PlexinD1 signaling controls morphological changes and migration termination in newborn neurons

Newborn neurons maintain a very simple, bipolar shape, while they migrate from their birthplace toward their destinations in the brain, where they differentiate into mature neurons with complex dendritic morphologies. Here, we report a mechanism by which the termination of neuronal migration is maintained in the postnatal olfactory bulb (OB). During neuronal deceleration in the OB, newborn neurons transiently extend a protrusion from the proximal part of their leading process in the resting phase, which we refer to as a filopodium‐like lateral protrusion (FLP). The FLP formation is induced by PlexinD1 downregulation and local Rac1 activation, which coincide with microtubule reorganization and the pausing of somal translocation. The somal translocation of resting neurons is suppressed by microtubule polymerization within the FLP. The timing of neuronal migration termination, controlled by Sema3E‐PlexinD1‐Rac1 signaling, influences the final positioning, dendritic patterns, and functions of the neurons in the OB. These results suggest that PlexinD1 signaling controls FLP formation and the termination of neuronal migration through a precise control of microtubule dynamics.     

Reelin induces EphB activation

The integration of newborn neurons into functional neuronal networks requires migration of cells to their final position in the developing brain, the growth and arborization of neuronal processes and the formation of synaptic contacts with other neurons. A central player among the signals that coordinate this complex sequence of differentiation events is the secreted glycoprotein Reelin, which also modulates synaptic plasticity, learning and memory formation in the adult brain. Binding of Reelin to ApoER2 and VLDL receptor, two members of the LDL receptor family, initiates a signaling cascade involving tyrosine phosphorylation of the intracellular cytoplasmic adaptor protein Disabled-1, which targets the neuronal cytoskeleton and ultimately controls the positioning of neurons throughout the developing brain. However, it is possible that Reelin signals interact with other receptor-mediated signaling cascades to regulate different aspects of brain development and plasticity. EphB tyrosine kinases regulate cell adhesion and repulsion-dependent processes via bidirectional signaling through ephrin B transmembrane proteins. Here, we demonstrate that Reelin binds to the extracellular domains of EphB transmembrane proteins, inducing receptor clustering and activation of EphB forward signaling in neurons, independently of the ''classical'' Reelin receptors, ApoER2 and VLDLR. Accordingly, mice lacking EphB1 and EphB2 display a positioning defect of CA3 hippocampal pyramidal neurons, similar to that in Reelin-deficient mice, and this cell migration defect depends on the kinase activity of EphB proteins. Together, our data provide biochemical and functional evidence for signal integration between Reelin and EphB forward signaling.     

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.     

Inhibition of Wnt and PI3K Signaling Modulates GSK-3β Activity and Induces Morphological Changes in Cortical Neurons: Role of Tau Phosphorylation

Glycogen synthase kinase GSK-3β has been identified as one of the major candidates mediating tau hyperphosphorylation at the same sites as those present in tau protein in brain from Alzheimer′s disease (AD) patients. However, the signal transduction pathways involved in the abnormal activation of GSK-3β, have not been completely elucidated. GSK-3β activity is repressed by the canonical Wnt signaling pathway, but it is also modulated through the PI3K/Akt route. Recent studies have suggested that Wnt signaling might be involved in the pathophysiology of AD. On the other hand, modulators of the PI3K pathway might be reduced during aging leading to a sustained activation of GSK-3β, which in turn would increase the risk of tau hyperphosphorylation. The role of Wnt and PI3K signaling inhibition on the extent of tau phosphorylation and neuronal morphology has not been completely elucidated. Thus, in the present investigation we analyzed the effects of different negative modulators of the Wnt and the PI3K pathways on GSK-3β activation and phosphorylation of tau at the PHF-1 epitope in cortical cultured neurons and hippocampal slices from adult rat brain. Changes in the microtubule network were also studied. We found that a variety of Wnt and PI3K inhibitors, significantly increased tau phosphorylation at the PHF-1 site, induced the disarrangement of the microtubule network and the accumulation of tau within cell bodies. These changes correlated with alterations in neuronal morphology. Special issue article in honor of Dr. Ricardo Tapia.     

The in vivo roles of STEF/Tiam1, Rac1 and JNK in cortical neuronal migration

The coordinated migration of neurons is a pivotal step for functional architectural formation of the mammalian brain. To elucidate its molecular mechanism, gene transfer by means of in utero electroporation was applied in the developing murine brain, revealing the crucial roles of Rac1, its activators, STEF/Tiam1, and its downstream molecule, c-Jun N-terminal kinase (JNK), in the cerebral cortex. Functional repression of these molecules resulted in inhibition of radial migration of neurons without affecting their proper differentiation. Interestingly, distinct morphological phenotypes were observed; suppression of Rac1 activity caused loss of the leading process, whereas repression of JNK activity did not, suggesting the complexity of the signaling cascade. In cultured neurons from the intermediate zone, activated JNK was detected along microtubules in the processes. Application of a JNK inhibitor caused irregular morphology and increased stable microtubules in processes, and decreased phosphorylation of microtubule associated protein 1B, raising a possibility of the involvement of JNK in controlling tubulin dynamics in migrating neurons. Our data thus provide important clues for understanding the intracellullar signaling machinery for cortical neuronal migration.     

Disabled-1-regulated adhesion of migrating neurons to radial glial fiber contributes to neuronal positioning during early corticogenesis

Disabled-1 regulates laminar organization in the developing mammalian brain. Although mutation of the disabled-1 gene in scrambler mice results in abnormalities in neuronal positioning, migratory behavior linked to Disabled-1 signaling is not completely understood. Here we show that newborn neurons in the scrambler cortex remain attached to the process of their parental radial glia during the entire course of radial migration, whereas wild-type neurons detach from the glial fiber in the later stage of migration. This abnormal neuronal-glial adhesion is highly linked to the positional abnormality of scrambler neurons and depends intrinsically on Disabled-1 Tyr220 and Tyr232, potential phosphorylation sites during corticogenesis. Importantly, phosphorylation at those sites regulates alpha3 integrin levels, which is critical for the timely detachment of migrating neurons from radial glia. Altogether, these results outline the molecular mechanism by which Disabled-1 signaling controls the adhesive property of neurons to radial glia, thereby maintaining proper neuronal positioning during corticogenesis.     

BPAG1a and b Associate with EB1 and EB3 and Modulate Vesicular Transport,Golgi Apparatus Structure,and Cell Migration in C2.7 Myoblasts

BPAG1a and BPAG1b (BPAG1a/b) constitute two major isoforms encoded by the dystonin (Dst) gene and show homology with MACF1a and MACF1b. These proteins are members of the plakin family, giant multi-modular proteins able to connect the intermediate filament, microtubule and microfilament cytoskeletal networks with each other and to distinct cell membrane sites. They also serve as scaffolds for signaling proteins that modulate cytoskeletal dynamics. To gain better insights into the functions of BPAG1a/b, we further characterized their C-terminal region important for their interaction with microtubules and assessed the role of these isoforms in the cytoskeletal organization of C2.7 myoblast cells. Our results show that alternative splicing does not only occur at the 5′ end of Dst and Macf1 pre-mRNAs, as previously reported, but also at their 3′ end, resulting in expression of additional four mRNA variants of BPAG1 and MACF1. These isoform-specific C-tails were able to bundle microtubules and bound to both EB1 and EB3, two microtubule plus end proteins. In the C2.7 cell line, knockdown of BPAG1a/b had no major effect on the organization of the microtubule and microfilament networks, but negatively affected endocytosis and maintenance of the Golgi apparatus structure, which became dispersed. Finally, knockdown of BPAG1a/b caused a specific decrease in the directness of cell migration, but did not impair initial cell adhesion. These data provide novel insights into the complexity of alternative splicing of Dst pre-mRNAs and into the role of BPAG1a/b in vesicular transport, Golgi apparatus structure as well as in migration in C2.7 myoblasts.     

Ndel1 operates in a common pathway with LIS1 and cytoplasmic dynein to regulate cortical neuronal positioning

Correct neuronal migration and positioning during cortical development are essential for proper brain function. Mutations of the LIS1 gene result in human lissencephaly (smooth brain), which features misplaced cortical neurons and disarrayed cerebral lamination. However, the mechanism by which LIS1 regulates neuronal migration remains unknown. Using RNA interference (RNAi), we found that the binding partner of LIS1, NudE-like protein (Ndel1, formerly known as NUDEL), positively regulates dynein activity by facilitating the interaction between LIS1 and dynein. Loss of function of Ndel1, LIS1, or dynein in developing neocortex impairs neuronal positioning and causes the uncoupling of the centrosome and nucleus. Overexpression of LIS1 partially rescues the positioning defect caused by Ndel1 RNAi but not dynein RNAi, whereas overexpression of Ndel1 does not rescue the phenotype induced by LIS1 RNAi. These results provide strong evidence that Ndel1 interacts with LIS1 to sustain the function of dynein, which in turn impacts microtubule organization, nuclear translocation, and neuronal positioning.     

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.     

Reelin promotes microtubule dynamics in processes of developing neurons

The extracellular matrix protein reelin controls radial migration and layer formation of cortical neurons, in part by modulation of cytoskeletal dynamics. A stabilizing effect of reelin on the actin cytoskeleton has been described recently. However, it is poorly understood how reelin modulates microtubule dynamics. Here, we provide evidence that reelin increases microtubule assembly. This effect is mediated, at least in part, by promoting microtubule plus end dynamics in processes of developing neurons. Thus, we treated primary neuronal cultures with nocodazole to disrupt microtubules. After nocodazole washout, we found microtubule reassembly to be accelerated in the presence of reelin. Moreover, we show that reelin treatment promoted the formation of microtubule plus end binding protein 3 (EB3) comets in developing dendrites, and that EB3 immunostaining in the developing wild-type neocortex is most intense in the reelin-rich marginal zone where leading processes of radially migrating neurons project to. This characteristic EB3 staining pattern was absent in reeler. Also reassembly of nocodazole-dispersed dendritic Golgi apparati, which are closely associated to microtubules, was accelerated by reelin treatment, though with a substantially slower time course when compared to microtubule reassembly. In support of our in vitro results, we found that the subcellular distribution of α-tubulin and acetylated tubulin in reeler cortical sections differed from wild-type and from mice lacking the very low density lipoprotein receptor (VLDLR), known to bind reelin. Taken together, our results suggest that reelin promotes microtubule assembly, at least in part, by increasing microtubule plus end dynamics.     

Neuronal pentraxin 1 induction in hypoxic-ischemic neuronal death is regulated via a glycogen synthase kinase-3α/β dependent mechanism

Intracellular signaling pathways that regulate the production of lethal proteins in central neurons are not fully characterized. Previously, we reported induction of a novel neuronal protein neuronal pentraxin 1 (NP1) in neonatal brain injury following hypoxia-ischemia (HI); however, how NP1 is induced in hypoxic-ischemic neuronal death remains elusive. Here, we have elucidated the intracellular signaling regulation of NP1 induction in neuronal death. Primary cortical neurons showed a hypoxic-ischemia time-dependent increase in cell death and that NP1 induction preceded the actual neuronal death. NP1 gene silencing by NP1-specific siRNA significantly reduced neuronal death. The specificity of NP1 induction in neuronal death was further confirmed by using NP1 (−/−) null primary cortical neurons. Declines in phospho-Akt (i.e. deactivation) were observed concurrent with decreased phosphorylation of its downstream substrate GSK-3α/β (at Ser21/Ser9) (i.e. activation) and increased GSK-3α and GSK-3β kinase activities, which occurred prior to NP1 induction. Expression of a dominant-negative inhibitor of Akt (Akt-kd) blocked phosphorylation of GSK-3α/β and subsequently enhanced NP1 induction. Whereas, overexpression of constitutively activated Akt (Akt-myr) or wild-type Akt (wtAkt) increased GSK-α/β phosphorylation and attenuated NP1 induction. Transfection of neurons with GSK-3α siRNA completely blocked NP1 induction and cell death. Similarly, overexpression of the GSK-3β inhibitor Frat1 or the kinase mutant GSK-3βKM, but not the wild-type GSK-3βWT, blocked NP1 induction and rescued neurons from death. Our findings clearly implicate both GSK-3α- and GSK-3β-dependent mechanism of NP1 induction and point to a novel mechanism in the regulation of hypoxic-ischemic neuronal death.     

DCX, a new mediator of the JNK pathway

Mutations in the X-linked gene DCX result in lissencephaly in males, and abnormal neuronal positioning in females, suggesting a role for this gene product during neuronal migration. In spite of several known protein interactions, the involvement of DCX in a signaling pathway is still elusive. Here we demonstrate that DCX is a substrate of JNK and interacts with both c-Jun N-terminal kinase (JNK) and JNK interacting protein (JIP). The localization of this signaling module in the developing brain suggests its functionality in migrating neurons. The localization of DCX at neurite tips is determined by its interaction with JIP and by the interaction of the latter with kinesin. DCX is phosphorylated by JNK in growth cones. DCX mutated in sites phosphorylated by JNK affected neurite outgrowth, and the velocity and relative pause time of migrating neurons. We hypothesize that during neuronal migration, there is a need to regulate molecular motors that are working in the cell in opposite directions: kinesin (a plus-end directed molecular motor) versus dynein (a minus-end directed molecular motor).     

Dishevelled-1 regulates microtubule stability: a new function mediated by glycogen synthase kinase-3beta

Dishevelled has been implicated in the regulation of cell fate decisions, cell polarity, and neuronal function. However, the mechanism of Dishevelled action remains poorly understood. Here we examine the cellular localization and function of the mouse Dishevelled protein, DVL-1. Endogenous DVL-1 colocalizes with axonal microtubules and sediments with brain microtubules. Expression of DVL-1 protects stable microtubules from depolymerization by nocodazole in both dividing cells and differentiated neuroblastoma cells. Deletion analyses reveal that the PDZ domain, but not the DEP domain, of DVL-1 is required for microtubule stabilization. The microtubule stabilizing function of DVL-1 is mimicked by lithium-mediated inhibition of glycogen synthase kinase-3beta (GSK-3beta) and blocked by expression of GSK-3beta. These findings suggest that DVL-1, through GSK-3beta, can regulate microtubule dynamics. This new function of DVL-1 in controlling microtubule stability may have important implications for Dishevelled proteins in regulating cell polarity.     

Neuronal migration and the role of reelin during early development of the cerebral cortex

During development, neurons migrate to the cortex radially from periventricular germinative zones as well as tangentially from ganglionic eminences. The vast majority of cortical neurons settle radially in the cortical plate. Neuronal migration requires an exquisite regulation of leading edge extension, nuclear translocation (nucleokinesis), and retraction of trailing processes. During the past few years, several genes and proteins have been identified that are implicated in neuronal migration. Many have been characterized by reference to known mechanisms of neuronal and non-neuronal cell migration in culture; however, probably the most interesting have been identified by gene inactivation or modification in mice and by positional cloning of brain malformation genes in humans and mice. Although it is impossible to provide a fully integrated view, some patterns clearly emerge and are the subject of this article. Specific emphasis is placed on three aspects: first, the role of the actin treadmill, with cyclic formation of filopodial and lamellipodial extensions, in relation to surface events that occur at the leading edge of radially migrating neurons; second, the regulation of microtubule dynamics, which seems to play a key role in nucleokinesis; and third, the mechanisms by which the extracellular protein Reelin regulates neuronal positioning at the end of migration.     

NMDA receptor regulates migration of newly generated neurons in the adult hippocampus via Disrupted-In-Schizophrenia 1 (DISC1)

In the mammalian brain, new neurons are continuously generated throughout life in the dentate gyrus (DG) of the hippocampus. Previous studies have established that newborn neurons migrate a short distance to be integrated into a pre-existing neuronal circuit in the hippocampus. How the migration of newborn neurons is governed by extracellular signals, however, has not been fully understood. Here, we report that NMDA receptor (NMDA-R)-mediated signaling is essential for the proper migration and positioning of newborn neurons in the DG. An intraperitoneal injection of the NMDA-R antagonists, memantine, or 3-(2-carboxypiperazin-4-yl)propyl-1-phosphonic acid (CPP) into adult male mice caused the aberrant positioning of newborn neurons, resulting in the overextension of their migration in the DG. Interestingly, we revealed that the administration of NMDA-R antagonists leads to a decrease in the expression of Disrupted-In-Schizophrenia 1 (DISC1), a candidate susceptibility gene for major psychiatric disorders such as schizophrenia, which is also known as a critical regulator of neuronal migration in the DG. Furthermore, the overextended migration of newborn neurons induced by the NMDA-R antagonists was significantly rescued by exogenous expression of DISC1. Collectively, these results suggest that the NMDA-R signaling pathway governs the migration of newborn neurons via the regulation of DISC1 expression in the DG.     

Phosphorylation of doublecortin by protein kinase A orchestrates microtubule and actin dynamics to promote neuronal progenitor cell migration

Doublecortin (DCX) is a microtubule-associated protein that is specifically expressed in neuronal cells. Genetic mutation of DCX causes lissencephaly disease. Although the abnormal cortical lamination in lissencephaly is thought to be attributable to neuronal cell migration defects, the regulatory mechanisms governing interactions between DCX and cytoskeleton in the migration of neuronal progenitor cells remain obscure. In this study we found that the G(s) and protein kinase A (PKA) signal elicited by pituitary adenylate cyclase-activating polypeptide promotes neuronal progenitor cells migration. Stimulation of G(s)-PKA signaling prevented microtubule bundling and induced the dissociation of DCX from microtubules in cells. PKA phosphorylated DCX at Ser-47, and the phospho-mimicking mutant DCX-S47E promoted cell migration. Activation of PKA and DCX-S47E induced lamellipodium formation. Pituitary adenylate cyclase-activating polypeptide and DCX-S47E stimulated the activation of Rac1, and DCX-S47E interacted with Asef2, a guanine nucleotide exchange factor for Rac1. Our data reveal a dual reciprocal role for DCX phosphorylation in the regulation of microtubule and actin dynamics that is indispensable for proper brain lamination.     

Centrosome positioning and primary cilia assembly orchestrate neuronal development

Establishment of axon and dendrite polarity, migration to a desired location in the developing brain, and establishment of proper synaptic connections are essential processes during neuronal development. The cellular and molecular mechanisms that govern these processes are under intensive investigation. The function of the centrosome in neuronal development has been examined and discussed in few recent studies that underscore the fundamental role of the centrosome in brain development. Clusters of emerging studies have shown that centrosome positioning tightly regulates neuronal development, leading to the segregation of cell factors, directed neurite differentiation, neuronal migration, and synaptic integration. Furthermore, cilia, that arise from the axoneme, a modified centriole, are emerging as new regulatory modules in neuronal development in conjunction with the centrosome. In this review, we focus on summarizing and discussing recent studies on centrosome positioning during neuronal development and also highlight recent findings on the role of cilia in brain development. We further discuss shared molecular signaling pathways that might regulate both centrosome and cilia associated signaling in neuronal development. Furthermore, molecular determinants such as DISC1 and LKB1 have been recently demonstrated to be crucial regulators of various aspects of neuronal development. Strikingly, these determinants might exert their function, at least in part, via the regulation of centrosome and cilia associated signaling and serve as a link between these two signaling centers. We thus include an overview of these molecular determinants.     

A Highlights from MBoC Selection: Global Up-Regulation of Microtubule Dynamics and Polarity Reversal during Regeneration of an Axon from a Dendrite

Axon regeneration is crucial for recovery after trauma to the nervous system. For neurons to recover from complete axon removal they must respecify a dendrite as an axon: a complete reversal of polarity. We show that Drosophila neurons in vivo can convert a dendrite to a regenerating axon and that this process involves rebuilding the entire neuronal microtubule cytoskeleton. Two major microtubule rearrangements are specifically induced by axon and not dendrite removal: 1) 10-fold up-regulation of the number of growing microtubules and 2) microtubule polarity reversal. After one dendrite reverses its microtubules, it initiates tip growth and takes on morphological and molecular characteristics of an axon. Only neurons with a single dendrite that reverses polarity are able to initiate tip growth, and normal microtubule plus-end dynamics are required to initiate this growth. In addition, we find that JNK signaling is required for both the up-regulation of microtubule dynamics and microtubule polarity reversal initiated by axon injury. We conclude that regulation of microtubule dynamics and polarity in response to JNK signaling is key to initiating regeneration of an axon from a dendrite.     

Cdk5 phosphorylation of FAK regulates centrosome-associated miocrotubules and neuronal migration

Cdk5 is a member of the cyclin-dependent kinase (Cdk) family. Unlike other Cdks that promote cell cycle, Cdk5 is activated in postmitotic neurons and critically regulates neuronal migration by phosphorylating its substrates during brain development. Recently, we found that Cdk5 phosphorylates focal adhesion kinase (FAK) at Serine 732 in vitro and is responsible for this phosphorylation in the developing brain. Our experiments using a phospho-specific antibody and an S732-unphosphorylatable mutant FAK suggest that S732 phosphorylation may regulate a centrosome-associated microtubule structure to promote nuclear translocation, a critical step in neuronal migration. S732 phosphorylation does not directly impact on the kinase activity of FAK, but appears to prevent the accumulation of FAK at the centrosome. Our study reveals a similarity between Cdk5 and Cdk1 in the regulation of neuronal migration and cell division, respectively. In addition, our study implicates FAK in a signaling pathway that directly regulates microtubules.     

Laminin/β1 integrin signal triggers axon formation by promoting microtubule assembly and stabilization

Axon specification during neuronal polarization is closely associated with increased microtubule stabilization in one of the neurites of unpolarized neuron, but how this increased microtubule stability is achieved is unclear. Here, we show that extracellular matrix (ECM) component laminin promotes neuronal polarization via regulating directional microtubule assembly through β1 integrin (Itgb1). Contact with laminin coated on culture substrate or polystyrene beads was sufficient for axon specification of undifferentiated neurites in cultured hippocampal neurons and cortical slices. Active Itgb1 was found to be concentrated in laminin-contacting neurites. Axon formation was promoted and abolished by enhancing and attenuating Itgb1 signaling, respectively. Interestingly, laminin contact promoted plus-end microtubule assembly in a manner that required Itgb1. Moreover, stabilizing microtubules partially prevented polarization defects caused by Itgb1 downregulation. Finally, genetic ablation of Itgb1 in dorsal telencephalic progenitors caused deficits in axon development of cortical pyramidal neurons. Thus, laminin/Itgb1 signaling plays an instructive role in axon initiation and growth, both in vitro and in vivo, through the regulation of microtubule assembly. This study has established a linkage between an extrinsic factor and intrinsic cytoskeletal dynamics during neuronal polarization.