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Cortical Folding: When, Where, How, and Why? Georg F. Striedter,1 Shyam Srinivasan,3,4 and Edwin S. Monuki2 1 Department of Neurobiology and Behavior, 2 Department of Pathology and Laboratory Medicine, University of California, Irvine, California 92697; email: [email protected], [email protected] 3

The Salk Institute, La Jolla, California 92037; email: [email protected]

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Kavli Institute for Brain and Mind, University of California San Diego, La Jolla, California 92037

Annu. Rev. Neurosci. 2015. 38:291–307

Keywords

The Annual Review of Neuroscience is online at neuro.annualreviews.org

cerebral cortex, neocortex, gyrification, sulcus, development, mechanism

This article’s doi: 10.1146/annurev-neuro-071714-034128

Abstract

c 2015 by Annual Reviews. Copyright  All rights reserved

Why the cerebral cortex folds in some mammals but not in others has long fascinated and mystified neurobiologists. Over the past century—especially the past decade—researchers have used theory and experiment to support different folding mechanisms such as tissue buckling from mechanical stress, axon tethering, localized proliferation, and external constraints. In this review, we synthesize these mechanisms into a unifying framework and introduce a hitherto unappreciated mechanism, the radial intercalation of new neurons at the top of the cortical plate, as a likely proximate force for tangential expansion that then leads to cortical folding. The interplay between radial intercalation and various biasing factors, such as local variations in proliferation rate and connectivity, can explain the formation of both random and stereotypically positioned folds.

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Contents

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INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EXTERNAL CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DIFFERENTIAL TANGENTIAL EXPANSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Folding the Telencephalic Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Folding the Cortical Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tangential Expansion by Radial Intercalation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DIFFERENTIAL PROLIFERATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AXONAL TENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EVOLUTIONARY GYRIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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INTRODUCTION The folds of the cerebral cortex in large mammalian brains are easy to observe but not so easy to explain. Imagine what would happen if the human neocortex were smooth (lissencephalic), rather than folded (gyrencephalic), but retained its normal thickness and areal extent. This smooth cortex would have to bulge outward, forming a huge balloon with dramatically enlarged cerebral ventricles (Striedter 2005). Such a ballooning brain would fail to pass through the mother’s birth canal and likely be impossible to balance on the neck. It would also require longer-than-normal axons to connect the cortical neurons to each other and to the rest of the brain, further increasing the brain’s substantial metabolic costs and reducing the speed of information processing. Folding solves these problems by allowing cortical surface area to scale almost linearly with brain volume (rather than the two-thirds scaling relationship one would expect without folding; Prothero & Sundsten 1984). Therefore, it is adaptive for large cortices to fold. Finding a proximate, mechanistic explanation for cortical folding is substantially more challenging. Researchers have proposed several hypotheses to explain the development of cortical folds (Figure 1). These hypotheses are not mutually exclusive. Instead, we view them as interacting with one another and with a hitherto neglected mechanism, namely the radial intercalation of young cortical neurons into the outer layer of the developing cortical plate. We propose that this radial intercalation causes the cortical plate to expand tangentially more rapidly than the underlying tissue. As a result, the cortical plate buckles, forming a series of folds. To explain folds that are conserved across individuals and species, we hypothesize that the cortical plate is biased to buckle at specific locations by various factors, including spatial variation in proliferation rate, cortical thickness, and axons that tether the cortical plate at stereotyped, specific locations. Compressive forces from the skull and meninges may also generate external constraints that shape cortical folds, at least at some specific stages of development.

EXTERNAL CONSTRAINTS Le Gros Clark (1945) and others had hypothesized that the cerebral cortex folds during embryogenesis, at least in part, because the skull provides external resistance to tangential expansion of the growing cortex. For an analogy, imagine a piece of paper expanding in surface area (tangentially) within a glass jar; the more the paper expands, the more crumpled it becomes. The cortical primordium likewise expands in surface area until it bumps up against the internal surface of 292

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Models of cortical folding

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Figure 1 A family of cortical folding models. Mechanistic explanations for cortical folding tend to focus either on forces external to the developing cortex or, more commonly, on intrinsic forces. The latter models tend to emphasize axonal tension, differential proliferation, or differential tangential expansion of developing structures that are bonded to one another. We stress that these various explanations are not mutually exclusive.

the developing skull. If this endocranial surface provides sufficient resistance to further cortical expansion, then the growing cortex must buckle, creating the folds we see in adulthood. This external constraint hypothesis is intuitively appealing, but some evidence speaks against it. One problem is that creating more space within the embryonic skull—by surgically removing noncortical brain areas—does not alter cortical folding patterns in sheep (Barron 1950). A second problem is that growth of the skull, which does not ossify until late in development, can clearly be influenced by growth of the brain. For example, genetic manipulations that cause mice to grow abnormally large brains also cause increased skull growth (Supplemental Figure 1) (Chenn & www.annualreviews.org • Cortical Folding

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Walsh 2002). Similarly, fetal hydrocephaly increases not only the size of the cerebral ventricles and the brain as a whole, but also the size of the skull. The finding that skull growth can be driven by brain growth decreases the likelihood that cortical folding is caused by external constraints, but it does not negate the possibility entirely. Skull constraints may, for example, explain experimentally induced folding of the normally smooth midbrain tectum in chicken embryos, which occurs without significant enlargement of the skull (McGowan et al. 2012). Moreover, the tops of outward cortical folds ( gyri) in large mammalian brains are frequently pressed flat against the overlying meninges, which in turn abut the overlying skull. These flattened gyral tops suggest that the skull, and possibly the meninges, provides some resistance to cortical tangential expansion, forcing the expanding cortex to buckle inward. We can conclude that external constraints may play a minor causal role in the growth of cortical folds, especially during late stages of development (Nie et al. 2010). Folds caused by external constraints tend to form at random positions; however, if the constraints are distributed unevenly across the cortex, then the folds would be most likely to develop in regions that experience the most pronounced constraints. As those constraints abate, some induced folds may disappear, becoming transient fissures (Ono et al. 1990).

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DIFFERENTIAL TANGENTIAL EXPANSION Disenchanted with models of cortical folding that rely on external constraints, researchers turned their attention to mechanisms that are intrinsic to the brain. An influential early idea was that the cortex folds because its superficial (outer) layers expand more rapidly than its deep layers (Richman et al. 1975). Modeling both layers as sheets that are bonded to a highly elastic underlying core of simulated white matter, the authors calculated that the bonded sheets should fold much as the real cortex does. An analogous mechanism has recently been used to explain the looping structure of vertebrate intestines (Savin et al. 2011). To visualize the core idea, imagine two stretched rubber sheets that are glued together, one on top of the other. When the stretch is released, both sheets shrink, but if one of them shrinks more than the other, both sheets will wrinkle. This rubber sheet analogy involves differential shrinkage, rather than differential expansion, but the forces that cause folding in both cases are functionally equivalent. The important question is how well the bonded cortical layers hypothesis applies to the brain. One major problem is that white matter is just as stiff as cortical gray matter in ferrets during the developmental stages when most cortical folds form (Xu et al. 2010). These data create a problem for the model of Richman et al. (1975) because both the inward and the outward buckling of the bonded layers require the inner core, to which the layers are attached, to change its shape. A second problem is that Richman et al. did not provide a developmental mechanism to explain why the superficial cortical layers expand tangentially more rapidly than the deep layers. Indeed, their model is based entirely on data from adults, when cortical expansion is essentially complete. A more developmental version of Richman’s model has been proposed by Arnold Kriegstein and his collaborators, who argue that cortical folding stems from an evolutionary expansion of cortical progenitors that preferentially give rise to neurons in the superficial cortical layers (Lui et al. 2011). However, this proposal also fails to explain why the superficial layers would expand tangentially, rather than radially, relative to the deeper layers. As a result of these uncertainties, the bonded cortical layers hypothesis has fallen out of favor. More recent models of cortical folding emphasize that folding may occur in systems where a single-layer, peripheral shell is bonded to a central core (Tanaka et al. 1987; Cao et al. 2011; Dervaux et al. 2011; Dervaux & Amar 2011, 2012; Li et al. 2011; Barros et al. 2012; Tallinen

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et al. 2014; Yang & Lin 2014). If the surface area of the shell expands more rapidly than that of the core, then the shell eventually buckles. The size and shape of the folds depend both on the thickness of the shell and on the stiffness of the core. Such buckling shell models have been examined mathematically and, quite productively, in synthetic hydrogels with outer shells that swell more than their cores (Supplemental Figure 2). They have been applied to a variety of natural phenomena, including the growth of various fruits (Yin et al. 2008), the development of fingertips (Kucken 2007), and tumor enlargement (Dervaux et al. 2011). ¨ If we want to apply the buckling shell models to cortical folding (see also Tallinen et al. 2014), we must be clear on what is core and what is shell inside the brain. This distinction, in turn, depends on the stage of brain development one is considering. At early stages of development, the entire telencephalic wall can be thought of as a shell that surrounds a ventricular core; later in development, it is better to think of the outer cortical plate—a cell-dense layer of immature cortical neurons—as a shell that surrounds the underlying brain tissue and buckles as it expands tangentially. These ideas are developed more fully in the following sections.

Folding the Telencephalic Wall At early stages of development, the dorsolateral walls of the telencephalon, where the cerebral cortex originates, consist almost exclusively of rapidly proliferating cells. As these progenitors divide, the telencephalic wall expands tangentially—“somewhat as a soap bubble expands from the bowl of a pipe under increasing pressure” (Le Gros Clark 1945, p. 6)—while remaining relatively constant in thickness. The inside of this growing balloon is filled with embryonic cerebrospinal fluid (CSF) that is under pressure and increases in volume as the telencephalon expands (Gato & Desmond 2009). Thus, one can think of the telencephalic wall as a thin shell around a fluid-filled core; they are bonded to one another in the sense that the telencephalic wall cannot peel away (delaminate) from the fluid. As long as the increase in CSF volume keeps pace with the tangential expansion of the telencephalic wall, the surface of the cortical primordium should remain smooth, which it does during normal development. However, if CSF is drained from early embryonic brains, the walls of the embryonic telencephalon (and other brain regions) buckle inward (Desmond & Jacobson 1977) (Supplemental Figure 3), just as the buckling shell models predict. Similar folds emerge in transgenic mice whose telencephalic progenitors divide abnormally often, causing increased tangential expansion of the proliferative zone (Chenn & Walsh 2002) (Supplemental Figure 1). Because the ventricles in these transgenic mice do not expand in concert with the telencephalic wall, the wall must fold. The artificial folds produced by decreased intraventricular pressure or increased proliferation are interesting, but they differ from most naturally occurring folds because the artificial folds involve the entire telencephalic wall. In contrast, in naturally occurring folds only the gray matter and the cortical surface exhibit prominent folds; the ventricular surface remains relatively smooth and does not extend into the individual folds (Figure 2). Therefore, folding occurs in the early embryonic telencephalon only in artificial, experimental situations (though one could argue that the choroid plexus and the hippocampus form as early inward folds). Under normal conditions, CSF production and tangential expansion of the telencephalic wall appear carefully matched to prevent most of the cortex from folding. The need for this balancing act may explain why the choroid plexus, which is critical for CSF production, is so enormous in embryonic human brains (Supplemental Figure 4).

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Postnatal day 1 Postnatal day 4

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Figure 2 Development of cortical folds in ferrets. Drawings of coronal sections through the telencephalon of ferrets at the indicated ages (at comparable rostrocaudal levels). Cortical gray matter is shown in blue, and the proliferative ventricular zone is shown in brown. Also shown is a lateral view of an adult ferret’s brain. Drawings based on data in Smart & McSherry (1986) and on an image at the Comparative Mammalian Brain Collections: http://brainmuseum.org.

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Youngest cortical plate cells Older cortical plate cells Migrating young neurons Intermediate progenitors Radial progenitors

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Subventricular zone Ventricular zone Early stages

Later stages

Figure 3 Growth of a cortical gyrus. At early stages of cortical development (left) the cortical plate is relatively thin, as are the proliferative ventricular and subventricular zones. At later stages (right), the cortical plate has thickened, although its outermost layer, containing the youngest cortical neurons, remains quite thin. Newborn neurons migrate into this layer along the processes of radial progenitors, some of which lack (or have lost) their attachment to the ventricular surface.

Folding the Cortical Plate At later stages of development, the walls of the telencephalon, including the primordial neocortex, thicken considerably (Figure 2). The progenitor cells remain near the ventricular surface, where they form distinct ventricular and subventricular zones (Figure 3), but the ventricles no longer expand in concert with the telencephalic walls. Young, immature neurons migrate radially away from their site of birth near the ventricles, climbing along the long processes of radial progenitor cells, also known as radial glia (Figure 3). When the young neurons reach the marginal zone, a cell-sparse layer just beneath the cortical surface, they stop their migration. Over time, the young neurons accumulate and form a cell-dense layer known as the cortical plate. It is this cortical plate, together with the overlying marginal zone and cortical surface, that folds as development proceeds. To apply the buckling shell model to these later stages of cortical development, we can define the shell as the cortical plate and the core as the underlying tissues, which are bonded to the cortical plate primarily through radial glial fibers (see Figure 3). Toro & Burnod (2005) developed a computational model of such a system and showed that its shell eventually buckles when it expands tangentially more quickly than the core. A conceptually similar model was developed by Bayly et al. (2013), the main difference being that the latter model allows the core to grow in the radial dimension when it experiences radial stress, which naturally arises when the shell buckles outward. Missing from these models is a developmental mechanism for the tangential expansion of the cortical plate. Some authors have suggested that the tangential expansion of the cortical plate is caused by the tangential migration of young cortical neurons (Lui et al. 2011, Reillo et al. 2011). However, tangential dispersion of individual neurons generates no net tangential spreading force; at best, it can cause the cortex to expand at its edges. Other authors have proposed that the cortical plate expands tangentially because individual neurons become larger as they mature (Knutsen et al. 2013, Ronan et al. 2013). However, such cytoplasmic growth would tend to thicken the cortical plate as much as it spreads the plate tangentially, which is not what happens in real www.annualreviews.org • Cortical Folding

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Outward buckling of the cortical plate Marginal zone

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Migrating neuron Radial glial cell

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Figure 4 Radial intercalation of newborn neurons drives cortical plate buckling. When the leading processes of young migrating neurons (red ) reach the marginal zone, the cells pull their cell body into the outer cortical plate, pushing neighboring cells aside. Because these other cells continue to pull their cell bodies toward the marginal zone (at least for some time), the cortical plate expands tangentially. Because this tangential expansion outpaces that of the underlying tissue, the cortical plate must buckle either outward (a) or inward (b), depending on the balance of tissue elasticities, tension-induced growth, and external restraining forces (e.g., from the brain-encasing meninges).

brains. Therefore, cytoplasmic growth cannot explain why the developing cortical plate expands tangentially so much more than it expands radially.

Tangential Expansion by Radial Intercalation To overcome these weaknesses of the existing buckling shell models of cortical folding, we propose that tangential expansion of the cortical plate is driven by the intercalation of radially migrating neurons into the cell-dense outer (most superficial) layer of the cortical plate (Figure 4; also known as the primitive cortical zone). Our hypothesis is based in part on observations by Sekine et al. (2011, 2014) of how young neurons migrate into the cortical plate (Supplemental Figure 5). When the cell body of a radially migrating neuron approaches the outer layer of the cortical plate, the neuron’s leading process rapidly shortens and the cell body is pulled into the outer cortical plate, a phenomenon dubbed terminal translocation. In the process, the translocating cell body pushes the neighboring cell bodies tangentially aside. As long as those neighboring cell bodies also remain in the outer cortical plate, before reverse intercalating and dropping down into the subjacent layers, the radial intercalation should cause the outer cortical

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plate to spread tangentially. Assuming that the outer cortical plate is bonded to the deeper layers of the cortical plate (through radial processes and intercellular adhesion), the entire cortical plate should spread, while increasing just slightly in thickness. Support for this radial intercalation hypothesis derives from an analogy to other developing tissues, where intercalation is thought to generate substantial tangential spreading (Warga & Kimmel 1990, Heller et al. 2014, Walck-Shannon & Hardin 2014). Particularly relevant is the process of epiboly, in which radial intercalation of deep cells into a more superficial position thins the embryonic blastoderm and causes it to spread across the yolk (Keller 1980, Keller et al. 2000). Unlike those other tissues, the cortical plate does not get thinner as it expands tangentially, but this difference can be attributed to the addition of new cells to the cortical plate. Radial intercalation in the cortical plate also resembles interkinetic nuclear migration in the brain’s ventricular zone (Sauer & Walker 1959), which involves the active pulling of cell nuclei toward the ventricular surface (Kosodo et al. 2011). To obtain more direct evidence for radial intercalation in the cortical plate, one could test the prediction that tangential spreading of the cortical plate should be reduced in embryos of transgenic mice with impaired cortical neuronal migration, including deficits specifically in the terminal translocation stage (Tonosaki et al. 2014). Similar deficits in species with folded cortices should reduce foliation. In that context, it is interesting that classic lissencephaly in human fetuses is thought to stem from neuronal migration deficits and that the number of neurons stuck below the cortical plate in lissencephaly is inversely correlated with the degree of cortical folding (Stewart et al. 1975, Moon & Wynshaw-Boris 2013). When lissencephaly affects only part of the brain (as in hemimegalencephaly), the abnormally smooth cortex also tends to be abnormally thick (Aronica et al. 2012). Even in normal brains, variations in the degree of local cortical folding are inversely correlated with local cortical thickness, irrespective of subject age (Hogstrom et al. 2013). One potential problem for the radial intercalation hypothesis is that cortical neurogenesis and neuron migration are thought to be largely complete in ferrets by 1–2 weeks after birth (Neal et al. 2007), whereas cortical folding continues at least through postnatal day 18 (Figure 2). The most likely explanation for this discrepancy is that some young neurons in ferrets are actually born as late as 2 weeks after birth ( Jackson et al. 1989) and probably do not arrive in the cortical plate until at least one week after that, in which case the timing of neuronal migration and cortical folding in ferrets would coincide remarkably well. In humans, too, many young neurons are still migrating “during the last trimester and even after birth” (Sidman & Rakic 1973, p. 7). That said, it is clear that little cortical folding occurs during early stages of tangential cortical expansion by radial intercalation, but this can be explained by the existence of a buckling threshold below which tangential expansion occurs without the formation of folds. It also seems likely that processes other than radial intercalation (e.g., increases in cell size and neuropil development) will magnify preexisting shallow folds. Another potential challenge is that buckling tends to generate randomly positioned folds, whereas real cortices exhibit at least some stereotyped sulci and gyri, particularly those that form early in development (Ono et al. 1990). We already know, however, that the location of folds in buckling shell models can be influenced by various factors, including the model’s initial shape. In ellipsoid models, for example, most folds run either parallel or orthogonal to the ellipsoid’s long axis (Todd 1982, Toro 2012). The location of buckling folds can also be influenced by spatial variation in the relative stiffness and thickness of the shell (Dervaux et al. 2011, Bayly et al. 2013), by local differences in the rate of tangential expansion (Toro & Burnod 2005, Xu et al. 2010), and by extrinsic constraints. As discussed in the next two sections, several of these factors appear at play in the developing cortex.

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DIFFERENTIAL PROLIFERATION

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Gustav Retzius proposed in 1896 that cortical gyri develop at proliferative hot spots. The idea received a major boost when Kriegstein et al. (2006) showed that the subventricular zone, which harbors neural progenitors that undergo mitoses away from the ventricular surface, is thicker under some developing gyri than under the adjacent emerging sulci in both macaques and humans. A later study confirmed this basic finding in ferrets (Reillo et al. 2011), although it remains unclear whether proliferative hot spots are found beneath every developing gyrus or just a few of them. A major limitation of this differential proliferation hypothesis of cortical folding is that increased proliferation (by itself ) can only build a gyrus by locally thickening the cortical plate, effectively creating bumps in the cortical surface; however, this is not how natural folds form. Instead, as shown in Figure 2, cortical folds develop because the cortical plate begins to undulate while remaining relatively constant in thickness. This weakness of the differential proliferation hypothesis can be overcome by combining the notion of differential proliferation with the radial intercalation and buckling shell hypotheses. Specifically, local increases in proliferation should (other things being equal) lead to local increases in tangential expansion of the cortical plate, which should (according to the buckling shell hypothesis) increase the probability of developing one or more folds in the expanded area. Consistent with this prediction, an experimental increase in the proliferation of cortical progenitors caused an increase in the degree of cortical folding, at least in ferrets (NonakaKinoshita et al. 2013). Such a synthesis predicts at least a general correlation between spatial variations in proliferation rates and the degree of cortical folding. It would, for example, explain why spatial variations in the degree of cortical folding correlate with the general anterior-posterior gradient of cortical neurogenesis, at least in monkeys (Zilles et al. 1988). The proposal is also consistent with the finding that the degree of tangential expansion, as inferred from the intrinsic (Gaussian) curvature of the cortical surface (Todd 1985; Ronan et al. 2011, 2013), varies across the cortical expanse. (Gaussian curvature is nonzero for bowl- or saddle-shaped surfaces and zero for cylinders or cones, which can be unfurled to form flat sheets). Although rates of radial intercalation and, consequently, tangential expansion generally correlate with rates of proliferation, this relationship can be altered by changes in migration distance or speed. If part of the ventricular zone, where new neurons are born, moves further and further away from the cortical plate, thus increasing the migration distance, then the rate of radial intercalation will be lower than the rate of neurogenesis (as in the Doppler effect for light or sound waves). When the relative movement between the ventricular zone and the cortical plate is spatially heterogeneous, tangential expansion will likewise vary spatially (other things being equal). This insight is relevant to cortical folding because the proliferative zone at the corticostriatal junction moves further and further away from the cortical plate as development proceeds, and does so to a much greater extent than neighboring regions (Bayer et al. 1991). Because of this displacement, young neurons destined for the insular and olfactory cortices migrate over progressively longer distances as development goes on (Supplemental Figure 6). Other things being equal, this increase in migration distance should lower the rate of radial intercalation in these cortical areas, potentially explaining why the insular cortex bulges outward much less than adjacent cortical areas and is relatively lissencephalic for most of its development.

AXONAL TENSION The most heavily cited model of cortical folding is that of Van Essen (1997), who pointed out that some cortical neurons emit axons while they are still migrating and that those axons probably resist being stretched. He then argued that “tension along obliquely oriented axonal trajectories 300

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between nearby cortical areas would generate tangential force components that tend to induce folds at specific locations” (p. 315). As the cortical plate expands tangentially, “populations of axons pulling together should have ample strength to cause folding of the highly pliable embryonic cortical sheet” (p. 315). A key prediction of this model is that the walls of a single gyrus should be more densely interconnected than the walls of different gyri. More generally, Van Essen proposed that the overall pattern of cortical folding is determined by the pattern of intracortical axonal connections, which engage in a global tug-of-war that minimizes total axonal tension. Consistent with this axonal tension hypothesis, several studies have shown that axonal connections in highly folded cortices tend to be relatively short and straight, connecting adjacent gyral walls more frequently than expected by chance (Van Essen 1997, Hilgetag & Barbas 2006, Rajimehr & Tootell 2009). Unfortunately, the connectional data cannot discriminate cause from effect. Short connections between adjacent gyral walls might result from axons pulling on nascent gyral walls, but they might also be a consequence of adaptive evolution. The longer axons are, the more space and energy they require, and the longer it takes for information to be exchanged between cortical areas. Therefore, it would have been adaptive for evolving species to minimize intracortical connection lengths, at least to some extent (Klyachko & Stevens 2003, Striedter 2005, Raj & Chen 2011). To test the axonal tension hypothesis, Xu et al. (2010) conducted microdissection experiments on fresh tissue slices through the developing cortex of ferrets. If axons exert tension between adjacent gyral walls, then making a cut radially down the center of a young gyrus should cause the cut to splay. Instead, the cuts stayed closed. Although these results run counter to the axonal tension hypothesis, the existing studies were more anecdotal than systematic. Moreover, axonal tension might influence cortical folding by tethering sulci, rather than pulling on gyral walls. For example, thalamocortical axons growing into a specific cortical region might make it more difficult for the cortical plate at that location to move radially outward, thereby creating a sulcus. Alternatively, or in addition, thalamocortical axons may influence cortical folding by modulating cortical proliferation rates. When thalamocortical axons first grow into the cortex, they closely approach the cortical progenitors (Dehay & Kennedy 2007), and diffusible factors released from embryonic thalamocortical axons can modulate cortical proliferation rates in tissue culture (Dehay et al. 2001). In addition, removal of the eyes during embryogenesis, thus reducing the size of the lateral geniculate nucleus and the number of thalamocortical axons, dramatically alters the pattern of cortical folding in the occipital cortex of monkeys (Rakic 1988, Dehay et al. 1996). An analogous study in ferrets reduced proliferation rates in the region giving rise to the primary visual cortex, which caused the associated cortical gyrus to become abnormally small (Reillo et al. 2011). Thus, axons may influence cortical folding by factors other than the tension that they may generate.

EVOLUTIONARY GYRIFICATION Across species, the degree of cortical folding (gyrification) correlates with brain weight and, more specifically, with cortical surface area. In all major mammalian lineages, the species with large brains tend to have more highly folded cortices than species with smaller brains (Hofman 1985, Zilles et al. 1989, Pillay & Manger 2007, Kelava et al. 2013, Zilles et al. 2013, Lewitus et al. 2014). Especially interesting is that the relationship between gyrification and cortical surface area is nonlinear, even when one or both of the variables are log-transformed (Figure 5a). Species with cerebral cortices smaller than 10 cm2 in surface area are generally lissencephalic, but above this threshold the degree of cortical folding tends to increase predictably with cortical surface area (Hofman 1985; Lewitus et al. 2013, 2014). www.annualreviews.org • Cortical Folding

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log (perimeter) Figure 5 The larger and thinner the cortex, the more folded it is. (a) The degree of cortical folding can be quantified by dividing total cortical surface area by smoothed cortical surface area (without following the surface into the depths of sulci). The higher this gyrification index, the more folded the cortex; an index of 1 denotes a lack of folds. The graph in panel a shows that cerebral cortices begin to fold once cortical surface area exceeds 10 cm2 and that cetaceans have both thinner and more folded cortices than other mammals with similarly extensive cortices. The graph in panel b summarizes results from a computational buckling shell model, showing that the buckling instability is reached at smaller shell perimeters (the two-dimensional equivalent to cortical surface area) in thinner cortices. Data in panel a are from Hofman (1985). Data in panel b are courtesy of Roberto Toro; see also Toro & Burnod (2005).

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The slope with which the gyrification index of a species scales against cortical surface area tends to vary between mammalian orders, a fact that seems to suggest some evolutionary changes in the underlying mechanisms of cortical folding. However, the nonlinear scaling is predicted by the buckling shell models (Toro & Burnod 2005), which show that a tangentially expanding shell stays smooth up to a point, beyond which it starts to fold progressively (Figure 5b). Although ontogeny need not recapitulate phylogeny (de Beer 1958), it seems likely that in small-brained species the cerebral cortex never expands beyond the point of buckling instability, whereas it does in larger-brained mammals. If this statement is true, then the fundamental mechanisms underlying cortical folding may be conserved across mammals, even if gyrification scales with different slopes in different orders. Nonetheless, species clearly do vary in their degree of cortical folding independently of cortical surface area. The factor most likely to account for this phylogenetic variation is cortical thickness. Dolphin and whales, for example, have an exceptionally thin cerebral cortex for the size of their brain, and those cortices are exceptionally folded (Figure 5a, Supplemental Figure 7) (Pillay & Manger 2007). Conversely, manatees have unusually thick cerebral cortices that are, despite their large size, almost completely smooth (Welker 1990). These data are consistent with a key insight from the buckling shell models: the thinner the shell, the earlier the system reaches the buckling instability and, beyond that threshold, the greater its degree of folding at a given surface area (Figure 5b) (Toro & Burnod 2005). More specifically, we predict a correlation in which species with thicker and smoother cortices should (other things being equal) exhibit lower rates of radial intercalation and tangential expansion in the cerebral cortex.

CONCLUSIONS We here provide a broad review of various mechanisms that have been proposed to explain cortical folding (for additional insights, see Prothero & Sundsten 1984, Striegel & Hurdal 2009, Garzon´ Alvarado et al. 2011, Mota & Herculano-Houzel 2012, Nie et al. 2012, Chen et al. 2013, Ribeiro et al. 2013, Stahl et al. 2013). In our view, these mechanisms are not alternatives but instead constitute an interacting set. We are not the first to propose that cortical folding involves multiple mechanisms (Welker 1990, Manger et al. 2012, Bayly et al. 2014, Sun & Hevner 2014), but we stress their interactions and propose a novel developmental mechanism—the radial intercalation of newborn neurons into the cortical plate—as providing a hitherto unrecognized proximate force that ties together many of the previously proposed mechanisms underlying cortical folding. Although we stress that cortical folding results from the interplay of multiple cellular mechanisms and mechanical forces, some of these processes are more important than others. For understanding variations in the overall degree of cortical folding, across individuals or species, the most important mechanism is the tangential expansion of the cortical plate relative to the underlying tissue, i.e., the buckling shell mechanism. The higher the expansion ratio, the greater the degree of cortical folding (assuming that the system has passed the buckling threshold). The degree of tangential expansion, in turn, depends most strongly on the rate at which new cells are intercalated into the cortical plate, the duration of this migration, and the duration over which young neurons remain in the outer cortical plate. To the extent that these factors are regulated homogeneously throughout the cortex, they affect gyrification globally. In contrast, localized variations in cortical folding, as well as the shape and orientation of specific gyri and sulci, are influenced by various additional factors, including spatial variations in proliferation, migration, axonal tension, and mechanical constraints. Our review is focused squarely on the cellular rather than the molecular level. Several molecules are already known to affect cortical folding (see Sun & Hevner 2014 for a recent review), but they www.annualreviews.org • Cortical Folding

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are likely just the tip of the proverbial iceberg. The cellular mechanisms that we have discussed certainly involve a plethora of genes, most of which likely affect cortical folding when they are disrupted or overexpressed. To make sense of these accumulating molecular data, it will be imperative to have a solid model of cortical folding at the cellular level. Without such a model, it is extremely difficult to discriminate central molecular factors (mediators) from permissive or modulatory ones (Sanes & Lichtman 1999). Given our model, the central molecular mediators of cortical folding are likely to include molecules that are essential for radial intercalation of newborn cells into the outer cortical plate. These would include cytoskeletal proteins implicated in lissencephaly (e.g., LIS1 and DCX) because lissencephaly is ascribed to impaired radial migration and probably involves defects in the cytoskeleton-dependent forces needed for radial intercalation. Other likely mediators are L1cam, assuming that it affects terminal translocation in gyrencephalic species as well as in mice (Tonosaki et al. 2014), and factors that have widespread effects on proliferation rate and duration, such as some members of the fibroblast growth factor family that can cause abnormal folding of otherwise normal-appearing brain tissue (e.g., McGowan et al. 2012, Rash et al. 2013). In the long run, we hope that molecular data from these and future studies will be integrated into our cellular-level model to provide a comprehensive understanding of cortical folding.

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DISCLOSURE STATEMENT The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS We thank Roberto Toro for access to some raw data and Charles Stevens, Stephen Noctor, and Jeffrey Golden for feedback on the draft. This work was supported by NSF grant IOS-1025434 to G.S. and by the Mathers Foundation and NSF award CCF-1212778 to S.S. LITERATURE CITED Aronica E, Becker AJ, Spreafico R. 2012. Malformations of cortical development. Brain Pathol. 22:380–401 Barron DH. 1950. An experimental analysis of some factors involved in the development of the fissure pattern of the cerebral cortex. J. Exp. Zool. 113:553–81 Barros W, de Azevedo EN, Engelsberg M. 2012. Surface pattern formation in a swelling gel. Soft Matter 8:8511–16 Bayer SA, Altman J, Russo RJ, Dai XF, Simmons JA. 1991. Cell migration in the rat embryonic neocortex. J. Comp. Neurol. 307:499–516 Bayly PV, Okamoto RJ, Xu G, Shi Y, Taber LA. 2013. A cortical folding model incorporating stress-dependent growth explains gyral wavelengths and stress patterns in the developing brain. Phys. Biol. 10:016005 Bayly PV, Taber LA, Kroenke CD. 2014. Mechanical forces in cerebral cortical folding: a review of measurements and models. J. Mech. Behav. Biomed. Mater. 29:568–81 Cao Y-P, Li B, Feng X-Q. 2011. Surface wrinkling and folding of core–shell soft cylinders. Soft Matter 8:556–62 Chen H, Zhang T, Guo L, Li K, Yu X, et al. 2013. Coevolution of gyral folding and structural connection patterns in primate brains. Cereb. Cortex 23:1208–17 Chenn A, Walsh CA. 2002. Regulation of cerebral cortical size by control of cell cycle exit in neural precursors. Science 297:365–69 de Beer G. 1958. Embryos and Ancestors. London: Oxford Univ. Press Dehay C, Giroud P, Berland M, Killackey H, Kennedy H. 1996. Contribution of thalamic input to the specification of cytoarchitectonic cortical fields in the primate: effects of bilateral enucleation in the fetal 304

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Cortical folding: when, where, how, and why?

Why the cerebral cortex folds in some mammals but not in others has long fascinated and mystified neurobiologists. Over the past century-especially th...
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