The protein Folds as Platonic Forms: New Support for … · The Protein Folds as Platonic Forms:...

J. theor. Biol. (2002) 219, 325–342doi:10.1006/yjtbi.3128, available online at http://www.idealibrary.com on

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The Protein Folds as Platonic Forms:New Support for the Pre-Darwinian Conception of Evolution

by Natural Law

Michael J. Dentonnw, Craig J. Marshallw and Michael Leggew

wDepartment of Biochemistry, University of Otago, P.O. Box 56, Dunedin, New Zealand

(Received on 27 November 2001, Accepted in revised form on 8 July 2002)

Before the Darwinian revolution many biologists considered organic forms to be determinedby natural law like atoms or crystals and therefore necessary, intrinsic and immutablefeatures of the world order, which will occur throughout the cosmos wherever there is life.The search for the natural determinants of organic formFthe celebrated ‘‘Laws ofForm’’Fwas seen as one of the major tasks of biology. After Darwin, this Platonicconception of form was abandoned and natural selection, not natural law, was increasinglyseen to be the main, if not the exclusive, determinant of organic form. However, in the case ofone class of very important organic formsFthe basic protein foldsFadvances in proteinchemistry since the early 1970s have revealed that they represent a finite set of natural forms,determined by a number of generative constructional rules, like those which govern theformation of atoms or crystals, in which functional adaptations are clearly secondarymodifications of primary ‘‘givens of physics.’’ The folds are evidently determined by naturallaw, not natural selection, and are ‘‘lawful forms’’ in the Platonic and pre-Darwinian sense ofthe word, which are bound to occur everywhere in the universe where the same 20 aminoacids are used for their construction. We argue that this is a major discovery which has manyimportant implications regarding the origin of proteins, the origin of life and the fundamentalnature of organic form. We speculate that it is unlikely that the folds will prove to be the onlycase in nature where a set of complex organic forms is determined by natural law, and suggestthat natural law may have played a far greater role in the origin and evolution of life than iscurrently assumed.

r 2002 Published by Elsevier Science Ltd.

Introduction

Before Darwin, the majority of leading biolo-gists adhered to a Platonic model of nature,referred to by Owen (1849) in his classicmonograph On the Nature of Limbs as ‘‘thePlatonic cosmogony.’’ According to this concep-

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tion, all the basic recurrent forms of the organicworld, such as the pentadactyl design of thevertebrate limb, the body plans of the majorphyla, the forms of leaves and so forth, as well asthe recurrent forms of the inorganic realm, suchas atoms, crystals, etc., represent the materialmanifestations of a finite set of immutableimmaterial archetypes or ‘‘ideas’’ termed byOwen (1849) ‘‘predetermined or primal pat-terns.’’ These pre-existing abstract types or ideasare materialized, or to cite Owen (1849) again,‘‘clothed in material garb,’’ by the agency of

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M. J. DENTON ET AL.326

natural law, or more precisely in the case oforganic forms by a special class of natural lawswhich applied uniquely to the vital realmFthecelebrated ‘‘Laws of Form.’’

And just as today we account rationally forthe diversity of inorganic forms such as atoms,crystals, chemical compounds, and even suba-tomic particles by various sets of laws orconstructional rulesFatom building rules, lawsof crystallography, laws of chemistry and soforthFwhich allow for a rational deductivederivation of all possible atoms, crystals, chemi-cal compounds, subatomic particles, etc., so pre-Darwinian biologists hoped to provide a rationaland lawful account of the diversity of organicforms via the ‘‘Laws of Biological Form’’(Driesch, 1929; Webster & Goodwin, 1982).

The fundamental goal of biologists in the pre-Darwinian era to seek rational and lawfulexplanations for biological form is reflected inGoeffroy St Hillaire’s attempt to derive all thebasic body plans of the major biological typesfrom a basic fundamental plan by a system ofsimple natural transformationsFhis most fa-mous being the derivation of the vertebratesfrom the invertebrates by simply turning theinvertebrate body plan on its back. The attemptof Carl Gustave Carus to provide a rational andlawful account of all skeletal forms in terms ofa set of simple geometric transformations isindicative of the same tendency. According toRussell (1916): ‘‘He was seeking to identify theinner law which presides over the formation ofthe skeleton throughout the animal kingdom.His system was y an attempt to work out ageometry of the skeleton y his thesis is that allforms of skeleton y can be deduced from ahollow sphere y every skeleton can be repre-sented schematically by a number of hollowspheres suitably modified in shape and suitablyarranged. We may expect then all skeletons to becomposed of spheres, cylinders and dicones indiverse arrangements.’’

Conceiving of organic forms to be naturalkinds, determined by natural law like inorganicforms, it is easy to see why the crystal was one ofthe most popular metaphors for organic formin the early 19th century. It was used widely byCarus (Russell, 1916) Theodore Schwann, Owenand Robert Chambers. Schwann, the co-founder

of the cell theory considered ‘‘cytogenesis as aform of organic crystallization’’ (Rupke, 1994)and in the last chapter of his MicroscopicalResearches he draws extensive parallels betweencells and crystals: ‘‘The process of crystallizationin inorganic nature y is y the nearest analogueto the formation of cells y should we nottherefore be justified in putting forward theproposition that the formation of the elementaryparts of organisms is nothing but a crystal-lization and the organism nothing but anaggregate of such crystals y if a number ofcrystals capable of imbibition [absorption] areformed, they must combine according to certainlaws so as to form a systematic whole, similar toan organism’’ (Schwann, 1847). Owen (1866)used the analogy unambiguously in the finalchapter of his Anatomy of Vertebrates in thecontext of a discussion of the causes ofsegmentation: ‘‘the repetition of similar segmentsin a vertebral column and of similar elements ina vertebral segment, is analogous to the repeti-tion of similar crystals.’’ And Chambers (1969)used the crystal as an analogy of organic formthroughout his popular Vestiges of the NaturalHistory of Creation, first published in 1840: ‘‘Insome crystallizations the mimicry [of biologicalform] is beautiful and complete; for example, theArbor Dianae is a crystallization resembling ashrub.’’ The fact that many different crystalforms can be generated from a small number ofbasic patterns added to the attraction of theanalogy. In the case of calcite, for example, therules permit the construction of about 600different molecular arrangements which can becombined to build over 2000 different combina-tions (Lima de Faria, 1988).

The widespread belief that organic forms arelawful ‘‘givens of nature’’ explains why it wasthat throughout the pre-Darwinian period fromthe naturphilosophie of the late 18th century,right up to the period just before the publicationof the Origin, although it was universallyaccepted that organisms exhibited functionaladaptations, for Goethe, Carus Goeffroy andOwen, it was always form which was of primaryconcern. Form came first and function wasviewed as a secondary and derived adaptivefeature (Russell, 1916; Richards, 1992). Owen(1866) believed that during evolution: ‘‘change

PROTEIN FOLDS AS PLATONIC FORMS 327

of structure would precede that of use andhabit.’’ Goethe, one of the foremost exponentsof the naturphilosophie, took the ‘‘form firstposition’’ to extraordinary extremes. He evenwent so far as to claim: ‘‘We are not to explainy the tusks of the Babirussa by their possibleuse, but we must first ask how it comes to havetusks. In the same way we must not suppose thata bull has horns in order to gore, but we mustinvestigate the process by which it comes to havehorns in the first place’’ (Russell, 1916). In otherwords it is form which is primary and ‘‘given,’’and adaptive functions are merely secondarymodifications.

It followed from this Platonic conception oforganic forms as ‘‘built-in’’ lawful givens ofphysics, like molecules or crystals, that the wholepattern of evolution was itself in a sense alreadypre-determined or pre-specified by natural lawFbeing the material manifestation of a pre-existingand eternal plan. As Owen (1866) put it in theconcluding chapter of his Anatomy of Verte-

brates, the path of evolution was ‘‘preordainedy due to an innate tendency y by whichnomogenously created [generated by law] proto-zoa have risen to the higher forms.’’ The ideathat the paths of evolution were all pre-ordainedby natural law was vigorously defended byChambers (1969) in his Vestiges. Discussing lifein the cosmos he comments: ‘‘Thus as one set oflaws produced all the orbs and their motions andgnognostic arrangements, so one set of lawsoverspread them with life.’’ And of course itfollowed that if biological forms were indeed theinevitable ends of natural lawF‘‘givens ofphysics’’Flife throughout the cosmos whereverit exists should be based on the same set oforganic forms. And this radical possibility wasraised by Owen (1849) in the concluding sectionof On the Nature of Limbs where he raises thepossibility of the vertebrate body plan havingbeen modified in different ways on differentplanets: ‘‘The laws of light as of gravitationbeing the same [on other planets] y theinference as to the possibility of the vertebratetype being the basis of organization of some ofthe inhabitants of other planets will not appearso hazardous.’’ And Chambers (1969) followingthe same logic considered it highly likely: ‘‘theinhabitants of all other globes of space bear not

only a general, but a particular resemblance tothose of our own.’’

The conception of evolution by natural lawalso raised the obvious possibilityFagain byanalogy with inorganic phenomenaFthat theevolution of organic forms might have occurredper saltum. Chambers (1969) for example putsforward the idea that the origin of life mighthave come about per saltum as the result of aprocess analogous to that of crystallization, aview which echoes some modern thinking in thisarea (Kauffman, 1993). The possibility of salta-tional evolution was also raised by Owen (1866)in Anatomy of Vertebrates in the discussion onthe evolution of the horse. Of course theconception of organic forms as lawful ‘‘crystal-like’’ features of the natural order did not ruleout alternative more gradual modes of origin viabuilt-in ‘‘pre-determined constructional or evo-lutionary paths.’’

Holding organic forms to be the result of a setof natural laws which applied uniquely to theorganic realm, nearly all the leading biologists ofthe pre-Darwinian era might be described as‘‘vitalists,’’ according to the definition of theterm given by Driesch (1929) in his Science and

Philosophy of the Organism, as the belief that life:‘‘has its elemental laws, laws of its own,’’ whichare additional to those which are known tooperate in the inanimate world. This type ofvitalism is however a very weak form of thedoctrine, and is obviously compatible with aquite materialistic conception of the nature oflife (McDougall, 1938). It amounts to little morethan the claim that the properties and structuresof organic forms which comprise the vital realmarise like the properties and structures of allother classes of natural formsFlike those ofatoms and molecules for exampleFfrom theintrinsic natural properties of their constituents.[Expressed in the jargon of today we might saythat they believed organic forms to be the resultof the self-organizing properties of the uniquebio-materials which comprise living systems.] AsRussell (1916) points out, Schwann’s interpreta-tion of cells as ‘‘crystals’’ was for example quitematerialistic. According to Schwann (1847), ifthere were vital laws, unique to the organicrealm, these were no less immaterial, no less partof the physical world than the laws of chemistry,


or the laws of crystallographyFwhich were alsounique to the realms of chemistry and crystal-lography respectively. Owen was also accused attimes of veering toward materialism (Rupke,1994). Indeed it seems he even considered thepossibility that the vertebrate body plan mightbe the result of the action of purely physicalforces such as electromagnetism, which impliedthat the laws of organic form are just a specialsubset of ordinary physical laws. As Rupke(1994) recounts, William Conybeare argues in aletter to Owen: ‘‘although you do excellentlydistinguish organic laws from the mere mechan-ical laws of inorganic natureFyet you areinclined to assign a very considerably largerinfluence to the inorganic forces in the organickingdom than I can persuade myself to do.’’ Andas Rupke continues: ‘‘Galvanism brought us toonear to the materialistic belief in the spontaneousgeneration of life advocated by such foreignfiends as Lamark and Oken. Such fears provedfully founded when at a later stage Owen indeedattributed the origin of life in its most primitiveand elementary form, not to any separate lifeforce y but to a constellation of organicparticles, like elementary dipoles concurring toproduce a magnet.’’ [Owen had more to fearfrom such charges than his continental fellowtravelers stationed as he was in England wherecreationism was so prevalent. For Owen wasquite aware that according to the Platonic/naturalistic conception of nature, the order ofbiology was an in-built necessary order and not acontingent artifactual order as the creationistdoctrine implied. This clash is nowhere clearerthan in On the Nature of Limbs where Owen hasto explain that because adaptations are ad hoc

functional modifications of the primal patternsgiven by natural law and not contrivancesdesigned specifically by God to serve particularfunctions, we should not expect organisms toexhibit perfect adaptations.]

The Platonic biology of the pre-Darwinian erawith its emphasis on evolution by natural lawand its conception of a rational order underlyingthe diversity of life, represented a grand scientificvision, whose heroic goal was nothing less thanthe unification of biology and physics. Itcollapsed primarily because it failed to identifythe elusive laws of form which might have

provided a rational account of organic formand explained how the evolution of the basicinvariant forms or types, from cell forms to thebody plans of the major phyla, and deephomologies such as the pentadactyl limb, mighthave come about as a result of natural law. Thatthey had no convincing explanation was expli-citly conceded by Owen (1849) in the finalparagraph of ‘‘On the Nature of Limbs’’: ‘‘Towhat natural laws or secondary causes thesuccession and progression of such organicphenomena may have been committed we asyet are ignorant.’’

POST-DARWINIAN BIOLOGY: THE ARTIFACT

AS METAPHOR OF LIFE

After 1859, the whole Platonic typologicalscheme was overthrown. Indeed the very conceptof organic forms as real natural existents, asnecessary parts of the eternal fabric of the worldorder, like atoms or crystals was abandoned.Instead a new model of organic form F that ofthe machine or artifact took its place. Necessitywas replaced by contingency and natural lawwas replaced by natural selection. Organic formswere now viewed as contingent mutable assem-blages of matter, like the constructs of a child’serector set such as Lego, put together during thecourse of evolution piece by piece by naturalselection for various biological functions. Such amodel implied in Driesch’s (1914) words that life‘‘ is distinctive as a [functional] combination andnot because of its own laws.’’

And because according to the new Darwinianframework, it is selection for function whichgenerates organic formFan inversion of theprevious Platonic ‘‘form first function secondconception’’Fthe great majority of biologistssince 1859 have come to see selection, inKauffman’s (1993) words ‘‘as the overwhelming,even the sole source of order in organisms.’’Even the deep homologous patterns whichunderlie the major body plans such as thevertebrate body plan or the pentadactyl limb,for which no convincing selectionist explanationhas ever been provided, are now assumed torepresent ancient adaptations entrapped bygenetic inertia and perpetuated as non-adaptivefeatures in their present-day descendents.


[We note in passing that there is some irony inthe fact that in adopting the metaphor of theartifact or machine, the Darwinists had adoptedthe same metaphor as their creationist oppo-nents. For both creationists and Darwinists,life’s order is contingent and artifactual, like theorder of a machine, like the order of Paley’swatch. Significantly, Darwin himself admittedhow impressed he was with Paley’s Evidences

(Darwin, 1958). For creationists it was God whohad contrived life’s contingent order for theDarwinists it was a ‘‘Blind Watchmaker’’(Daw-kins, 1986) who relied on time and chance.]

The adoption of the ‘‘contingent mutableartifact’’as the metaphor of organic form ush-ered in the modern era of biology and changedthe whole explanatory framework of biologicalscience. It was truly a change of revolutionaryimport. The very naturalness of lifeFthe idea oforganic forms as necessary parts of nature wasabandoned. The metaphor of the crystal wasreplaced by that of the watch! Where beforeDarwin the order of life and its unique propertieshad been an ‘‘element of nature’’ (Driesch, 1929)‘‘freely given from within’’ by natural law, thesame order and properties now arose like thoseof an artifact from special functional contingentcombinations of matter which had to beinstructed or specified from outside of nature,like an artifact, from information in a blueprintor program (Webster & Goodwin, 1983; Yockey,1992; Keller, 2000; Davies, 2001). And becausethe order and properties of machines aredetermined from the bottom up by their parts,the focus of biology shifted away from the studyof organisms and higher forms to the study oflife’s most elementary components.

And it is implicit in the new Darwinian view oforganic forms as ‘‘artifact-like assemblages,’’that the actual biological forms that make upthe organic realm of earthFmolecular forms,cell forms, body plans, etc.Frepresent a tiny

finite set of all possible forms which have beendrawn by selection during the evolution of life on

earth from a potentially infinite set. Organicforms on other planets should be, on this theory,quite different from those on earthFif the tapeof life were to be replayed (Gould, 1989) wewould not expect to see vertebrates on extra-terrestrial planets, as Owen inferred.

However the pre-Darwinian conception oforganic forms as intrinsic features of the naturalorder was never completely laid to rest after1859. It survived well into the 20th centuryparticularly on the continent of Europe (Gould& Lewontin, 1979). Much of Driesch’s (1929)Science and Philosophy of the Organism was notso much an argument for an indwelling non-material vital force as what Driesch terms the‘‘autonomy of life’’ by which he meant theexistence of natural laws peculiar to or autono-mous to the biological realm. D’Arcy Thomp-son’s On Growth and Form (1942), first publishedin 1917, represents a great classic in the Platonictradition and contains more than an echo inmany sections of the thinking of Goethe, Carusand Goeffroy. In the final chapter of On Growth

and Form, where Thompson shows how theforms of many animals can be related by simplemathematical transformations, one is instantlyreminded of the attempt of Carus to create auniversal geometry of all skeletal forms. Tworecent authors who must also count as belongingto the Platonic tradition are Brian Goodwin andStuart Kauffman (Webster & Goodwin, 1983;Kauffman, 1993; Goodwin, 1994).

Of course no serious biologist doubts thatsome biological forms may be given by naturallaw and arise spontaneously out of the intrinsicself-organizing properties of their constituentsand may not need any genetic program for theirspecification. The spherical form of the cell andthe flat form of the cell membrane are two well-known examples. Other more complex examplescited by Waddington (1962) are the variouscytoplasmic structures made up of multiplelayers of membranes such as the grana andintergrana regions of chloroplasts, the hexagonalarrangement of the rhabdomeres in the eyes ofinsects and the many forms described byThompson (1942) in Growth and Form, includingradiolarian skeletons, the shapes of molluskshells, the curved shape of animal horns. Buton the whole, natural law is considered to play avery trivial role in the generation of biologicalform and particularly in the generation ofcomplex seemingly asymmetric biological formssuch as protein folds, cell forms, body plans, etc.

The only area of modern biology where astrong deterministic and naturalistic element is


still evident is the ‘‘origin of life’’ with manyresearchers viewing life’s origin as an inevitableand determined end of planetary and cosmicevolution (Kenyon & Steinman, 1969; Lehnin-ger, 1982; De Duve, 1991; Morowitz et al., 2000;Sowerby et al., 2001). Here we argue that inanother important area of modern biology, onerelated to the origin of life, that involves theevolution and origin of one of the mostimportant classes of complex biological for-msFthe basic protein folds F the pre-Darwi-nian concept of organic forms as ‘‘built-in’’intrinsic features of nature determined bynatural law provides a more powerful explana-tory framework than its selectionist successor(Denton & Marshall, 2001).

The Platonic Nature of the Protein Folds

The protein folds are the basic building blocksof proteins and therefore of the cell and indeedof all life on earth. Each is a polymer between 80and 200 amino acids long consisting of fromabout 1000 to 3000 atoms folded up into acomplex intricate three-dimensional shape. Mostfolds exhibit a hierarchical structure composedof basic secondary structural elements such as ahelices and b sheet conformations which areoften arranged into more complex motifs whichare in turn combined together to make up thenative conformation of the fold. The elucidationof the atomic structure of the protein folds hasbeen one of the triumphs of 20th century science.Many different folds have now been identifiedand together they form an exotic and beautifulset of organic forms. The strangeness and beautyof these enigmatic abstract forms (see Fig. 1)is apparent to anyone on even a cursoryexamination.

It is important at this stage to note that thegreat majority of functional proteins in the cellconsist of two or more basic folds linkedtogether into multidomain or multifold com-plexes. In this paper we are considering only thefundamental nature and evolutionary origin ofthe folds and not of the higher order adaptivestructures into which they are combined. Thesehigher order complexes resembleF‘‘Lego-like’’-Fcontingent assemblages put together by nat-ural selection for various biological functions

during the course of evolution by gene duplica-tion and fusion (Brandon & Tooze, 1999).

FOLD TYPOLOGY

For most of the first half of the 20th centurythe structure of proteins was a subject of greatspeculation. It had been known since 1910, afterthe pioneering work of the great Germanchemist Emile Fischer, that proteins were longpolymers consisting of amino acids. But it wasonly in 1957 when the first 3D structure of aprotein, whale myoglobin, was finally deter-mined by X-ray crystallography that the 3Darrangement of the polypeptide backbone of atleast one protein was finally revealed. By the late1960s several other proteins had been deter-mined including hemoglobin and lysozyme.Despite these early successes the lack of anyapparent regularity in protein structures, and thegreat dissimilarity among those that had beendetermined, provided no basis for a rationalclassification (Ptitsyn & Finkelstein, 1980; Ri-chardson, 1981). The picture was still in thoseearly days compatible with the Lego modelFthat the folds in living organisms on earth mightbe individual members of a near infinite set ofcontingent material assemblages put together bynatural selection over millions of years ofevolution.

It was only during the 1970s, as the number of3D structures began to grow significantly, that itfirst became apparent that there might not be anunlimited number of protein foldsFthat thefolds might not belong to a potentially infiniteset of artifactual Lego-like constructs. On thecontrary, it became increasingly obvious as morestructures were determined that the protein foldscould be classified into a finite number of distinctstructural families containing a number ofrelated but variant forms, i.e. that the classifica-tion system of fold structures was typological(Ptitsyn & Finkelstein, 1980; Richardson, 1981;Orengo et al., 1997). This was an importantfinding as the very fact that protein folds can begrouped in such a way was itself significant, for itprovided the first line of evidence that the foldsmight be natural forms determined by physicallaw.

Fig. 1. Structural classes of protein folds. (Top row) Three basic fold classesFa, containing only a helices; a and b,containing a helices and b sheets; and b, containing only b sheets. (Middle row) Three different architectural subclasses ofthe a and b classFTIM barrel, three-layer sandwich and roll. (Bottom row) Two different arrangements of the three-layersandwich. The spiral conformations are the a helices, the broad arrows are the b sheets. (Reprinted with permission fromOrengo et al. (1997). Copyright 1997, with permission from Elsevier Science.)

doi:10.1006 yjtbi.3128

M. J. DENTON ET AL.


It also became apparent that the 3D structuresof individual folds were essentially invar-iantFsome such as the Globin fold and theRossman fold for example, having remainedessentially unchanged for thousands of millionsof years. Both their invariance and the typolo-gical classification schemes into which they couldbe grouped argued for their being a finite set of‘‘real timeless structures’’ determined by physicsrather than being mutable ‘‘Lego-like’’ aggre-gates of amino acids determined by selection.

LAWS OF FORM

Additional support for the Platonic idea thatthe protein folds represent a set of natural kindsis provided by the fact that their structures canbe accounted for by what amounts to a rationaland generative morphology consisting of a set ofrules which govern the way that the varioussecondary structural motifs such as a helices andb sheets can be combined and packed intocompact 3D structures (Ptitsyn & Finkelstein,1980; Finkelstein & Ptitsyn, 1987; Chothia, 1993;Chothia et al., 1997; Taylor et al., 2001). In thewords of Chothia et al. (1997): ‘‘In most proteinsthe a helices and b sheets pack together in one ofa small number of ways. The connectionsbetween secondary structures obey a set ofempirical topological rules in almost all casesy Subsequently it was argued that thesesimilarities arise from the intrinsic physical andchemical properties of proteins and a great dealof work was carried out to demonstrate that thisis the case.’’

It is impossible here not to be reminded of theconstructional rules which govern the assemblyof subatomic particles into atomic structures,and generate the finite set of 92 atoms whichmake up the periodic table of the elements, orthe rules of grammar, which restrict grammaticalletter strings to a tiny finite set of all possiblesequences. These ‘‘laws of fold form’’ represent aset of pre-existing abstract prescriptions, specify-ing a finite set of allowable ‘‘material’’ forms andthey therefore provide for a rational deductivederivation of all possible fold morphologies. Theyself evidently represent a set of ‘‘Laws ofBiological Form’’ of precisely the kind sought

after by Geoffroy, Carus and many otherPlatonic biologists of the pre-Darwinian era.

The Platonic ethos of the field is captured inthe title of a recent paper by Taylor (2000)entitled ‘‘Searching for the ideal forms ofproteins’’ in which he talks of: ‘‘unifyingstructural principles that can be represented asidealized proteins–protein archetypes, or theirunderlying Platonic forms’’ and goes on to citethe Platonic approach of other researchers in thefield (Murzin & Finkelstein, 1988) who: ‘‘repre-sented the all a helix class of folds, by a set ofquasi-regular polyhedra.’’

Consideration of the various physical con-straints which restrict the folded spatial arrange-ments of linear polymers of amino acidsFthelaws of fold formFsuggests that the totalnumber of permissible folds is bound to berestricted to a very small number. One recentestimate based on possible arrangements oftypical structural elements gave a maximum of4000 folds (Lingard & Bohr, 1996). Based onsimilar considerations, the authors of anotherrecent paper suggested that the maximum islikely to be no more than a few thousand(Chothia et al., 1997). A different type ofestimate based on the rate of discovery of newfoldsFrather than permissible spatial arrange-mentsFsuggests that the total number of foldsutilized by organisms on earth might not bemore than 1000 (Chothia, 1993). In many recentreports the total number of different folds isoften cited to be somewhat less than 1000 (Holm& Sander, 1996; Orengo et al., 1997; Zhang &DeLisi, 1999; Holm & Sander, 1999).

Whatever the actual figure, the fact that thetotal number of folds represents a tiny stablefraction of all possible polypeptide conforma-tions, determined by the laws of physics,reinforces further the notion that the folds likeatoms, represent a finite set of allowable physicalstructures which would recur throughout thecosmos wherever there is carbon-based lifeutilizing the same 20 amino acids.

Some idea of how enormously restricting these‘‘laws of fold form’’ are may be gained byconsideration of the fact that the total number oftheoretically possible protein structures that anindividual amino acid chain 150 residues longmight adopt, assuming that each peptide group


has only three conformations, is 3150 or 1068

(Brandon & Tooze, 1999). And the total numberof possible 3D conformations that all possibleamino acid sequences 150 residues long couldtheoretically adopt would be vastly greater,while, as we see, the total number of stable 3Dstructures allowed by physics would appear to berestricted to a tiny finite set of about 1000 uniqueconformations.

FUNCTIONAL ADAPTATIONS: SECONDARY

MODIFICATIONS OF PRIMARY FORMS

Further evidences consistent with the Platonicconception that the protein folds represent a setof lawful immutable natural forms, ‘‘primarygivens of physics,’’ are those many cases whereprotein functions are clearly secondary adapta-tions of a primary, immutable form (Gerlt &Babbitt, 2001). This is spectacularly true in thecase of some of the more common folds alsoknown as superfolds (Orengo et al., 1994; Gerlt& Babbitt, 2001). In the case of one superfold theso-called triosephosphate isomerase (TIM) bar-rel, an eight-stranded alpha/beta bundle (seeFig. 1), essentially the same fold, has beensecondarily modified for many completely un-related enzymic functions occurring in suchdiverse enzymes as F triosephosphate isomer-ase, enolase and glycolate oxidase (Orengo et al.,1994). Another example, where a basic fold hasbeen secondarily modified for various biochem-ical functions, in this case closely related func-tions, is the various elegant functionaladaptations to oxygen uptake and carriageexhibited by the globin fold in myoglobin andthe various vertebrate hemoglobins. The factthat in many cases where the same fold isadapted to different functions, no trace ofhomology can be detected in the amino acidsequences, suggesting multiple separate discov-eries of the same basic structure during thecourse of evolution (Orengo et al., 1994;Brandon & Tooze, 1999), further reinforces theconclusion that the folds are a finite set ofahistoric physical forms.

Moreover even the extreme Platonic positionof some of the pre-Darwinian biologists, such asGoetheFthat form directly determines function,without any or only minimal selective modifica-

tionFmay also be true in certain cases. Considerthose cases where a particular protein function,such as that of hemoglobin or cytochrome c,arises from the association of a particular foldwith a particular prosthetic group, co-factor ormetal ion. Because these associations are ulti-mately determined by the unique 3D forms ofthe folds, then in all such cases the biochemicalfunction is in effect given deterministically, bythe spontaneous combination of the basic foldwith its prosthetic group.

PROTEIN FOLDING: MATTER DRAWN INTO

A PRE-EXISTING PLATONIC MOLD

During folding the amino acid sequence of aprotein appears to be searching conformationspace for increasingly stable intermediates whichlead it step wise toward the deepest energyminimum for that sequence, which correspondsto its final native conformation (Ptitsyn &Finkelstein, 1980; Finkelstein & Ptitsyn, 1987).The process is driven thermodynamically via asuccession of free energy decreases (Dinner et al.,2000). The process of folding is often pictured asbeing analogous to a ball finding its way downthe sides of a complex rather irregularly shapedbowl to the bottom of the bowl, its final pre-ordained and natural resting place, where thebottom of the bowl represents the natural freeenergy minimum of the fold. Extending thisanalogy we can think of there being a pre-existing energy landscape containing 1000 or souniquely shaped bowls or free energy minima.This picture lends itself to Platonic interpreta-tion. Even the terms used in the literature reflectthe Platonic concept of matter ‘‘finding’’ or‘‘filling’’ a pre-existing mold. Thus the foldingprocess is often described as a mechanism bywhich ‘‘sequence selects structure.’’ As a recentauthor commented: ‘‘Thus the notion thatsequence determines structure might be moreprecisely formulated with the concept thatsequence chooses between the limited numberof secondary structures available to the poly-peptide backbone’’ (Honig, 1999). In otherwords, it is not the sequence which specifies themold but the mold which specifies whichsequences can be accommodated. For the moldis prior to the sequence, although of course


during folding each particular sequence is priorin time to the form which it finally makesmanifest. The ubiquitous text book claim that‘‘the amino acid sequence determines the 3Dform of the protein’’ is a mechanistic interpreta-tion of the folding process which might be moreaccurately stated Platonically as ‘‘the prior lawsof form determine which amino acid sequencescan fold into a stable 3D form.’’ If the sequencecontains any information, it is not informationto create or generate a unique artifact-likeassemblage analogous to a Lego construct or awatch, but more of a guide through a pre-existing Platonic landscape to an already pre-figured end.

Aristotle expressed this Platonic conception ofnature (and of the folds) in his Parts of Animals

(Aristotle, 1937) in the famous analogy, wherehe envisages the pre-existing plan of a houseacting as an ‘‘attractor’’ molding the materialconstituents, the bricks and stones, duringbuilding of the house into conformity with thepre-existing plan of the house: ‘‘Now the orderof things in the process of formation is thereverse of their real and essential order y bricksand stone come chronologically before the houseybut logically the real essence and the Form ofthe thing [the pre-existing plan of the house orthe pre-existing Form of the fold] comes first.’’

However we may wish to interpret the foldingof a protein, there is no question that the processis nothing like the assembly of a contingentmechanical construct like a Lego model or awatch.

ROBUSTNESS: THE MAINTENANCE OF FORM

The free energy difference between the nativeconformation of the fold and its denatured stateis small. A consequence of this is that folds areonly marginally stable. This allows for a crucialdegree of structural flexibility, which is necessaryfor many catalytic and other functional activ-ities, which often necessitate the fold adoptingslightly different conformations. But it alsomeans that because of the continual buffetingand bombardment arising from molecular colli-sions in the turbulent interior of the cell, theconfiguration of each fold is continually subjectto conformational disturbances which may

involve anything from the movement of a fewatoms to the unfolding of sections of the aminoacid chain (Brandon & Tooze, 1999).

However a fold is able to maintain and regainits native conformation in the face of thesemicrochallenges because its native conformation,being a natural free energy minimum, acts as anatural attractor ‘‘continually drawing’’ all theparts of the fold back into its proper nativeconformation (the natural free energy minimumof the fold). And just as a ball in a bowl alwaysends up at the bottom of the bowl, a fold is alsoable to get back ‘‘home’’ or to recover its properconformation along an infinity of different paths.In short, the folds are robust natural existents,whose proper forms are under the governanceand supervision of natural law.

In the case of artifactual contingent assem-blages of matter such as a watch or ‘‘Legoconstruct,’’ there is no natural agency or naturalguarantor of ‘‘proper form’’Fno eternally pre-sent Platonic mold or free energy minimumacting as an attractor continually drawing orguiding the assembly of its components to a pre-ordained end. Consequently artifacts are notrobust and are incapable of recovering theirform after rearrangements of their components.Natural forms are robust, contingent artificialforms are fragile. In the case of natural forms,the agency of natural law acts ‘‘freely’’ as theguarantor of form. In the case of artifacts thereis no such guarantor.

These considerations highlight an interestingdifference between natural and artificial forms.In the case of artifactual forms such as Legoassemblages or watches or other types ofmachines which are put together from thebottom up mechanically, we have an infinity offorms, but each is led up to or assembled by onlya few or even only one unique constructionalpath. In the case of natural forms on the otherhandFand the folds are classic examplesFthereis a finite number of forms but an infinite numberof paths via which their actualization may beachieved.

ROBUSTNESS: RESISTANCE TO MUTATION

The 3D conformations of the folds exhi-bit another sort of robustnessFthey are


remarkably resistant to evolutionary changes intheir amino acid sequences (Brandon & Tooze,1999). As referred to above, although there areonly a limited number of folds permitted byphysics, many very different apparently unre-lated amino acid sequences can fold into thesame form (Gerlt & Babbitt, 2001). Becauseprotein functions depend on the maintenance ofa stable scaffold, the tolerance of the folds tosequential changes may well confer anothercrucial element of robustness making them‘‘immune to most mutational insults’’ and henceevolutionarily reliable constructional units of thecell. The self-organization of the same fold fromvery different amino acid sequences again under-scores the natural autonomy and Platonicprimacy of the fold over its material constituentsand highlights the fact that the folds are naturalexistents and not artifactual aggregates of matterlike machines, which do not possess any naturalautonomy over their components, and arefar less tolerant of variations in their basicconstituents.

We speculate that the fact that the robustnessof the folds [which enables them to maintaintheir forms and dependent functions in the faceof both mutational challenges and conforma-tional disturbances due to the turbulence of thecell’s interior] is ‘‘natural’’ may have deepevolutionary implications. The robustness ofbiological systems is generally conceived of asbeing analogous to that of advanced machinesutilizing such devices as feedback control,parallel circuitry, error fail-safe devices, redun-dancy and so forth (Keller, 2000; Kitano, 2002;Csete & Doyle, 2002). But such robustness whichwe suggest might be termed ‘‘artifactual robust-ness’’ is inherently complex and can only bearrived at after millions of years of evolution andis necessarily a secondary and derived feature ofany biological system or structure. The robust-ness of the folds is a natural intrinsic feature ofthe folds themselves and not a secondarilyevolved feature. Robustness of this sort is ‘‘forfree’’ and does not require the intervention ofnatural selection. Such robustness has theenormous evolutionary advantage in that itprovides evolution with ‘‘ready-made’’ stablestructures upon which to build more complexstructures and functions. We speculate that an

element of natural robustness may be a neces-sary feature of all biological forms utilized byevolution from the molecular to the organismiclevel.

PARTS AND WHOLES: A UNIQUE RECIPROCAL

FORMATIVE RELATIONSHIP

If the folds were contingent assemblages ofmatter like Lego constructs, watches or othersorts of artifactsFwhere the parts are theprimary things and pre-exist the wholeFthenthe various parts of each fold, the constituent ahelices and b sheet conformations and higherorder submotifs which make up the wholeshould be stable structures (like Lego bricks)which should exist prior to and independent ofthe wholes in which they occur. And if this werethe case then the structure of the whole foldshould be easily predictable (as in the case of anartifactual assemblage like Lego) from thecharacter and properties of its parts in isolation.But this is evidently not the case.

On the contrary, many of the unique second-ary structural motifs which make up a maturefold are in most cases, either highly metastableoutside the fold or non-existent. We can statethis formally by saying that most submotifswhich make up a fold are existentially dependenton being part of the native conformation of thewhole fold, outside of which they have noindependent existence.

Evidence that the specific confirmationadopted by particular segments of the aminoacid chain is determined by the whole was gainedsome time ago in the classic complementationexperiments of Anfinsen, which showed that theisolated S-peptide of ribonuclease, which com-prises residues 1–20 of the enzyme, is a randomcoil in isolation, whereas most of it forms an ahelix in combination with the rest of themolecule. Similarly, the fragments of myoglobinreleased from the molecule after cyanogenbromide treatment, the so-called peptides 1, 2and 3, have very little residual secondarystructure after their removal from the myoglobinmolecule. Peptide 1 aggregates, peptide 2 is arandom coil and the large central peptide,peptide 3, has only residual a helical properties(Anfinsen, 1973). Evidently the structures


adopted by the different sections of the aminoacid sequence are ‘‘context dependent.’’ The caseof the prion proteins illustrates again that thesame sequence may fold into two alternativestructures depending on context (Prusiner, 1995;Manson, 1999). Studies on the Arc repressormolecule (Cordes et al., 2000) have revealed thatone section of the protein can switch from ahelical to a sheet conformation depending onminor environmental changes, including tem-perature and solvent conditions. The fact thatthe same or very similar sequences may adoptdifferent secondary structures dependent oncontext is at the heart of the whole problem ofpredicting the 3D structure of a protein from itsamino acid sequence. If the same sequencesalways adopted the same structures whatever thecontextFif in other words the substructures ofproteins were like the building blocks of Lego, orthe cogs of a watchFthen the problem ofprediction of ‘‘global form’’ from the formof the building blocks would be easyFbut ofcourse this is not the case and the problem is farfrom solved.

The linguistic analogy again springs to mind.The meaning of a word in a sentence may varydepending on the sentence in which it occursFits context. In a spoken sentence of Englishfor example, the sound represented by the letters‘‘rite’’ or ‘‘right’’ may refer from anything from amedieval ritual to a movement or a moraljudgement. Outside the context in which itoccurs it is impossible to determine its meaning.Consequently it is impossible to determine themeaning of a ‘‘whole’’ sentence from the study ofits constituent words in isolation.

Proteins, like sentences, are intensely holisticentities. All the current evidence suggests thatthe various parts of the foldFthe variousconstituent a helices and b sheet conformationsand higher order submotifsFexert what appearsto be a mutual and reciprocal formative influence

on each other and on the whole, which itself in itsturn exerts a reciprocal formative influence on all

its constituent parts. In this characteristic pro-teins are unlike any other material objects withwhich we are familiar.

It is interesting to recall that Kant (1790), in awell-known section of his Critique of Judgement

argues that the formative reciprocity of parts

and whole is the defining characteristic of anatural unity. In such a unity: ‘‘the partscombine themselves into the unity of a wholeby being reciprocally cause and effect of theirform y [and] the whole may conversely, orreciprocally determine in its turn the form andcombination of all its parts y [in other words ashe continues] every part may be thought of asowing its presence to the agency of the remainingparts, and also as existing for the sake of theothers, and of the whole y [and he concludes]an organized natural product is one in which everypart is reciprocally both end and means.’’ [ouremphasis].

Kant also pointed out that objects whose partsexhibit such a reciprocal formative influence oneach other belong to a completely different orderof being to that of the contingent artifactualassemblages. In the case of a watch for example,although it is true that each part is there for thesake of the othersFso that they might coher-ently function together for a purpose (telling thetime)Fthe parts do not owe their presence tothe agency of the others. In Kant’s words:‘‘Hence one wheel in the watch does not producethe other, and still less does one watch produceother watches y An organized being is nottherefore, a mere machine y An organizedbeing possesses inherent formative power.’’

Whatever may be the merits of Kant’s views,there is no doubt that the parts to wholerelationship in the case of the folds is nothinglike that of any contingent artifact ever built orconceived ofFas Kant insists: ‘‘no instrument ofart can answer to this description’’ and the typeof organization ‘‘has nothing analogous to anycausality known to us.’’

Evolution by Natural Law

If the folds are indeed lawful natural formsarising out of the intrinsic physical properties ofamino acid sequences, it is hard to see howselection for function can have played a sig-nificant role in their origin or evolution. Theproblem is somewhat like trying to provide aselectionist/functional explanation for the sphe-rical shape of a cell, or the flat shape of the cellmembrane! Selection may select a whole fold andthen modify it for function and this is clearly


what has happened in many cases, but it is veryhard to see how selection for biological functioncan put together a fold in the first place. Toexplain the origin and evolution of the folds weare forced, it seems, to turn to explanations interms of natural law, as we would in the case ofother types of natural forms, such as atoms,crystals or galaxies and more specifically to thetwin 19th century concepts of origin by saltationor via Owen’s ‘‘preordained paths.’’

PER SALTUM

In the case of the folds, origin per saltum or inFinkelstein’s (1994) words ‘‘by choice fromrandom [amino acid] sequences’’ is only afeasible mechanism if the protein folds are easyto find by chance and therefore common inamino sequence space. There is no doubt thatindividual a helices and b sheets are verycommon in sequence space and as the folds arisenaturally from combinations of these subunitsone might presume that the folds themselveswould be relatively common. Whether they areor not has been a subject of considerablediscussion (Finkelstein, 1994; Cordes et al.,1996; Sauer, 1996; Axe, 2000). Thermodynamicconsiderations of the random characteristics offold sequences support the contention that stablefolds are common in sequence space (Finkelstein& Ptitsyn, 1987; Finkelstein, 1994; Finkelsteinet al., 1995). In Finkelstein’s (1994) words ‘‘littleediting of a random sequence is necessary for theformation of the protein globule itself.’’ Inlibraries of random amino acid sequences, ahelical proteins displaying cooperative thermaldenaturation and specific oligomeric states havebeen recovered at frequences of 1% (Cordeset al., 1996). Evidence that different stablestructures may be close in sequence space issupported by the case of the prion proteins andother cases where different structures may beadopted by the same sequence, such as the Arcrepressor mutant, referred to above. Discussingthe implications of the conformational switch inthe Arc repressor the authors (Cordes et al.,2000) comment: ‘‘The intermediate can adopteither fold y Thus distinct protein folds neednot be isolated islands in sequence space, but canbe linked by evolutionary bridges where multiple

native structures coexist.’’ Another line ofevidence which suggests that the folds must berelatively common in sequence space is theexistence of overlapping genes. These appear tooccur in the genomes of almost all organisms.New functional proteins could never have beendiscovered or evolved, embedded in existing genesequences, if the folds were not relativelycommon in sequence space.

The current consensus view (Finkelstein, 1994;Plaxco et al., 1998; Brandon & Tooze, 1999) isthat stable folds are in fact quite common inamino acid sequence space. Brandon & Tooze(1999) have even speculated that as many as onein a hundred random amino acid sequences mayfold into a stable form. If indeed folds are thatcommon in sequence spaceFoccurring, say, at afrequency of one in a hundred random sequen-cesFthen, this might mean that whereverrandom polypeptides are synthesized anywherein the cosmosFin the laboratory, in a pre-bioticsoup or in a primeval cellFall the basic foldsutilized by life on earth would be bound to begenerated after only a few thousand trials. Andthis leads us to surmise that if at some stage incellular evolution ‘‘random polypeptides’’ weresynthesized in great numbers, then all the foldsmight have been discovered quite easily bychance. This would mean that in the rightenvironment, just as atoms are assembled inthe stars and crystals form when rocks coolslowly, so the protein folds would also be formedautomatically, wherever conditions permittedthe synthesis of any quantity of polypeptides tooccur. And because the association of manyproteins with their prosthetic groups is basicallyspontaneous, and does not require the interven-tion of an enzyme, this raises the possibility thatmany protein functions may also have beengenerated deterministically in the protocell with-out the necessity for selection, by the directassociation of small organic compounds withparticular protein folds. In effect this means thatmerely by synthesizing a few thousand randompolypeptides in a ‘‘broth’’ containing the basicbiochemicals used by life on earth, includingenzymic prosthetic groups, all the necessaryproto-functional enzymes needed for cellularmetabolism might be generated per saltum bynatural law. These primitive enzymes could then


be fine tuned by selection to generate the highlyefficient enzymes of modern cells. In effect theorigin and evolution of the protein-based bio-chemistry of modern cells may be ‘‘a free lunch.’’Evidence that intermediary metabolism may alsohave been given deterministically in the protocellwas obtained in a recent study (Morowitz et al.,2000) which concluded that: ‘‘The chemistry atthe core of the metabolic chart is necessary anddeterministic and would likely characterize anyaqueous carbon based life anywhere it is foundin this universe.’’

PRE-ORDAINED PATHS

The alternative to per saltum models is toenvisage physically determined ‘‘constructionalseries’’ or evolutionary pathways starting fromsay, a simple single a helix structure and leadingvia a series of small motifs to the final fold. Oneexample of a simple, two-step ‘‘constructionalsequence’’ for the evolution of the classic TIMbarrel from a half barrel was reported recently(Lang et al., 2000). But how feasible might suchconstructional pathways be in the case of manyfolds? In the case of some foldsFthe globin foldfor exampleFno one has yet been able toprovide a credible constructional sequence fromsimple motif to final fold to show how the foldmight have come about via a series of stableintermediate forms. Some folds, like perhaps theTIM fold, may lend themselves to constructionfrom simpler motifs but this may not be true ofall folds. Of course as any set of small stablemotifs and constructional sequences in pre-fold space would also be a finite set andvery much given by physics, then such construc-tional sequences if they exist, would be no less‘‘built-in’’ than the final set of stable folds towhich they lead. However as there would bedifferent routes through this pre-fold space tothe 1000 folds, there would inevitably be anelement of contingency in the actual routestaken. Nonetheless, the 1000 protein folds wouldstill represent a physically determined or ‘‘built-in’’ bottle neck through which protein evolutionhad to pass and through which it would have topass on any earth-like planet, where life usesproteins constructed out of the same 20 aminoacids.

If it is possible to derive folds via evolutionaryconstructional sequences starting from say asimple a helix and leading via a double helicalmotif and so on, then selection for biologicalfunctions may have played at least some role.However as many authors have pointed out, inthe context of protein evolution, selection musthave a detectable proto-function to start with(Ohno, 1970, 1984; Keese & Gibbs, 1992). Thismeans that before selection begins there must beat least some sort of stable scaffold on which afunction can be hung. And in the case of somefunctions, this might necessitate a stable scaffoldplus a prosthetic group! In the end, whatever roleselection might have played it must obviouslyhave been highly constrained by the various typesof stable submotifs permitted by physics.

The idea that the origin and evolution of thefolds occurred essentially ‘‘for free’’Feither persaltum or via physically pre-determined construc-tional paths, because of the essential ‘‘natural-ness’’ of the folds and their frequency in aminoacid spaceFis enormously attractive because itprovides a plausible framework for understandingthe origin of protein-based life. Such a modelcontrasts very favorably with the traditionalselectionist scenario and the need for a longinvolved process of cumulative selection (Daw-kins, 1986) to direct the assembly of highlyimprobable contingent ‘‘artifact-like’’ structures.If the folds were indeed ‘‘artifact-like’’ structures,if their complexity entailed what Davies (2001)terms ‘‘instructed complexity’’ it is not onlydifficult to see how they could possess the pre-requisite robustness to function reliably as theconstructional units of the cell (discussed above)but also difficult to see how they could ever haveoriginated naturally (Davies, 2001). The re-adop-tion of the 19th century metaphor of the crystaland the reassigning of biological order as ‘‘natur-al’’ rather than ‘‘artificial,’’ at least in the case ofthe folds, goes a long way to solving the problemof the origin of protein-based life and may providea general naturalistic explanatory framework forunderstanding other aspects of the origin of life.

LIFE AS INTEGRAL TO NATURE

The discovery that the folds are naturalforms, whose evolution is determined largely


by physical law and which are bound to arisespontaneouslyF‘‘for free’’Fin any large set ofrandom amino acid sequences, strongly supportsthe widely held belief among origin of liferesearchers (already mentioned above) that lifeis itself an inevitable end of chemistryFaphenomenon which is bound to arise in thecorrect environmental conditions, perhaps inspace or perhaps on the surfaces of newlyformed planets (Lehninger, 1982; De Duve,1991; Sowerby et al., 2001). It also providesnew support for the currently fashionableAnthropic view that the laws of nature appearto be fine tuned for life (Barrow & Tippler, 1986;Denton, 1998; Davies, 2001). For the lawfulnature of the folds provides for the first timeevidence that the laws of nature may not only befine tuned to generate an environment fit for life(the stage) but may also be fine tuned to generatethe organic forms (the actors) as well, in otherwords that the cosmos may be even morebiocentric than is currently envisaged!

The lawful nature of the folds together withthe intriguing fact that many of the 20 proto-genic amino acidsFout of which the folds areconstructedFare amongst the commonest ami-no acids found in meteorites and the easiestamino acids to generate in pre-biotic syntheses(Miller & Orgel, 1974) is surely of considerablesignificance, consistent with and supporting adeterministic theory of the origin of life (or atleast of proteins) and by extrapolation the wholePlatonic cosmogonyFraising the possibility thatall organic forms and indeed the whole patternof life may finally prove to be the determined endof physics and life a necessary feature of thefundamental order of nature. In their bookBiochemical Predestination, the authors Kenyon& Steinman (1969) echoing the early 19thcentury views of Owen and Schwann, concludewith sentiments consistent with the pre-Darwi-nian concept of evolution by natural law and theviewpoint defended in this paper: ‘‘the ultimatedevelopment of the living cell is determined bythe physiochemical properties possessed by thestarting compounds from which these systemsevolved. In other words the ultimate character-istics of the living cell can be traced back to thenature of the starting compounds from which itwas produced. Therefore we should not look

upon the appearance and development of theliving cell as an improbable phenomenon butrather as one which followed a definite coursegoverned and promoted by the properties of thesimple compounds from which the processbegan.’’

Discussion

The protein folds clearly represent a finite setof about 1000 natural forms determined likeatoms and crystals and other natural forms bythe laws of physics. They can be classified intodistinct structural types, their structures can beaccounted for in terms of a rational morphologyof constructional rules, they have remainedinvariant for billions of years, and in many casestheir functional adaptations are clearly second-ary modifications of what are evidently ahistoricprimary forms. They are robust both in theircapacity to resist long-term evolutionary muta-tional challenges and in their capacity tomaintain and regain their proper form in theface of the destabilizing challenges posed by thebuffeting and turbulence of the cell’s interior.Depending on their frequency in sequence space,their evolutionary origin may have occurredeither by saltation, or via physically determinedintermediates, in other words by pre-ordainedconstructional pathways. In short, they do notconform in any way to the Darwinian concep-tion of organic forms as contingent ‘‘Lego-like’’functionally contrived assemblages of matter.On the contrary, they are wonderful exemplarsof the pre-Darwinian and Platonic conception oforganic forms as abstract, lawful and rationalfeatures of the eternal world order, which willoccur throughout the cosmos wherever the same20 protogenic amino acids are used to makeproteins.

This is a remarkable, even historic discovery.For the folds represent the first case in the historyof biology where a set of complex organic forms

can be shown to be unambiguously lawful naturalforms in the classic pre-Darwinian sense. In therealm of the proteins, Owen’s metaphor ofthe crystal has displaced Darwin’s metaphor ofthe watch. That what are perhaps the mostimportant set of forms in the biological realm,the fundamental constructional units of life and


more specifically of the protein-based biochem-istry of the modern cell, the most thoroughlycharacterized of all known organic forms todate, known and understood to the ultimateatomic level, should have turned out to be suchperfect exemplars of the pre-Darwinian Platoniccosmogony, and the idea of natural law as themajor determinant of organic form and evolu-tion, is an important and intriguing discovery inits own right. But the real significance of thisfinding lies in the deep implications it holds fortwo key areas of biology, namely the origin oflife and the fundamental nature of organic form.We have already seen that in the area of theorigin of life this new ‘‘naturalistic’’ conceptionof the folds goes a long way to providing arational explanation for the origin of protein-based life. No less significant is the radicalchallenge it poses to the current deeply heldDarwinian presumption, that all complex or-ganic forms (like the folds?) are the contingentartifact-like products of selectionF‘‘chancecaught on the wing’’Fto cite Monod’s (1972)famous phrase, and that natural law has playedno role in directing the course of evolution or inthe determination of organic form. In thecontext of the ‘‘folds’’ these presumptions areno longer secure.

It is more than anything else the complexhierarchic structure of the foldsFtheir beingcomposed of clearly defined substructures andsubmotifs combined together into what appearseemingly to be irregular complex hierarchicwholes, the sort of order which is so character-istic of that of a machine or artifactFwhichconveys the irresistible feeling that such formscould not possibly be natural or lawful. The factthat such structures should be lawful natural andin essence ‘‘simple’’ is entirely counterintuitive.And the question obviously arises, might therebe other sets of lawful self-organizing organicforms which arise like the folds out of theintrinsic properties of their basic material con-stituents? A number of considerations suggestthat this possibility cannot be so easily dis-missed. We believe that in the case of at least twoother classes of self-organizing formsFmicro-tubular and cell formsFthere is at least somepreliminary and intriguing evidence for believingthat these might turn out to represent like the

folds, preferred arrangements of matter whichare determined by various ‘‘constructional rules’’or ‘‘organizational laws.’’

There is no doubt that the bipolar aster arisesby the self-organization of microtubules andmolecular motors (Kirschner & Mitchison, 1986,Kirschner et al., 2000) or in the words of Hyman& Karsenti (1996) from ‘‘the intrinsic character-istics of its parts.’’ And the aster is not the onlymicrotubular form that arises in this way. This isbeautifully shown by studies of the variousforms which arise in vitro out of the interactionof molecular motors and microtubules (Nedelecet al., 1997). The results are very instructive.Merely by altering the concentration of themotor protein kinesin in the presence of stabi-lized microtubules, a variety of spatially orga-nized structures, including the aster can begenerated. Clearly these forms are not specifieddirectly in the DNA, nor does any geneticprogram direct their assembly. They are to beexplained as the ‘‘lawful’’ outcome of localdynamic interactions between a few basic com-ponents in the cell. They appear to be another setof natural forms no less natural than the proteinfolds, although the laws involved are of coursevery different. The authors (Nedelec et al., 1997)summarized the results of their work thus:‘‘These simplified experiments show that thebasic structural ‘‘vocabulary’’ used by the cell isextremely rich. By using just two basic compo-nents and simple local rules of interaction weobtained a large variety of assembled structures.By extending our system to include otherinteracting components, such as nucleationcenters for microtubules or different motors, itwill be possible to explore the conditions neededfor the formation of other structures. Anotherdirection of study would be to introduce someelements of regulation, making it possible tosearch for rules underlying the choice of different‘‘words’’ from this large vocabulary of selforganized structures.’’

These results are consistent with the notionthat microtubular forms represent another set oflawful forms which arises spontaneously, like thefolds, out of the intrinsic properties of their basicmaterial constituents and where it may bepossible eventually to derive them deduc-tively from a unique set of contructional rules


(analogous to those that apply to the folds)which we might term ‘‘laws of microtubularform.’’ It is surely not so far fetched to see theaster (like a protein fold) as a primary ‘‘given ofphysics’’ which has been secondarily co-optedand modified by selection for its crucial func-tional role in cell division.

Might cell forms also be lawful? The observa-tion that some cell forms are almost as ancientand invariant as the protein folds lends somesupport to the notion. The cell form of Tetra-

hymena for example, has remained basicallyunchanged for perhaps 1000 million yearsamong the set of sibling species termed theTetrahymena swarm (Nanney, 1982). Even de-tails of the arrangements of the cilia round theoral apparatus have remained constant over themillions of years since the various species ofTetrahymena divergedFalmost certainly sometime before the origin of the vertebrates, deepin pre-Cambrian times, hundreds of millions ofyears ago (Nanney, 1982). What makes thesituation even more curious is the fact that themolecular constituents which generate the iden-tical forms vary tremendously. So there isinvariance of cell form with considerable varia-tion in the building blocks. (Again the similarityhere to the folds is striking, where as we haveseen, the same 3D form may be specified bymany different sequences, sometimes so diversethat no sequential relationship can even bedetected.) Frankel (1983) has speculated thatpart of the explanation may be that develop-mental constraints impose restrictions on allow-able forms. But this may not be the whole story.As Nanney (1982) has commented: ‘‘It must beconcluded that few, if any, improvements arepossible, at least by the usual one-step opportu-nistic methods of microevolutionary progres-sion. The phenotype is prevented, by its very,perhaps arbitrary complexity, from any kind ofsubstantial change.’’ This is close to acknowl-edging that certain features of Tetrahymena cellform may be lawful afunctional structures, givenby physics not selection.

Reinforcing the possibility that ciliate cellforms may be lawful is the extraordinary abilityof ciliate cells like Stentor to recover their‘‘proper form’’ after microsurgical manipula-tions. These recoveries are consistent with the

possibility that the whole cell is behaving like anatural form, which can recover its proper formby searching a conformational space for itscorrect conformation, just like a folding protein,or a self-assembling aster. In the case of Stentorthe process can take up to 40 hr (Tatar, 1961) farlonger than the time taken by a protein (1 s) oran aster (several minutes) to search theirrespective conformational spaces.

Commenting in a recent Cell review Kirschnerand his colleagues (Kirschner et al., 2000)remark: ‘‘In the case of Stentor pattern reforma-tion after surgery suggests that incorrect assem-bly states of the cortical cytoskeleton are lessstable than correct ones, and that off ratessufficient to explore new configurations mustexist.’’ This is consistent with the view that theregeneration of cell form in Stentor involves (asis the case in the self-assembly of proteins or theself-assembly of the bipolar aster) an energy-dependent exploration of a higher order struc-tural landscape which leads eventually as in thecase of a fold to a preferred state or free energyminimum.

Conclusion

Whether or not there are other sets of lawfulorganic forms, there is no doubt that theuniverse of protein folds represents a Platonicuniverse of precisely the kind sought after bypre-Darwinian biology. There is no question thatin this universe, functional adaptations aresecondary and trivial modifications of what areevidently essentially invariant crystal-like ‘‘gi-vens of physics’’ and evolution is by law notselection for function. It would have delightedGoethe and Owen! It is a universe where abstractrules, like the rules of grammar, define a set ofunique immaterial templates which are materi-alized into a thousand or so natural formsFaworld of rational morphology and pre-ordainedevolutionary paths. We may have as yet, noevidence to support Owen’s belief in the ex-istence of vertebrates on extraterrestrial planets,but at least as far as the 1000 protein folds areconcerned, we may be sure that they will bepresent everywhere in the cosmos where there iscarbon-based life, utilizing the same 20 proto-genic amino acids.


The possibility that organic forms may proveeventually to be intrinsic features of naturerather than contingent artifacts has of courseimmense intellectual appeal. For it holds out theprospect that the study of organic form, mighteventually become as the pre-Darwinian biolo-gists such as Goethe, Goeffroy and Owen hadalways hoped, a fully rational and predictivescience, and that biology may in the end beunified with physics in Plato’s timeless realm ofthe gods.

We wish to thank Dr G. Kumaramanickavel,Reader and Head, Department of Genetics andMolecular Biology, Vision Research Foundation, 18College Road, Chennai 600 006, India, and othermembers of his staff, especially Dr V. L. Ramprasadfor critically reading the manuscript and for editorialassistance.

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