RESEARCH I REPORTS

RESEARCH I REPORTS to record the responses from individual layer 2/3 pyramidal cells together with their presynaptic partners in different cortical layers. Presynaptic cells within layers 2/3 and 4 (and, to some ex- tent, layer 5) are tuned similarly for motion di- rection and orientation, forming layer-specific functional modules. The preferred direction and orientation of different layer modules can be aligned, resulting in presynaptic networks that are "feature-locked," or can be shifted rela- tive to each other, giving rise to "feature-varianr networks (Fig. 4C). The existence of feature-locked and feature- variant networks may explain why some studies found more variability than others in the tuning of dendritic input sites of layer 2/3 pyramidal cells (6-8) and may suggest that variability is likely due to inputs from deeper cortical layers. The combination of distinct layer modules in feature-variant networks is consistent with pre- vious studies in brain slices showing cross-talk between different subnetworks in layer 2/3 and layer 5 (78, 19). In the visual cone; the strength of connections among neurons correlates with similarity in visual responses (20), raising the possibility that feature-locked networks have a higher density of strong connections compared with feature-variant networks. Also, whether dif- ferent subtypes of cortical interneurons (27, 22) are differentially represented in feature-locked and feature-variant networks remains an open 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 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 to align, resulting in a transition from a feature- variant to a feature-locked network. This recruit- ment of relevant circuits could allow more robust feature representations of behaviorally impor- tant stimuli. Another possibility is that variant layer modules enhance responses of the post- synaptic cell during object motion. Approaching and receding objects, for example, have edges moving in different directions. Some of these edges may stimulate inputs from deeper layers, which are not strong enough to drive responses of the postsynaptic cell alone but could boost responses of the postsynaptic cell to an edge moving in its preferred direction. Indeed, re- sponses to combinations of orientations have been demonstrated in primate V2 (25). REFERENCES AND NOTES I. D. It Hutel. 1. N. Mesd.1 Physiot 148 574-591(1959). 2. U. C Draget.f. CØ Need. 1W. 269-290 (197» 3. T. Halting, M. Fyhrt S Mott M.43. Moser. E. I. »Net /Wu* 436.801-8C6 (2006). 4. W. A. Froward D. Y. %so. M. S. Lfringslwe. Nat Mina /2. 1187-U96(2009) 5. H. Ito et at. liatum 473.87-91 (2011). & & L. Swilh. I. T. With. 1. &aØ M. Muss«. Nature 503. 115-120 (2013). 7. H. Ja N L Rodefort L Orion. A. Moren» feolum 464. 1307-1312 (20I0). & T Ohm el al.. failure 499.295-300 (2013). 9. J. H. MUSA T. Mad. X. J. Nielsen. E. M Callaway. Newon 67. 562-574(2010). la I. R. Welinsham d W. Neuron 51 639-647 (2007). IL E. A. Rana el W. na1. flekrosci. 14.527-532 (MI). 12. M. Yelenforl et at. neuron 811431-1443 (20141 11 S. Schad. 1. Bonhoelln. M. N'tbbne.l Nana& 22 6549-6559 (2002). 14. Y: J. Liu et at. Cut BIM n 1746-1755 (2013). 15 K. D. Harris. G M. G Shepherd Nal. IleureSei. It 170-181 (2015). 16. U. Maur& M. Kaye. S. D. Van Hemet Front /legal &curls 8.92 (2014). 17. G. Ketone et at. Alit Methods 9.201-203 (2012). 18 B. LI Karnpa. J. J. Islam. G I Slunk Ma fieurosa 9. 1472-1473 (2006). 19 Y. noshimua. J. L M. Dartzkirt E. ILL Callaway. nature 433. 868-873 (2005). 20. L Casual el a.. natar. 518.399-403 (2015). 21. C. A. Runyan el ak Much 67.847-857 (2010). 22. A. St Kuhn. M L. Anderinann. V. K. Bereansiti. R. C. Red. Neuron 67.858-871 (2010). 23. M. Okun et at. Nature 521.511-515 (20151 24. J. P. Gomm& M. F. Beat Nat Neuman V. 732-737 (2014). 25. A. Anzio. X. Peng, D. C. Van (sun. Mt akurcisa 10. 1313-1321 Waal. 2& K. Manua B. Julkeretz. M. Kano. W. Denk. IA Munn. NM. Methods 5.61-67 (2000. 27. B. Judkew4L M. Run. K. Mama. M. Haute,. Ala. Prolix. 4. 862-869 (2009). ACKNOWLEDGMENTS We Runk R da &helm ha henlul 0503.541, &out possible knaiwal roles for feature-laked ad .varhad nedaks. We that S Oakdey and A. Drinnenberg lot whmertege on the inanuStript ard members ol the Factily for Advanced Imaging and Microscopy at Ily Fierlich Meschei rolilule (RAI) kw assistance with awtorritd dala amt.:anon and image processing. O&M data se eurXid ad sifted n the server of rUl. Al manikin described in this paper. with the emepten of the rabies virus. cal Co oblened ler ilnOrrininWal pupates alter agning a material Nate vetoed (UTA) with Fill. The rabies rims can be obtained for noncommercial puposes after awing an MIA Ma the LudeagattaximlianoUnheisity Munidt Me plasma can be obtaned from Addgene (addgene.oigy We a:knowledge Me Mown& grants. Hurler, Rooter Science Program POoldcolcral Felbwinp (L7000171'2013) to 5.7.: Japan Society for the Piomotgnol Stance Postdoctoral felbvdhip for Research Abroad to KY_ Euopean Molecular EtolOgy Organization Postdoctoral Felbrirstip to M.: Swiss National Science Foundation giant to GX.: Swiss~an. Hungarianf french CadiatHungarian Region. Research and Technological Innovation Fund al European then 3x3D Magna Valle to & 45231 German Reseach FeurglatiOn Neuronal Circuit grad (SFB 870) to &KC. al A.G. GetedOul Foundation. Swiss Whom' Science Fount:tali:4. Europam Reseach Wax* Natrona Cadres ol Competence XI Reseach UdeoJai Systems Enorteing. Sineiga. Swale itirnsian. and European Union 3/(30 mageg grants to B. Roska Adhor contraulkok In vho elecutexemal and 'rus tracing techniques were optimized by A.W. Experiments were &s hed by A.W.. 5.7.. and B. Rothe. Experimeits were performed by A.W. and 5.1. Image data analysis was pertained by A.W. Innunohatochernistry was peiloirned by A.W. ard 5.1. MaiphOlOstal data analysis was performed by 5.T. Shmi.latnn sonwaie was written by Z.P. Two-photon MiCIOSICIXS were deiekiped by B. Rena and optimized by GS. ard S iboeslartls win dembped by A.G. and &KC. flasmds were nu* by KY. The intrinsic imagng was performed by All... ad GK. The won was written by A.W.. S.7.. and B. ROSIA SUPPLEMENTARY MATERIALS wintscifficernagoig/cortenV349/6241/70/stepriDCI Matenals and Methods figs. SI to 515 References (Z8-35) 20 Mach 2015 accepted 29 May 2015 10.U26/sciencesab1687 BRAIN STRUCTURE Cortical folding scales universally with surface area and thickness, not number of neurons Bruno Mot& and Suzana Herculano-Hournes• Larger brains tend to have more folded cortices, but what makes the cortex fold has remained unknown. We show that the degree of cortical folding scales uniformly across lissencephalic and gyrencephalic species, across individuals. and within individual cortices as a function of the product of cortical surface area and the square root of cortical thickness. This relation is derived from the minimization of the effective free energy associated with cortical shape according to a simple physical model, based on known mechanisms of axonal elongation. This model also explains the scaling of the folding index of crumpled paper balls. We discuss the implications of this finding for the evolutionary and developmental origin of folding. including the newfound continuum between lissencephaly and gyrencephaly. and for pathologies such as human lissencephaly. T he expansion of the cerebral cortex, the most obvious feature of mammalian brain evolution, is generally accompanied by in- creasing degrees of folding of the cortical surface into sold and gyri (1). Cortical fold- ing has been considered a means of allowing numbers of neurons in the cerebral cortex to expand beyond what would be possible in a lissencephalic cortex, presumably as the cortical sheet expands laterally with a constant number of neurons beneath the surface (2, 3). Although some models have shown conical convolutions rInshluto de Rao& Unheadade Federal di RD de Janeiro. Rio de Janeiro. Brazil. ''Instituto de OtoCiaS Becnktolicas. Uriversidaie Federal do Rio de Janeiro. Rio de Janeiro. Brat, Nrisbluto National de Neurocltncaa TranslationaL INCT/IXT. Sao Patio. &Ant •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 mechanisms that drive gyrification remain to be determined, and the field still lacks a mechanis- tic and predictive, quantitative explanation for how the degree of cortical folding scales across species. Moreover, recent systematic analyses of cortical folding have made clear that vilification actually scales differently across mammalian or- ders, across clades within an order, and across individuals as a function of increasing brain vol- ume (6-9). These apparent discrepancies have led to the view that different mechanisms must regulate cortical folding at the evolutionary, species- specific, and ontogenetic levels (7). We undertook a systematic analysis of the var- iation in cortical folding across a large sample of mammalian species in search of a universal, uni- fying relationship between cortical folding and morphological properties of the cerebral cortex. We examined two data sets: our own, which in- cludes numbers of cortical neurons and cortical surface areas (10-21), and another consisting of published data on cortical surface area, thickness, brain volume. and folding index, but not numbers of cortical neurons (1, 22-24) (table SI). In the combined data set, there is a general correlation between total brain mass and the degree of cortical folding, and the two data sets overlap in their distribution (Fig. IA. compare A ID- x 7 ' a; I ,• C ro. 3. 0 • se 01 1 10 icio 1.000 10.000 Brain mass (g) 100 bioo 10,000 loo:coo total cortkal surface area (mm2I black and colored data points). However, the power function that relates the folding index of gyrencephalic species to brain mass has a fairly low r2 and a 05% confidence interval that ex- cludes many species (Fig. IA). Striking and well- known outliers in this relationship are cetaceans (as a whole) and the manatee, but the capybara, the greater kudu, and humans also lie outside of the confidence interval (Fig. IA). This indicates that cortical folding is not a homogeneous func- tion of brain mass. Although all cortical hemispheres with fewer than 30 million neurons are lissencephalic in our data set, and the correlation between folding in- dex and number of neurons is significant across gyrencephalic species (Spearman correlation, p = 0.7741, P < 0.0001), the degree of gyrification is much larger in artiodactyls than in primates for similar numbers of cortical neurons (Fig. IS). Ad- ditionally, the elephant cortex Ls about twice as folded as the human cortex, although the former has only about onethird the number of neurons found in the latter (Fig. IS, "e" and "h"). The cor- tical surface area across species expands sublin- early with the number of cortical neurons in primates and supralinearly in other species (Fig. IC). As a consequence, the average number of neurons per mm2 of cortical surface is highly variable across species, ranging in our data set B , '5 01 E x C a 0 u. • • h 0•41 • • • • e •ft S. .••••••• 103 105 100 1010 Number of cortical neurons 1- . 1 • • • • • • • • •" 5$ • ••:••0 • • • • • • • • • • • 05 1.0 I'S 2.0 21.1 35 Cortical thicknesstrim) Fig. 1. Scaling of cortical folding index and total cortical surface area. Data pants ri blxk are taken from the •.terature. pants in colas are Iran Cu' own data set. except for cetaceans. (Ato Folding index scales across all gyrencephale species in the cornbned data sets as power functions of (A) brain mass. with exponent 0.221 t 0.018 (r2 = 0.751. P < 0.0001): (8) comber of cortical neurons. with exponent 0.168 t 0.032 (r2 = 0.573. P < 0.0001: not plotted): (D) total cortical area. with exponent 0.257 t 0.014 (r2 = 0.872. P < 0.0001): and (E) average cortical thickness, with a nonsignificant exponent 0'2 = C hom10752 in the African elephant (15) to 138,606 in the squirrel monkey (20). Cortical expansion and folding are therefore neither a direct conse- quence of increasing numbers of neurons nor a requirement for increasing numbers of neurons in the cortex. In comparison to the poor fit between folding index and total brain mass (Fig. IA), a better fit is found for total surface area of the cerebral cortex in the two data sets (Fig. ID). In this case, there is better overlap across afrotherians. glims, primates, and artiodactyls, although cetaceans, the manatee, and humans are still major outliers. Interest- ingly, all species with a cortical surface area be- low 400 mm2 are lissencephalic in the two data sets. Similarly, all species with average cortical thickness below 1.2 mm are lissencephalic, but the folding index does not vary as a signifi- cant power function of cortical thickness across gyrencephalic species (Fig. 1E). The folding index shows a sharp inflection be- tween smooth and gyrated cortices, so it is unlikely that a universal model in terms of this variable alone could be derived. Because the folding index is the ratio of total surface area AG to exposed sur- face area AE, we next examined directly how AE scales With AG (Fig. 11') In the combined data sets, for the species with small AG (<400 mm2) there is no folding, such that AE equals AG (Fig. IF, green F 1.000.000 new Z 10'000 •C a O 102 to, i09 ion Number of conical neurons 1003 IO 100 1,1103 10:03 100,000 Exposed cortical surface area fmm2) 0.054. P = 0.1430: not plotted). (C) Total cortical surface area of the cerebral cortex scales across primate species with an exponent of 0.911 s 0.083 (12 = 0.938. P < 0.0001) and across nonprimate species with an exponent of 1.248 t 0.037 (r2 = 0.989. P < 0.0001). (F) Total cortical surface area varies across lissencephalic species as a linear function of the exposed surface area. but as a power function with an exponent of 1.242 t 0.018 across noncetacean gyrencephalic species (r2 = 0.992. P < 0.0001). Dashed lines 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- atee cerebral cortex, even though its AG is much larger than 1000 me. In contrast, for all non- cetaccan gyrencephalic species. AG increases with AE12. (r2 = 0992. P < 0.0001), significantly above linearity (Fig. IF, red line), meaning that as total surface area increases, it becomes increas- ingly folded. Cetaceans fall above the 95% confi- dence interval of the function, which indicates that these cortices are more folded than sim- ilarly sized cortices in noncetaceans. The finding thatAc scales as a power law MAE means that gnification is a property of a cortical surface that is self-similar down to a fundamental scale (the limit area between lissencephaly and gyrencephaly). This strongly suggests the existence of a single universal mechanism responsible for cortical folding (the alternative being some im- probable multiscale fine-tuning) that over a range of scales generates self-similar, or fractal, surfaces. Frodals can be characterized by the power-law scaling between intrinsic and extrinsic measures of an object's size, such asAc and A• In this case, the fractal dimension d of the cortical surface is twice the value of the exponent relatingAG to AB (given that AR in turn scales with the square of the linear dimension of the cortex). Given that 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- mension 23 of crumpled sheets of paper (25), which are fractal-like self-avoiding surfaces thin enough to fokl under external compression while maintaining structural integrity. Empirically, we conceive the fractal folding (or lack thereof) of the cortical surface as a conse- quence of the minimization of the effective free energy of a self-avoiding surface of average thick- ness T that bounds a volume composed of fibers connecting distal regions of said surface. Our model incorporates the known mechanics and organization of elongating axonal fibers (26, 27), as described in the supplementary materials. It predicts that from a purely physical perspective, AGAR, and Tare related by the power law TV2Ar = kAti. (The exponent 5/4 is the only value for which the constant A- is adimensional) We first tested whether our model baked on the minimization of the effective free energy of a self-avoiding surface could explain the well-known fractal folding of a self-avoiding surface: paper. We examined how the exposed surface area of crumpled paper balls, At. scales with increasing total surface area, AT, and thickness, T, of office 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- cates that the coarse-grained folding of a sheet of paper subjected to external compression depends simply on a combination of its surface area and thickness. We next examined whether our model predicts the folding of the mammalian cerebral cortex by plotting the product Tv2AG as a function ofA5 for the combined data sets. This yielded a power function with an exponent of 1229 i 0.014s with a very high r2 of 0.996 for the noncetacean gyrenceploilic species in the combined data sets (Fig 3A, red line). Note that this function, although calculated for gyrencephalic species, overlaps with lissencephalic species. Including lissencephalic species (but still excluding cetaceans) actually improved the fit, with r2 = 0_998, and yielded an exponent of 1305 i amo, which is dose to the expected value of 1.25. Adding cetaceans to the analysis resulted in a small change of the fit (Fig. 3A, black line). Remarkably, the function fitted exdusively for lissencephalic species also predicted the relationship between Tv2AG and AT in gyrencephalic species (Fig. 3A, green line)—and species such as the manatee and other afrotherians are no longer outliers. Given the theoretical relation 74/2A0 it follows that lissencephalic species (for which 103 goo room Exposed surface area (mm2) B 3 3 2 1 • • • • I • 0) • • 0.4 • • • • • • 0.6 • • S• • • • • II I . • • • • • 1000 10.000 Total surface area (mm') Exposed surface area (rnm2) AG = AO are those that meet the condition T = PAGI12. In contrast, all species for which T< k2AcIn are predicted to be gytencephalic, with Ac > AE (the alternative where T> it2AGI/2 would result in AG < An which is geometrically impossible). Indeed, in the combined data set, we find that rnAr filwa (Pc 0.0001) across lissencephalic species (Fig. 3B, green line). All gyrencephalic species data points fall to the right of the Bs- sencephalic distribution; that is, their AG values are larger than predicted for a cortical thickness that would allow lissencephaly. The precise rela- tionship between T and AG across girrencephalic speciesdiffers across orders, with a much smaller exponent for primates than for artiodactyls (Fig. 3B, red and pink lines). Thus, within the single universal relationship that describes cortical ex- pansion, there isa transition point between smooth and folded cortices: Gyrencephaly ensues when Ac expands in area faster than 7'2. For gyrence- phalic species, the rate of expansion of cortical thickness relative to expansion of the conical surface varies across orders, but the product T1J2Ac still varies as a universal function offlp.us to Alt1-33. We also found the same universality between the product 71/24 : and AT across corona! sections Fig. 2. The degree of folding of crumpled paper balls is a function of surface area and thickness as predicted by our model. (A) Relationship between total surface area of A4 to All sheets of office paper and the exposed surface area of the crumpled sheet of paper. with a power function of exponent 1234 ± 0.033 for a single sheet of thickness 01 inn. (B) Increasing the thickness of the paper to be crumpled by stacking two to eight sheets dis- places the curves to the right. that is. decreases the folding index of the resulting paper balls. (C) However. all crumpled paper balls of varying total surface area and thickness exhibit the same rela- tionship. with the product TV2Ar varying proper tionateiy to Acu°5'°°22 (r2 = 0.983. P< 0.0001). Color gradations correspond to thickness in millimeters. as shown in each panel. 76 3 JULY 2015 • VOL a'9 ISSUP. 6233 501011001111g.01• SCIENCE EFTA01190687 RESEARCH I REPORTS along the anteroposterior axis of the cortical hemi- sphere of a single individual, of different individ- uals, and even different specks ranging from small rodents to human and elephant (fig. Sh. The finding that AI,. scales across all lissen- cephalic and gyrencephalic mammals (and even across species usually regarded as outliers such as the manatee and cetaceans) as a single power law of T inAG indicates that gyrification is an in- trinsic property of any mammalian cortex Further, because the degree of folding can be described by the simple equation generated by our model (which also applies to crumpled sheets of paper), folding must occur as it minimizes the effective free energy of the cortical surface. Folding is therefore an intrinsic, fractal property of a self- avoiding surface, whether biological or not, sub- jected to crumpling forces. As such, this scaling of cortical folding does not depend on numbers of neurons or how they are distributed in the cortical sheet, but simply on the relative lateral expansion of this sheet relative to its thickness, regardless of how densely neurons are distrib- uted within IL The finding that conical folding scales univer- sally across dades, species, individuals, and parts of the same cortex implies that the single mecha- nism based on the physics of minimization of effective free energy of a growing surface subject to inhomogeneous bulk stresses applies across cortical development and evolution.This Is in stark contrast to previous conclusions that different mechanisms regulated folding at different lev- els (7); such conclusions may reflect the tradi- tional emphasis on the relationship between folding degree and brain volume (1, 8), which is indeed diverse across orders, across species, and across individuals of a sante species (6, 8). Also, the dependence of cortical folding on a simple combination of AG and T implies that any al- Fig. 3. The degree of folding of the mammalian cerebral cortex is a single function of surface area and thickness across lissencephalic and gyrence- phalic species alike. although thickness scales as order-specific fisictions of cortical surface area (A) The product TV2A0 varies with Aci229P° 'G(r2 = 0.9%. P < 0.0001) across noncetacean gyrence- phalic species in the combined data set (red line). with AE1325'0009 (r2= 0.997.P < 0.0001, k = O157, 0.012) across all species (including cetaceans: black line). and with AEL292'°°27 (r2 = 0.994. P < 0.0001) across lissencephalic species alone (green line). Note that the function plotted for lissencephalic species predicts the product 7 V2Ae for gyrencephalic species equaly well as the functions plotted for gyrencephalic species themselves. (B) Cortical thickness varies with cortical surface areaAG°565'°°w (r2 = 0287 P< 0.0001) across lissencephalic species in the corn- bined data set (green line). but with AG°16°'° 0.25 (+2 = 0.703.P< 0.0001)acrossprrnates (red line). and with AG°13""°22 (r2 = 0.879. P = 0.0185) across artio- dactyl species (pink line). NI fits exclude cetaceans. Dashed lines indicate the 95% confidence intervals for the fitted functions. teratIons, such as defects in cell migration, that lead to increased Tor decreased A0 (or both) are expected to decrease cortical folding, exactly as found in human pathological lhasmeephaly (28). This might also be the case for the lissencephalic brain of birds, where a very thick telencephalon of small surface area surrounds the subpalllal structures. Finally, our findings indicate that cortical fold- ing did not evolve, in the sense of a new property specific to some dades but not others. Similarly, there is no such thing as -secondary lissencephaly (29), nor are there two clusters of gyrencephaly (9). Rather, what has evolved, we propose, is a faster increase in AG relative to T2 in development— and at different rates in different mammalian clades, which thus become gyrencephalic at dif- ferent functions of Ao or different numbers of neurons. Remarkably, there is no a priori reason for lissencephaly, considering that AG and T ulti- mately result from different biological pi oet.sses. lateral expansion of the progenitor cell popula- tion tarifa, radial neurogenesis and cell growth for T (30). Similarly, there Is no a priori reason for the cortex to become gaTencephalie once past a certain surface area—unless the rate of (lateral) progenitor cell expansion inevitably outpaces the rate of (radial) neurogenesis at this point, which apparently occurs typically when Ac reaches 400 mm2. We propose that, starting from the ear- liest and smallest (and smooth) mammalian brains 04 the cortical surface initially scaled isometri- cally, with Ao a Ta Gyrencephaly ensued in each Glade as soon as this lockstep growth changed, with AG now increasing faster than T. Prob- able mechanisms involved are those that con- trol the rate of neurogenesis and increases in cell size relative to the rate of progenitor and intermediate progenitor cell proliferation in A 190004 3 1000, B Cortical thickness Iran) 10 toci moo maxi maxi Exposed surface area (mm2) Total surface area (mm2) early cortical development. Rapid increases in numbers of intermediate progenitor cells would lead to grencephdy, although not through the gen- eration of larger numbers of neurons, as previ- ously thought (7, 30, 32), but rather through the simple lateral expansion of the resulting cortical surface area at a rate faster than the cortical thickness squared. REFERENCES AND NOTES I. U. A. Holman. Bran BMW. 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Data reputed in de pmer are presaged in PK supplemotry rnaltrISS SUPPLEMENTARY MATERIALS wsne.sekommagogiconen1/349/6241/74/supg/DC1 Materials and Methods Turk SI References (33-38) 13 February 2015 accepted 1113e, 2015 10.1126/science.so9101 SCIENCE scleneemag.org 3 JULY 2016 • VOL 349 ISSUE 6243 77 EFTA01190688 Science tlAAAS Cortical folding scales universally with surface area and thickness, not number of neurons Bruno Mota and Suzana Herculano-Houzel Science 349, 74 (2015); 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. 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