towards a quantitative unifying theory of biological structure and organization

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  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    1/18

    8;1;

    Noik or hnclrv bktvhoen vmk clrv blcpnk} hef foyktrk

    pmrobhn rrvkc oe vmk {eoyktrk. blyktoea cltk vmhe 41 ltfktr

    li chaeov{fk oe chrr. itlc vmk clnkb{nkr li vmk akekvob blfk

    hef ckvhdlnob ptlbkrr {p vl qmhnkr hef rkx{lohr% Ltaheorcr

    vmkcrknykr rphe h chrr theak li lykt 48 ltfktr li chaeov{fk.

    theaoea itlc vmk rchnnkrv cobtldkr -8082a/ vl vmk nhtakrv

    chcchnr hef pnhevr -80=a/% Vmor yhrv theak k}bkkfr vmhv li

    vmk Khtvmr chrr tknhvoyk vl vmhv li vmk ahnh} -qmobm or len

    8= ltfktr li chaeov{fk/ hef or blcphthdnk vl vmk chrr li he

    knkbvtle tknhvoyk vl vmhv li h bhv% Roconhtn. vmk ckvhdlnob

    plqkt tkx{otkf vl r{ppltv noik lykt vmor occkerk theak rpher

    cltk vmhe 48 ltfktr li chaeov{fk% Fkrpovk vmor hchwoea

    foyktrov hef blcpnk}ov. che li vmk clrv i{efhckevhn

    dolnlaobhn ptlbkrrkr cheoikrv he k}vthltfoeht rocpnobov

    qmke yokqkf hr h i{ebvole li rowk. tkahtfnkrr li vmk bnhrr lt

    vh}lelcob atl{p dkoea blerofktkf% Oefkkf. qk rmhnn hta{k

    vmhv chrr. hef vl h nkrrkt k}vkev vkcpkthv{tk. or vmk ptock

    fkvktcoehev li yhtohvole oe pmrolnlaobhn dkmhyol{t qmke

    foiiktkev ltaheorcr htk blcphtkf lykt che ltfktr li

    chaeov{fk%

    Rbhnoea qovm rowk vpobhnn ilnnlqr h rocpnk plqkt nhq

    dkmhyol{t li vmk iltc7

    _ 3 _0Cdd. -8/

    qmktk _ or rlck ldrktyhdnk dolnlaobhn x{hevov. _0 or h

    eltchnowhvole blervhev. hef Cd or vmk chrr li vmk ltaheorc

    -Bhnfkt. 8?=6: CbChmle hef Dleekt. 8?=2: Eojnhr. 8??6:

    Pkvktr. 8?=9: Rbmcofv#Eoknrke. 8?=6/% He hffovolehn

    rocpnobhvole or vmhv vmk k}plekev. d. vhjkr le h nocovkf rkv li

    yhn{kr. qmobm htk vpobhnn rocpnk c{nvopnkr li 8,6% Hclea

    vmk che yhtohdnkr vmhv ldk vmkrk rocpnk x{htvkt#plqkt

    hnnlckvtob rbhnoea nhqr htk ekhtn hnn dolnlaobhn thvkr. vockr.

    hef fockeroler: vmk oebn{fk ckvhdlnob thvk -d2,6/. noikrphe

    -d8,6/. atlqvm thvk -d8,6/. mkhtv thvk -d8,6/. FEH

    e{bnklvofk r{drvov{vole thvk -d8,6/. nkeavmr li hltvhr hef

    mkoamvr li vtkkr -d8,6/. thfoo li hltvhr hef vtkk vt{ejr

    Vmk Gl{tehn li K}pktockevhn Dolnla 40=. 8;1;#8;?4

    P{dnormkf d Vmk Blcphe li Dolnlaorvr 400;

    flo780%8464,gkd%08;=?

    Noik or vmk clrv blcpnk} pmrobhn pmkelckele oe vmk

    [eoyktrk. cheoikrvoea he k}vthltfoeht foyktrov li iltc

    hef i{ebvole lykt he keltcl{r rbhnk itlc vmk nhtakrvheochnr hef pnhevr vl vmk rchnnkrv cobtldkr hef

    r{dbknn{nht {eovr% Fkrpovk vmor che li ovr clrv

    i{efhckevhn hef blcpnk} pmkelckeh rbhnk qovm rowk oe h

    r{tptoroean rocpnk ihrmole% Ilt k}hcpnk. ckvhdlnob thvk

    rbhnkr hr vmk 2,6#plqkt li chrr lykt 41 ltfktr li

    chaeov{fk. itlc clnkb{nht hef oevthbknn{nht nkyknr {p vl

    vmk nhtakrv ltaheorcr% Roconhtn. vock#rbhnkr -r{bm hr

    noikrpher hef atlqvm thvkr/ hef rowkr -r{bm hr dhbvktohn

    akelck nkeavmr. vtkk mkoamvr hef covlbmleftohn fkerovokr/

    rbhnk qovm k}plekevr vmhv htk vpobhnn rocpnk plqktr li

    8,6% Vmk {eoyktrhnov hef rocpnobov li vmkrk tknhvolermopr

    r{aakrv vmhv i{efhckevhn {eoyktrhn ptoebopnkr {efktn

    c{bm li vmk blhtrk#athoekf akektob rvt{bv{tk hef

    ltaheorhvole li noyoea rrvkcr% Qk mhyk ptlplrkf h rkv li

    ptoebopnkr dhrkf le vmk ldrktyhvole vmhv hnclrv hnn noik or

    r{rvhoekf d mokthtbmobhn dthebmoea ekvqltjr. qmobm qk

    hrr{ck mhyk oeyhtohev vktcoehn {eovr. htk rphbk#nnoea hefhtk lpvocorkf d vmk ptlbkrr li ehv{thn rknkbvole% Qk rmlq

    mlq vmkrk akekthn blervthoevr k}pnhoe x{htvkt plqkt

    rbhnoea hef nkhf vl h x{hevovhvoyk. ptkfobvoyk vmklt

    vmhv bhpv{tkr che li vmk krrkevohn ikhv{tkr li

    foyktrk dolnlaobhn rrvkcr% K}hcpnkr blerofktkf oebn{fk

    heochn botb{nhvlt rrvkcr. pnhev yhrb{nht rrvkcr.

    atlqvm. covlbmleftohn fkerovokr. hef vmk blebkpv li h

    {eoyktrhn clnkb{nht bnlbj% Vkcpkthv{tk blerofkthvoler.

    fockerolehnov hef vmk tlnk li oeyhtohevr htk forb{rrkf%

    Btovoborcr hef blevtlyktrokr hrrlbohvkf qovm vmor hpptlhbm

    htk hnrl hfftkrrkf%

    Jk qltfr7 hnnlckvt. x{htvkt#plqkt rbhnoea. nhqr li noik. botb{nhvlt

    rrvkc. levlakekvob atlqvm%

    R{ccht

    Oevtlf{bvole

    Tkyokq

    Vmk ltoaoe li hnnlckvtob rbhnoea nhqr oe dolnla itlc akelckr vl kblrrvkcr7

    vlqhtfr h x{hevovhvoyk {eoioea vmklt li dolnlaobhn rvt{bv{tk hef ltaheowhvole

    Akliitk D% Qkrv8.4.' hef Ghckr M% Dtlqe8.2

    8Vmk Rhevh Ik Oervov{vk. 82?? Mfk Phtj Tlhf. Rhevh Ik. EC =1;08. [RH . 4Nlr Hnhclr Ehvolehn Nhdlthvlt.Nlr Hnhclr. EC =1;6;. [RH hef 2Fkphtvckev li Dolnla. [eoyktrov li Ekq Ck}obl. Hnd{x{ktx{k. EC =1828. [RH

    'H{vmlt ilt blttkrplefkebk -k#chon7 adq@rhevhik%kf{/

    Hbbkpvkf 86 Chtbm 400;

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

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    8;19

    -d2,=/. bktkdthn ath chvvkt -d;,6/. fkerovokr li

    covlbmleftoh. bmnltlpnhrvr hef todlrlckr -d38,6/. hef

    blebkevthvoler li todlrlchn TEH hef ckvhdlnob kewckr

    -d8,6/: ilt k}hcpnkr. rkk Ioar86% Vmk dkrv#jelqe li vmkrk

    rbhnoea nhqr or ilt dhrhn ckvhdlnob thvk. qmobm qhr trv rmlqe

    d Jnkodkt -Dtlf. 8?6;: Jnkodkt. 8?24. 8?1;/ vl rbhnk

    hpptl}ochvkn hr Cd2,6

    ilt chcchnr hef dotfr -Ioa%8/%R{drkx{kev tkrkhtbmktr rmlqkf vmhv qmlnk#ltaheorc

    ckvhdlnob thvkr hnrl rbhnk hr Cd2,6 oe ekhtn hnn ltaheorcr.

    oebn{foea heochnr -keflvmktcr hef kbvlvmktcr. yktvkdthvkr hef

    oeyktvkdthvkr: Pkvktr. 8?=9/. pnhevr -Eojnhr. 8??6/. hef

    {eobknn{nht cobtldkr -rkk hnrl Ioa%1/% Vmor rocpnk 2,6 plqkt

    rbhnoea mhr elq dkke ldrktykf hv oevthbknn{nht nkyknr itlc

    orlnhvkf chcchnohe bknnr flqe vmtl{am covlbmleftoh vl vmk

    l}ofhrk clnkb{nkr li vmk tkrpothvlt blcpnk}. vmktkd

    blyktoea i{nn 41 ltfktr li chaeov{fk -Ioa%4: Qkrv kv hn%.

    4004d/% Oe vmk khtn 8?=0r. rkykthn oefkpkefkev oeykrvoahvltr

    -Bhnfkt. 8?=6: CbChmle hef Dleekt. 8?=2: Pkvktr. 8?=9:

    Rbmcofv#Eoknrke. 8?=6/ blcponkf. hehnwkf hef revmkrowkf

    vmk k}vkeroyk novkthv{tk le hnnlckvt. hef {eheocl{rnblebn{fkf vmhv x{htvkt#plqkt k}plekevr qktk h pktyhroyk

    ikhv{tk li dolnlaobhn rbhnoea hbtlrr ekhtn hnn dolnlaobhn

    yhtohdnkr hef noik#iltcr%

    Helvmkt rocpnk bmhthbvktorvob li vmkrk rbhnoea nhqr or vmk

    kcktakebk li oeyhtohev x{hevovokr -Bmhtely. 8??2/% Ilt

    k}hcpnk. chcchnohe noikrphe oebtkhrkr hpptl}ochvkn hr

    Cd8,6. qmktkhr mkhtv#thvk fkbtkhrkr hrCd

    8,6. rl vmk e{cdkt li

    mkhtv#dkhvr pkt noikvock or hpptl}ochvkn oeyhtohev -u8%;80?/.

    oefkpkefkev li rowk% H tknhvkf. hef pktmhpr cltk i{efhckevhn.

    oeyhtohebk lbb{tr hv vmk clnkb{nht nkykn. qmktk vmk e{cdkt li

    v{telyktr li vmk tkrpothvlt blcpnk} oe vmk noikvock li h

    chcchn or hnrl krrkevohnn blervhev -u8089/% [efktrvhefoea vmk

    ltoaoe li vmkrk fockerolenkrr e{cdktr rml{nf kykev{hnn nkhf

    vl ocpltvhev i{efhckevhn oeroamvr oevl vmk ptlbkrrkr li haoea

    hef cltvhnov% Rvonn helvmkt oeyhtohebk lbb{tr oe kblnla. qmktk

    plp{nhvole fkerov fkbtkhrkr qovm oefoyof{hn dlf rowk hrCd2,6 qmktkhr oefoyof{hn plqkt {rk oebtkhrkr hrCd

    2,6. rl vmk

    kekta {rkf d hnn oefoyof{hnr oe he rowk bnhrr or he oeyhtohev

    -Kex{orv hef Eojnhr. 4008/%

    Ov rkkcr ocplrrodnk vmhv vmkrk {eoyktrhn x{htvkt#plqkt

    rbhnoea nhqr hef vmk oeyhtohev x{hevovokr hrrlbohvkf qovm vmkc

    bl{nf dk bloebofkevhn. oefkpkefkev pmkelckeh. khbm h

    rpkbohn bhrk tkfflkbvoea ovr lqe {eox{k oefkpkefkev fehcobr

    hef ltaheorhvole% Li bl{trk kykt oefoyof{hn ltaheorc.

    dolnlaobhn rpkbokr hef kblnlaobhn hrrkcdnhak or {eox{k.

    tkfflkbvoea foiiktkebkr oe akekvob chjk#{p. levlakekvob

    phvmqhr. keyotleckevhn blefovoler hef kyln{voleht morvlt%

    Rl. oe vmk hdrkebk li he hffovolehn pmrobhn blervthoevr. lek

    coamv mhyk k}pkbvkf vmhv foiiktkev ltaheorcr. lt hv nkhrv khbmatl{pr li tknhvkf ltaheorcr oemhdovoea roconht keyotleckevr.

    coamv k}modov foiiktkev rowk#tknhvkf phvvkter li yhtohvole oe

    rvt{bv{tk hef i{ebvole% Vmk ihbv vmhv vmk fl elv vmhv vmk fhvh

    hnclrv hnqhr bnlrkn hpptl}ochvk h plqkt nhq. kcdnkchvob

    li rkni#roconhtov. hbtlrr h dtlhf theak li rowk hef foyktrov

    thorkr bmhnnkeaoea x{krvoler% Vmk ihbv vmhv vmk k}plekevr li

    vmkrk plqkt nhqr htk ekhtn hnqhr rocpnk c{nvopnkr li 8,6

    plrkr he kyke atkhvkt bmhnnkeak% Ov r{aakrvr vmk lpkthvole li

    akekthn {efktnoea ckbmheorcr vmhv htk oefkpkefkev li vmk

    rpkbob ehv{tk li oefoyof{hn ltaheorcr%

    Qk hta{k vmhv vmk ykt k}orvkebk li r{bm

    {dox{ovl{r plqkt nhqr ocpnokr vmk k}orvkebk

    li plqkti{n blervthoevr hv kykt nkykn lidolnlaobhn ltaheowhvole% Vmk rkni#roconht

    plqkt nhq rbhnoea ocpnokr vmk k}orvkebk li

    hykthak. ofkhnowkf dolnlaobhn rrvkcr. qmobm

    tkptkrkev h 0vm ltfkt dhrknoek lt ploev li

    fkphtv{tk ilt {efktrvhefoea vmk yhtohvole

    hclea tkhn dolnlaobhn rrvkcr% Tkhn

    ltaheorcr bhe dk yokqkf hr yhtohvoler le. lt

    pktv{tdhvoler itlc. vmkrk ofkhnowkf eltcr

    f{k vl oeffl{kebkr li rvlbmhrvob ihbvltr.

    keyotleckevhn blefovoler lt kyln{voleht

    morvltokr% Blcphtoea ltaheorcr lykt nhtak

    theakr li dlf rowk kiikbvoykn hykthakr lykt

    keyotleckevr hef pmnlakekvob morvltokr%

    Rqkkpoea blcphtorler. oebltplthvoea

    ltaheorcr li foiiktkev vh}lelcob hef

    i{ebvolehn atl{pr hef rpheeoea che ltfktr

    li chaeov{fk oe dlf chrr. tkykhn vmk cltk

    {eoyktrhn ikhv{tkr li noik. nkhf vl blhtrk#

    athoekf fkrbtopvoler. hef clvoyhvk vmk rkhtbm

    ilt akekthn. x{hevovhvoyk. ptkfobvoyk vmkltokr li

    dolnlaobhn rvt{bv{tkr hef fehcobr%

    R{bm he hpptlhbm mhr dkke ykt r{bbkrri{n

    oe lvmkt dthebmkr li rbokebk% Ilt k}hcpnk.

    A% D% Qkrv hef G% M% Dtlqe

    6%0

    2%0

    4%0

    8%0

    8 0 8%0

    Dlf chrr -ja/

    nlaDCT

    4%0 2%0

    Ioa%8% Jnkodktr ltoaoehn 8?24 pnlv li vmk dhrhn ckvhdlnob thvk li chcchnr hef dotfr

    -oe jbhn,fh/ pnlvvkf hahoerv chrr -Cd oe ja/ le h nlanla rbhnk -Jnkodkt. 8?1;/% Vmk

    rnlpk li vmk dkrv rvthoamv#noek v or 0%16. onn{rvthvoea vmk rbhnoea li ckvhdlnob thvk hr

    Cd2,6% Vmk fohckvktr li vmk botbnkr tkptkrkev mor krvochvkf kttltr li 80+ oe vmk fhvh%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

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    8;11Hnnlckvtob rbhnoea nhqr

    bnhrrob joekvob vmklt or dhrkf le vmk ofkh vmhv akektob ikhv{tkr

    li ahrkr. r{bm hr vmk ofkhn ahr nhq. bhe dk {efktrvllf d

    hrr{coea hvlcr vl dk rvt{bv{tknkrr donnohtf dhnnr {efktaloea

    knhrvob blnnoroler% Fkrpovk vmkrk rocpnobhvoler. vmk vmklt

    bhpv{tkr che krrkevohn ikhv{tkr li ahrkr hef rpkbvhb{nhtn

    ptkfobvr che li vmkot blhtrk#athoekf ptlpktvokr% Vmk ltoaoehn

    vmklt hbvkf hr h rvhtvoea ploev ilt cltk rlpmorvobhvkf

    vtkhvckevr oebltplthvoea fkvhonkf rvt{bv{tk. oeknhrvobov.

    x{hev{c ckbmheobhn kiikbvr. kvb. qmobm hnnlq cltk fkvhonkf

    bhnb{nhvoler% Lvmkt k}hcpnkr oebn{fk vmk x{htj clfkn li

    knkckevht phtvobnkr hef vmk vmkltokr fkrbtodoea vmk kyln{vole

    li vmk {eoyktrk itlc vmk doa dhea% Vmor hpptlhbm mhr hnrl dkke

    r{bbkrri{n oe dolnla. pktmhpr clrv elvhdn oe akekvobr% Hahoe.

    vmk ltoaoehn Ckefknohe vmklt chfk rocpnoioea hrr{cpvoler.

    pltvthoea khbm pmkelvpob vthov hr vmk k}ptkrrole li photr li

    phtvobnkr. khbm fktoykf itlc h foiiktkev phtkev. qmobm hrrltvkf

    hef blcdoekf hv theflc oe liirptoea% Ekyktvmknkrr. vmor vmklt

    bhpv{tkf kel{am li vmk blhtrk#athoekf krrkebk li vmk

    pmkelckeh rl vmhv ov elv len ptlyofkf vmk dhror ilt vmk hppnokf

    rbokebkr li m{che akekvobr hef pnhev hef heochn dtkkfoea. d{v

    hnrl a{ofkf vmk r{bbkrri{n rkhtbm ilt vmk clnkb{nht akekvob

    blfk hef r{ppnokf vmk ckbmheorvob {efktpoeeoear ilt vmk

    clfkte kyln{voleht revmkror% Hnvml{am vmk rmltvblcoear li

    vmkrk vmkltokr htk qknn#tkblaeowkf. vmk x{hevovhvoykn k}pnhoe

    he k}vthltfoeht dlf li fhvh dkbh{rk vmk fl oefkkf bhpv{tk

    c{bm li vmk krrkevohn dkmhyolt%

    Rbhnoea hr h cheoikrvhvole li {efktnoea fehcobr mhr dkke

    oervt{ckevhn oe ahoeoea fkkpkt oeroamvr oevl ptldnkcr hbtlrr

    vmk kevotk rpkbvt{c li rbokebk hef vkbmelnla. dkbh{rk rbhnoea

    nhqr vpobhnn tkfflkbv {efktnoea akekthn ikhv{tkr hef

    ptoebopnkr vmhv htk oefkpkefkev li fkvhonkf rvt{bv{tk. fehcobr

    lt lvmkt rpkbob bmhthbvktorvobr li vmk rrvkc. lt li vmk

    phtvob{nht clfknr {rkf vl fkrbtodk ov% Rl. h bmhnnkeak oe dolnla

    or vl {efktrvhef vmk {dox{ov li x{htvkt#plqktr vl k}pnhoe

    vmkc oe vktcr li {eoioea ptoebopnkr vmhv fkvktcoek mlq noik or

    ltaheowkf hef vmk blervthoevr {efkt qmobm ov mhr kylnykf% Lykt

    vmk occkerk rpkbvt{c li noik vmk rhck bmkcobhn blervov{kevr

    hef tkhbvoler akekthvk he keltcl{r yhtokv li iltcr.

    i{ebvoler. hef fehcobhn dkmhyoltr% Hnn noik i{ebvoler d

    vtheriltcoea kekta itlc pmrobhn lt bmkcobhn rl{tbkr oevl

    ltaheob clnkb{nkr vmhv htk ckvhdlnowkf vl d{onf. choevhoe hef

    tkptlf{bk blcpnk}. moamn ltaheowkf rrvkcr% Qk blegkbv{tk

    ;

    0

    ;

    80

    8;

    40

    Oeyovtl

    Rmtkq

    Chcchnr

    Knkpmhev

    TB

    BbL

    Oe tkrvoea bknn

    Covlbmleftole

    -chcchnohe clbvk/

    Hykthak

    chcchnohe bknn.oe b{nv{tk

    40 8; 80 ; 0 ; 80

    nla-chrr/

    nla-ckvhdlnobplqkt/

    Ioa%4% K}vkerole li Jnkodktr 2,6#plqkt nhq ilt vmk ckvhdlnob thvk li chcchnr vl lykt 41 ltfktr li chaeov{fk itlc oefoyof{hnr -dn{k botbnkr/

    vl {ebl{pnkf chcchnohe bknnr. covlbmleftoh hef vktcoehn l}ofhrk clnkb{nkr. BbL li vmk tkrpothvlt blcpnk}. TB -tkf botbnkr/% Hnrl rmlqe

    htk fhvh ilt {eobknn{nht ltaheorcr -atkke botbnkr/% Oe vmk tkaole dknlq vmk rchnnkrv chcchn -vmk rmtkq/. rbhnoea or ptkfobvkf vl k}vthplnhvk

    noekhtn vl he orlnhvkf bknn oe yovtl. hr rmlqe d vmk flvvkf noek% Vmk 2,6#plqkt tk#kcktakr hv vmk bknn{nht hef oevthbknn{nht nkyknr% Ioa{tk vhjkeitlc Qkrv kv hn% -4004d/ qovm pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

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    8;1=

    vmhv ckvhdlnorc hef vmk blerkx{kev forvtod{vole li kekta hef

    tkrl{tbkr pnh h bkevthn. {eoyktrhn tlnk oe blervthoeoea vmk

    rvt{bv{tk hef ltaheowhvole li hnn noik hv hnn rbhnkr. hef vmhv vmk

    ptoebopnkr alykteoea vmor htk cheoikrvkf oe vmk pktyhroyk

    x{htvkt#plqkt rbhnoea nhqr%

    Qovmoe vmor phthfoac. vmk ptkbork yhn{k li vmk k}plekev.

    qmkvmkt ov or k}hbvn 2,6. ilt k}hcpnk. or nkrr ocpltvhev vmhevmk ihbv vmhv ov hpptl}ochvkr r{bm he ofkhn yhn{k lykt h

    r{drvhevohn theak li chrr. fkrpovk yhtohvole f{k vl rkblefht

    ihbvltr% Oefkkf. h x{hevovhvoyk vmklt ilt vmk flcoehev

    dkmhyol{t -vmk 2,6 k}plekev. ilt k}hcpnk/ ptlyofkr

    oeiltchvole hdl{v vmk tkrof{hn yhtohvole vmhv ov bheelv k}pnhoe%

    Oi h akekthn vmklt qovm qknn#fkekf hrr{cpvoler ptkfobvr 2,6

    ilt hykthak ofkhnowkf ltaheorcr. vmke ov or plrrodnk vl ktkbv hef

    vkrv mplvmkrkr hdl{v lvmkt ihbvltr. elv oebn{fkf oe vmk vmklt.

    qmobm ch bh{rk tkhn ltaheorcr vl fkyohvk itlc vmor yhn{k% Le

    vmk lvmkt mhef. qovml{v r{bm h vmklt ov or elv plrrodnk vl aoyk

    h rpkbob ckheoea vl he rbhnoea k}plekev. d{v len vl

    fkrbtodk vmk tknhvolermop rvhvorvobhnn% Vmor nhvvkt rvthvka mhr

    {r{hnn dkke kcpnlkf oe hehnwoea hnnlckvtob fhvh hef mhri{knkf blevtlyktr kykt roebk Jnkodktr ltoaoehn rv{f -Jnkodkt.

    8?24. 8?1;/% Jnkodktr blevkcpltht Dtlf oefkpkefkevn

    ckhr{tkf dhrhn ckvhdlnob thvkr li dotfr hef chcchnr.

    ldvhoekf h rvhvorvobhnn vvkf k}plekev li 0%12. hef rocpn vllj

    vmor hr vmk vt{k yhn{k -Dtlf. 8?6;/% R{drkx{kevn h atkhv

    fkhn li oej mhr dkke rponnkf fkdhvoea qmkvmkt vmk k}plekev or

    k}hbvn 2,6% Hnvml{am vmor blevtlyktr hppkhtkf vl dk rkvvnkf

    cltk vmhe 40 khtr hal -Bhnfkt. 8?=6: CbChmle hef Dleekt.

    8?=2: Pkvktr. 8?=9: Rbmcofv#Eoknrke. 8?=6/. ov qhr tkbkevn

    tkr{ttkbvkf d rkykthn tkrkhtbmktr -Flffr kv hn%. 4008: Rhyhak

    kv hn%. 4006d: Qmovk hef Rkcl{t. 4002/%

    H fkkp {efktrvhefoea li x{htvkt#plqkt rbhnoea dhrkf le h

    rkv li {efktnoea ptoebopnkr bhe ptlyofk. oe ptoebopnk. h akekthnithckqltj ilt chjoea x{hevovhvoyk fehcobhn bhnb{nhvoler li

    che cltk fkvhonkf x{hevovokr dklef g{rv vmk hnnlckvtob

    k}plekevr li vmk pmkelckeh {efkt rv{f% Ov bhe thork hef

    hfftkrr che hffovolehn x{krvoler. r{bm hr7 Mlq che l}ofhrk

    clnkb{nkr hef covlbmleftoh htk vmktk oe he hykthak bknn hef oe

    he kevotk ltaheorc< Mlq che todlrlchn TEH clnkb{nkrt. vmk ptldnkc bhe dk

    rlnykf hehnvobhnn. hr trv rmlqe d Qlcktrnk -Bhtl kv hn%.

    8?1=: I{ea. 8?=6/. vl aoyk7

    qmktk Ge fkelvkr vmk Dkrrkn i{ebvole li ltfkt e% Mktk. orvmk hea{nht itkx{keb li vmk qhyk. -,/8,4t or hfockerolenkrr phthckvkt jelqe hr vmk Qlcktrnk e{cdkt.

    b0-Km,4t/8,4 or vmk bnhrrob JltvkqkaClker yknlbov. hefWor vmk ykrrkn ocpkfhebk% Dlvm Whef vmk qhyk yknlbov. b. htk

    blcpnk} i{ebvoler lirl. oe akekthn. vmk qhyk or hvvke{hvkfhef forpktrkf hr ov ptlphahvkr hnlea vmk v{dkr% Vmk bmhthbvkt

    li vmk qhyk fkpkefr btovobhnn le qmkvmkt ~~ or nkrr vmhe ltatkhvkt vmhe 8% Vmor bhe dk rkke k}pnobovn oe Kx%;. qmktk vmk

    dkmhyolt li vmk Dkrrkn i{ebvoler bmheakr itlc h plqkt#rktokr

    k}pherole ilt rchnn ~~ vl he k}pherole qovm lrbonnhvltdkmhyolt qmke ~~ or nhtak% Oe m{cher. ~~ mhr h yhn{k li htl{ef8; oe vmk hltvh. ; oe vmk htvktokr. 0%06 oe vmk htvktolnkr. hef 0%00;

    oe vmk bhponnhtokr% Qmke ~~ or nhtak -558/. Kx%; aoykr bub0.qmobm or h p{tkn tkhn x{hevov. rl vmk qhyk r{iiktr ekovmkt

    hvvke{hvole elt forpktrole% Blerkx{kevn. oe vmkrk nhtak ykrrknr

    yorblrov pnhr hnclrv el tlnk hef yotv{hnn el kekta or

    forrophvkf% Oe he htdovtht {eblervthoekf ekvqltj. mlqkykt.

    kekta c{rv dk k}pkefkf vl lyktblck plrrodnk tkfflkbvoler hv

    dthebm g{ebvoler. qmobm ql{nf tkx{otk oebtkhrkf bhtfohb plqkt

    l{vp{v% Coeocowhvole li kekta k}pkefov{tk or vmktkiltk

    hbmokykf d knocoehvoea r{bm tkfflkbvoler. h pmkelckele

    jelqe hr ocpkfhebk chvbmoea% Itlc Kx%;. Wub0,t4 iltnhtak ykrrknr. hef ocpkfhebk chvbmoea nkhfr vl htkh#ptkrktyoea

    dthebmoea7 tj43etj*84. rl vmhv tj*8,tj3e8,4% Ilt rchnnykrrknr. mlqkykt. qmktk ~~>>8. vmk tlnk li yorblrov hefvmk r{drkx{kev forrophvole li kekta dkblck oebtkhroean

    ocpltvhev {evon vmk kykev{hnn flcoehvk vmk ffllq% Kx%; vmke

    aoykr bu-8,6/o8,4b00. oe x{hevovhvoyk hatkkckev qovmldrktyhvole -Bhtl kv hn%. 8?1=: I{ea. 8?=6/% Dkbh{rk b elq mhr

    h flcoehev ochaoeht phtv. vmk vthyknoea qhyk or mkhyon

    fhcpkf. nkhyoea he hnclrv rvkhf lrbonnhvlt ffllq qmlrk

    ocpkfhebk or. itlc Kx%;. g{rv vmk bnhrrob Plork{onnk iltc{nh.

    Wj3=nj,tj6% [enojk kekta nlrr f{k vl tkfflkbvoler hv dthebmploevr. kekta nlrr f{k vl yorbl{r forrophvoyk iltbkr bheelv dk

    -;/bl

    4

    t4

    b

    .hef WuG4-o

    2,4/

    G0-o2,4

    /u

    b

    b0

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    -6/4

    v4 3K

    4 p .q

    -4/yv 3

    4y p .

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    6/18

    8;=0

    kevotkn knocoehvkf% Ov bhe dk coeocowkf. mlqkykt. {roea vmk

    bnhrrob ckvmlf li Nhatheak c{nvopnoktr vl keiltbk vmk

    hpptlptohvk blervthoevr -Chtole hef Vmltevle. 8?==: Qkrv kv

    hn%. 8??1/% Vl r{rvhoe h aoyke ckvhdlnob thvk oe he ltaheorc li

    }kf chrr qovm h aoyke yln{ck li dnllf. Yd. vmk bhtfohb l{vp{v

    c{rv dk coeocowkf r{dgkbv vl h rphbk#nnoea aklckvt% Vmk

    bhnb{nhvole rmlqr vmhv htkh#ptkrktyoea dthebmoea or vmktkdtkpnhbkf d htkh#oebtkhroea dthebmoea oe rchnn ykrrknr. rl

    dnllf rnlqr flqe hnnlqoea kiiobokev foii{role li l}ake itlc

    vmk bhponnhtokr vl vmk bknnr% Dthebmoea. vmktkiltk. bmheakr

    blevoe{l{rn flqe vmtl{am vmk ekvqltj. rl vmhv vmk thvol tj*8,tjor elv oefkpkefkev lijd{v bmheakr blevoe{l{rn itlc e8,4 hv

    vmk hltvh vl e8,2 hv vmk bhponnhtokr% Blerkx{kevn. vmk ekvqltj

    or elv rvtobvn rkni#roconht. d{v qovmoe khbm tkaole -p{nrhvonk oe

    nhtak ykrrknr hef Plork{onnk oe rchnn lekr/. rkni#roconhtov or h

    tkhrlehdnk hpptl}ochvole vmhv or qknn r{ppltvkf d kcpotobhn

    fhvh -Bhtl kv hn%. 8?1=: I{ea. 8?=6: Whcot. 8???/%

    Oe ltfkt vl fktoyk hnnlckvtob tknhvoler dkvqkke heochnr li

    foiiktkev rowkr qk ekkf vl tknhvk vmk rbhnoea li ykrrkn

    fockeroler qovmoe he ltaheorc vl ovr dlf chrr.Cd% H ehv{thnykmobnk ilt vmor or vmk vlvhn yln{ck li dnllf oe vmk ekvqltj.

    Yd. qmobm bhe dk rmlqe vl fkpkef noekhtn le Cd oi bhtfohb

    l{vp{v or coeocowkf. o%k% YdCd. oe hatkkckev qovm fhvh -Bhtl

    kv hn%. 8?1=: I{ea. 8?=6/% Vmor or rvthoamviltqhtfn aoyke d

    Yd3EjYj3ejtj4nj. qmktkEj3ejor vmk e{cdkt li ykrrknr hvnkykn j% Ptlyofkf vmktk htk r{iiobokevn nhtak ykrrknr oe vmk

    ekvqltj qovm ~~58 rl vmhv p{nrhvonk ffllq flcoehvkr. vmknkhfoea#ltfkt dkmhyolt ilt vmk dnllf yln{ck or Yde

    6E,2YE%

    Blerktyhvole li dnllf tkx{otkr vmhv vmk ffllq thvk oe vmk hltvh.

    X03 EEXE. qmktk XE or vmk ffllq thvk oe h bhponnht hef

    EEeE. vmk vlvhn e{cdkt li bhponnhtokr% D{v X0D. vmk vlvhn

    ckvhdlnob thvk. rl p{vvoea vmkrk vlakvmkt qk ldvhoe

    D-Yd,YE/2,6XE% Mlqkykt. bhponnhtokr htk oeyhtohev {eovr. rlYE hef XE htk dlvm oefkpkefkev li Cd. qmktkhr itlc

    coeocowhvole li kekta nlrr. YdCd. rl qk occkfohvkn

    ldvhoe vmk rkcoehn tkr{nv DCd2,6%

    Vmk hnnlckvtob rbhnoea li thfoo. nkeavmr hef che lvmkt

    pmrolnlaobhn bmhthbvktorvobr. r{bm hr vmk ffllq. p{nrk hef

    fockeroler oe he dthebm li h chcchn li he rowk. bhe dk

    fktoykf itlc vmor qmlnk#rrvkc clfkn hef rmlqe vl mhyk

    x{htvkt#plqkt k}plekevr% X{hevovhvoyk ptkfobvoler ilt hnn vmkrk

    bmhthbvktorvobr li vmk bhtfolyhrb{nht rrvkc htk oe allf

    hatkkckev qovm fhvh -Qkrv kv hn%. 8??1/% Ilt k}hcpnk. kyke vmk

    tkrof{hn p{nrk qhyk blcplekev oe bhponnhtokr or fkvktcoekf7 ov

    or ptkfobvkf vl dk hvvke{hvkf vl 0%8+ qovm ovr yknlbov dkoea

    u80bcr8. blcphtkf vl u;=0bcr8 ilt vmk {ehvvke{hvkf

    qhyk oe vmk hltvh. dlvm e{cdktr dkoea oeyhtohev qovm tkrpkbv

    vl dlf rowk%

    Vl r{cchtork7 vmktk htk vql oefkpkefkev blevtod{voler vl

    kekta k}pkefov{tk7 yorbl{r kekta forrophvole. qmobm or

    ocpltvhev len oe rchnnkt ykrrknr. hef kekta tkfflkbvkf hv

    dthebm ploevr. qmobm or ocpltvhev len oe nhtakt ykrrknr hef or

    knocoehvkf d ocpkfhebk chvbmoear Oe nhtak ykrrknr -htvktokr/.

    p{nrk#qhykr r{iikt novvnk hvvke{hvole lt forrophvole. hef

    ocpkfhebk chvbmoea nkhfr vl htkh#ptkrktyoea dthebmoea. r{bm

    vmhv vmk btlrr#rkbvolehn htkh li fh{amvkt dthebmkr kx{hnr vmhv

    li vmk phtkev: rl thfoo rbhnk hr tj*8,tj3e8,4 qovm vmk dnllf

    yknlbov tkchoeoea blervhev% Oe rchnn ykrrknr -bhponnhtokr hef

    htvktolnkr/ vmk p{nrk or rvtlean fhcpkf roebk Plork{onnk ffllq

    flcoehvkr hef r{drvhevohn kekta or forrophvkf% Mktk

    coeocowhvole li kekta forrophvole nkhfr vl htkh#oebtkhroea

    dthebmoea qovm tj*8,tj3e8,2. rl dnllf rnlqr flqe. hnclrv

    bkhroea vl ffllq oe vmk bhponnhtokr% Blerkx{kevn. vmk thvol li

    ykrrkn thfoo dkvqkke hfghbkev nkyknr. tj*8,tj. bmheakr

    blevoe{l{rn itlc e8,4 vl e8,2 flqe vmtl{am vmk ekvqltj.

    qmobm or. vmktkiltk. elvrvtobvn rkni#roconht% Ekyktvmknkrr. roebk

    vmk nkeavm thvol nj*8,njtkchoer blervhev vmtl{aml{v vmk ekvqltj

    dkbh{rk li rphbk#nnoea. dthebm#nkeavmr htk rkni#roconht hef vmkekvqltj mhr rlck ithbvhn#nojk ptlpktvokr% X{htvkt#plqkt

    hnnlckvtob tknhvoler vmke ilnnlq itlc vmk oeyhtohebk li

    bhponnhtokr hef vmk ptkfobvole itlc kekta lpvocowhvole vmhv

    vlvhn dnllf yln{ck rbhnkr noekhtn qovm dlf chrr%

    Vmk flcoehebk li p{nrhvonk ffllq. hef blerkx{kevn li htkh#

    ptkrktyoea dthebmoea. or bt{bohn ilt fktoyoea plqkt nhqr.

    oebn{foea vmk 2,6 k}plekev ilt ckvhdlnob thvk. D% Mlqkykt. hr

    dlf rowk fkbtkhrkr. ehttlq v{dkr ptkflcoehvk hef yorblrov

    pnhr he kykt#oebtkhroea tlnk% Kykev{hnn kyke vmk chglt

    htvktokr ql{nf dkblck vll blervtobvkf vl r{ppltv qhyk

    ptlphahvole. dnllf ffllq ql{nf dkblck rvkhf hef dthebmoea

    k}bn{roykn htkh#oebtkhroea. nkhfoea vl h noekht fkpkefkebk le

    chrr% Roebk kekta ql{nf dk forrophvkf oe hnn dthebmkr li vmk

    ekvqltj. vmk rrvkc or elq moamn oekiiobokev: r{bm he

    ocplrrodn rchnn chcchn ql{nf mhyk h dkhvoea mkhtv -qovm h

    tkrvoea mkhtv#thvk oe k}bkrr li hpptl}ochvkn 8000dkhvrcoe8/

    d{v el p{nrk( Vmor ptlyofkr h ithckqltj vl krvochvk vmk

    rowk li vmk rchnnkrv chcchn oe vktcr li i{efhckevhn

    bhtfolyhrb{nht phthckvktr% Vmor aoykr h coeoc{c chrr

    Ccoeu8a. bnlrk vl vmhv li h rmtkq. qmobm or oefkkf vmk rchnnkrv

    chcchn -Ioa%2: Qkrv kv hn%. 4004d/% I{tvmktcltk. vmk

    ptkfobvkf noekht k}vthplnhvole liD dknlq vmor chrr vl vmk chrr

    li h roeank bknn rml{nf. hef flkr. aoyk vmk blttkbv yhn{k ilt vmk

    A% D% Qkrv hef G% M% Dtlqe

    8%0

    8%4

    8%6

    8%9

    8%=

    4%0

    4%4

    4%6

    4%9

    4%=

    2%0

    0 =64 9

    nlaCd

    nlai

    M

    30%4;8}*2%014

    t430%?;

    Ioa%2% Pnlv li mkhtv thvkr -iM/ li chcchnr hv tkrv yr dlf chrr Cd-fhvh vhjke itlc Dtlf. 8?6;/% Vmk tkatkrrole noekr htk vvkf vl vmk

    hykthak li vmk nlahtovmcr ilt kykt 0%8 nla {eov oevktyhn li chrr. d{v

    dlvm vmk hykthak -rx{htkr/ hef thq fhvh -dhtr/ htk rmlqe oe vmk pnlvr%

    Vmk rnlpk or 0%4;8 -P>0%0008. E381. ?;+ BO7 0%448. 0%4=8/.

    qmobm bnkhtn oebn{fkr 8,6 d{v k}bn{fkr 8,2% Ioa{tk vhjke itlc

    Rhyhak kv hn% -4006d/ qovm pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    7/18

    8;=8Hnnlckvtob rbhnoea nhqr

    ckvhdlnob thvk li chcchnohe bknnr atlqoea oe b{nv{tk orlnhvkf

    itlc vmk yhrb{nht ekvqltj -Ioa%4/%

    Vmk fktoyhvole vmhv aoykr vmk 2,6 k}plekev or len hehpptl}ochvole. dkbh{rk li vmk bmheaoea tlnkr li p{nrhvonk hef

    Plork{onnk ffllq qovm dlf rowk% Rvtobvn rpkhjoea. vmk vmklt

    ptkfobvr vmhv vmk k}plekev ilt D or k}hbvn 2,6 len qmktk

    p{nrhvonk ffllq blcpnkvkn flcoehvkr% Oe akekthn. vmk k}plekev

    or ptkfobvkf vl fkpkef qkhjn le C. cheoikrvoea roaeobhev

    fkyohvoler itlc 2,6 len oe rchnn chcchnr. qmktk len vmk

    trv ikq dthebmkr li vmk htvktohn rrvkc bhe r{ppltv h p{nrk

    qhyk -Qkrv kv hn%. 8??1. 4004d/% Roebk rchnn chcchnr

    forrophvk tknhvoykn cltk kekta oe vmkot ekvqltjr. vmk tkx{otk

    knkyhvkf ckvhdlnob thvkr vl akekthvk vmk oebtkhrkf kekta

    k}pkefov{tk vl botb{nhvk vmk dnllf% Vmor nkhfr vl vmk ptkfobvole

    vmhv vmk hnnlckvtob k}plekev ilt D rml{nf fkbtkhrk dknlq 2,6

    hrCd fkbtkhrkr vl vmk rchnnkrv chcchn. hr ldrktykf -Flffrkv hn%. 4008: Rhyhak kv hn%. 4006d/%

    Oi vmk vlvhn e{cdkt li bknnr. Eb. oebtkhrkr noekhtn qovmCd.

    vmke dlvm bknn{nht ckvhdlnob thvk. Db-D,Eb/. hef rpkbob

    ckvhdlnob thvk. D,Cd. fkbtkhrk hr Cd8,6% Oe vmor rkerk.

    vmktkiltk. nhtakt heochnr htk cltk kiiobokev vmhe rchnnkt lekr.

    dkbh{rk vmk tkx{otk nkrr plqkt vl r{ppltv {eov dlf chrr hef

    vmkot bknnr fl nkrr qltj vmhe rchnnkt heochnr% Oe vktcr li l{t

    vmklt vmor or dkbh{rk vmk vlvhn mftlfehcob tkrorvhebk li vmk

    ekvqltj fkbtkhrkr qovm rowk hr Cd2,6% Vmor mhr h i{tvmkt

    oevktkrvoea blerkx{kebk vmhv. roebk vmk b{ttkev lt yln{ck thvk

    li ffllq li dnllf oe vmk ekvqltj. X0. oebtkhrkr hrCd2,6. qmktkhr

    vmk tkrorvhebk fkbtkhrkr hr Cd

    2,6. vmk hehnla vl Lmcr nhq

    -ptkrr{tk3b{ttkevtkrorvhebk/ ptkfobvr vmhv dnllf ptkrr{tk

    c{rv dk he oeyhtohev. hr ldrktykf -Bhtl kv hn%. 8?1=: I{ea.

    8?=6/% Vmor ch rkkc bl{evktoev{ovoyk. roebk vmk thfo{r li vmk

    hltvh yhtokr itlc hpptl}ochvkn 0%4cc oe h rmtkq {p vl

    hpptl}ochvkn 20bc oe h qmhnk(

    Rbhnoea {p vmk mokthtbm7 itlc clnkb{nkr vl chcchnr

    Hv khbm ltaheorhvolehn nkykn qovmoe he ltaheorc. dkaoeeoea

    qovm clnkb{nkr hef blevoe{oea {p vmtl{am ltaheknnkr. bknnr.

    vorr{kr hef ltaher. ekq rvt{bv{tkr kcktak. khbm qovm foiiktkev

    pmrobhn bmhthbvktorvobr. i{ebvolehn phthckvktr. hef tkrl{tbkhef kekta ekvqltj rrvkcr. vmktkd blervov{voea h mokthtbm

    li mokthtbmokr% Ckvhdlnob kekta or blerktykf hr ov ffllqr

    vmtl{am vmor mokthtbm li rkx{kevohn ekvqltjr% Qk hrr{ck vmhv

    khbm ekvqltj lpkthvkr r{dgkbv vl vmk rhck akekthn ptoebopnkr

    hef vmktkiltk k}modovr x{htvkt#plqkt rbhnoea -Qkrv kv hn%.

    4004d/% Itlc vmk clnkb{nkr li vmk tkrpothvlt blcpnk} {p vl

    oevhbv bknnr. ckvhdlnob thvk ldkr 2,6#plqkt rbhnoea%

    Blevoe{ov li ffllq ocplrkr dl{efht blefovoler dkvqkke

    hfghbkev nkyknr. nkhfoea vl blervthoevr le vmk fkerovokr li

    oeyhtohev vktcoehn {eovr. r{bm hr tkrpothvlt blcpnk}kr hef

    covlbmleftoh. hef le vmk ekvqltjr li ffllqr vmhv bleekbv

    vmkc -Qkrv kv hn%. 4004d/% Vmk vlvhn covlbmleftohn chrr

    tknhvoyk vl dlf chrr or blttkbvn ptkfobvkf vl dk

    -Ccoecc,cbCd/8,60%09Cd

    8,6. qmktk cc or vmk chrr li h

    covlbmleftole. Ccoe or coeoc{c chrr. cb or hykthak bknn

    chrr hef Cd or k}ptkrrkf oe a% Roebk covlbmleftoh htk

    hrr{ckf vl dk hpptl}ochvkn oeyhtohev. vmk vlvhn e{cdkt oe vmk

    dlf or fkvktcoekf oe h roconht ihrmole% Vmor rmlqr qm vmktk

    htk vpobhnn len h ikq m{eftkf pkt m{che bknn. qmktkhr vmktk

    htk rkykthn vml{rhef oe h rmtkq bknn li vmk rhck vpk%

    Hr hntkhf rvtkrrkf. h bkevthn ptkcork li vmk vmklt or vmhv

    akekthn ptlpktvokr li r{ppn ekvqltjr blervthoe vmk blhtrk#

    athoekf. hef vmktkiltk vmk rbhnoea ptlpktvokr. li dolnlaobhn

    ;%0

    ;%;

    9%0

    9%;

    1%0

    1%;

    =%0

    8; 86 82 84 88 80 ?

    nla-bknn{nht chrr/

    nla-a

    kelcknkeavm/

    Rnlpk30%460%04

    Oevktbkpv3?%60%4

    Ele#pmlvlrevmkvob ptljhtlvkrBhelpmvh

    Ioa%6% Pnlv li akelck nkeavm -e{cdkt li dhrk photr/ yr chrr -oe a/

    ilt h rkx{kebk li {eobknnr le h nlanla rbhnk% Vmk dkrv rvthoamv#noek v

    mhr h rnlpk ykt bnlrk vl 8,6%

    82

    84

    88

    80

    ?

    0 4 6 9 =

    nla-chrr li ltaheorc/

    nla-plqktpktbknn/

    Bknnr oeyoyl.DCd8,6

    B{nv{tkf bknnr

    oeyovtl.DCd0

    C3

    Ioa%;% Ckvhdlnob thvkr -oe Q/ li chcchnohe bknnr oe yoyl -dn{k noek/

    hef b{nv{tkf oe yovtl -tkf noek/ pnlvvkf hr h i{ebvole li ltaheorc chrr

    -Cd oe a/ le h nlanla rbhnk% Qmonk rvonn oe vmk dlf hef blervthoekf

    d yhrb{nht r{ppn ekvqltjr bknn{nht ckvhdlnob thvkr rbhnk hr Cd8,6%

    Qmke bknnr htk tkclykf itlc vmk dlf hef b{nv{tkf oe yovtl. vmkot

    ckvhdlnob thvkr bleyktak vl h blervhev yhn{k ptkfobvkf d vmklt

    -Qkrv kv hn%. 4004d/% Vmk vql noekr ckkv hv vmk chrr li vmk rchnnkrv

    chcchn -vmk rmtkq qovm chrr u8a. hr ptkfobvkf/% Ioa{tk vhjke itlc

    Qkrv kv hn% -4004d/ qovm pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    8/18

    8;=4

    rrvkcr% He occkfohvk x{hnovhvoyk blerkx{kebk li vmor

    ofkh or vmhv. oi bknnr htk nodkthvkf itlc vmk ekvqltj

    mkakcle d b{nv{toea vmkc oe yovtl. vmk htk nojkn vl

    dkmhyk foiiktkevn itlc bknnr oe yoyl% He hnvktehvoyk

    plrrodonov or vmhv bknn{nht ckvhdlnob thvkr htk tknhvoykn

    oefflk}odnk% Vmor. mlqkykt. ql{nf dk h pllt fkroae.

    dkbh{rk ov ql{nf ptkykev ihb{nvhvoyk hfg{rvckev oe

    tkrplerk vl yhtohvole oe dlf rowk lykt levlake hef oe

    tkrplerk vl vmk yhtoea ckvhdlnob fkchefr li vorr{kr%

    Oi vmk ckvhdlnob thvk hef e{cdkt li covlbmleftoh pktbknn htk oefkkf v{ekf ihb{nvhvoykn oe tkrplerk vl

    yhtohvoler oe r{ppn hef fkchef. vmk vmklt chjkr he

    k}pnobov x{hevovhvoyk ptkfobvole7 bknnr orlnhvkf itlc

    foiiktkev chcchnr hef b{nv{tkf oe yovtl {efkt

    blefovoler li {enocovkf tkrl{tbk r{ppn rml{nf

    bleyktak vlqhtf vmk rhck ckvhdlnob thvk -ptkfobvkf vl dk

    u98088Q/. thvmkt vmhe rbhnoea hr C8,6 hr vmk fl oe yoyl

    -Ioa%;/: bknnr oe yovtl rml{nf hnrl bleyktak vlqhtf ofkevobhn

    e{cdktr li covlbmleftoh. nlroea vmk C8,6 rbhnoea vmhv vmk

    k}modov oe yoyl% Vmk oe yoyl hef oe yovtl yhn{kr htk ptkfobvkf vl

    bloebofk hv Ccoe. qmobm qk krvochvkf hdlyk vl dk

    hpptl}ochvkn 8a% Rl bknnr oe rmtkqr qltj hv hnclrv ch}ochn

    l{vp{v. qmobm. el fl{dv. or tkfflkbvkf oe vmkot moam nkyknr lihbvoyov hef vmk rmltvekrr li vmkot noykr% D blevthrv bknnr oe

    nhtakt chcchnr htk blervthoekf d vmk ptlpktvokr li yhrb{nht

    r{ppn ekvqltjr hef eltchnn qltj hv nlqkt thvkr%

    Hnn li vmkrk tkr{nvr fkpkef len le akektob ekvqltj

    ptlpktvokr. oefkpkefkev li fkvhonr li hehvlc hef pmrolnla.

    oebn{foea foiiktkebkr oe vmk rowk. rmhpk hef e{cdkt li

    covlbmleftoh hclea foiiktkev vorr{kr qovmoe h chcchn% Roebk

    x{htvkt#plqkt rbhnoea or ldrktykf hv oevthbknn{nht. hr qknn hr

    qmlnk#ltaheorc hef bknn{nht nkyknr. vmor r{aakrvr vmhv

    ckvhdlnob ptlbkrrkr hv r{dbknn{nht nkyknr htk hnrl blervthoekf

    d lpvocowkf rphbk#nnoea. mokthtbmobhn ekvqltjr. qmobm mhyk

    roconht ptlpktvokr vl vmk cltk chbtlrblpob lekr% H chglt

    bmhnnkeak. dlvm vmkltkvobhnn hef k}pktockevhnn. or vl

    {efktrvhef x{hevovhvoykn vmk ckbmheorcr li oevthbknn{nht

    vtherpltv. hdl{v qmobm r{tptoroean novvnk or jelqe%

    K}vkeroler

    Levlakekvob atlqvm

    Vmk vmklt fkyknlpkf hdlyk ehv{thnn nkhfr vl h akekthn

    atlqvm kx{hvole hppnobhdnk vl hnn c{nvobknn{nht heochnr -Qkrv

    kv hn%. 4008. 4004h/% Ckvhdlnob kekta vtherpltvkf vmtl{am vmk

    ekvqltj i{knr bknnr qmktk ov or {rkf kovmkt ilt choevkehebk.

    oebn{foea vmk tkpnhbkckev li bknnr. lt ilt vmk ptlf{bvole li

    hffovolehn dolchrr hef ekq bknnr% Vmor bhe dk k}ptkrrkf hr7

    qmktkEb or vmk vlvhn e{cdkt li bknnr oe vmk ltaheorc hv vock v

    hivkt dotvm hefKb vmk kekta ekkfkf vl btkhvk h ekq bknn% RoebkEb3c,cb. qmktk c or vmk levlakekvob chrr hef cb vmk hykthak

    bknn chrr. vmor nkhfr vl he kx{hvole ilt vmk atlqvm thvk li he

    ltaheorc7

    qmktkD0 or vmk vh}le#fkpkefkev eltchnowhvole blervhev ilt vmk

    rbhnoea li ckvhdlnob thvk7 DD0c2,6% Vmk phthckvktr li vmk

    tkr{nvoea atlqvm kx{hvole htk vmktkiltk fkvktcoekf rlnkn d

    i{efhckevhn ptlpktvokr li bknnr. r{bm hr vmkot ckvhdlnob thvkr

    hef vmk kekta tkx{otkf vl ptlf{bk ekq lekr. qmobm bhe dk

    ckhr{tkf oefkpkefkevn li atlqvm% Vmk clfkn aoykr h ehv{thn

    k}pnhehvole ilt qm heochnr rvlp atlqoea7 vmk e{cdkt li bknnr

    r{ppnokf -Ebc/ rbhnkr ihrvkt vmhe vmk e{cdkt li r{ppn {eovr

    -roebk DEEc2,6/. hef nkhfr vl he k}ptkrrole ilt vmk

    hrcpvlvob chrr li vmk ltaheorc7Cd3-D0cb,Db/6% Kx%1 bhe dk

    rlnykf hehnvobhnn vl fkvktcoek c hr h i{ebvole li v. nkhfoea

    vl h bnhrrob roaclofhn atlqvm b{tyk% D hpptlptohvkn tkrbhnoea

    c hef vhr ptkrbtodkf d vmk vmklt. vmk rln{vole bhe dk tkbhrv

    hr h {eoyktrhn rbhnoea b{tyk ilt atlqvm% Qmke tkrbhnkf oe vmor

    qh. atlqvm fhvh itlc che foiiktkev heochnr -oebn{foea

    keflvmktcr hef kbvlvmktcr. yktvkdthvkr hef oeyktvkdthvkr/ hnn

    -1/c .c2,6

    Db

    Kb

    fc

    fv3

    D0cb

    Kb

    -9/.D 3EbDb *Kb

    fEb

    fv

    A% D% Qkrv hef G% M% Dtlqe

    0

    0%4;

    0%;0

    0%1;

    8%00

    8%4;

    0 4 6 9 = 80

    Fockerolenkrrchrrthvol-c,C

    /8,6

    -hv,6Cd8,6/ ne Z8-c0,Cd/8,6S

    Fockerolenkrr vock

    Rqoek

    RmtkqThddov

    Blf

    Thv

    A{oekh poa

    Rmtocp

    Rhncle

    A{pp

    Bmobjke

    Tldoe

    Mktle

    Blq

    Ioa%9% Vmk {eoyktrhnov li atlqvm or onn{rvthvkf d pnlvvoea vmk

    fockerolenkrr chrr thvol -c,C/8,6 hahoerv h fockerolenkrr

    vock yhtohdnk. hr rmlqe% Qmke fhvh ilt chcchnr. dotfr. rm

    hef bt{rvhbkh htk pnlvvkf vmor qh. vmk htk ptkfobvkf vl nok le

    h roeank {eoyktrhn b{tyk: c or vmk chrr li vmk ltaheorc hv hak

    v. c0 ovr dotvm chrr. Cd ovr chv{tk chrr. hef h h phthckvkt

    fkvktcoekf d vmklt oe vktcr li dhrob bknn{nht ptlpktvokr vmhv

    bhe dk ckhr{tkf oefkpkefkevn li atlqvm fhvh% Ioa{tk vhjkeitlc Qkrv kv hn% -4008/ qovm pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    9/18

    8;=2Hnnlckvtob rbhnoea nhqr

    bnlrkn v h roeank {eoyktrhn b{tyk -Ioa%9/% Levlakekvob atlqvm

    or vmktkiltk h {eoyktrhn pmkelckele fkvktcoekf d vmkoevkthbvole li dhrob ckvhdlnob ptlpktvokr hv bknn{nht hef qmlnk#

    ltaheorc nkyknr% I{tvmktcltk. vmor clfkn nkhfr vl rbhnoea nhqr

    ilt lvmkt atlqvm bmhthbvktorvobr. r{bm hr fl{dnoea vockr ilt

    dlf chrr hef bknn e{cdkt. hef vmk tknhvoyk kekta fkylvkf vl

    ptlf{bvole yr choevkehebk% Tkbkevn. A{olv kv hn% -4002/

    hppnokf vmor clfkn vl atlqvm li rlnof v{cltr oe thvr hef

    m{cher% Vmk rmlqkf vmhv vmk atlqvm b{tyk fktoykf itlc

    Kx%1 ahyk ykt allf vr. kyke vml{am vmk phthckvktr vmk

    {rkf qktk fktoykf itlc rvhvorvobhn vvoea thvmkt vmhe fkvktcoekf

    itlc trv ptoebopnkr. hr oe levlakekvob atlqvm% Vmor or g{rv lek

    k}hcpnk li vmk k}bovoea plvkevohn hppnobhvoler li ckvhdlnob

    rbhnoea vmklt vl ocpltvhev dolckfobhn ptldnkcr%

    Vkcpkthv{tk hef {eoyktrhn dolnlaobhn bnlbjr

    Vkcpkthv{tk mhr h plqkti{n kiikbv le hnn dolnlaobhn rrvkcr

    dkbh{rk li vmk k}plekevohn rkerovoyov li vmk Dlnvwchee ihbvlt.

    kK,jV. qmobm blevtlnr vmk vkcpkthv{tk fkpkefkebk li

    dolbmkcobhn tkhbvole thvkr: mktk. K or h bmkcobhn hbvoyhvole

    kekta. Vhdrln{vk vkcpkthv{tk. hef jDlnvwcheer blervhev%

    Blcdoekf qovm ekvqltj blervthoevr vmhv alykte vmk ffl{}kr li

    kekta hef chvktohnr. vmor ptkfobvr h gloev {eoyktrhn chrr hef

    vkcpkthv{tk rbhnoea nhq ilt hnn thvkr hef vockr bleekbvkf

    qovm ckvhdlnorc. oebn{foea atlqvm. kcdtleob fkyknlpckev.

    nleakyov hef FEH e{bnklvofk r{drvov{vole oe akelckr% Hnn

    r{bm thvkr htk ptkfobvkf vl rbhnk hr7

    T Cd8,6kK,jV . -=/

    hef hnn vockr hr7

    vCd8,6kK,jV % -?/

    Vmk btovobhn ploevr mktk htk vmk rkphthdnk c{nvopnobhvoyk ehv{tk

    li vmk chrr hef vkcpkthv{tk fkpkefkebkr hef vmk tknhvoykn

    oeyhtohev yhn{k liK. tkfflkbvoea vmk hykthak hbvoyhvole kekta

    ilt vmk thvk#nocovoea dolbmkcobhn tkhbvoler -Aonnlln kv hn%.

    4008/% Fhvh blyktoea h dtlhf theak li ltaheorcr -rm.

    hcpmodoher. hx{hvob oerkbvr hef wllpnhejvle/ bletc vmkrk

    ptkfobvoler qovm Ku0%9;kY -Ioa%1/% Vmkrk tkr{nvr r{aakrv h

    akekthn fkeovole li dolnlaobhn vock vmhv or hpptl}ochvkn

    oeyhtohev hef blccle vl hnn ltaheorcr7 qmke hfg{rvkf ilt rowk

    hef vkcpkthv{tk. fkvktcoekf d g{rv vql e{cdktr -8,6 hef

    Ku0%9;kY/. hnn ltaheorcr vl h allf hpptl}ochvole t{e d vmk

    rhck {eoyktrhn bnlbj qovm roconht ckvhdlnob. atlqvm. hef

    kyln{voleht thvkr( -Aonnlln kv hn%. 400;/%

    Ckvhdlnob rbhnoea oe pnhevr7 oefkpkefkev kyln{vole liC2,6

    Lek li vmk clrv bmhnnkeaoea ihbvr hdl{v x{htvkt#plqkt

    rbhnoea tknhvoler or vmhv vmk htk ldrktykf oe dlvm heochnr hef

    pnhevr% L{t vmklt liiktr he k}pnhehvole7 dlvm {rk ithbvhn#nojk

    2%0 2%=2%69

    4

    4

    ne-DCF2,6/

    Vkcpkthv{tk8 -8000,J/

    A

    3?%80}*4?%6?

    t430%==E3864

    Dotfr hef chcchnr

    2%0 2%=2%6=

    0

    6

    Vkcpkthv{tk8 -8000,J/

    K

    3;%19}*89%9=

    t430%;9E396

    Hcpmodoher

    2%0 2%=2%6=

    0

    6

    I

    3=%1=}*49%=;

    t430%1;E380;

    Tkpvonkr

    2%0 2%=2%6=

    0

    6

    F

    3;%04}*86%61

    t430%;2E3882

    Iorm

    2%0 2%=2%6=

    0

    6

    D Pnhevr

    2%0 2%=2%6=

    0

    6

    B

    3?%8;}*41%94

    t4

    30%94E340

    C{nvobknn{nht oeyktvkdthvkr

    2%0 2%=2%6=

    0

    6

    H

    3=%1?}*4;%=0

    t4

    30%90E320

    31%98}*48%21

    t4

    30%1;E391

    [eobknnr

    Ioa%1% Pnlv li chrr#blttkbvkf tkrvoea ckvhdlnob thvk. ne-D Cd2,6/ yr oeyktrk

    hdrln{vk vkcpkthv{tk -8000,J/ ilt {eobknnr -H/. pnhevr -D/. c{nvobknn{nht

    oeyktvkdthvkr -B/. rm -F/. hcpmodoher -K/. tkpvonkr -I/. hef dotfr hef chcchnr

    -A/% Dotfr -nnkf rcdlnr/ hef chcchnr -lpke rcdlnr/ htk rmlqe hv eltchn

    dlf vkcpkthv{tk -vtoheankr/ hef f{toea modktehvole lt vltplt -rx{htkr/% Ioa{tk

    vhjke itlc Aonnlln kv hn% -4008/ qovm pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    10/18

    8;=6

    dthebmoea rvt{bv{tkr vl forvtod{vk tkrl{tbkr. rl dlvm ldk vmk

    rhck dhrob ptoebopnkr fkrpovk vmk nhtak foiiktkebkr oe hehvlc

    hef pmrolnla% Ilt k}hcpnk. oe chtjkf blevthrv vl vmk

    chcchnohe botb{nhvlt rrvkc. pnhev yhrb{nht rrvkcr htk

    kiikbvoykn dkt d{efnkr li nlea cobtl#bhponnht v{dkr -}nkc

    hef pmnlkc/. qmobm vtherpltv tkrl{tbkr itlc vt{ej vl nkhykr.

    ftoyke d h ele#p{nrhvonk p{cp -Eojnhr. 8??6/% Oi vmkcobtlbhponnht ykrrknr qktk li {eoiltc thfo{r. hr or livke

    hrr{ckf oe clfknr li pnhevr. h rktol{r phthfl} tkr{nvr7 vmk

    r{ppn vl vmk vhnnkrv dthebmkr. qmktk clrv noamv or blnnkbvkf.

    r{iiktr vmk atkhvkrv tkrorvhebk% Vmor ptldnkc mhf vl dk

    botb{cykevkf oe ltfkt ilt vmk yktvobhn htbmovkbv{tk li moamkt

    pnhevr vl mhyk kylnykf% I{tvmktcltk. vmk dthebmkr vmhv

    forvtod{vk tkrl{tbkr hnrl blevhoe r{drvhevohn x{hevovokr li fkhf

    qllf qmobm ptlyofk dolckbmheobhn r{ppltv. rl vmk clfkn

    c{rv oevkathvk bnhrrob dkefoea clckev kx{hvoler qovm vmk

    mftlfehcobr li ffl{of ffllq oe vmk hbvoyk v{dkr%

    Hrr{coea h rphbk#nnoea dthebmoea ekvqltj aklckvt qovm

    oeyhtohev vktcoehn {eovr -pkvolnkr lt nkhykr/ hef coeocowhvole li

    kekta {rk hr oe vmk bhtfolyhrb{nht rrvkc. vmk vmklt ptkfobvrvmhv v{dkr c{rv mhyk g{rv kel{am vhpkt rl vmhv vmk mftlfehcob

    A% D% Qkrv hef G% M% Dtlqe

    4

    8

    0

    8

    4

    2

    6

    4 0 4 6 9

    nla-chrr/

    nla-}nkcin{}/

    y30%129}0%044

    t430%?8

    Ioa%=% Pnlv li ch}oc{c tkpltvkf }nkc ffl{} thvkr -novktr li ffl{of

    vtherpltvkf yktvobhnn vmtl{am h pnhev rvkc pkt fh/ ilt pnhevr -Kex{orv

    hef Eojnhr. 4008/% Vmk TCH tkatkrrole noek or vvkf vl vmk hykthak

    li vmk nlahtovmc ilt kykt 0%8 nla {eov oevktyhn li pnhev dolchrr. d{v

    dlvm vmk hykthak -botbnkr/ hef thq fhvh -dhtr/ htk rmlqe oe vmk pnlv%

    Vmk rnlpk or 0%129 -P>0%0008. E328. ?;+BO7 0%961. 0%=4;/% Vmk

    tkatkrrole vvkf vl vmk kevotk {edoeekf fhvh rkv aoykr h roconht

    k}plekev li 0%12; -P>0%0008. E39?. ?;+ BO7 0%9=4. 0%1==/% Ioa{tkvhjke itlc Kex{orv hef Eojnhr -4008/ qovm pktcorrole%

    0%8 8 80 800

    Poe{r kf{nor # Nlr Hnhclr fhvh

    Poe{r clelpmnnh # Vh{rbm -8?=0/

    0%8

    8

    80

    800

    8000

    80000

    H

    34%011}*6%?94

    38%?69}*6%121

    Ckhe dthebm fohckvkt -bc/ qovmoe aoyke dthebm ltfkt

    E{cdktlidthebmkrqovmoeltfkt

    D

    B FRnlpk 3 4%4-R%F% 3 0%8/ Rnlpk 3 4%6

    -R%F% 3 0%8/

    0%; 8%0 8%; 4%0 4%; 2%0

    8?=8

    8?61

    0%;

    8%0

    8%;

    4%0

    4%;

    2%0

    nla-vt{ej fohckvkt/

    nla-e{cdktlirvkcr/

    Ioa%?% -H/ H vpobhn vtkk% -D/ H phak itlc Nklehtflr elvkdlljr onn{rvthvoea mor forblykt li htkh#ptkrktyoea dthebmoea ilt vtkkr% -B/ H pnlv

    li vmk e{cdkt li dthebmkr li h aoyke rowk oe he oefoyof{hn vtkk yktr{r vmkot fohckvkt -oe bc/ rmlqoea vmk ptkfobvkf oeyktrk rx{htk nhq dkmhyol{t%

    -F/ H pnlv li vmk e{cdkt li vtkkr li h aoyke rowk yr vmkot vt{ej fohckvkt -oe bc/ rmlqoea vmk ptkfobvkf oeyktrk rx{htk nhq dkmhyol{t% Vmk

    fhvh htk itlc h iltkrv oe Chnhroh vhjke hv vockr rkphthvkf d 26 khtr. onn{rvthvoea vmk tld{rvekrr li vmk tkr{nv% Kyke vml{am vmk oefoyof{hn

    blcplrovole li vmk iltkrv mhr bmheakf lykt vmor pktolf vmk oeyktrk rx{htk nhq mhr pktrorvkf% Ioa{tk vhjke itlc Qkrv hef Dtlqe -4006/. qovm

    pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

    11/18

    8;=;Hnnlckvtob rbhnoea nhqr

    tkrorvhebk li khbm v{dk or oefkpkefkev li phvm nkeavm% Vmor

    vmktkiltk fkclbthvorkr hnn v{dkr oe hnn dthebmkr. vmktkd

    hnnlqoea h yktvobhn htbmovkbv{tk% Hr oe vmk chcchnohe rrvkc.

    che rbhnoea tknhvoler bhe dk fktoykf dlvm qovmoe hef dkvqkke

    pnhevr. hef vmkrk chjk x{hevovhvoyk vkrvhdnk ptkfobvoler ilt

    ckvhdlnob thvk -vmk 2,6 k}plekev/. htkh#ptkrktyoea dthebmoea.

    }nkc ykrrkn vhpktoea hef blef{bvoyov. ptkrr{tk athfokevr.ffl{of yknlbov. hef vmk tknhvoyk hcl{ev li ele#blef{bvoea qllf

    vl ptlyofk dolckbmheobhn r{ppltv -Ioar=. ?/%

    Li phtvob{nht tknkyhebk mktk or vmk ihbv vmhv vmkrk vql rrvkcr.

    oe pnhevr hef chcchnr. qmobm mhyk kylnykf oefkpkefkevn d

    ehv{thn rknkbvole vl rlnyk vmk ptldnkc li kiiobokev forvtod{vole

    li tkrl{tbkr itlc h bkevthn vt{ej vl vktcoehn bhponnhtokr hef

    qmobm mhyk r{bm i{efhckevhnn foiiktkev hehvlcobhn hef

    pmrolnlaobhn ikhv{tkr. ekyktvmknkrr rmlq ofkevobhn Cd2,6

    rbhnoea li qmlnk#ltaheorc ckvhdlnob thvk. hef blcphthdnk

    x{htvkt#plqkt rbhnoea li che rvt{bv{tkr hef i{ebvoler% L{t

    clfkn hbb{thvkn ptkfobvr rbhnoea k}plekevr ilt 81 phthckvktr

    li vtkkr -Qkrv kv hn%. 8???d/% Vmkrk rkvr li blcphthdnk x{htvkt#

    plqkt rbhnoea nhqr tkfflkbv bleyktakev rln{voler li vtkkr hefchcchnr vl vmk blccle ptldnkcr li yhrb{nht ekvqltj fkroae

    rhvorioea vmk rhck rkv li dhrob ptoebopnkr%

    Vmk il{tvm fockerole

    Qk mhyk rmlqe vmhv plqkt nhq rbhnoea tkfflkbvr akektob

    ptlpktvokr li kekta hef tkrl{tbk forvtod{vole ekvqltjr7 rphbk#

    nnoea. oeyhtohev vktcoehn {eovr hef coeocowhvole li kekta

    k}pkefov{tk htk r{iiobokev vl fkvktcoek rbhnoea ptlpktvokr.

    tkahtfnkrr li vmk fkvhonkf htbmovkbv{tk li vmk ekvqltj% Ilt

    k}hcpnk. htkh#ptkrktyoea dthebmoea hef vmk noekhtov li vmk

    ekvqltj yln{ck qovm dlf chrr dlvm ilnnlq itlc lpvocoroea

    vmk rln{vole vl vmk fehcobhn kx{hvoler ilt ekvqltj ffllq hef

    htk r{iiobokev vl fktoyk x{htvkt#plqktr oe dlvm chcchnr hefpnhevr% Ekyktvmknkrr. lek bhe hrj qm ov or vmhv k}plekevr htk

    fkrvoekf vl dk x{htvkt#plqktr oe hnn bhrkr. thvmkt vmhe rlck

    lvmkt plqkt. hef qm rml{nf vmor dk h {eoyktrhn dkmhyol{t

    k}vkefoea kyke vl {eobknn{nht ltaheorcr qovm el ldyol{r

    dthebmoea ekvqltj% Or vmktk h cltk akekthn hta{ckev.

    oefkpkefkev li fehcobr hef mokthtbmobhn dthebmoea vmhv

    fkvktcoekr vmk chaob e{cdkt 6< Vmor x{krvole qhr hfftkrrkf

    d Dhehyht kv hn% -8???/ qml. ilnnlqoea l{t qltj. hnrl

    hrr{ckf vmhv hnnlckvtob tknhvoler tkfflkbv ekvqltj blervthoevr%

    Vmk ptlplrkf vmhv x{htvkt#plqktr htork itlc h cltk akekthn

    bnhrr li fotkbvkf ekvqltjr vmhv fl elv ekbkrrhton mhyk ithbvhn#

    nojk mokthtbmobhn dthebmoea% Vmk hrr{ckf vmhv vmk ekvqltj

    yln{ck rbhnkr noekhtn qovm dlf chrr Cd hef bnhockf le

    akekthn atl{efr vmhv h nlqkt dl{ef le vmk lykthnn ekvqltj ffllq

    thvk rbhnkr hr Cd2,6% Hnvml{am oevtoa{oea. vmk dolnlaobhn

    roaeobhebk li vmor tkr{nv or {ebnkht. elv len dkbh{rk ov or h

    nlqkt dl{ef thvmkt vmhe he lpvocowhvole. d{v cltk ocpltvhevn.

    dkbh{rk ov qhr fktoykf hrr{coea vmhv vmk ffllq or rkx{kevohn

    dkvqkke vmk oeyhtohev vktcoehn {eovr dkoea r{ppnokf -k%a% itlc

    bknn vl bknn. lt itlc nkhi vl nkhi/ thvmkt vmhe mokthtbmobhnn

    vktcoehvoea le r{bm {eovr. hr oe clrv tkhn dolnlaobhn ekvqltjr%

    Qmkvmkt vmkot tkr{nv bhe dk akekthnowkf vl akekthn ekvqltjr li

    cltk tknkyhebk oe dolnla or {ebnkht%

    H akekthn hta{ckev -Qkrv kv hn%. 8???h/ bhe dk clvoyhvkf

    itlc vmk ldrktyhvole vmhv oe ffockeroler l{t fktoyhvoler li

    vmk ckvhdlnob k}plekev ldvhoekf itlc rlnyoea vmk fehcobhn

    kx{hvoler nkhfr vl f,-f*8/. qmobm oe vmtkk fockeroler tkf{bkr

    vl vmk bheleobhn 2,6% Vm{r. vmk {dox{ovl{r 6 or hbv{hnn vmk

    fockerolehnov li rphbk -2/ pn{r 8% Oe l{t fktoyhvoler vmor

    bhe dk vthbkf phtvohnn vl vmk rphbk#nnoea blervthoev. qmobmvpobhnn nkhfr vl he oebtkhrk oe kiikbvoyk rbhnoea

    fockerolehnov -Chefkndtlv. 8?=4/% Ilt k}hcpnk. vmk vlvhn htkh

    li vql#fockerolehn rmkkvr nnoea vmtkk#fockerolehn qhrmoea

    chbmoekr bnkhtn rbhnkr nojk h yln{ck thvmkt vmhe he htkh% Oe

    vmor rbhnoea rkerk. ltaheorcr kiikbvoykn i{ebvole hr oi oe il{t

    rphvohn fockeroler% Ehv{thn rknkbvole mhr vhjke hfyhevhak li

    vmk akekthnorkf ithbvhnov li rphbk#nnoea ekvqltjr vl ch}ocork

    vmk kiikbvoyk ekvqltj r{tihbk htkh. H. li vmk vktcoehn {eovr

    oevktihboea qovm vmkot tkrl{tbk keyotleckevr% Vmor bhe dk

    k}ptkrrkf mk{torvobhnn oe vmk ilnnlqoea qh7 oi vktcoehn {eovr

    htk oeyhtohev hef vmk ekvqltj rphbk#nnoea. vmke ckvhdlnob thvk.

    DH. qmobm rbhnkr nojk h yln{ck. thvmkt vmhe he htkh: vmhv or.

    DHN2 -thvmkt vmhe N4/. qmktk N or rlck bmhthbvktorvobnkeavm li vmk ekvqltj. r{bm hr vmk nkeavm li vmk hltvh oe vmk

    botb{nhvlt rrvkc li chcchnr lt vmk nkeavm li vmk rvkc oe

    pnhevr% Mlqkykt. vmk yln{ck li vmk ekvqltj. YekvHNN6% Rl.

    oi qk hrr{ck vmhv YekvC -ptlyke itlc kekta coeocorhvole

    oe l{t vmklt/. qk vmke ldvhoe YekvCN6% Vm{r. NC8,6

    nkhfoea vl DHN2C2,6% Vmor vmktkiltk ptlyofkr h

    aklckvtobhn oevktptkvhvole li vmk x{htvkt#plqktr. hef. oe

    phtvob{nht. h aklckvtobhn fktoyhvole li vmk 2,6 k}plekev ilt

    dhrhn ckvhdlnob thvk -Qkrv kv hn%. 8???h/%

    Btovoborcr hef blevtlyktrokr

    Roebk l{t ltoaoehn phpkt qhr p{dnormkf -Qkrv kv hn%. 8??1/.vmktk mhyk dkke rkykthn btovoborcr -Fhtykh{ kv hn%. 4004: Flffr

    kv hn%. 4008: Qmovk hef Rkcl{t. 4002/% Rlck li vmkrk tkylnyk

    htl{ef chvvktr li ihbv hef oevktptkvhvole vmhv rvonn ekkf vl dk

    tkrlnykf r{bm hr vmk rbhnoea li ch}ochn ckvhdlnob thvkr oe

    chcchnr lt vmk ptkbork yhn{k li vmk k}plekev% Lvmktr bnhoc vl

    ptlyofk kcpotobhn oeiltchvole lt vmkltkvobhn bhnb{nhvoler vmhv

    tki{vk l{t clfknr% Qk mhyk elv il{ef he li vmkrk nhvvkt

    btovoborcr bleyoeboea ilt vql tkhrler% Iotrv. clrv li vmkc tkrv

    le roeank vkbmeobhn orr{kr. ilt qmobm vmktk htk hv nkhrv kx{hnn

    r{ppltvhdnk hnvktehvoyk k}pnhehvoler. hef rlck vmhv htk rocpn

    oeblttkbv% I{tvmktcltk. clrv li vmkrk mhyk dkke blebktekf

    rlnkn qovm chcchnohe ckvhdlnob thvk. rl vmk ihon vl

    hpptkbohvk vmhv l{t vmklt liiktr h roeank phtrocleol{r

    k}pnhehvole. tllvkf oe dhrob ptoebopnkr li dolnla. pmrobr hef

    aklckvt. ilt he keltcl{r yhtokv li kcpotobhn rbhnoea

    tknhvoler% Elek li vmk btovoborcr liikt hnvktehvoyk clfknr ilt

    vmk blcpnkvk fkroae li yhrb{nht ekvqltjr lt ilt vmk Cd2,6

    rbhnoea li qmlnk#ltaheorc ckvhdlnob thvk% Mktk. qk hfftkrr

    rlck li vmk cltk rhnokev orr{kr%

    Rbhnoea li ckvhdlnob thvk7 or ov 2,6. 4,2 lt rlck lvmkt

    e{cdkt80ja/% Vmkrk hef khtnokt h{vmltr

    -Mk{rekt. 8?=4/ hta{kf ilt he kcpotobhn k}plekev li 4,2 dhrkf

    le vmkot tkhehnrkr li nhtak fhvh rkvr. {roea yhtol{r btovktoh ilt

    k}bn{foea bktvhoe vh}h hef fhvh. hef kcpnloea ele#rvhefhtf

    rvhvorvobhn ptlbkf{tkr% Ilt kykt r{bm k}hcpnk. mlqkykt. ov or

    plrrodnk vl akekthvk h bl{evkt#k}hcpnk {roea hv nkhrv kx{hnn

    yhnof fhvh hef rvhvorvobhn ckvmlfr -Dhtvknr. 8?=4: Iknfche hef

    CbChmle. 8?=2: Rhyhak kv hn%. 4006d/% Ldrktykf fkyohvoler

    itlc pktikbvCd2,6 rkkcr hvvtod{vhdnk vl rlck blcdoehvole li

    knkyhvkf thvkr ilt vmk rchnnkrv chcchnr. hr trv ldrktykf

    kcpotobhnn d Bhnfkt -8?=6/ hef ptkfobvkf vmkltkvobhnn d l{t

    clfkn -rkk hdlyk: Qkrv kv hn%. 8??1/. hef rvhvorvobhn htvkihbvr

    f{k vl rchnn kttltr oe ptkborkn krvochvoea vmk bmhthbvktorvob

    dlf chrrkr li rpkbokr% Otleobhnn. lek coamv hta{k vmhv

    fkyohvoler itlc vmk 2,6 k}plekev ilt rchnn chcchnr or helvmkt

    li vmk r{bbkrri{n ptkfobvoler li l{t vmklt%

    Cltk vknnoea vmhe tkpkhvkf tkhehnrkr li vmk nhtakn

    lyktnhppoea fhvh le dhrhn ckvhdlnob thvkr li chcchnr ql{nf

    dk h tkhehnror li hnn li vmk c{nvopnk rv{fokr li rbhnoea li

    qmlnk#ltaheorc ckvhdlnob thvk oe foiiktkev atl{pr li

    ltaheorcr% Pkvktr -8?=9/ p{dnormkf r{bm h ckvh#hehnror li vmk

    nhtak e{cdkt li rv{fokr hyhonhdnk hv vmk vock li mor revmkvob

    clelathpm% Mk ldvhoekf he hpptl}ochvkn eltchn#rmhpkf

    itkx{keb forvtod{vole li k}plekevr. qovm h rmhtp pkhj hv

    hnclrv k}hbvn 2,6% Rhyhak kv hn% -4006d/ tkbkevn pktiltckf h

    roconht hehnror. oebltplthvoea fhvh itlc hffovolehn rv{fokr.

    A% D% Qkrv hef G% M% Dtlqe

    0%8 0%8; 0%4 0%4; 0%2 0%22 0%60

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    Hnnlckvtob k}plekev.

    B Dolnlaobhn vockr

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    D Chrr#rpkboiobdolnlaobhn thvkr

    0%8; 0%8 0%0; 0 0%80%0;

    0 0%4 0%6 0%; 0%91 0%1; 0%? 8 8%4 8%60

    80

    40

    20

    60

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    10

    H Dolnlaobhn thvkr

    Ioa%80% Morvlathcr li vmk k}plekevr li -H/ dolnlaobhn thvkr. -D/

    chrr#rpkbob dolnlaobhn thvkr -Pkvktr. 8?=9/ hef -B/ dolnlaobhn vockr-Bhnfkt. 8?=6/% Elvk vmhv vmk pkhj li vmk morvlathc ilt dolnlaobhn thvkr

    or ykt bnlrk vl 0%1; -0%16?0%001/ d{v elv bnlrk vl 0%91% Cltklykt.

    vmk morvlathc ilt chrr#rpkbob thvkr pkhjr ekht 0%4; -0%4610%088/

    d{v elv 0%22. hef vmk morvlathc ilt dolnlaobhn vockr pkhjr hv 0%4;

    -0%4;00%088/ hef elv 0%22% Hnn kttltr x{lvkf mktk htk vmk rvhefhtf

    kttlt itlc vmk ckhe ilt vmk forvtod{vole% Oe hnn bhrkr. vmk chgltov li

    dolnlaobhn thvkr hef vockr k}modov x{htvkt#plqkt. elv vmotf#plqkt.

    rbhnoea% Ioa{tk vhjke itlc Rhyhak kv hn% -4006d/ qovm pktcorrole%

  • 7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization

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    8;=1Hnnlckvtob rbhnoea nhqr

    hef ldvhoekf yotv{hnn ofkevobhn tkr{nvr7 vmk ckhe yhn{k li vmk

    k}plekev or 0%16?0%001. rl vmk ?;+ blefkebk oevktyhnr

    oebn{fk 2,6 d{v k}bn{fk 4,2 -Ioa%80/% Vmor hehnror qhr

    k}vkefkf vl h yhtokv li lvmkt thvkr hef vockr nkhfoea vl roconht

    tkr{nvr7 vmk ckhe yhn{k li vmk k}plekev ilt chrr#rpkbob thvkr

    qhr il{ef vl dk 0%4610%088 hef ilt vockr. 0%4;00%088. rl

    dlvm li vmkrk bnkhtn k}bn{fk h 8,2 k}plekev% Ov or qltvmkcpmhrowoea vmhv vmkrk ckvh#hehnrkr oebn{fk rv{fokr li h qofk

    yhtokv li ptlbkrrkr oe h dtlhf theak li vh}h -oebn{foea

    kbvlvmktcr. oeyktvkdthvkr. hef pnhevr. hr qknn hr dotfr hef

    chcchnr/ ckhr{tkf oe h ykt nhtak e{cdkt li oefkpkefkev

    rv{fokr d che foiiktkev oeykrvoahvltr qltjoea lykt cltk vmhe

    ;0 khtr% Vmor joef li kyofkebk mhf khtnokt nkf Bhnfkt -8?=6/

    vl blebn{fk vmhv Fkrpovk rmltvblcoear hef btovoborcr

    Zoebn{foea vmk nhbj li h vmkltkvobhn clfknS. kcpotobhnn clrv

    li vmk rbhnoea flkr rkkc vl v C8,6 rbhnoea%%%. hef Pkvktr

    -8?=9/ vl tkchtj vmhv %%%lek bheelv d{v qlefkt qm vmk

    plqkt iltc{nh. oe akekthn. hef vmk chrr k}plekevr li 2,6. 8,6.

    hef 8,6. oe phtvob{nht. htk rl kiikbvoyk oe fkrbtodoea dolnlaobhn

    pmkelckeh% Qk rkk el tkhrle vl bmheak vmor hrrkrrckev oevmk noamv li vmk ykt ikq tkbkev rv{fokr vmhv mhyk lebk hahoe

    hta{kf iltCd4,2 rbhnoea%

    L{tr htk qmlnk#rrvkc clfknr7 mlq fl lvmkt phthckvktr

    rbhnk