.8 Hydrogen-Like Atoms and Beyond... 67 2.9 Concluding Remarks................................. 72 References............................................. 72 3 Fundamentals of Biological Thermodynamics, Biomolecules, Cellular Genetics, and Bioenergetics... 75 3.1 Biological Thermodynamics............................ 75 3.1.1 The First Law of Thermodynamics, Perfect Gas, Enthalpy of the System.......................... 76 3.1.2 Gibbs Boltzmann Distribution Law, Second Law of Thermodynamics, and Third Law of Thermodynamics... 78 3.1.3 Biochemical Reaction Energetics... 83 3.2 Biomolecules....................................... 87 3.2.1 Amino Acids, Peptides, and Proteins................ 90 3.2.2 Carbohydrates and Corresponding Polymers......... 104 3.2.3 Lipids, Phospholipids, Membranes, and Vesicles........ 108 3.2.4 Nucleic Acids, Nucleosides, and Nucleotides... 111 3.3 Cellular Genetics.................................... 115 3.3.1 DNA Structure and DNA Replication Process... 115 3.3.2 Genetic Code, RNA Molecules, Transcription, and Translation... 118 3.3.3 Gene Anatomy and Regulation of Gene Expression..... 122 3.4 Mutations, Evolution, and DNA Repair... 128 3.5 Bioenergetics of the Cell.... 134 3.6 Concluding Remarks................................. 140 References............................................. 141 4 Quantum Information Theory and Quantum Mechanics-Based Biological Modeling and Biological Channel Capacity Calculation... 143 4.1 Introduction........................................ 143 4.2 Quantum Biological Channel Models Suitable for Study of Quantum Information Transfer from DNA to Proteins...... 144

Contents xi 4.3 Sources of Genetic Errors and Genetic Noise: A Quantum-Mechanical Perspective... 156 4.4 Quantum Biological Channel Capacity Evaluation............ 166 4.5 Quantum Modeling of Bird Navigation Compass... 170 4.6 Quantum Aspects of Photosynthesis...... 175 4.7 Concluding Remarks................................. 191 References............................................. 192 5 Quantum-Mechanical Modeling of Mutations, Aging, Evolution, Tumor, and Cancer Development... 197 5.1 Quantum-Mechanical and Quantum Mechanics-Like Models for Mutations and Evolution... 197 5.2 Markovian Chain-Like Quantum-Mechanical Modeling of Mutations and Aging...... 207 5.3 Classical, Semiclassical, and Quantum Modeling of Tumor and Cancer Development....................... 222 5.4 Concluding Remarks................................. 232 References............................................. 233 6 Classical and Quantum Error-Correction Coding in Genetics... 237 6.1 Classical/Quantum Information Theory in Genetics and Evolution... 238 6.2 Classical/Quantum Error-Correction Coding in Genetics and Evolution... 244 6.3 Topological Codes.... 256 6.4 Subsystem Codes... 259 6.5 Nonbinary Quantum Stabilizer Codes...... 261 6.6 Classical/Quantum DNA Error Correction Robust to Tumor and Cancer Introducing Mutation Errors...... 264 6.7 Concluding Remarks................................. 265 References............................................. 266