EFTA01190685.pdf

RESEARCH I REPORTS to record the responses from individual layer 2/3 & T Ohm el al.. failure 499.295-300 (2013). manikin described in this paper. with the emepten of the rabies pyramidal cells together with their presynaptic 9. J. H. MUSA T. Mad. X. J. Nielsen. E. M Callaway. Newon 67. virus. cal Co oblened ler ilnOrrininWal pupates alter agning 562-574(2010). a material Nate vetoed (UTA) with Fill. The rabies rims partners in different cortical layers. Presynaptic la I. R. Welinsham d W. Neuron 51 639-647 (2007). can be obtained for noncommercial puposes after awing an MIA cells within layers 2/3 and 4 (and, to some ex- IL E. A. Rana el W. na1. flekrosci. 14.527-532 (MI). Ma the LudeagattaximlianoUnheisity Munidt Me plasma can tent, layer 5) are tuned similarly for motion di- 12. M. Yelenforl et at. neuron 811431-1443 (20141 be obtaned from Addgene (addgene.oigy We a:knowledge Me rection and orientation, forming layer-specific 11 S. Schad. 1. Bonhoelln. M. N'tbbne.l Nana& 22 Mown& grants. Hurler, Rooter Science Program POoldcolcral 6549-6559 (2002). Felbwinp (L7000171'2013) to 5.7.: Japan Society for the functional modules. The preferred direction 14. Y:J. Liu et at. Cut BIM n 1746-1755 (2013). Piomotgnol Stance Postdoctoral felbvdhip for Research Abroad and orientation of different layer modules can 15 K. D. Harris. G M. G Shepherd Nal. IleureSei. It 170-181 to KY_ Euopean Molecular EtolOgy Organization Postdoctoral be aligned, resulting in presynaptic networks (2015). Felbrirstip to M.: Swiss National Science Foundation giant to that are "feature-locked," or can be shifted rela- 16. U. Maur& M. Kaye. S. D. Van Hemet Front /legal &curls GX.: Swiss~an. Hungarianffrench CadiatHungarian 8.92 (2014). Region. Research and Technological Innovation Fund al European tive to each other, giving rise to "feature-varianr 17. G. Ketone et at. Alit Methods 9.201-203 (2012). then 3x3D Magna Valle to & 45231 German Reseach networks (Fig. 4C). 18 B. LI Karnpa. J. J. Islam. G I Slunk Ma fieurosa 9. FeurglatiOn Neuronal Circuit grad (SFB 870) to &KC. al A.G. The existence of feature-locked and feature- 1472-1473 (2006). GetedOul Foundation. Swiss Whom' Science Fount:tali:4. variant networks may explain why some studies 19 Y. noshimua. J. L M. Dartzkirt E. ILL Callaway. nature 433. Europam Reseach Wax* Natrona Cadres ol Competence XI 868-873 (2005). Reseach UdeoJai Systems Enorteing. Sineiga. Swale found more variability than others in the tuning 20. L Casual el a.. natar. 518.399-403 (2015). itirnsian. and European Union 3/(30 mageg grants to B. Roska of dendritic input sites of layer 2/3 pyramidal 21. C. A. Runyan el ak Much 67.847-857 (2010). Adhor contraulkok In vho elecutexemal and 'rus tracing cells (6-8) and may suggest that variability is 22. A. St Kuhn. M L. Anderinann. V. K. Bereansiti. R. C. Red. techniques were optimized by A.W. Experiments were &shed likely due to inputs from deeper cortical layers. Neuron 67.858-871 (2010). by A.W.. 5.7.. and B. Rothe. Experimeits were performed by 23. M. Okun et at. Nature 521.511-515 (20151 A.W. and 5.1. Image data analysis was pertained by The combination of distinct layer modules in 24. J. P. Gomm& M. F. Beat Nat Neuman V. 732-737 (2014). A.W. Innunohatochernistry was peiloirned by A.W. ard feature-variant networks is consistent with pre- 25. A. Anzio. X. Peng, D. C. Van (sun. Mt akurcisa 10. 5.1. MaiphOlOstal data analysis was performed by 5.T. Shmi.latnn vious studies in brain slices showing cross-talk 1313-1321 Waal. sonwaie was written by Z.P. Two -photon MiCIOSICIXS were between different subnetworks in layer 2/3 and 2& K. Manua B. Julkeretz. M. Kano. W. Denk. IA Munn. deiekiped by B. Rena and optimized by GS. ard S iboeslartls NM. Methods 5.61-67 (2000. win dembped by A.G. and &KC. flasmds were nu* by KY. layer 5 (78, 19). In the visual cone; the strength 27. B. Judkew4L M. Run. K. Mama. M. Haute,. Ala. Prolix. 4. The intrinsic imagng was performed by All... ad GK. The of connections among neurons correlates with 862-869 (2009). won was written by A.W.. S.7.. and B. ROSIA similarity in visual responses (20), raising the possibility that feature-locked networks have a ACKNOWLEDGMENTS SUPPLEMENTARY MATERIALS higher density of strong connections compared We Runk R da &helm ha henlul 0503.541, &out possible wintscifficernagoig/cortenV349/6241/70/stepriDCI knaiwal roles for feature-laked ad .varhad nedaks. We Matenals and Methods with feature-variant networks. Also, whether dif- figs. SI to 515 that S Oakdey and A. Drinnenberg lot whmertege on the ferent subtypes of cortical interneurons (27, 22) inanuStript ard members ol the Factily for Advanced Imaging References (Z8-35) are differentially represented in feature-locked and Microscopy at Ily Fierlich Meschei rolilule (RAI) kw and feature-variant networks remains an open assistance with awtorritd dala amt.:anon and image processing. 20 Mach 2015 accepted 29 May 2015 O&M data se eurXid ad sifted n the server of rUl. Al 10.U26/sciencesab1687 question. Finally, it will be interesting to test whether postsynaptic cells in feature-locked and featurevariant networks exhibit different pop- ulation coupling strengths (23). What could be the role of feature-variant BRAIN STRUCTURE presynaptic networks? One possibility is that feature-variant networks are plastic. Top-down modulation or learning (24) could force the pre- ferred direction and orientation of layer modules Cortical folding scales universally to align, resulting in a transition from a feature- variant to a feature-locked network. This recruit- with surface area and thickness, not ment of relevant circuits could allow more robust feature representations of behaviorally impor- number of neurons tant stimuli. Another possibility is that variant layer modules enhance responses of the post- Bruno Mot& and Suzana Herculano-Hournes• synaptic cell during object motion. Approaching and receding objects, for example, have edges Larger brains tend to have more folded cortices, but what makes the cortex fold has moving in different directions. Some of these remained unknown. We show that the degree of cortical folding scales uniformly across edges may stimulate inputs from deeper layers, lissencephalic and gyrencephalic species, across individuals. and within individual cortices which are not strong enough to drive responses as a function of the product of cortical surface area and the square root of cortical of the postsynaptic cell alone but could boost thickness. This relation is derived from the minimization of the effective free energy responses of the postsynaptic cell to an edge associated with cortical shape according to a simple physical model, based on known moving in its preferred direction. Indeed, re- mechanisms of axonal elongation. This model also explains the scaling of the folding index sponses to combinations of orientations have of crumpled paper balls. We discuss the implications of this finding for the evolutionary and been demonstrated in primate V2 (25). developmental origin of folding. including the newfound continuum between lissencephaly and gyrencephaly. and for pathologies such as human lissencephaly. REFERENCES AND NOTES T I. D. It Hutel. 1. N. Mesd.1Physiot 148 574-591(1959). he expansion of the cerebral cortex, the sheet expands laterally with a constant number 2. U. C Draget.f. CØ Need. 1W. 269-290 (197» most obvious feature of mammalian brain of neurons beneath the surface (2, 3). Although 3. T. Halting, M. Fyhrt S Mott M.43. Moser. E. I. »Net /Wu* 436.801-8C6 (2006). evolution, is generally accompanied by in- some models have shown conical convolutions 4. W. A. Froward D. Y. %so. M. S. Lfringslwe. Nat Mina /2. creasing degrees of folding of the cortical 1187-U96(2009) surface into sold and gyri (1). Cortical fold- rInshluto de Rao& Unheadade Federal di RD de Janeiro. 5. H. Ito et at. liatum 473.87-91 (2011). ing has been considered a means of allowing Rio de Janeiro. Brazil. ''Instituto de OtoCiaS Becnktolicas. & & L. Swilh. I. T. With. 1. &aØ M. Muss«. Nature 503. Uriversidaie Federal do Rio de Janeiro. Rio de Janeiro. 115-120 (2013). numbers of neurons in the cerebral cortex to Brat, Nrisbluto National de Neurocltncaa TranslationaL 7. H. Ja N L Rodefort L Orion. A. Moren» feolum 464. expand beyond what would be possible in a INCT/IXT. Sao Patio. &Ant 1307-1312 (20I0). lissencephalic cortex, presumably as the cortical •Correspending author. Email: 74 3 JULY zois • VOL 349 ISSUE 6243 sclencemag.org SCIENCE EFTA01190685  RESEARCH I REPORTS to form as a result of cortical growth (4, 5), the black and colored data points). However, the hom10752 in the African elephant (15) to 138,606 mechanisms that drive gyrification remain to be power function that relates the folding index of in the squirrel monkey (20). Cortical expansion determined, and the field still lacks a mechanis- gyrencephalic species to brain mass has a fairly and folding are therefore neither a direct conse- tic and predictive, quantitative explanation for low r2 and a 05% confidence interval that ex- quence of increasing numbers of neurons nor a how the degree of cortical folding scales across cludes many species (Fig. IA). Striking and well- requirement for increasing numbers of neurons species. Moreover, recent systematic analyses of known outliers in this relationship are cetaceans in the cortex. cortical folding have made clear that vilification (as a whole) and the manatee, but the capybara, In comparison to the poor fit between folding actually scales differently across mammalian or- the greater kudu, and humans also lie outside of index and total brain mass (Fig. IA), a better fit is ders, across clades within an order, and across the confidence interval (Fig. IA). This indicates found for total surface area of the cerebral cortex individuals as a function of increasing brain vol- that cortical folding is not a homogeneous func- in the two data sets (Fig. ID). In this case, there is ume (6-9). These apparent discrepancies have tion of brain mass. better overlap across afrotherians. glims, primates, led to the view that different mechanisms must Although all cortical hemispheres with fewer and artiodactyls, although cetaceans, the manatee, regulate cortical folding at the evolutionary, species- than 30 million neurons are lissencephalic in our and humans are still major outliers. Interest- specific, and ontogenetic levels (7). data set, and the correlation between folding in- ingly, all species with a cortical surface area be- We undertook a systematic analysis of the var- dex and number of neurons is significant across low 400 mm2 are lissencephalic in the two data iation in cortical folding across a large sample of gyrencephalic species (Spearman correlation, p = sets. Similarly, all species with average cortical mammalian species in search of a universal, uni- 0.7741, P < 0.0001), the degree of gyrification is thickness below 1.2 mm are lissencephalic, but fying relationship between cortical folding and much larger in artiodactyls than in primates for the folding index does not vary as a signifi- morphological properties of the cerebral cortex. similar numbers of cortical neurons (Fig. IS). Ad- cant power function of cortical thickness across We examined two data sets: our own, which in- ditionally, the elephant cortex Ls about twice as gyrencephalic species (Fig. 1E). cludes numbers of cortical neurons and cortical folded as the human cortex, although the former The folding index shows a sharp inflection be- surface areas (10-21), and another consisting of has only about onethird the number of neurons tween smooth and gyrated cortices, so it is unlikely published data on cortical surface area, thickness, found in the latter (Fig.IS, "e" and "h"). The cor- that a universal model in terms of this variable brain volume. and folding index, but not numbers tical surface area across species expands sublin- alone could be derived. Because the folding index of cortical neurons (1, 22-24) (table SI). early with the number of cortical neurons in is the ratio of total surface area AG to exposed sur- In the combined data set, there is a general primates and supralinearly in other species (Fig. face area AE, we next examined directly how AE correlation between total brain mass and the IC). As a consequence, the average number of scales With AG (Fig. 11') In the combined data sets, degree of cortical folding, and the two data sets neurons per mm2 of cortical surface is highly for the species with small AG (<400 mm2) there is overlap in their distribution (Fig. IA. compare variable across species, ranging in our data set no folding, such that AE equals AG (Fig. IF, green A ID- B , C x I7 ' a; ,• C • • h ro. 3. '5 0•41 • • 0 e•ft .•••••••••S. • se 01 01 1 10 icio 1.000 10.000 103 105 100 1010 102 to, i09 ion Brain mass (g) Number of cortical neurons Number of conical neurons E F 1.000.000 • x • • • new • • Z 10'000 C • • • a .1• •C 0 u. • • • a • • O • • 1003 •" 5$ • 1- ••:••0 • IO 100 bioo 10,000 loo:coo 05 1.0 I'S 2.0 21.1 35 100 1,1103 10:03 100,000 total cortkal surface area (mm2I Cortical thicknesstrim) Exposed cortical surface area fmm2) Fig. 1. Scaling of cortical folding index and total cortical surface area. 0.054.P = 0.1430: not plotted). (C) Total cortical surface area of the cerebral Data pants ri blxk are taken from the •.terature. pants in colas are Iran Cu' own cortex scales across primate species with an exponent of 0.911s 0.083 (12 = data set.except for cetaceans. (Ato Folding index scales across all gyrencephale 0.938. P < 0.0001) and across nonprimate species with an exponent of species in the cornbned data sets as power functions of (A) brain mass. with 1.248 t 0.037 (r2 = 0.989. P < 0.0001). (F) Total cortical surface area varies exponent 0.221 t 0.018 (r2 = 0.751. P < 0.0001): (8) comber of cortical across lissencephalic species as a linear function of the exposed surface neurons. with exponent 0.168 t 0.032 (r2 = 0.573. P < 0.0001: not plotted): area. but as a power function with an exponent of 1.242 t 0.018 across (D) total cortical area. with exponent 0.257 t 0.014 (r2 = 0.872. P < 0.0001): noncetacean gyrencephalic species (r2 = 0.992. P < 0.0001). Dashed lines and (E) average cortical thickness, with a nonsignificant exponent 0'2 = are 95% confidence intervals for the fitted functions. SCIENCE selencemag.org 3 JULY 2015 • VOL 34P ISSUE 3243 75 EFTA01190686 RESEARCH I REPORTS line). This linear relationship extends to the man- cates that the coarse-grained folding of a sheet of AG = AO are those that meet the condition T = atee cerebral cortex, even though its AG is much paper subjected to external compression depends PAGI12. In contrast, all species for which T< k2AcIn larger than 1000 me. In contrast, for all non- simply on a combination of its surface area and are predicted to be gytencephalic, with Ac > AE cetaccan gyrencephalic species. AG increases with thickness. (the alternative where T> it2AGI/2 would result in AE12. (r2 = 0992. P < 0.0001), significantly We next examined whether our model predicts AG < An which is geometrically impossible). above linearity (Fig. IF, red line), meaning that as the folding of the mammalian cerebral cortex by Indeed, in the combined data set, we find that total surface area increases, it becomes increas- plotting the product Tv2AG as a function ofA5 for rnAr filwa (Pc 0.0001) across lissencephalic ingly folded. Cetaceans fall above the 95% confi- the combined data sets. This yielded a power species (Fig. 3B, green line). All gyrencephalic dence interval of the function, which indicates function with an exponent of1229 i 0.014s with species data points fall to the right of the Bs- that these cortices are more folded than sim- a very high r 2 of 0.996 for the noncetacean sencephalic distribution; that is, their AG values ilarly sized cortices in noncetaceans. gyrenceploilic species in the combined data sets are larger than predicted for a cortical thickness The finding thatAc scales as a power law MAE (Fig 3A, red line).Note that this function, although that would allow lissencephaly. The precise rela- means that gnification is a property of a cortical calculated for gyrencephalic species, overlaps with tionship between T and AG across girrencephalic surface that is self-similar down to a fundamental lissencephalic species. Including lissencephalic speciesdiffers across orders, with a much smaller scale (the limit area between lissencephaly and species (but still excluding cetaceans) actually exponent for primates than for artiodactyls (Fig. gyrencephaly). This strongly suggests the existence improved the fit, with r2 = 0_998, and yielded an 3B, red and pink lines). Thus, within the single of a single universal mechanism responsible for exponent of 1305 i amo, which is dose to the universal relationship that describes cortical ex- cortical folding (the alternative being some im- expected value of 1.25. Adding cetaceans to the pansion, there isa transition point between smooth probable multiscale fine-tuning) that over a range analysis resulted in a small change of the fit (Fig. and folded cortices: Gyrencephaly ensues when of scales generates self-similar, or fractal, surfaces. 3A, black line). Remarkably, the function fitted Ac expands in area faster than 7'2. For gyrence- Frodals can be characterized by the power-law exdusively for lissencephalic species also predicted phalic species, the rate of expansion of cortical scaling between intrinsic and extrinsic measures the relationship between Tv2AG and A T in thickness relative to expansion of the conical ofan object's size, such asAc and A• In this case, gyrencephalic species (Fig. 3A, green line)—and surface varies across orders, but the product the fractal dimension d of the cortical surface is species such as the manatee and other afrotherians T1J2Ac still varies as a universal function offlp.us twice the value of the exponent relatingAG to AB are no longer outliers. to Alt1-33. (given that AR in turn scales with the square of Given the theoretical relation 74/2A0 We also found the same universality between the linear dimension of the cortex). Given that it follows that lissencephalic species (for which the product 71/24 : and AT across corona! sections AG scales with Ag.2e2'0 . 016 across noncetacean gyrencephalic brains, then d = 2.484 i 0.036. This value is remarkably close to the fractal di- Fig. 2. The degree of folding of crumpled paper mension 23 of crumpled sheets of paper (25), balls is a function of surface area and thickness which are fractal-like self-avoiding surfaces thin as predicted by our model. (A) Relationship enough to fokl under external compression while between total surface area of A4 to All sheets of maintaining structural integrity. office paper and the exposed surface area of the Empirically, we conceive the fractal folding (or crumpled sheet of paper. with a power function of lack thereof) of the cortical surface as a conse- exponent 1234 ± 0.033 for a single sheet of thickness quence of the minimization of the effective free 01inn. (B) Increasing the thickness of the paper to energy of a self-avoiding surface of average thick- be crumpled by stacking two to eight sheets dis- ness T that bounds a volume composed of fibers places the curves to the right. that is. decreases connecting distal regions of said surface. Our the folding index of the resulting paper balls. (C) 103 goo room However. all crumpled paper balls of varying total model incorporates the known mechanics and Exposed surface area (mm2) surface area and thickness exhibit the same rela- organization of elongating axonal fibers (26, 27), as described in the supplementary materials. It B 3 • tionship. with the product TV2Ar varying proper • tionateiy to Acu°5'°°22 (r2 = 0.983.P< 0.0001).Color predicts that from a purely physical perspective, AGAR, and Tare related by the power law TV2Ar = gradations correspond to thickness in millimeters. kAti. (The exponent 5/4 is the only value for as shown in each panel. • which the constant A- is adimensional) • We first tested whether our model baked on • • • • I • • the minimization of the effective free energy of a 3 0) • • II I . self-avoiding surface could explain the well-known • • • 2 0.4 • • • • fractal folding of a self-avoiding surface: paper. 0.6 • • • • We examined how the exposed surface area of 1 •S • crumpled paper balls, At . scales with increasing 1000 10.000 total surface area, AT, and thickness, T, of office Total surface area (mm') paper (in this case, under forces applied exter- nally by the experimenter's hands). As shown in Fig. 2A, Ara Ar s'°433 for crumpled single sheets, a value similar to that for gyrencephalie cortices. Increasing T(by narking sheets before crumpling) displaces the curves to the right (Fig. 2A) but leaves their slope largely unaltered, re- sulting in similar-looking but less folded paper balls (Fig. 2B). However, the product TV2Ar varies proportionately to Ag'105i0.°6R as a single, uni- versal power function across all paper balls of different surface areas and thicknesses (Fig. 2C), as predicted by our model. This conformity inch- Exposed surface area (rnm2) 76 3 JULY 2015 • VOL a'9 ISSUP. 6233 501011001111g.01• SCIENCE EFTA01190687  RESEARCH I REPORTS along the anteroposterior axis of the cortical hemi- teratIons, such as defects in cell migration, that early cortical development. Rapid increases in sphere of a single individual, of different individ- lead to increased Tor decreased A0 (or both) are numbers of intermediate progenitor cells would uals, and even different specks ranging from small expected to decrease cortical folding, exactly as lead to grencephdy, although not through the gen- rodents to human and elephant (fig. Sh. found in human pathological lhasmeephaly (28). eration of larger numbers of neurons, as previ- The finding that AI,. scales across all lissen- This might also be the case for the lissencephalic ously thought (7, 30, 32), but rather through the cephalic and gyrencephalic mammals (and even brain of birds, where a very thick telencephalon simple lateral expansion of the resulting cortical across species usually regarded as outliers such of small surface area surrounds the subpalllal surface area at a rate faster than the cortical as the manatee and cetaceans) as a single power structures. thickness squared. law of T inAG indicates that gyrification is an in- Finally, our findings indicate that cortical fold- trinsic property of any mammalian cortex Further, ing did not evolve, in the sense of a new property REFERENCES AND NOTES because the degree of folding can be described specific to some dades but not others. Similarly, I. U. A. Holman. Bran BMW. Ent 27.28-40 (1985). by the simple equation generated by our model there is no such thing as -secondary lissencephaly 2. A. J Radial. R. W. Horns. r P. Panel. Bran 101 221-244 (which also applies to crumpled sheets of paper), (29), nor are there two clusters ofgyrencephaly (9). (1980). 3. P. Nile. riendt ffettoso. It 383-38809953 folding must occur as it minimizes the effective Rather, what has evolved, we propose, is a faster 4. R loo. Y. Burn* With Carter 15. 1930-1913 (2006). free energy of the cortical surface. Folding is increase in AG relative to T2 in development— 5. 7. Tanen. S Y. Chung J. S. Begirt L Maluderat F744 NW therefore an intrinsic, fractal property of a self- and at different rates in different mammalian Aced Sol USA. 111. 12667-12672 (20143 avoiding surface, whether biological or not, sub- clades, which thus become gyrencephalic at dif- 6. K 2ibes. N Paornero-Gdlastitt. K. AniurdS. french Mau/46d. jected to crumpling forces. As such, this scaling ferent functions of Ao or different numbers of 36. 275-284(2013) 7 E. Lenitus. I. Kelm. W. B. Hubner. Front. Man. Ueorosol 7. of cortical folding does not depend on numbers neurons. 424 (2013). of neurons or how they are distributed in the Remarkably, there is no a priori reason for 8. P. Fillay. P. R. Ming.. fur. J. Worm 1. 28 2705-2712 cortical sheet, but simply on the relative lateral lissencephaly, considering that AG and T ulti- (2007) expansion of this sheet relative to its thickness, mately result from different biological pioet.sses. 9_ E. Lemnos. I. Kara A. T. KAMA P. %mutat. W. B. Huttner. regardless of how densely neurons are distrib- lateral expansion of the progenitor cell popula- PLUS War 12 e1002000 (2014). 10. F. A. C Aimed° el at. J. Wept Minot 5B.532-531 uted within IL tion tarifa, radial neurogenesis and cell growth (2003). The finding that conical folding scales univer- for T (30). Similarly, there Is no a priori reason II. U. Gab ce at. Brain BMW. Ent 76. 32-44 (2010) sally across dades, species, individuals, and parts for the cortex to become gaTencephalie once past 12. S. HttalamWesel. B. Mota.R. Let Proc. NaK Acad. Sri U.S.A. of the same cortex implies that the single mecha- a certain surface area—unless the rate of (lateral) 111 12138-12143(2006) nism based on the physics of minimization of progenitor cell expansion inevitably outpaces 13. S. HercSano'Hoozd. C. E_ Catins. P. %bog J. H. EMS. Noe. !Olt Aced So. USA. 104. 3562-3567 (2007). effective free energy of a growing surface subject the rate of (radial) neurogenesis at this point, 14. S. HerculartrHouzd et et. 8(40 Mien foot 71 302-314 to inhomogeneous bulk stresses applies across which apparently occurs typically when Ac reaches (20115 cortical development and evolution.This Is instark 400 mm2. We propose that, starting from the ear- 15. S. HeroAartrHouzd et et. Emit Nein690.11. 8.46 (2014). contrast to previous conclusions that different liest and smallest (and smooth) mammalian brains 16. R S. Kam. J. Llinamsdo. B. Ucla. P. R. Mega. S. sercastosolsa. Fiat El9a030.11. 8.128 (2014). mechanisms regulated folding at different lev- 04 the cortical surface initially scaled isometri- 17. K Hems et 41.. &ant fitufainal $ 5 (2014). els (7); such conclusions may reflect the tradi- cally, with Ao a Ta Gyrencephaly ensued in each 18. D. K. S343). K C. Calleia. D. B. Leitch J. H. Ea* tional emphasis on the relationship between Glade as soon as this lockstep growth changed, S. Herodanottouzd. Fiat Aburcomf. 3.8 (2009). folding degree and brain volume (1, 8), which is with AG now increasing faster than T. Prob- It S. Herodanottouzd. B Mots P. %tog. J. H. EMS. Plot NW.. indeed diverse across orders, across species, and able mechanisms involved are those that con- Aced So'. USA. 107. 19008-19013 (2010). 20. L Ifenturmentttes. 6 Mats S.HeragnaliototEmit Murata? across individuals of a sante species (6, 8). Also, trol the rate of neurogenesis and increases in 7.3(2013) the dependence of cortical folding on a simple cell size relative to the rate of progenitor and 21. P. F. M Rbeiro ef at. Front Neural's!. 7.28 (2013). combination of AG and T implies that any al- intermediate progenitor cell proliferation in 22. H. Dias. D. Saturant Z. Siebertid. 36 147-163 (1971). 23. IT L. Eeep. 7.1. O'Shea. Brain Behar. Lot 35.185-194 (1930). Fig. 3. The degree of folding of the mammalian A 24. 7. It Maybes.. G. L. "'warrantee. V. Darter. S. %hams. J. Anal. 188 53-58 (1996). cerebral cortex is a single function of surface area 25. Y. Kantor. M Kardar. D. R. !fetich Phys. Rev. A 35.3056-3071 and thickness across lissencephalic and gyrence- (1987). phalic species alike. although thickness scales 26. D. H. Smith. Nog. Neurchor 89. 231-239 (2009). as order-specific fisictions of cortical surface area 190004 27. D. H. Smith. J. A WcU. D. F. Meaty. Tissue Erg. 7.131-139 (A) The product TV2A0 varies with Aci229P° 'G(r2 = 3 (2001). 1000, 28. S. E. Hong el at. Mal. Genet 26 93-96 (2000). 0.9%. P < 0.0001) across noncetacean gyrence- 24 I. Kelwa. L Lentils. W. B. Runner. front Neuronal. 7. 16 phalic species in the combined data set (red line). (2013). with AE1325'0009 (r2= 0.997.P < 0.0001, k = O157 , 30. J. H. LS. D. V. Baden. A. R. Krieggen Cul 146.18-36 0.012) across all species (including cetaceans: black 10 (20115 line). and with AEL292'°°27 (r2 = 0.994. P < 0.0001) toci moo maxi maxi 31. 7. Rose. T. E. Mttrini. Z. X. Lux Science 331955-957 (20115 across lissencephalic species alone (green line). Note Exposed surface area (mm2) 32. I. Redo. C de Jan Erner0. M. A. Eardataberas. E. 60943. that the function plotted for lissencephalic species B Ceth Goan 211674-1694 (2011). predicts the product 7 V2Ae for gyrencephalic species equaly well as the functions plotted for gyrencephalic ACKNOWLEDGMENTS Cortical thickness Iran) species themselves. (B) Cortical thickness varies Supported by Camila Nacional de Deserntienwolo Derek° e 1KnologKa knack de Ampana a Pesquaa do Estado do Mode with cortical surface areaAG°565'°°w (r2 = 0287 P< Intim tia/UCT. and the Janes S McOomdi Foto:Moo. Data 0.0001) across lissencephalic species in the corn- reputed in de pmer are presaged in PK supplemotry rnaltrISS bined data set (green line). but with AG°16°'° 0.25 (+2 = 0.703.P< 0.0001)acrossprrnates (red line). and with SUPPLEMENTARY MATERIALS AG°13""°22 (r2 = 0.879. P = 0.0185) across artio- wsne.sekommagogiconen1/349/6241/74/supg/DC1 Materials and Methods dactyl species (pink line). NI fits exclude cetaceans. Turk SI Dashed lines indicate the 95% confidence intervals References (33-38) for the fitted functions. 13 February 2015 accepted 1113e, 2015 Total surface area (mm2) 10.1126/science.so9101 SCIENCE scleneemag.org 3 JULY 2016 • VOL 349 ISSUE 6243 77 EFTA01190688  Cortical folding scales universally with surface area and thickness, Science not number of neurons Bruno Mota and Suzana Herculano-Houzel Science 349, 74 (2015); tlAAAS DOI: 10.1126/science.aaa9101 This copy is for your persona!, non-commercial use only. If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here. Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here. The following resources related to this article are available online at www.sciencemag.org (this information is current as of August 24, 2015): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/349/6243/74.full.html Downloaded from www.sciencemag.org on August Supporting Online Material can be found at: http://www.sciencemag.org/content/suppl/2015/07/01/349.6243.74.DC1.html A list of selected additional articles on the Science Web sites related to this article can be found at: http://www.sciencemag.org/content/349/6243/74.full.html#related This article cites 37 articles, 10 of which can be accessed free: http://www.sciencemag.org/content/349/6243/74.full.html#ref-hst-1 This article has been cited by 1 articles hosted by HighWire Press; see: http://www.sciencemag.org/content/349/6243/74.full.html#related-urls This article appears in the following subject collections: Neuroscience http://www.sciencemag.org/cgi/collection/neuroscience Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington. DC 20005. Copyright 2015 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS.