Combinatorial rules of icosahedral capsid growth(6)

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

Figure3:Nextagglomerationstep:fromtripletstoquadruplets

Theresultingsolutionsforthelimitvaluesofxandforauxiliaryvariablesξ=(W56)/(W66),η=(W56,6)/(W66,5),ζ=(W66,6)/(W66,5),etc.,althoughusuallynotintheformofsimplefractions,giveverygoodhintsconcerningtheassemblyrulesleadingtoparticularcapsidstructures.

Now,asthecapsidproductionratefrominitialproteinmaterialiscloseto100%,forfullerene-like(T=3)capsidsweshouldhavetheinitialrateofpentamersversusallcapsomersas3:8.Inordertokeepthesameratiointhegrown-upcapsids,simple“stickingrules”willsu ce.

Letusdenotepentamers’sidesbysymbolp,whereastwodi erentkindsofsidesonhexamers’edgeswillbecalledaandb(Fig.4).Supposethatahexamercansticktoapentamerwithonly(p+a)-combination;thentwohexamersmuststicktoeachotheronlythrougha(b+b)combination,withboth(p+b)and(a+b)combinationsbeingforbiddenbychemicalpotentialbarrier.Withtheseassumptionswegetthefollowingstatisticalfactors:W56=15,W66=9W56,6=3,W66,5=5andW66,6=0.Withtheserulesthestatisticsinclusterswillconvergetothe nalvaluex=3/8asshowninFig.4below:

Similarly,withamoredi erentiatehexamerscheme,(abcabc),andwiththeassemblingrulesallowingonlyassociationsofp+aandb+c,wegetwitha100%probabilitytheT=4capsid,withx=2/7,asshowninFig.5.

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