towards a quantitative unifying theory of biological structure and organization
TRANSCRIPT
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7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization
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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;
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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%
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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%
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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
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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%
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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%
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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%
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7/31/2019 Towards a Quantitative Unifying Theory of Biological Structure and Organization
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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%
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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%
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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
8
4
2
6
;
9
1
E{cdktckhr{tkfvlmhyk
Hnnlckvtob k}plekev.
B Dolnlaobhn vockr
0%;0%;; 0%60%6; 0%22 0%4; 0%40
4
6
9
=
8084
86
89
8=
40
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
;0
90
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
13/18
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