Cytoskeletal-associated proteins in the migration of cortical neurons

Neuronal migration is a hallmark of cerebral cortical development as neurons born deep within the brain migrate to the surface in a highly choreographed process. The cytoskeleton extends throughout the cell, mediating the dramatic morphological changes that accompany migration. On a cellular level, proper migration is accompanied by polarization of the cytoskeleton and cellular contents and by dynamic reorganization that generates the force for cell locomotion. Genetic analyses of human brain malformations, as well as genetically engineered mouse mutants, have highlighted a number of cytoskeletal-associated proteins underlying these functions, which are necessary for proper cortical development. While these proteins are involved in diverse molecular mechanisms, disruption during development results in the ectopic placement of neurons in the cortex. We review key cytoskeletal events and the critical cytoskeletal-associated proteins involved in cortical neuronal migration.     

Developmental mechanisms of gyrification

Folding of the cerebral cortex is a fundamental milestone of mammalian brain evolution associated with dramatic increases in size and complexity. Cortex folding takes place during embryonic and perinatal development and is important to optimize the functional organization and wiring of the brain, while allowing fitting a large cortex in a limited cranial volume. Cortex growth and folding are the result of complex cellular and mechanical processes that involve neural stem progenitor cells and their lineages, the migration and differentiation of neurons, and the genetic programs that regulate and fine-tune these processes. Here, we provide an updated overview of the most significant and recent advances in our understanding of developmental mechanisms regulating cortical gyrification.     

Dab2ip Regulates Neuronal Migration and Neurite Outgrowth in the Developing Neocortex

Dab2ip (DOC-2/DAB2 interacting protein) is a member of the Ras GTPase-activating protein (GAP) family that has been previously shown to function as a tumor suppressor in several systems. Dab2ip is also highly expressed in the brain where it interacts with Dab1, a key mediator of the Reelin pathway that controls several aspects of brain development and function. We found that Dab2ip is highly expressed in the developing cerebral cortex, but that mutations in the Reelin signaling pathway do not affect its expression. To determine whether Dab2ip plays a role in brain development, we knocked down or over expressed it in neuronal progenitor cells of the embryonic mouse neocortex using in utero electroporation. Dab2ip down-regulation severely disrupts neuronal migration, affecting preferentially late-born principal cortical neurons. Dab2ip overexpression also leads to migration defects. Structure-function experiments in vivo further show that both PH and GRD domains of Dab2ip are important for neuronal migration. A detailed analysis of transfected neurons reveals that Dab2ip down- or up-regulation disrupts the transition from a multipolar to a bipolar neuronal morphology in the intermediate zone. Knock down of Dab2ip in neurons ex-vivo indicates that this protein is necessary for proper neurite development and for the expression of several major neuronal microtubule associated proteins (MAPs), which are important for neurite growth and stabilization. Thus, our study identifies, for the first time, a critical role for Dab2ip in mammalian cortical development and begins to reveal molecular mechanisms that underlie this function.     

Complement inhibition and statins prevent fetal brain cortical abnormalities in a mouse model of preterm birth

Premature babies are particularly vulnerable to brain injury. In this study we focus on cortical brain damage associated with long-term cognitive, behavioral, attentional or socialization deficits in children born preterm. Using a mouse model of preterm birth (PTB), we demonstrated that complement component C5a contributes to fetal cortical brain injury. Disruption of cortical dendritic and axonal cytoarchitecture was observed in PTB-mice. Fetuses deficient in C5aR (−/−) did not show cortical brain damage. Treatment with antibody anti-C5, that prevents generation of C5a, also prevented cortical fetal brain injury in PTB-mice. C5a also showed a detrimental effect on fetal cortical neuron development and survival in vitro. Increased glutamate release was observed in cortical neurons in culture exposed to C5a. Blockade of C5aR prevented glutamate increase and restored neurons dendritic and axonal growth and survival. Similarly, increased glutamate levels – measured by ¹HMRS – were observed in vivo in PTB-fetuses compared to age-matched controls. The blockade of glutamate receptors prevented C5a-induced abnormal growth and increased cell death in isolated fetal cortical neurons. Simvastatin and pravastatin prevented cortical fetal brain developmental and metabolic abnormalities -in vivo and in vitro. Neuroprotective effects of statins were mediated by Akt/PKB signaling pathways. This study shows that complement activation plays a crucial role in cortical fetal brain injury in PTL and suggests that complement inhibitors and statins might be good therapeutic options to improve neonatal outcomes in preterm birth.     

Ena/VASP proteins regulate cortical neuronal positioning

Development of the multilayered cerebral cortex involves extensive regulated migration of neurons arising from the deeper germinative layers of the mammalian brain. The anatomy and formation of the cortical layers has been well characterized; however, the underlying molecular mechanisms that control the migration and the final positioning of neurons within the cortex remain poorly understood. Here, we report evidence for a key role of Ena/VASP proteins, a protein family implicated in the spatial control of actin assembly and previously shown to negatively regulate fibroblast cell speeds, in cortical development. Ena/VASP proteins are highly expressed in the developing cortical plate in cells bordering Reelin-expressing Cajal-Retzius cells and in the intermediate zone through which newly born cells migrate. Inhibition of Ena/VASP function through retroviral injections in utero led to aberrant placement of early-born pyramidal neurons in the superficial layers of both the embryonic and the postnatal cortex in a cell-autonomous fashion. The abnormally placed pyramidal neurons exhibited grossly normal morphology and polarity. Our results are consistent with a model in which Ena/VASP proteins function in vivo to control the position of neurons in the mouse neocortex.     

The unfolding story of two lissencephaly genes and brain development

Formation of our highly structured human brain involves a cascade of events, including differentiation, fate determination, and migration of neural precursors. In humans, unlike many other organisms, the cerebral cortex is the largest component of the brain. As in other mammals, the human cerebral cortex is located on the surface of the telencephalon and generally consists of six layers that are formed in an orderly fashion. During neuronal development, newly born neurons, moving in a radial direction, must migrate through previously formed layers to reach their proper cortical position. This is one of several neuronal migration routes that takes place in the developing brain; other modes of migration are tangential. Abnormal neuronal migration may in turn result in abnormal development of the cortical layers and deleterious consequences, such as Lissencephaly. Lissencephaly, a severe brain malformation, can be caused by mutations in one of two known genes:LIS1 anddoublecortin (DCX). Recent in vitro and in vivo studies, report on possible functions for these gene products.     

Pocket proteins pRb and p107 are required for cortical lamination independent of apoptosis

Pocket proteins (pRb, p107 and p130) are well studied in their role of regulating cell cycle progression. Increasing evidence suggests that these proteins also control early differentiation and even later stages of cell maturation, such as migration. However, pocket proteins also regulate apoptosis, and many of the developmental defects in knock out models have been attributed to increased cell death. Here, we eliminate ectopic apoptosis in the developing brain through the deletion of Bax, and show that pocket proteins are required for radial migration independent of their role in cell death regulation. Following loss of pRb and p107, a population of cortical neurons fails to pass through the intermediate zone into the cortical plate. Importantly, these neurons are born at the appropriate time and this migration defect cannot be rescued by eliminating ectopic cell death. In addition, we show that pRb and p107 regulate radial migration through a cell autonomous mechanism since pRb/p107 deficient neurons fail to migrate to the correct cortical layer within a wild type brain. These results define a novel role of pocket proteins in regulating cortical lamination through a cell autonomous mechanism independent of their role in apoptosis.     

Emerging roles of neural stem cells in cerebral cortex development and evolution

Expansion and folding of the cerebral cortex are landmark features of mammalian brain evolution, which are recapitulated during embryonic development. Neural stem cells and their derived germinal cells are coordinated during cerebral cortex development to produce the appropriate amounts and types of neurons. This process is further complicated in gyrencephalic species, where newborn neurons must disperse in the tangential axis to expand the cerebral cortex in surface area. Here, we review advances that have been made over the last decade in understanding the nature and diversity of telencephalic neural stem cells and their roles in cortical development, and we discuss recent progress on how newly identified types of cortical progenitor cell populations may have evolved to drive the expansion and folding of the mammalian cerebral cortex.     

MACF1 regulates the migration of pyramidal neurons via microtubule dynamics and GSK-3 signaling

Neuronal migration and subsequent differentiation play critical roles for establishing functional neural circuitry in the developing brain. However, the molecular mechanisms that regulate these processes are poorly understood. Here, we show that microtubule actin crosslinking factor 1 (MACF1) determines neuronal positioning by regulating microtubule dynamics and mediating GSK-3 signaling during brain development. First, using MACF1 floxed allele mice and in utero gene manipulation, we find that MACF1 deletion suppresses migration of cortical pyramidal neurons and results in aberrant neuronal positioning in the developing brain. The cell autonomous deficit in migration is associated with abnormal dynamics of leading processes and centrosomes. Furthermore, microtubule stability is severely damaged in neurons lacking MACF1, resulting in abnormal microtubule dynamics. Finally, MACF1 interacts with and mediates GSK-3 signaling in developing neurons. Our findings establish a cellular mechanism underlying neuronal migration and provide insights into the regulation of cytoskeleton dynamics in developing neurons.     

Supersize me—new insights into cortical expansion and gyration of the mammalian brain

EMBO J 32 13, 1817–1828 doi:10.1038/emboj.2013.96; published online April262013During evolution, the mammalian brain massively expanded its size. However, the exact roles of distinct neural precursors, identified in the developing cortex during embryogenesis, for size expansion and surface folding (i.e., gyration) remain largely unknown. New findings by Nonaka-Kinoshita et al advance our understanding of embryonic neural precursor function by identifying cell type-selective functions for size expansion and folding, and challenge previously held concepts of mammalian brain development.Over the course of evolution, the mammalian brain massively expanded its size and complexity, which is believed to be responsible for an increase in cognitive functions and intellectual skills. The increase in brain size and number of cortical neurons is primarily due to an increased surface area by generating folds (gyrations) while the cortical thickness remained relatively constant (Lui et al, 2011). In the last decade, substantial progress has been made in identifying the cellular sources of cortex development. Using genetic lineage tracing of individual cell populations and time-lapse imaging of rodent and human slices of the embryonic cortex, radial glial cells (RGCs) were identified as the primary progenitors or neural stem cells (NSCs) in the developing cortex (Gotz and Huttner, 2005). Simplified, RG in the ventricular zone (VZ) line the ventricular surface and self-renew through symmetric divisions or give rise to basal progenitors (BPs; also called intermediate progenitors) in the subventricular zone (SVZ) that typically divide symmetrically and generate neurons. In contrast to the lissencephalic rodent brain, the developing cortex of gyrated mammals (e.g., humans and ferrets) contains a large number of basal radial glial (bRG) cells that reside in the outer subventricular zone (OSVZ), retain a cellular process that is connected to the pial surface and that are, in contrast to BPs, multipotent, meaning that they have the potency to generate diverse neural cell types (Fietz et al, 2010; Hansen et al, 2010; Reillo et al, 2011).Largely based on the anatomical differences between the developing cortex of lissencephalic and gyrencephalic brains, several hypotheses have been formulated aiming to explain the massive increase in size and induction of brain folding during mammalian evolution. One prominent hypothesis, called the radial unit hypothesis, suggests that the expansion of RGCs lining the ventricle leads to an increase of radial units that generate neurons and thus is responsible for the increase of surface area (Rakic, 1995). Others proposed that the increase in size and folding could be due to an increase in BP expansion in the SVZ compared to RGC numbers in the VZ, a hypothesis called the intermediate progenitor model (Kriegstein et al, 2006). These hypotheses were helpful to start explaining mammalian brain evolution, but testing the exact role of different neural precursors remained extremely challenging due to technical difficulties to selectively manipulating the proliferative activity of distinct precursor populations. Even though previous approaches were successful in enhancing brain size/neuron numbers in mouse models (e.g., by ectopically enhancing WNT signalling activity or manipulating the activity of the small RhoGTPase Cdc42 in neural precursors), these strategies had the drawback that the normal six-layered cortical topography was disrupted, making it difficult to draw definite conclusions (Chenn and Walsh, 2002; Cappello et al, 2006).In a collaborative work from the Calegari and Borrell laboratories, Nonaka-Kinoshita et al, 2013 now used an elegant approach to selectively enhance proliferation of distinct precursor populations in the mouse and ferret developing cortex. They used a previously described approach manipulating cell cycle length and subsequently proliferation by overexpressing the cell cycle regulators cdk4 and cyclinD1 that is sufficient to enhance neurogenesis without affecting cortical layering (a system called 4D) (Lange et al, 2009). For their mouse experiments, Nonaka-Kinoshita et al used a transgenic strategy to transiently overexpress 4D in nestin-expressing precursors using a tetracycline-controlled gene expression system (nestin^rtTA/tetbi^4D). With this approach, they selectively enhanced proliferation of BPs in the SVZ without affecting the number or proliferation of RGCs in the VZ (Nonaka-Kinoshita et al, 2013). Strikingly, targeted expansion of BPs induced a substantial increase in surface area but was not sufficient to induce cortical folding in the otherwise smooth mouse cortex, challenging the radial unit hypothesis and the intermediate progenitor model with regard to their predictions on the effects on size and/or gyration of the cortex upon expansion of the BP pool. Complementing their findings of BP expansion in the lissencephalic mouse brain, Nonaka-Kinoshita et al used retroviral vectors and electroporation of 4D expression constructs to target 4D expression to neural precursors in the developing ferret cortex that is gyrated under physiological conditions. In the ferret, 4D expression induced proliferation of multipotent bRG located in the OSVZ, as outlined above, a cell type that is found predominantly in gyrated cortices compared to lissencephalic brains. Notably, enhanced proliferation of bRG triggered the formation of novel cortical folds, suggesting that indeed the expansion of bRG may represent a key event during evolution to induce gyration and subsequent surface expansion of the mammalian brain (Borrell and Reillo, 2012; Nonaka-Kinoshita et al, 2013) (Figure 1). This now experimentally supported hypothesis is strongly reinforced by two recent publications: one from (Tuoc et al, 2013) who found that deletion of the chromatin remodelling protein BAF170 increases the BP pool and subsequently enhances brain size; and another one from the Götz laboratory where it was found that experimentally reduced expression levels of the DNA-associated protein Trnp1 substantially increased the expansion of bRG and BPs, inducing folding of the normally lissencephalic mouse brain (Stahl et al, 2013). Taken together, these studies suggest that bRG in the OSVZ play an important role in cortical folding by enhancing the generation of neurons and by providing a glial scaffold for newborn neurons to disperse more laterally and thus to form folds in the developing brain (Reillo et al, 2011).Open in a separate windowFigure 1How different neural precursors appear to regulate size expansion and folding during mammalian brain development. (A) Shown are the main cellular components of the cortex of the lissencephalic mouse brain during embryonic development with RGCs (blue) lining the lateral ventricles in the VZ that generate BPs (yellow) in the SVZ and provide a scaffold for migrating neurons (left; green). Note that the mouse developing brain contains only a few bRG in the OSVZ (red). Notably, expansion of BPs using the 4D strategy developed in the Calegari laboratory increases surface area of the murine cortex without inducing the folding of the smooth mouse brain surface (right panel). (B) In contrast to lissencephalic animals, the developing cortices of species with gyrated brains (e.g., humans and ferrets) contain a substantial number of bRG located in the OSVZ (left panel). 4D-based, virus-mediated expansion of bRG in the ferret cortex leads to the induction of additional folds in the ferret cortex, indicating that the proliferative activity of bRG is critically involved in the extent of folding in physiologically gyrated brains (right panel).Even though this new study challenges previously held concepts regarding size expansion and folding of the mammalian brain, future studies are required that even more selectively enhance the proliferation and expansion of distinct precursor subtypes with high temporal and spatial control. Thus, the combination of sophisticated genetic tools to enhance precursor activity with detailed molecular analyses (e.g., analysing gene expression in highly folded versus unfolded brain regions, an approach that already showed differential levels of Trnp1 expression; Stahl et al, 2013) and live-imaging studies in the developing mammalian cortex will further enhance the understanding how our brains developed during evolution.     

C3G/Rapgef1 Is Required in Multipolar Neurons for the Transition to a Bipolar Morphology during Cortical Development

The establishment of a polarized morphology is essential for the development and function of neurons. During the development of the mammalian neocortex, neurons arise in the ventricular zone (VZ) from radial glia cells (RGCs) and leave the VZ to generate the cortical plate (CP). During their migration, newborn neurons first assume a multipolar morphology in the subventricular zone (SVZ) and lower intermediate zone (IZ). Subsequently, they undergo a multi-to-bipolar (MTB) transition to become bipolar in the upper IZ by developing a leading process and a trailing axon. The small GTPases Rap1A and Rap1B act as master regulators of neural cell polarity in the developing mouse neocortex. They are required for maintaining the polarity of RGCs and directing the MTB transition of multipolar neurons. Here we show that the Rap1 guanine nucleotide exchange factor (GEF) C3G (encoded by the Rapgef1 gene) is a crucial regulator of the MTB transition in vivo by conditionally inactivating the Rapgef1 gene in the developing mouse cortex at different time points during neuronal development. Inactivation of C3G results in defects in neuronal migration, axon formation and cortical lamination. Live cell imaging shows that C3G is required in cortical neurons for both the specification of an axon and the initiation of radial migration by forming a leading process.     

Reelin is essential for neuronal migration but not for radial glial elongation in neonatal ferret cortex

Numerous functions related to neuronal migration are linked to the glycoprotein reelin. Reelin also elongates radial glia, which are disrupted in mutant reeler mice. Our lab developed a model of cortical dysplasia in ferrets that shares features with the reeler mouse, including impaired migration of neurons into the cerebral cortex and disrupted radial glia. Explants of normal ferret cortex in coculture with dysplastic ferret cortex restore the deficits in this model. To determine if reelin is integral to the repair, we used explants of P0 mouse cortex either of the wild type (WT) or heterozygous (het) for the reelin gene, as well as P0 reeler cortex (not containing reelin), in coculture with organotypic cultures of dysplastic ferret cortex. This arrangement revealed that all types of mouse cortical explants (WT, het, reeler) elongated radial glia in ferret cortical dysplasia, indicating that reelin is not required for proper radial glial morphology. Migration of cells into ferret neocortex, however, did not improve with explants of reeler cortex, but was almost normal after pairing with WT or het explants. We also placed an exogenous source of reelin in ferret cultures at the pial surface to reveal that migrating cells move toward the reelin source in dysplastic cortex; radial glia in these cultures were also improved toward normal. Our results demonstrate that the normotopic position of reelin is important for proper neuronal positioning, and that reelin is capable of elongating radial glial cells but is not the only radialization factor.     

Cortical deficiency of laminin γ1 impairs the AKT/GSK-3β signaling pathway and leads to defects in neurite outgrowth and neuronal migration

Laminins have dramatic and varied actions on neurons in vitro. However, their in vivo function in brain development is not clear. Here we show that knockout of laminin γ1 in the cerebral cortex leads to defects in neuritogenesis and neuronal migration. In the mutant mice, cortical layer structures were disrupted, and axonal pathfinding was impaired. During development, loss of laminin expression impaired phosphorylation of FAK and paxillin, indicating defects in integrin signaling pathways. Moreover, both phosphorylation and protein levels of GSK-3β were significantly decreased, but only phosphorylation of AKT was affected in the mutant cortex. Knockout of laminin γ1 expression in vitro, dramatically inhibited neurite growth. These results indicate that laminin regulates neurite growth and neuronal migration via integrin signaling through the AKT/GSK-3β pathway, and thus reveal a novel mechanism of laminin function in brain development.     

PEA15 loss of function and defective cerebral development in the domestic cat

Cerebral cortical size and organization are critical features of neurodevelopment and human evolution, for which genetic investigation in model organisms can provide insight into developmental mechanisms and the causes of cerebral malformations. However, some abnormalities in cerebral cortical proliferation and folding are challenging to study in laboratory mice due to the absence of gyri and sulci in rodents. We report an autosomal recessive allele in domestic cats associated with impaired cerebral cortical expansion and folding, giving rise to a smooth, lissencephalic brain, and that appears to be caused by homozygosity for a frameshift in PEA15 (phosphoprotein expressed in astrocytes-15). Notably, previous studies of a Pea15 targeted mutation in mice did not reveal structural brain abnormalities. Affected cats, however, present with a non-progressive hypermetric gait and tremors, develop dissociative behavioral defects and aggression with age, and exhibit profound malformation of the cerebrum, with a 45% average decrease in overall brain weight, and reduction or absence of the ectosylvian, sylvian and anterior cingulate gyrus. Histologically, the cerebral cortical layers are disorganized, there is substantial loss of white matter in tracts such as the corona radiata and internal capsule, but the cerebellum is relatively spared. RNA-seq and immunohistochemical analysis reveal astrocytosis. Fibroblasts cultured from affected cats exhibit increased TNFα-mediated apoptosis, and increased FGFb-induced proliferation, consistent with previous studies implicating PEA15 as an intracellular adapter protein, and suggesting an underlying pathophysiology in which increased death of neurons accompanied by increased proliferation of astrocytes gives rise to abnormal organization of neuronal layers and loss of white matter. Taken together, our work points to a new role for PEA15 in development of a complex cerebral cortex that is only apparent in gyrencephalic species.

SummaryGyrification is the neurodevelopmental process in certain mammalian species during which the cerebral cortex expands and folds resulting in the classic wrinkled appearance of the brain. Abnormalities in this process underlie many congenital malformations of the brain. However, unlike many other human malformations, genetic insight into gyrification is not possible in laboratory mice because rodents have a lissencephalic or smooth cerebral cortex. We identified a pathogenic variant in domestic cats that likely causes failure of the cerebral cortex to expand and fold properly, and discovered that the pathogenic variant impairs production of a protein, PEA15 (phosphoprotein expressed in astrocytes-15), involved in intracellular signaling. Affected cats have profound abnormalities in brain development, with minimal changes in their superficial behavior and neurologic function. Additional studies of tissue and cultured cells from affected animals suggest a pathophysiologic mechanism in which increased death of neurons accompanied by increased cell division of astrocytes gives rise to abnormal organization of neuronal layers and loss of white matter. These results provide new insight into a developmental process that is unique to animals with gyrencephalic brains.     

Oscillation of Cdc20–APC/C–mediated CAMDI stability is critical for cortical neuron migration

Radial migration during cortical development is required for formation of the six-layered structure of the mammalian cortex. Defective migration of neurons is linked to several developmental disorders such as autism and schizophrenia. A unique swollen structure called the dilation is formed in migrating neurons and is required for movement of the centrosome and nucleus. However, the detailed molecular mechanism by which this dilation forms is unclear. We report that CAMDI, a gene whose deletion is associated with psychiatric behavior, is degraded by cell division cycle protein 20 (Cdc20)–anaphase-promoting complex/cyclosome (APC/C) cell-cycle machinery after centrosome migration into the dilation in mouse brain development. We also show that CAMDI is restabilized in the dilation until the centrosome enters the dilation, at which point it is once again immediately destabilized. CAMDI degradation is carried out by binding to Cdc20–APC/C via the destruction box degron of CAMDI. CAMDI destruction box mutant overexpression inhibits dilation formation and neuronal cell migration via maintaining the stabilized state of CAMDI. These results indicate that CAMDI is a substrate of the Cdc20–APC/C system and that the oscillatory regulation of CAMDI protein correlates with dilation formation for proper cortical migration.     

Cortical Folding of the Primate Brain: An Interdisciplinary Examination of the Genetic Architecture,Modularity, and Evolvability of a Significant Neurological Trait in Pedigreed Baboons (Genus Papio)

Folding of the primate brain cortex allows for improved neural processing power by increasing cortical surface area for the allocation of neurons. The arrangement of folds (sulci) and ridges (gyri) across the cerebral cortex is thought to reflect the underlying neural network. Gyrification, an adaptive trait with a unique evolutionary history, is affected by genetic factors different from those affecting brain volume. Using a large pedigreed population of ∼1000 Papio baboons, we address critical questions about the genetic architecture of primate brain folding, the interplay between genetics, brain anatomy, development, patterns of cortical–cortical connectivity, and gyrification’s potential for future evolution. Through Mantel testing and cluster analyses, we find that the baboon cortex is quite evolvable, with high integration between the genotype and phenotype. We further find significantly similar partitioning of variation between cortical development, anatomy, and connectivity, supporting the predictions of tension-based models for sulcal development. We identify a significant, moderate degree of genetic control over variation in sulcal length, with gyrus-shape features being more susceptible to environmental effects. Finally, through QTL mapping, we identify novel chromosomal regions affecting variation in brain folding. The most significant QTL contain compelling candidate genes, including gene clusters associated with Williams and Down syndromes. The QTL distribution suggests a complex genetic architecture for gyrification with both polygeny and pleiotropy. Our results provide a solid preliminary characterization of the genetic basis of primate brain folding, a unique and biomedically relevant phenotype with significant implications in primate brain evolution.     

A new method to measure cortical growth in the developing brain

Folding of the cerebral cortex is a critical phase of brain development in higher mammals but the biomechanics of folding remain incompletely understood. During folding, the growth of the cortical surface is heterogeneous and anisotropic. We developed and applied a new technique to measure spatial and directional variations in surface growth from longitudinal magnetic resonance imaging (MRI) studies of a single animal or human subject. MRI provides high resolution 3D image volumes of the brain at different stages of development. Surface representations of the cerebral cortex are obtained by segmentation of these volumes. Estimation of local surface growth between two times requires establishment of a point-to-point correspondence ("registration") between surfaces measured at those times. Here we present a novel approach for the registration of two surfaces in which an energy function is minimized by solving a partial differential equation on a spherical surface. The energy function includes a strain-energy term due to distortion and an "error energy" term due to mismatch between surface features. This algorithm, implemented with the finite element method, brings surface features into approximate alignment while minimizing deformation in regions without explicit matching criteria. The method was validated by application to three simulated test cases and applied to characterize growth of the ferret cortex during folding. Cortical surfaces were created from MRI data acquired in vivo at 14 days, 21 days, and 28 days of life. Deformation gradient and Lagrangian strain tensors describe the kinematics of growth over this interval. These quantitative results illuminate the spatial, temporal, and directional patterns of growth during cortical folding.