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Masanari 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 LibraryofCongressControlNumber:2015933361 SpringerDordrechtHeidelbergNewYorkLondon ©SpringerScience+BusinessMediaDordrecht2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 dissimilarmethodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis 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 hereinorforanyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerScience+BusinessMediaB.V.DordrechtispartofSpringerScience+BusinessMedia (www.springer.com) 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 mathematics. 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 philosophy 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 individual or a species at extraordinary speed. As a consequence, an overwhelming volume of genomic sequences is generated that await detailed analysis by bioinformatics.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 quantum 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 biological 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 cognitive 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 statistical 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 applications, 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.