Quantum Biological Information Theory

278 Pages·2016·8.411 MB·English

by  Ivan B. Djordjevic (auth.)

Ivan B. Djordjevic
Quantum
Biological
Information
Theory
Quantum Biological Information Theory

Ivan B. Djordjevic
Quantum Biological
Information Theory
IvanB.Djordjevic
DepartmentofElectricalandComputerEngineering
UniversityofArizona
Tucson,AZ,USA
ISBN978-3-319-22815-0 ISBN978-3-319-22816-7 (eBook)
DOI10.1007/978-3-319-22816-7
LibraryofCongressControlNumber:2015947789
SpringerChamHeidelbergNewYorkDordrechtLondon
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Preface
Recent evidence suggests that quantum mechanics is relevant in photosynthesis,
magnetoreception, enzymatic catalytic reactions, olfactory reception, photorecep-
tion,genetics,electrontransferinproteins,andevolution,tomentionafew.Ithas
become evident that certain organisms can harness some of the quantum-
mechanical features for a biological advantage over competitors. On the other
hand, the standard DNA template-replication paradigm is not able to explain
neitherthelong-termstorageofthegeneticinformationnortheevolutionofgenetic
material through generations. Classical/quantum information theory provides the
limits,knownaschannelcapacity,beyondbiologicalerrorsthatcannotbecorrected
for. Any correction mechanism in communication systems has the limits on error
correctioncapability.TheDNApolproofreadingandDNArepairmechanismsare
weakerrorcorrectionconcepts,farawayfrombiologicalchannelcapacity,andas
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
explainthefaithfulpreservationsofimportantgenesthroughgenerations.However,
this genetic stability is not absolute, regardless ofgenetic error correctionmecha-
nism.Ontheotherhand,theimperfectstabilityingeneticmaterialisalsorespon-
sible 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
geneticcodeandtransferofinformationfromDNAtoproteinbyusingtheconcepts
ofclassicalinformationtheory.However,giventhatmanybiologicalprocessesin
organismsarequantummechanicsdependent,classicalinformationtheoryisinsuf-
ficient to provide proper answers to many open problems today. Moreover, given
thatShannon(classical)entropyisjustthespecialcaseofvonNeumann(quantum)
entropy,itappearsthatonlyquantuminformationtheoryeffortsarerelevant.
Thekeyideainthisbookistodescribevariousbiologicalprocessesascommu-
nication 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
communicationchannelproblem.Inthismodel,DNAreplication,DNAtomRNA
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 informa-
tion 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 approxima-
tion of the operator sum representation. This indicates that the quantum channel
model description given byoperatorsum representation andthe 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 particularuse ofrepresentationis dictated bythe 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
calledthequantumbiologicalinformationtheory.
ThebookQuantumBiological InformationTheoryis aself-contained,tutorial-
basedintroductiontoquantuminformationtheoryandquantumbiology.Itservesas
asingle-sourcereferencetothetopicforresearchersinbioengineering,communi-
cations engineering, electrical engineering, applied mathematics, biology, com-
puter science, and physics. The book provides all the essential principles of the
quantumbiological informationtheoryrequiredtodescribethe quantum informa-
tiontransferfromDNAtoproteins,thesourcesofgeneticnoiseandgeneticerrors,
as well as their effects. For additional details on the book, an interested reader is
referredtotheintroductionchapterandcontents.
Theuniquefeaturesofthebookinclude:
• Itintegratesquantuminformationandquantumbiologyconcepts.
• Thebookdoesnotrequirethepriorknowledgeofquantummechanics.
• The book does not require any prerequisite material except basic concepts of
vectoralgebraatundergraduatelevel.
• Thebookdoesnotrequirepriorknowledgeingeneticsorcellbiology.
• Thisbookoffersin-depthdiscussionofthequantumbiologicalchannelmodel-
ing,quantumbiologicalchannelcapacitycalculation,quantummodelsofaging,
quantum models of evolution, quantum models on tumor and cancer develop-
ment, quantum modeling of bird navigationcompass, quantum aspects ofpho-
tosynthesis,andquantumbiologicalerrorcorrection.
• Thesuccessfulreaderofthebookwillbewellpreparedforfurtherstudyinthis
areaandwillbequalifiedtoperformindependentresearch.
Finally,theauthorwouldliketothankCharlesGlaser,JeffreyTaub,andNicole
LowaryofSpringerUSfortheirtremendouseffortinorganizingthelogisticsofthe
book including editing and promotion, which is indispensible to make this book
happen.
Tucson,AZ IvanB.Djordjevic
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 QuantumBiologyPerspective. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 QuantumInformationTheoryandBiology. . . . . . . . . . . . . . . . . . 7
1.3 OrganizationoftheBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 ConcludingRemarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 QuantumInformationTheoryFundamentals. . . . . . . . . . . . . . . . . . 21
2.1 StateVectors,Operators,ProjectionOperators,
andDensityOperators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.1 StateVectorsandOperators. . . . . . . . . . . . . . . . . . . . . . . 22
2.1.2 ProjectionOperators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.3 Photon,Spin-½Systems,andHadamardGate. . . . . . . . . . 24
2.1.4 DensityOperators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Measurements,UncertaintyRelations,andDynamics
ofaQuantumSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 UncertaintyPrinciple. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Time-EvolutionSchr€odingerEquation. . . . . . . . . . . . . . . 33
2.3 QuantumInformationProcessing(QIP)Fundamentals. . . . . . . . . 36
2.3.1 SuperpositionPrinciple,QuantumParallelism,
QuantumGates,andQIPBasics. . . . . . . . . . . . . . . . . . . . 37
2.3.2 No-CloningTheoremandDistinguishing
theQuantumStates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.3 QuantumEntanglement. . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.4 OperatorSumRepresentation. . . . . . . . . . . . . . . . . . . . . . 46
2.3.5 DecoherenceEffects,Depolarization,
andAmplitudeDampingChannelModels. . . . . . . . . . . . . 48
2.4 Classical(Shannon)andQuantum
(vonNeumann)Entropies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
ix