Wingless/Int （Wnt） signaling pathways are signal transduction mechanisms that have been widely studied In the field of embryogen- esis. Recent work has established a critical role for these pathways in brain develop...Wingless/Int （Wnt） signaling pathways are signal transduction mechanisms that have been widely studied In the field of embryogen- esis. Recent work has established a critical role for these pathways in brain development, especially of midbrain dopaminergic neu- rones, However, the fundamental importance of Wnt signaling for the normal function of mature neurones in the adult central nervous system has also lately been demonstrated by an increasing number of studies. Parkinson＇s disease （PD） is the second most prevalent neurodegenerative disease worldwide and is currently incurable. This debilitating disease is characterized by the progres- sive loss of a subset of midbrain dopaminergic neurones in the substontla nigm leadingto typical extrapyramidal motor symptoms. The aetiology of PD is poorly understood but work performed over the Last two decades has identified a growing number of genetic defects that underlie this condition. Herewe review a growing body of data connecting genes implicated in PD--most notablythe PARKgenes-- with Wnt signaling. These observations provide clues to the normal function of these proteins in healthy neurones and suggest that deregulated Wnt signaling might be a frequent pathomechanlsm leading to PD. These observations have implications for the patho- genesis and treatment of neurodegenerative diseases in general.展开更多
During the past three decades, Wingtess/Int （Wnt）signaling has emerged as an essential regu{ator crucial for neuronal development and maintenance （Inestrosa and Arenas, 201_0）. In addition, Wnt signal- ing was rec...During the past three decades, Wingtess/Int （Wnt）signaling has emerged as an essential regu{ator crucial for neuronal development and maintenance （Inestrosa and Arenas, 201_0）. In addition, Wnt signal- ing was recently shown to be involved in the regula- tion of synaptic function and plasticity, which is critical for learning and memory （Oliva et aL, 2013）. Deregulation of Wnt signaling has been proposed as a key contributor to the pathogenesis of neurode- generative disorders including Alzheimer＇s disease （AD） and Parkinson＇s disease （PD）. This increasing knowledge of the specific roles of Wnt signaling cascades during different stages of life has suggested innovative therapeutic strategies for the treatment of neurodegenerative diseases.展开更多
A new loop algebra and a new Lax pair are constructed, respectively. It follows that the integrable coupling of the TC hierarchy of equations, which is also an expanding integrable model, is obtained. Specially, the i...A new loop algebra and a new Lax pair are constructed, respectively. It follows that the integrable coupling of the TC hierarchy of equations, which is also an expanding integrable model, is obtained. Specially, the integrable coupling of the famous KdV equation is presented.展开更多
A hierarchy of Hamiltonian systems obtained from the Lax pair of KdV hierarchy under theconstraint condition on potential u = (q, q) is. presented. The independent integrals for theseHamiltonian systems are constructe...A hierarchy of Hamiltonian systems obtained from the Lax pair of KdV hierarchy under theconstraint condition on potential u = (q, q) is. presented. The independent integrals for theseHamiltonian systems are constructed by using recursion operator and shown to be in involution.Thus this hierarchy of Hamiltonian systems is completely integrable in the sense of Liouville. andthey commute with each other.展开更多
文摘Wingless/Int （Wnt） signaling pathways are signal transduction mechanisms that have been widely studied In the field of embryogen- esis. Recent work has established a critical role for these pathways in brain development, especially of midbrain dopaminergic neu- rones, However, the fundamental importance of Wnt signaling for the normal function of mature neurones in the adult central nervous system has also lately been demonstrated by an increasing number of studies. Parkinson＇s disease （PD） is the second most prevalent neurodegenerative disease worldwide and is currently incurable. This debilitating disease is characterized by the progres- sive loss of a subset of midbrain dopaminergic neurones in the substontla nigm leadingto typical extrapyramidal motor symptoms. The aetiology of PD is poorly understood but work performed over the Last two decades has identified a growing number of genetic defects that underlie this condition. Herewe review a growing body of data connecting genes implicated in PD--most notablythe PARKgenes-- with Wnt signaling. These observations provide clues to the normal function of these proteins in healthy neurones and suggest that deregulated Wnt signaling might be a frequent pathomechanlsm leading to PD. These observations have implications for the patho- genesis and treatment of neurodegenerative diseases in general.
文摘During the past three decades, Wingtess/Int （Wnt）signaling has emerged as an essential regu{ator crucial for neuronal development and maintenance （Inestrosa and Arenas, 201_0）. In addition, Wnt signal- ing was recently shown to be involved in the regula- tion of synaptic function and plasticity, which is critical for learning and memory （Oliva et aL, 2013）. Deregulation of Wnt signaling has been proposed as a key contributor to the pathogenesis of neurode- generative disorders including Alzheimer＇s disease （AD） and Parkinson＇s disease （PD）. This increasing knowledge of the specific roles of Wnt signaling cascades during different stages of life has suggested innovative therapeutic strategies for the treatment of neurodegenerative diseases.
文摘A new loop algebra and a new Lax pair are constructed, respectively. It follows that the integrable coupling of the TC hierarchy of equations, which is also an expanding integrable model, is obtained. Specially, the integrable coupling of the famous KdV equation is presented.
基金This project is supported by the National Natural Science Foundation of China
文摘A hierarchy of Hamiltonian systems obtained from the Lax pair of KdV hierarchy under theconstraint condition on potential u = (q, q) is. presented. The independent integrals for theseHamiltonian systems are constructed by using recursion operator and shown to be in involution.Thus this hierarchy of Hamiltonian systems is completely integrable in the sense of Liouville. andthey commute with each other.
