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The JNK family of MAPKs is involved in a large variety of physiological and pathological processes in brain development, such as neural survival, migration, and polarity as well as axon regeneration. However, whether JNK activation is involved in axon guidance remains unknown. Here, we provide evidence indicating the JNK pathway is required for Netrin signaling in the developing nervous system. Netrin-1 increased JNK1, not JNK2 or JNK3, activity in the presence of deleted in colorectal cancer (DCC) or Down syndrome cell adhesion molecule (DSCAM), and expression of both of them further enhanced Netrin-1-induced JNK1 activity in vitro. Inhibition of JNK signaling either by a JNK inhibitor, SP600125, or expression of a dominant negative form of MKK4, a JNK upstream activator, blocked Netrin-1-induced JNK1 activation in HEK293 cells. Netrin-1 increased endogenous JNK activity in primary neurons. Netrin-1-induced JNK activation was inhibited either by the JNK inhibitor or an anti-DCC function-blocking antibody. Combination of the anti-DCC function-blocking antibody with expression of DSCAM shRNA in primary neurons totally abolished Netrin-1-induced JNK activation, whereas knockdown of DSCAM partially inhibited the Netrin-1 effect. In the developing spinal cord, phospho-JNK was strongly expressed in commissural axons before and as they crossed the floor plate, and Netrin-1 stimulation dramatically increased the level of endogenous phospho-JNK in commissural axon growth cones. Inhibition of JNK signaling either by JNK1 RNA interference (RNAi) or the JNK inhibitor suppressed Netrin-1-induced neurite outgrowth and axon attraction. Knockdown of JNK1 in ovo caused defects in spinal cord commissural axon projection and pathfinding. Our study reveals that JNK1 is important in the coordination of DCC and DSCAM in Netrin-mediated attractive signaling.  相似文献   

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The netrin axon guidance genes have previously been implicated in fertility in C. elegans and in vertebrates. Here we show that adult Drosophila lacking both netrin genes, NetA and NetB, have fertility defects in both sexes together with an inability to fly and reduced viability. NetAB females produce fertilized eggs at a much lower rate than wild type. Oocyte development and ovarian innervation are unaffected in NetAB females, and the reproductive tract appears normal. A small gene, hog, that resides in an intron of NetB does not contribute to the NetAB phenotype. Restoring endogenous NetB expression rescues egg-laying, but additional genetic manipulations, such as restoration of netrin midline expression and inhibition of cell death have no effect on fertility. NetAB males induce reduced egg-laying in wild type females and display mirror movements of their wings during courtship. Measurement of courtship parameters revealed no difference compared to wild type males. Transgenic manipulations failed to rescue male fertility and mirror movements. Additional genetic manipulations, such as removal of the enabled gene, a known suppressor of the NetAB embryonic CNS phenotype, did not improve the behavioral defects. The ability to fly was rescued by inhibition of neuronal cell death and pan-neural NetA expression. Based on our results we hypothesize that the adult fertility defects of NetAB mutants are due to ovulation defects in females and a failure to properly transfer sperm proteins in males, and are likely to involve multiple neural circuits.  相似文献   

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How axons in the developing nervous system successfully navigate to their correct targets is a fundamental problem in neurobiology. Understanding the mechanisms that mediate axon guidance will give important insight into how the nervous system is correctly wired during development and may have implications for therapeutic approaches to developmental brain disorders and nerve regeneration. Achieving this understanding will require unraveling the molecular logic that ensures the proper expression and localization of axon guidance cues and receptors, and elucidating the signaling events that regulate the growth cone cytoskeleton in response to guidance receptor activation. Studies of axon guidance at the midline of many experimental systems, from the ventral midline of Drosophila to the vertebrate spinal cord, have led to important mechanistic insights into the complex problem of wiring the nervous system. Here we review recent advances in understanding the regulation of midline axon guidance, with a particular emphasis on the contributions made from molecular genetic studies of invertebrate model systems.  相似文献   

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Netrins and their classical receptors - DCC and neogenin - play key roles in neuronal guidance. Recent developments identify new roles for netrins in epithelial and vascular morphogenesis. Netrins accomplish these effects, at least in part, through binding to integrins and/or activating integrin-associated kinases such as FAK and Fyn. Here we discuss these recent findings and propose that integrins and classical netrin receptors cooperate to regulate multiple aspects of development.  相似文献   

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Eph receptors and their ephrin ligands are key conserved regulators of axon guidance and can function in a variety of signaling modes. Here we analyze the genetic and cellular requirements for Eph signaling in a Caenorhabditis elegans axon guidance choice point, the ventral guidance of axons in the amphid commissure. The C. elegans Eph receptor EFN-1 has both kinase-dependent and kinase-independent roles in amphid ventral guidance. Of the four C. elegans ephrins, we find that only EFN-1 has a major role in amphid axon ventral guidance, and signals in both a receptor kinase-dependent and kinase-independent manner. Analysis of EFN-1 and EFN-1 expression and tissue-specific requirements is consistent with a model in which VAB-1 acts in amphid neurons, interacting with EFN-1 expressed on surrounding cells. Unexpectedly, left-hand neurons are more strongly affected than right-hand neurons by loss of Eph signaling, indicating a previously undetected left–right asymmetry in the requirement for Eph signaling. By screening candidate genes involved in Eph signaling, we find that the Eph kinase-independent pathway involves the ABL-1 nonreceptor tyrosine kinase and possibly the phosphatidylinositol 3-kinase pathway. Overexpression of ABL-1 is sufficient to rescue EFN-1 ventral guidance defects cell autonomously. Our results reveal new aspects of Eph signaling in a single axon guidance decision in vivo.  相似文献   

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The regenerative capacity of injured adult mammalian central nervous system (CNS) tissue is very limited. Disease or injury that causes destruction or damage to neuronal networks typically results in permanent neurological deficits. Injury to the spinal cord, for example, interrupts vital ascending and descending fiber tracts of spinally projecting neurons. Because neuronal structures located proximal or distal to the injury site remain largely intact, a major goal of spinal cord injury research is to develop strategies to reestablish innervation lost as a consequence of injury. The growth inhibitory nature of injured adult CNS tissue is a major barrier to regenerative axonal growth and sprouting. An increasing complexity of molecular players is being recognized. CNS inhibitors fall into three general classes: members of canonical axon guidance molecules (e.g., semaphorins, ephrins, netrins), prototypic myelin inhibitors (Nogo, MAG, and OMgp) and chondroitin sulfate proteoglycans (lecticans, NG2). On the other end of the spectrum are molecules that promote neuronal growth and sprouting. These include growth promoting extracellular matrix molecules, cell adhesion molecules, and neurotrophic factors. In addition to environmental (extrinsic) growth regulatory cues, cell intrinsic regulatory mechanisms exist that greatly influence injury-induced neuronal growth. Various degrees of growth and sprouting of injured CNS neurons have been achieved by lowering extrinsic inhibitory cues, increasing extrinsic growth promoting cues, or by activation of cell intrinsic growth programs. More recently, combination therapies that activate growth promoting programs and at the same time attenuate growth inhibitory pathways have met with some success. In experimental animal models of spinal cord injury (SCI), mono and combination therapies have been shown to promote neuronal growth and sprouting. Anatomical growth often correlates with improved behavioral outcomes. Challenges ahead include testing whether some of the most promising treatment strategies in animal models are also beneficial for human patients suffering from SCI.  相似文献   

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Regulation of cell signaling by Wnt proteins is critical for the formation of neuronal circuits. Wnts modulate axon pathfinding, dendritic development, and synaptic assembly. Through different receptors, Wnts activate diverse signaling pathways that lead to local changes on the cytoskeleton or global cellular changes involving nuclear function. Recently, a link between neuronal activity, essential for the formation and refinement of neuronal connections, and Wnt signaling has been uncovered. Indeed, neuronal activity regulates the release of Wnt and the localization of their receptors. Wnts mediate synaptic structural changes induced by neuronal activity or experience. New emerging evidence suggests that dysfunction in Wnt signaling contributes to neurological disorders. In this article, the attention is focused on the function of Wnt signaling in the formation of neuronal circuits in the vertebrate central nervous system.The formation of neuronal connections requires the navigation of axons to their appropriate synaptic targets, the formation of terminal branches, and the assembly of functional synapses. These processes greatly depend on the proper dialogue between axons and their environment as they navigate to their target, and between axons and their postsynaptic dendrites during synapse assembly. A combination of secreted molecules and transmembrane proteins modulates these processes. Studies over the last 10 years have revealed an essential role for Wnt signaling in axon pathfinding, dendritic development, and synapse assembly in both central and peripheral nervous systems. Wnts also modulate basal synaptic transmission and the structural and functional plasticity of synapses in the central nervous system. Studies of Wnts in the nervous system have significantly contributed to our current understanding of the molecular mechanisms that control neuronal circuit assembly. These studies have also shed light into fundamental aspects of cell signaling such as novel mechanisms of protein secretion (Korkut et al. 2009) and receptor dynamics (Sahores et al. 2010). Here I review the mechanisms by which Wnts modulate axon guidance and synapse formation in the vertebrate central nervous system. I also discuss the increasing evidence in support for a role of Wnts in basal synaptic transmission, synaptic plasticity, and neurological disorders.  相似文献   

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How extracellular molecules influence the direction of axon guidance is poorly understood. The HSN axon of Caenorhabditis elegans is guided towards a ventral source of secreted UNC-6 (netrin). The axon’s outgrowth response to UNC-6 is mediated by the UNC-40 (DCC) receptor. We have proposed that in response to the UNC-6 molecule the direction of UNC-40-mediated axon outgrowth is stochastically determined. The direction of guidance is controlled by asymmetric cues, including the gradient of UNC-6, that regulate the probability that UNC-40-mediated axon outgrowth is directed on average, over time, in a specific direction. Here we provide genetic evidence that a specialized extracellular matrix, which lies ventral to the HSN cell body, regulates the probability that UNC-40-mediated axon outgrowth will be directed ventrally towards the matrix. We show that mutations that disrupt the function of proteins associated with this matrix, UNC-52 (perlecan), UNC-112 (kindlin), VAB-19 (Kank), and UNC-97 (PINCH), decrease the probability of UNC-40-mediated axon outgrowth in the ventral direction, while increasing the probability of outgrowth in the anterior and posterior directions. Other results suggest that INA-1 (α integrin) and MIG-15 (NIK kinase) signaling mediate the response in HSN. Although the AVM axon also migrates through this matrix, the mutations have little effect on the direction of AVM axon outgrowth, indicating that responses to the matrix are cell-specific. Together, these results suggest that an extracellular matrix can regulate the direction of UNC-6 guidance by increasing the probability that UNC-40-mediated axon outgrowth activity will be oriented in a specific direction.  相似文献   

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This article reviews symptoms and signs of aberrant axon connectivity in humans, and summarizes major human genetic disorders that result, or have been proposed to result, from defective axon guidance. These include corpus callosum agenesis, L1 syndrome, Joubert syndrome and related disorders, horizontal gaze palsy with progressive scoliosis, Kallmann syndrome, albinism, congenital fibrosis of the extraocular muscles type 1, Duane retraction syndrome, and pontine tegmental cap dysplasia. Genes mutated in these disorders can encode axon growth cone ligands and receptors, downstream signaling molecules, and axon transport motors, as well as proteins without currently recognized roles in axon guidance. Advances in neuroimaging and genetic techniques have the potential to rapidly expand this field, and it is feasible that axon guidance disorders will soon be recognized as a new and significant category of human neurodevelopmental disorders.The human brain is highly organized and contains a myriad of axon tracts that follow precise pathways and make predictable connections. Model organism research has provided tremendous advances in our understanding of the principles and molecules governing axon growth and guidance. Remarkably, however, only a handful of human disorders resulting from primary errors in these processes have been identified.Traditional tools of the physician have limited sensitivity and specificity to detect human disorders of axon guidance. In particular, congenital synkinesis may be the only physical examination finding that has been attributed to such disorders. Synkinesis is the involuntary and pathological contraction of a muscle simultaneously with contraction of the intended muscle, and is typically reported with hand/finger or eye/eyelid movements and confirmed by electrophysiological studies. Mirror movement synkinesis refers to the contraction of homologous hand/finger muscles bilaterally when one attempts to move only one hand (Schott and Wyke 1981). In humans, 75%–90% of corticospinal tract (CST) fibers normally decussate in the lower medulla. Mirror movement synkinesis occurs in several human disorders with pathological, neuroimaging, and/or electrophysiological evidence of reduced CST decussation, including Joubert, Kallmann, and Klippel-Feil syndromes (Vulliemoz et al. 2005; Cincotta and Ziemann 2008). In some individuals with mirror movements, electrophysiological data are also consistent with bilateral engagement of the motor corticies (Leinsinger et al. 1997). Ocular synkinesis refers to aberrant patterns of eye movement and accompanies various congenital cranial dysinnervation disorders (CCDDs) (Gutowski et al. 2003; Engle 2007), including CFEOM, Duane syndrome, and Marcus Gunn jaw-winking phenomenon (Fig. 1). Finger and ocular movements require precise motor control, and errors in innervation of these muscles may be more easily detected than errors in the wiring of larger muscle groups. If true, this suggests that the clinical exam could fail to recognize many guidance errors in both the peripheral and central nervous system.Open in a separate windowFigure 1.Ocular synkinesis. (A) Child with CFEOM1 and Marcus Gunn jaw-winking phenomenon harboring a KIF21A mutation. His superior branch of the oculomotor nerve is hypoplastic/absent, resulting in bilateral ptosis from lack of appropriate innervation of the levator palpebrae superioris (LPS) muscle, and a downward position of each eye from absent innervation of the superior rectus muscle (left). Marcus Gunn phenomenon (right) is seen as the synkinetic elevation of the left eyelid with a subtle change in jaw position associated with a volitional increase in pterygoid muscle tension. This results from aberrant innervation of the LPS by axons from the motor branch of the trigeminal nerve that also innervates the intended ipsilateral pterygoid muscle. (B) Adult with Duane retraction syndrome harboring a CHN1 mutation. Central gaze reveals mild exotropia (middle). On attempted right gaze (left) and left gaze (right), there is limited horizontal excursion with globe retraction and secondary palpebral fissure narrowing of the adducting eye. Globe retraction results from synkinesis of the medial and lateral recti muscles. (A) Modified with permission from Yamada et al. 2005. Copyright © (2005) American Medial Association. All rights reserved. (B) Modified from Demer et al. 2007. Copyright © (2007) Association for Research in Vision and Ophthalmology. All rights reserved.The physician’s ability to detect disorders of axon guidance has been augmented by classical pathological, radiological, and electrophysiological techniques. Diagnostic radiologic and postmortem neuropathological studies detect overall changes in white matter volume and major abnormalities of axon tracts demarcated from the background such as the corpus callosum, anterior and posterior commissures, optic chiasm, and cerebellar peduncles. Neuropathological studies can also detect absence of axons that normally cross the midline at many points in the brain stem and spinal cord, which are more difficult to visualize by standard magnetic resonance imaging (MRI). Electrophysiological studies such as evoked potentials can reveal aberrant central connections of peripheral sensory or motor nerves.The genetic disorders with aberrant axon connectivity presented in this article have been defined primarily using traditional approaches described above. Exciting advances in neuroimaging and genetics, however, are revolutionizing the ability to define axon guidance disorders, and it is likely that these syndromes are only the first of an important new category of such human neurodevelopmental disorders. Detailed fiber tract anatomy can now be visualized using noninvasive tractography such as diffusion tensor imaging (DTI) and diffusion spectrum imaging (DSI). These techniques provide tract orientation by determining the anisotropic properties of water diffusion, and can be used to reconstruct the trajectories of fiber systems in three-dimensional space (Tovar-Moll et al. 2007; Wahl et al. 2009). Tractography has successfully confirmed aberrant projections in several of the disorders discussed below (Fig. 2). At the same time, human genetics now provides an unbiased approach to identify the etiologies of disorders with aberrant axon tracts. For some syndromes, animal and in vitro studies have confirmed that the encoded protein has a primary role in axon guidance. For others, such studies reveal a primary role in neuronal specification and/or migration rather than, or in addition to, a role in axon guidance. Finally, some neurodevelopmental disorders without clinical, pathologic, or radiologic evidence of aberrant axon tracts have been found to result from mutations in genes that contribute to axon guidance in animal models.Open in a separate windowFigure 2.Tractography studies in patients with partial agenesis of the corpus callosum (pACC). T1-weighted anatomic images and DTI tractography of six subjects with pACC (top panels) and two representative controls (bottom panel). Axial (left) and midline sagittal (middle) T1 sections are shown for each subject. Callosal fragments are identified with yellow arrows, and heterotopic fibers visible on T1-weighted images are denoted by red arrows. Midline sagittal DTI color maps are shown with segmented callosal fibers (right). For subjects with pACC, connectivity ranged from anterior frontal connections (subject 3) to only posterior frontal and occipitotemporal connections (subject 4). One individual (subject 5) displayed a discontinuous set of homotopic callosal connections, with anterior frontal and occipitotemporal connectivity without any posterior frontal or parietal connections. Control subjects (bottom panel) display normal callosal morphology and tractography results. Tracts are segmented and colored according to their cortical projections: homotopic anterior frontal, blue; homotopic posterior frontal, orange; homotopic parietal, pink; homotopic occipitotemporal, green; heterotopic left anterior-right posterior, yellow; heterotopic right anterior-left posterior, red. (Reprinted, with permission, from Wahl et al. 2009 [© AJNR].)The major human genetic disorders that result, or are proposed to result, from defective axon guidance are ordered below from rostral to caudal based on the location of the aberrant axons tracts. These include genetic mutations that alter axon growth cone ligands and receptors, downstream signaling molecules, and axon transport, as well as proteins without currently recognized roles in axon guidance (Fig. 3) (Open in a separate windowFigure 3.Schematic representation of gene products implicated in human disorders of axon guidance. KAL1 (anosmin) and PROK2 are shown as secreted ligands. ROBO3, L1, and PROKR2 are shown as transmembrane receptors on the growth cone. CHN1 is depicted with 3 green domains (SH2, C1, RacGAP), responding to an unknown activated receptor and altering a microtubule, which is depicted as a brown line. KIF21A dimers are depicted walking down MTs. The OCA/OA and JSRD gene products are not depicted. Note: these gene products are not necessarily expressed in the same neurons or function in the same pathways.

Table 1

Summary of major human genetic disorders resulting, or hypothesized to result, from errors in axon growth and guidance
DisorderL1JSRDHGPPSKSAlbinismCFEOM1DRSPTCD
InheritanceX-LARARX-L, ARX-L, ARADADSporadic
Gene(s)L1AHI1
NPHP1
CEP290
TMEM67
RPGRIP1L
ARL13B
CC2D2A
ROBO3KAL1
FGFR1
PROKR2
PROK2
CDH7
FGF8
TYR
OCA2
TYRI1
MATP
KIF21ACHN1
SynkinesisNoOccursNoOccurs (KAL1)NoOccursOccursNo
CC+/− ThinRarely thin
SCPThick, Mal-orientedSmallMal-oriented
SCP-DReduced to AbsentAbsentAbsent
MCPSmallSmall
ICPSmallSmall
CST-PFlatFlat
CST-D+/− ReducedReduced to AbsentAbsentAbnormal (KAL1)
CPT-DReducedAbsentAbsent
CN IAberrant
CN IISmallSmall
CN II-DIncreased
CN IIIAberrant+/− Aberrant
CN IV
CN V
CN VI+/− AberrantAberrant
CN VIISmall
CN VIIISmall
Open in a separate windowKey: X-L, X-linked; AR, autosomal recessive; AD, autosomal dominant; CC, corpus callosum; SCP, superior cerebellar peduncle; SCP-D, SCP midline decussation; MCP, middle cerebellar peduncle; ICP, inferior cerebellar peduncle; CST-P, corticospinal tract pyramids; CST-D, corticospinal tract midline decussation; CPT-D, central pontine tract decussation; CN I, olfactory nerve; CN II, optic nerve; CN II-D, optic chiasm decussation; CN III, oculomotor nerve; CN VI, abducens nerve; CN VII, facial nerve; CN VIII, vestibulocochlear nerve.  相似文献   

14.
Pioneer axons in insect legs are experimentally accessible model systems for the molecular identification and cellular localization of guidance cues regulating the path of axon growth. A detailed study of the Fe2 pioneer axons in the legs of the cockroach was performed to examine the diversity of guidance mechanisms. A detailed microscopic analysis of the axons at various points in their trajectory indicates that the Fe2 axons grow on a mesodermal substratum which contains the cues guiding their growth along a stereotyped path. An identified pair of muscle pioneer cells (MPC) are likely to play an important role in enabling the Fe2 growth cones to respond to mesodermal guidance cues. The addition of heparan sulfate, heparitinase, and phosphatidylinositol-specific phospholipase C to the medium perturbs thein situpath of growth of the Fe2 axons and the location of the MPC in cultured embryos. This indicates a role for heparan sulfate proteoglycans and glycosylphosphatidylinositol-anchored proteins in axon guidance. When these results are compared to those of similar experiments performed on the well-characterized Ti1 axons, they indicate significant differences in the mechanisms that are used for axon guidance. The Fe2 neurons are a good model for elucidating the mechanisms used to guide axon growth on nonmuscle mesodermal substrates often encountered in the periphery of vertebrate embryos.  相似文献   

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Guiding axon growth cones towards their targets is a fundamental process that occurs in a developing nervous system. Several major signaling systems are involved in axon-guidance, and disruption of these systems causes axon-guidance defects. However, the specific role of the environment in which axons navigate in regulating axon-guidance has not been examined in detail. In Drosophila, the ventral nerve cord is divided into segments, and half-segments and the precursor neuroblasts are formed in rows and columns in individual half-segments. The row-wise expression of segment-polarity genes within the neuroectoderm provides the initial row-wise identity to neuroblasts. Here, we show that in embryos mutant for the gene midline, which encodes a T-box DNA binding protein, row-2 neuroblasts and their neuroectoderm adopt a row-5 identity. This reiteration of row-5 ultimately creates a non-permissive zone or a barrier, which prevents the extension of interneuronal longitudinal tracts along their normal anterior-posterior path. While we do not know the nature of the barrier, the axon tracts either stall when they reach this region or project across the midline or towards the periphery along this zone. Previously, we had shown that midline ensures ancestry-dependent fate specification in a neuronal lineage. These results provide the molecular basis for the axon guidance defects in midline mutants and the significance of proper specification of the environment to axon-guidance. These results also reveal the importance of segmental polarity in guiding axons from one segment to the next, and a link between establishment of broad segmental identity and axon guidance.  相似文献   

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氧化修饰在调控细胞凋亡信号转导中的作用   总被引:2,自引:0,他引:2  
氧化修饰是细胞内的活性氧诱导生物大分子发生氧化反应引起的结构及构象改变,发挥调控信号转导和对应激作出反应的功能。氧化修饰发生在凋亡信号转导中的多个生物大分子,包括凋亡相关蛋白质的氧化,如caspase-9、线粒体通透性转变孔及电压依赖的阴离子通道(voltagedependent anion channel,VDAC),同时也包括膜磷脂的氧化修饰,如磷脂酰丝氨酸及线粒体特异的心磷脂。氧化修饰作用也涉及凋亡诱导因子、促凋亡的凋亡信号调控激酶1(apoptosis signalregulatin gkinasel,ASK1)信号转导途径及抗凋亡的转录因子NF—kB的激活和活性。所以氧化修饰可能是调控凋亡信号转导机制中除磷酸化、泛素化外的另一个新的分子机制。  相似文献   

19.
Navigation of retinal projections towards their targets is regulated by guidance molecules and growth cone transduction mechanisms. Here, we present in vitro and in vivo evidences that the cannabinoid receptor 2 (CB2R) is expressed along the retino-thalamic pathway and exerts a modulatory action on axon guidance. These effects are specific to CB2R since no changes were observed in mice where the gene coding for this receptor was altered (cnr2 −/−). The CB2R induced morphological changes observed at the growth cone are PKA dependent and require the presence of the netrin-1 receptor, Deleted in Colorectal Cancer. Interfering with endogenous CB2R signalling using pharmacological agents increased retinal axon length and induced aberrant projections. Additionally, cnr2 −/− mice showed abnormal eye-specific segregation of retinal projections in the dorsal lateral geniculate nucleus (dLGN) indicating CB2R’s implication in retinothalamic development. Overall, this study demonstrates that the contribution of endocannabinoids to brain development is not solely mediated by CB1R, but also involves CB2R.  相似文献   

20.
In this paper, a simulation tool for modeling axon guidance is presented. A mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms. In our framework, models can be defined that consist of concentration fields of guidance molecules in combination with finite-dimensional state vectors. These vectors can characterize migrating growth cones, target neurons that release guidance molecules, or other cells that act as sources of membrane-bound or diffusible guidance molecules. The underlying mathematical framework is presented as well as the numerical methods to solve them. The potential applications of our simulation tool are illustrated with a number of examples, including a model of topographic mapping.  相似文献   

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