Table Of ContentMasanari Asano · Andrei Khrennikov
Masanori Ohya · Yoshiharu Tanaka
Ichiro Yamato
Quantum Adaptivity
in Biology: From
Genetics to Cognition
Quantum Adaptivity in Biology:
From Genetics to Cognition
Masanari Asano Andrei Khrennikov
(cid:129)
Masanori Ohya Yoshiharu Tanaka
(cid:129)
Ichiro Yamato
Quantum Adaptivity
in Biology: From Genetics
to Cognition
123
MasanariAsano Yoshiharu Tanaka
LiberalArts Division InformationScience
TokuyamaCollege of Technology TokyoUniversity ofScience
Tokuyama Tokyo
Japan Japan
Andrei Khrennikov Ichiro Yamato
International Center forMathematical Department of Biological Science
Modelingin PhysicsandCognitive andTechnology
Sciences TokyoUniversity ofScience
Linnaeus University Tokyo
Växjö Japan
Sweden
Masanori Ohya
InformationScience
TokyoUniversity ofScience
Tokyo
Japan
ISBN 978-94-017-9818-1 ISBN 978-94-017-9819-8 (eBook)
DOI 10.1007/978-94-017-9819-8
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Science is beautiful when it makes simple
explanations of phenomena or connections
between different observations. Examples
include the double helix in biology and the
fundamental equations of physics.
Stephen Hawking
I’m fascinated by the idea that genetics is
digital. A gene is a long sequence of coded
letters, like computer information. Modern
biology is becoming very much a branch of
information technology.
Richard Dawkins
Foreword
Unlike any other discipline in the natural sciences, Biology has benefitted
tremendously from intriguing ideas and novel concepts from outside the subject’s
area throughout the last century. The apparently distinct topics of chemistry,
physics,mathematicsandinformaticsbecameintegralandindispensablemattersof
biologicalresearchthatblendedsurprisinglywellwithorganismalstudiesofthelast
centuries’Biology.Inthisveryaspect,Biologyisreminiscentoftheprincipalideas
ofancientPhilosophy, asboth fields specializeintheirquest for understandingthe
essence of ‘life’, ‘meaning’ and ‘truth’.
As an inherent consequence of organismal plasticity and diversity, ‘truth’ in
biological findings is given support by studying the probability of a discrete or
gradual trait in a population, which uses stochastic expressions of classical math-
ematics. Here, again, striking similarities between biology and philosophy exist:
While modern deductive biology uses mathematics to describe processes as pre-
cisely as possible such as the dynamics of chemical reactions inside a cell or even
growth and development of organs, pure mathematical formalism dominated phi-
losophy and ruled deductive reasoning for almost two millennia.
Established by Aristotle’s logic, especially inhis theory ofsyllogismabout300
BC,themeaningofwordsandthoughtscanbeexpressedincommonmathematical
formalism to deliver significance. This pure logic is bijective and unbiased from
feelings or subjective observations. Besides its influence on natural sciences,
Aristotle’sformallogicandtheresultingAristotelianphilosophyhadagreatimpact
on theology, especially Islamic and Christian religion. In addition, he introduced
deductive reasoning also into his own biological studies and, hence, Aristotle can
beconsideredasthefounderofmoderndeductivebiology.Hewasevenambitious
enough to adopt his theory of pure logic to the operational processes in the brain.
Ironically, the period of Aristotle’s logic formalism faced an end during the
epochofEnlightenmentthatclimaxedinCharlesDarwin’sandAlfredR.Wallace’s
biological ideas of speciation and evolution!
Duringaperiodofalmost200years,theoriesofmodernmathematicallogicand
Aristotelian logic were seemingly incompatible. In recent years, however, it is
statedthatmodernmathematicalformalismandAristotle’stheoriesoflogicdisclose
vii
viii Foreword
strikingsimilarities.Moreover,biologicalconceptionsmergedwiththeseideasand
formed the current basis of modern biology that superficially splits into overlap-
ping, but yet distinct disciplines such as bioethics, biochemistry, biophysics,
biostatistics or bioinformatics.
Modern biologists still aim at finding scientific ‘truth’, at identifying how ‘life’
functions or how nerve cells compute ‘meaning’. Intriguingly, with high-through-
put methods at hand, biologists accumulate an enormous amount of data within a
short period of time that gives a renaissance to descriptive biology of pre-Aristo-
telianreasoningoroftheepochofEnlightenment.Methodsofclassicalprobability
areimposedtomineallkindsofobservablesforstatistical significance,butalarge
amount of information remains cryptic.
Especially,next generation sequencingtechnologies providestrings ofgenomic
DNA-sequences that encode for all the genetic make-up that determines an indi-
vidual or a species at extraordinary speed. As a consequence, an overwhelming
volume of genomic sequences is generated that await detailed analysis by bioin-
formatics.Thislargeamountofinformationproduceshugeproblemsindatastorage
and evaluation that might benefit from novel ground-breaking ideas or progress in
technology.
The present monograph by Masanari Asano, Andrei Khrennikov, Masanori
Ohya, Yoshiharu Tanaka and Ichiro Yamato pursues such novel ground-breaking
ideas in approaching phenomena of modern biology by quantum probabilistic
formalism.Unlikethedescriptionofquantumphysicalprocessesatmolecularscale,
e.g. the processes of exciton transfer in photosynthesis or fluorescence resonance
energy transfer between different molecules, the authors use the operational
formalismofquantumtheorytoaddressbiologicalproblemsatdiversemacroscopic
biological scales. They discuss and describe the application of quantum-like
probability to various biological examples such as sequence and gene expression
analysis, bacterial growth or epigenetics studies as well as cognitive science.
The book highlights the similarities between mathematical formalism of quan-
tum probability in physics and statistical experimental data by quantum bio-infor-
matics. The authors carefully discuss current limitations of the general quantum
information theory and propose that an extended formalism might be required to
suit special biological problems. More importantly, however, they convincingly
explain that some biological observations violate classical mathematic formalism,
which might successfully be addressed by quantum-like probability or quantum
bioinformatics.
This monograph emphasizes the great potential of quantum-like probability in
life science, especially for the many dynamical processes in biological studies.
While classical stochastic formalism is rather static, quantum probability is more
advanced and allows the representation of dynamical biological processes as
different states in a framework of quantum fluctuations.
Finally, the authors provide a vital debate about how evolutionary aspects can
possibly be described by quantum-like models. Therefore, it is not surprising that
the authors address how quantum-like formalism and probability can support bio-
logical research in clarifying what ‘life’, ‘meaning’ and ‘truth’ is. Following
Foreword ix
Aristotelian logic, they concluded that quantum-like models hold the potential for
unifying Neo-Darwinism and Neo-Lamarckism theories in modern deductive
biology.
Although this book does not solve the problems of modern biological data
analysis, it constitutes an extraordinary attempt to show the applicability of quan-
tumtheoryandquantum-likeformalismtomacroscopicobservables,whichisnovel
and a very stimulating read.
Dierk Wanke
Saarland University and University of Tübingen
Germany
Preface
The aim of this book is to introduce a theoretical/conceptual principle (based on
quantuminformationtheoryandnon-Kolmogorovprobabilitytheory)tounderstand
informationprocessingphenomenainbiologyasawhole—theinformationbiology
—anewresearchfield,whichisbasedontheapplicationofopenquantumsystems
(and, more generally, adaptive dynamics [173, 26, 175]) outside of physics as a
powerful tool. Thus this book is about information processing performed by bio-
systems.Sincequantuminformationtheorygeneralizesclassicalinformationtheory
and presents the most general mathematical formalism for the representation of
informationflows,weusethisformalism.Inshort,thisbookisaboutquantumbio-
information. However, it is not about quantum physical processes in bio-systems.
We apply the mathematical formalism of quantum information as an operational
formalism to bio-systems at all scales: from genomes, cells, and proteins to cog-
nitive and even social systems.
F. Crick proposed a central dogma in molecular biology to understand the
genetic coding problem in biology in 1970 [62]. So far researchers in biological
sciences have elucidated individual molecular mechanisms of any information
processing phenomena in biology, such as signal transduction, differentiation,
cognition and even evolution. However, we do not have basic/unified principles
underlying such information flows in biology from genes to proteins, to cells, to
organisms, to ecological systems and even to human social systems. It seems that
we are now at the brink of the crisis (catastrophe) of the integrity of our earth
systemincludinghumansocieties.Wearelongingforanypossibletoolstopredict
our state in the future.
Nowadays, quantum information theory is widely applied for microscopic
physical carriers of information such as photons and ions. This is definitely one
of the most rapidly developing domains of physics. Classical information theory
is based on a special model of probability theory, namely the model proposed by
A.N. Kolmogorov in 1933 [148]. Quantum information theory is based on the
quantum probability model—the calculus of complex probability amplitudes. The
latter was elaborated by the founders of quantum mechanics, first of all, by
M. Born and J. von Neumann. Quantum probabilities exhibit many unusual
xi
xii Preface
(even exotic and mystical) features. In particular, they violate the main laws of
classical Kolmogorovian probability. As was emphasized by R. Feynman (one
of the physical genies of the twentieth century), the quantum interference phe-
nomenon demonstrated in the two slit experiment (where a quantum particle
interferes with itself) can be probabilistically interpreted as violation of the for-
mula of total probability. The latter is one of the most fundamental laws of
classical probability theory, the heart of Bayesian analysis with corresponding
applications to the game theory and decision making. Thus quantum physics has
demonstrated that the classical probability model (as any mathematical model) has
a restricted domain of application. In particular, it can be used in classical sta-
tistical mechanics, but not in quantum mechanics.
Thesituationinprobabilitytheoryissimilartothesituationingeometry.During
two thousand years Euclidean geometry was considered as the only possible
mathematical model of physical space. (We recall that E. Kant even claimed that
thisgeometrywas oneofthebasic elements ofreality.)However,thediscovery of
N.Lobachevskyshowedthatotherconsistentmathematicalgeometricmodelswere
possible as well. Later, Riemann by inventing geometric models known nowadays
as Riemann manifolds opened the doors to a variety of geometric worlds. Finally,
the genial mind of A. Einstein coupled these mathematical models of geometry to
the physical reality by developing the theory of general relativity. (And Lob-
achesvky’s geometry has applications in special relativity).
Physics was one of the first scientific disciplines that were mathematically for-
malized.Plentyofmathematicaltheories,whichwereborninphysicalstudies,have
later found applications in other domains of science. The best example is the
differential calculus originally developed by Newton for purely physical applica-
tions, but nowadays is applied everywhere, from biology to finances. A natural
questionarises:Canquantumand,moregenerally,non-Kolmogorovprobabilitybe
appliedanywherebesidesquantumphysics?Inthisbookweshalldemonstratethat
the answer is positive and that biology is a novel and extended field for such
applications. We noticed that biological phenomena, from molecular biology to
cognition, often violate classical total probability conservation law [26]. There is
plenty of corresponding experimental statistical data.1 Therefore, it is natural to
apply non-Kolmogorovian probability to biology (in the same way as non-
Euclidean geometric models are applied in physics). Since the quantum probabi-
listicmodelisthemostelaboratedamongnon-Kolmogorovianmodels,itisnatural
to start with quantum probabilistic modelling of biological phenomena. However,
sincebiologicalphenomenahavetheirowndistinguishingfeatures,onecanexpect
that the standard quantum formalism need not match completely with biological
applications. Novel generalizations of this formalism may be required. And this is
really the case, see Chap. 4.
1Alotofdatahasbeencollectedincognitivescienceandpsychology;unfortunately,inmolecular
biology we have just a few experimental data collections which can be used for comparison of
classical and nonclassical probabilistic models. We hope that the present book will stimulate
correspondingexperimentalresearchinmolecularbiology.
