CEJP 3(2003)516{555 AnIntroduction to Physical Theory ofMolecular Evolution BartoloLuque ¤ DepartamentoMatem¶ aticaAplicada y Estad¶³stica, EscuelaSuperior de Ingenieros Aeron¶ auticos, UniversidadPolit¶ ecnicade Madrid, PlazaCardenal Cisneros 3,Madrid 28040, Spain. Received 5March2003; revised 10July Abstract: This workis atutorial in Molecular Evolution fromthe point ofview of Physics. Wediscuss Eigen’s model, alink between evolutionary theory andphysics. We will begin by assumingthe existence of(macro)molecules orreplicators with the template property,that is, the capacity to self-replicate. According to this assumption, information will be randomlygenerated and destroyed by mutations in the code(i.e., errors in the copyingprocess) andnew bits ofinformation will be­xed (madestable) by the existence ofan external pressure onthe system (i.e.,selection), andthe ability ofthe molecules to replicate themselves. Our aimis to build amodelin order to describe molecularevolution fromas general a standpoint aspossible. As wewill see, even very simple modelsfrom the theoretical point ofview will havesurprisingly deep consequences. c Central EuropeanScience Journals. All rights reserved. ® Keywords:Mole cular Evolution, Quasi-species, Hypercycles, Biological Physics; Adaptationand Self-Organizing Systems;Soft CondensedMatter; Statistical Mechanics PACS(2000): 87.10.+e, 87.23.-n, 89.75.-k 1Thebirth of information The question of how lifearose onEarth isone of the most engaging intellectualchallenges in sciencetoday [1,2]. During recent yearswe havebeen ableto reconstruct atentative phylogenetictree starting from acommon ancestor by putting together the data provided both by Paleontology and MolecularBiology [3]. The particular historical order in which di®erent branches haveappeared and disappeared from this tree is,however, still subject to much debate. Furthermore, sincethe concretehistory oflifeon this planet isprobably ¤ E-mail:[email protected] B.Luque /CentralEuropean Journal of Physics3 (2003)516{555 517 full ofaccidentalsituations, hardly reproducible by their own nature, itislikelythat this willcontinue to be the state of a®airs for along timeindeed. Unless we are willingto acceptEarth’s uniqueness inthe Universe,there must be aset ofgeneral principles that makelife a viablephenomenon [4].It isabout these general principles that we should concern ourselves,and it isin this spirit that we willtry to tacklethe problems put forward in this introduction. The latenineteenth century Biology,developedin the midst of the industrial revo- lution, put forward avisionof livingsystems in which their internal mechanisms and energytransformations were the keyelements. However, the telecommunications domi- nated societyof today seeslife as adynamicalstate of matter organized by and around information. Energy transformations are not enough. Today we know that the genetic codestores information, and we are learning to decodeit. The letters of this alphabet are the chemicalbases that form the DNA, codons maybe thought ofaswords, operons as paragraphs. Thus, we can rephrase the old question about the origin oflifeas: What isthe origin of the information stored inlivingsystems, and why isit stable? [5] Afew preliminary conclusions can already be established by examiningthe physical and informational constraints that (pre)living systems need to achieve: First, one should observe that all° uctuations are absorbed, eliminated,in asystem in ° thermodynamic equilibrium.The spontaneous generation of order and information in this picture seemsa verydi± cult (if not impossible) feat to accomplish.Our ¯rst conclusion therefore isthat we willneed to model processes that takeplace out of equilibrium [6]. As the second pieceof the puzzle,classical Thermodynamics tellsus about the un- ° stoppable increaseof entropy that takesplace in isolated systems,about information loss.Any way out of this second constraint needs thus to provide an energy° ux, an open system.In principle,this energy° ux could be used either to prevent the degradation of the information carrying units or to fabricate new replicasof them (in atimescaleshorter than their lifetime,obviously). In the prebiotic stage, how- ever,these units (prebiotic molecules)will be smalland easyto build. Therefore, in our context the latter route willtend to be the most e±cient way to prevent the information loss associated with entropy increase. The third and central component of the picture isthe need for evolution. An im- ° mediate re°ection about what evolution means in the biologicalsense leads to the conclusion that we must havetwo di®erent mechanisms acting atoncein an evolving system.First, the information contained in itmust bemodi¯able, and must beable to change. Secondly,aparticular direction ofchange must beselectedby anexternal pressure or force exertedon the system,i.e., there must be a selection mechanism at work. Wewant to emphasizethat evolution does occur in everypopulation of entities with three characteristics: reproduction, heredity and mutation [2]. In this introduction we willassume the existenceof (macro)molecules or replicators with the template property,that is,the capacityto self-replicate.On the basis of this assumption, information willbe randomly generated and destroyed by mutations in the 518 B.Luque /CentralEuropean Journal of Physics3 (2003)516{555 codei.e., errors in the copying process, and new bits of information willbe made stable due to the existenceof an external pressure on the system i.e.,selection, and the ability of the moleculesto replicatethemselves. The availableexperimental evidencepoints towards RNAchains as the components of this ancient prebiotic world on Earth: the so-called"RNA world" scenario [7].There are at leastthree main questions in the RNA world scenario:¯ rst the synthesis of ancient nucleotides,second the emergenceof the ¯rst self-replicating molecules,and third the error-catastrophe [8].In this introduction we shall focus our attention onthe last point. What isofrealimportance to us, however, isthat until the work of Manfred Eigen [9]in the 70’sthere had been no convincing model for the evolution of complexityof this earlyreplicators. Eigen has created alink between evolutionary theory and physics.This area iswell-known today asthe Physical Theory of MolecularEvolution and isthe main focus of this work. Our aimwill be to tacklethe subject from atheoretical point ofview.Thus, we aimto build amodel which can describe molecularevolution from averygeneral framework. As we shall see,even simpletheoretical models havesurprisingly deep consequences. Afew words before we start: this work isnot an extensivereview and can beregarded as afriendly introduction to MolecularEvolution to those who liketo be initiated into the ¯eld.Many interesting issues are just mentioned and can be complemented with updated bibliography.Complex details havebeen removed for the sakeof simplicity and clarity.Three excellentreviews which go in depth are:"Biological evolution and statistical physics" by Barbara Drossel [10],"Introduction to the statistical theory of Darwinian evolution" by Luca Peliti[11] and "Molecularreplicator dynamics" by B.M. R.Stadler and P.F.Stadler [12]. 2Experimentalevolution? There are two well-known criticismsto the Darwinian evolutionary theory: the selection concept impliesa tautology,and that it cannot be checkedexperimentally .However, it isalready possible today to observe evolutionary processes in short timescales: the evolution ofthe in°uenza or RNAviruses [13]are wellknown examples. Oneof the ¯rst well-known examplewas the phago Q- ­ ,aRNAvirus that attacks bacteria. It stores its own information in RNAform and uses inversetranscriptasa to makeits complementary copy.In the 60’s,Haruna and Spiegelman cut o®the phago Q-­ ’scatalyst, the Q- ­ replicasa.This enzymeis the one responsible for the RNAcopy . If we combine together in atest tube Q- ­ replicasaalong with monomers likeA TP,GTP, UTP orCTP,the viralRNA no longer needs hosts for its self-reproduction. Inthis way it iseasy to de¯ne the ¯tness of amoleculeby simplycalculating its replication and decomposition rate. Thus, the tautology isavoided. Note that this isobviously not a natural environment for avirus. The capsule construction instructions stored inthe RNA havebecome unnecessary sincethe now reproduction capsid isnot needed any more,for example.As in the replicating process somemistakes may occur, the next generation of copiescould conceivablyobtain somereproduction bene¯ts in this new environment B.Luque /CentralEuropean Journal of Physics3 (2003)516{555 519 due to mutations. Thus, for example,the now accessorycapsid instructions could be detached from the chain and dismissed, in order to shorten the length of the chain and increaseits reproduction rate. Aexperiment (see¯ gure 1) with the samedesign as the one just described was carried out by Spigelman and collaborators [14].A Q- ­ phage was inserted inthe ¯rst test tube. After afew hours, part of the population of the tube was extracted and subsequently inserted in anew test tube. The end result after seventyrepetitions of this process was that the chains had reached astable con¯guration inwhich they had lost their infective capabilities.The RNAvirus had only17% its original length, and was reproducing at arate 15 times faster than its initialreplication rate. Nowadays, molecularor viral evolution experiments similarto the one described here yieldspectacular results, and are providing us with awealth of information onevolution