Combinatorial rules of icosahedral capsid growth(8)

A model of growth of icosahedral viral capsids is proposed. It takes into account the diversity of hexamers' compositions, leading to definite capsid size. We show that the observed yield of capsid production implies a very high level of self-organization

justforbidden.Incontrast,theBoltzmannfactorsresultingfromenergybarriersbetweentheallowedprocessesshouldnotbeverydi erentattem-peraturesbetween20oand37oC.

Whatremainsthenarepurestatisticalfactors,whichmustplaythedeci-siveroleinordertoensurethatthe”correct”con gurationsareproducedateachconsecutivestepalmostwithoutexception,i.e.practicallywitha100%yield.Letusshownowhowthesestatisticalfactorscanbeevaluated,andwhatconstraintstheyimplyonthecapsomerstructure.

Fromsymmetryconsiderations(andcon rmedbychemicalanalysis)itresultsthatthepentamersarecomposedfrom veidenticaldimers,sothattheir veedgesareperfectlyequivalent,andthattheypossessade nedorientation,i.e.itisknownwhichoneofthetwofaceswillbeontheoutersideofthecapsid.Allthe vesidesofapentamershouldbeequivalent(identical),because5isaprimenumber,andanydivisionintopartswillbreakthesymmetry.Concerningthehexamers,as6isdivisibleby2and3,onecanhavethefollowingfoursituations:

-All6sidesequivalent,(aaaaaa)

-Twotypesofsides,disposedas(ababab)

-Threetypesofsides,disposedas(abcabc)

-Sixdi erentsides,(abcdef)

Thehexamersarealsooriented,withonefacebecomingexternal,andtheotheroneturnedtotheinteriorofthecapsid.Thethreedi erentiatedhexamersarerepresentedinFigure6below.

Figure6:Threedi erentiationsofhexamers

Iftheviruseswereusingundi erentiatedhexamerswithalltheirsidesequivalent,thentherewouldbenoreasonfornotcreatinganykindofstruc-turesasshowninFig.3,andthe nalyieldwouldbeverylow(atbest

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