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He Q, Li R, Zhong N, Ma J, Nie F, Zhang R. The role and molecular mechanisms of the early growth response 3 gene in schizophrenia. Am J Med Genet B Neuropsychiatr Genet 2024; 195:e32969. [PMID: 38327141 DOI: 10.1002/ajmg.b.32969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 01/15/2024] [Accepted: 01/22/2024] [Indexed: 02/09/2024]
Abstract
Schizophrenia is a chronic, debilitating mental illness caused by both genetic and environmental factors. Genetic factors play a major role in schizophrenia development. Early growth response 3 (EGR3) is a member of the EGR family, which is associated with schizophrenia. Accumulating studies have investigated the relationship between EGR3 and schizophrenia. However, the role of EGR3 in schizophrenia pathogenesis remains unclear. In the present review, we focus on the progress of research related to the role of EGR3 in schizophrenia, including association studies between EGR3 and schizophrenia, abnormal gene expressional analysis of EGR3 in schizophrenia, biological function studies of EGR3 in schizophrenia, the molecular regulatory mechanism of EGR3 and schizophrenia susceptibility candidate genes, and possible role of EGR3 in the immune system function in schizophrenia. In summary, EGR3 is a schizophrenia risk candidate factor and has comprehensive regulatory roles in schizophrenia pathogenesis. Further studies investigating the molecular mechanisms of EGR3 in schizophrenia are warranted for understanding the pathophysiology of this disorder as well as the development of new therapeutic strategies for the treatment and control of this disorder.
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Affiliation(s)
- Qi He
- School of Basic Medicine, Shaanxi Key Laboratory of Acupuncture and Medicine, Shannxi University of Chinese Medicine, Xianyang, Shaanxi, China
| | - Ruochun Li
- Department of Medical Technology, Guiyang Healthcare Vocational University, Guiyang, Guizhou, China
| | - Nannan Zhong
- Department of Medical Technology, Guiyang Healthcare Vocational University, Guiyang, Guizhou, China
| | - Jie Ma
- Department of Electron Microscope, School of Basic Medical Sciences, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, China
| | - Fayi Nie
- School of Basic Medicine, Shaanxi Key Laboratory of Acupuncture and Medicine, Shannxi University of Chinese Medicine, Xianyang, Shaanxi, China
| | - Rui Zhang
- Department of Medical Technology, Guiyang Healthcare Vocational University, Guiyang, Guizhou, China
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2
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Obi-Nagata K, Suzuki N, Miyake R, MacDonald ML, Fish KN, Ozawa K, Nagahama K, Okimura T, Tanaka S, Kano M, Fukazawa Y, Sweet RA, Hayashi-Takagi A. Distorted neurocomputation by a small number of extra-large spines in psychiatric disorders. SCIENCE ADVANCES 2023; 9:eade5973. [PMID: 37294752 PMCID: PMC10256173 DOI: 10.1126/sciadv.ade5973] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Accepted: 05/05/2023] [Indexed: 06/11/2023]
Abstract
Human genetics strongly support the involvement of synaptopathy in psychiatric disorders. However, trans-scale causality linking synapse pathology to behavioral changes is lacking. To address this question, we examined the effects of synaptic inputs on dendrites, cells, and behaviors of mice with knockdown of SETD1A and DISC1, which are validated animal models of schizophrenia. Both models exhibited an overrepresentation of extra-large (XL) synapses, which evoked supralinear dendritic and somatic integration, resulting in increased neuronal firing. The probability of XL spines correlated negatively with working memory, and the optical prevention of XL spine generation restored working memory impairment. Furthermore, XL synapses were more abundant in the postmortem brains of patients with schizophrenia than in those of matched controls. Our findings suggest that working memory performance, a pivotal aspect of psychiatric symptoms, is shaped by distorted dendritic and somatic integration via XL spines.
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Affiliation(s)
- Kisho Obi-Nagata
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama 351-0106, Japan
- Gunma University Graduate School of Medicine, Maebashi City, Gunma 371-8512, Japan
| | - Norimitsu Suzuki
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama 351-0106, Japan
| | - Ryuhei Miyake
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama 351-0106, Japan
| | - Matthew L. MacDonald
- Departments of Psychiatry, Neurology, Statistics, and Neurobiology, Translational Neuroscience Program, University of Pittsburgh, School of Medicine, Pittsburgh, PA 15213, USA
| | - Kenneth N. Fish
- Departments of Psychiatry, Neurology, Statistics, and Neurobiology, Translational Neuroscience Program, University of Pittsburgh, School of Medicine, Pittsburgh, PA 15213, USA
| | - Katsuya Ozawa
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama 351-0106, Japan
| | - Kenichiro Nagahama
- Department of Neurophysiology, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, Tokyo, Japan
| | - Tsukasa Okimura
- Medical Institute of Developmental Disabilities Research, Showa University, Tokyo 157-8577, Japan
| | - Shoji Tanaka
- Department of Information and Communication Sciences, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan
| | - Masanobu Kano
- Department of Neurophysiology, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, Tokyo, Japan
| | - Yugo Fukazawa
- Division of Brain Structure and Function, Faculty of Medical Science, University of Fukui, Yoshida, Fukui, 910-1193, Japan
| | - Robert A. Sweet
- Departments of Psychiatry, Neurology, Statistics, and Neurobiology, Translational Neuroscience Program, University of Pittsburgh, School of Medicine, Pittsburgh, PA 15213, USA
| | - Akiko Hayashi-Takagi
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama 351-0106, Japan
- Gunma University Graduate School of Medicine, Maebashi City, Gunma 371-8512, Japan
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KASAI H. Unraveling the mysteries of dendritic spine dynamics: Five key principles shaping memory and cognition. PROCEEDINGS OF THE JAPAN ACADEMY. SERIES B, PHYSICAL AND BIOLOGICAL SCIENCES 2023; 99:254-305. [PMID: 37821392 PMCID: PMC10749395 DOI: 10.2183/pjab.99.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2023] [Accepted: 07/11/2023] [Indexed: 10/13/2023]
Abstract
Recent research extends our understanding of brain processes beyond just action potentials and chemical transmissions within neural circuits, emphasizing the mechanical forces generated by excitatory synapses on dendritic spines to modulate presynaptic function. From in vivo and in vitro studies, we outline five central principles of synaptic mechanics in brain function: P1: Stability - Underpinning the integral relationship between the structure and function of the spine synapses. P2: Extrinsic dynamics - Highlighting synapse-selective structural plasticity which plays a crucial role in Hebbian associative learning, distinct from pathway-selective long-term potentiation (LTP) and depression (LTD). P3: Neuromodulation - Analyzing the role of G-protein-coupled receptors, particularly dopamine receptors, in time-sensitive modulation of associative learning frameworks such as Pavlovian classical conditioning and Thorndike's reinforcement learning (RL). P4: Instability - Addressing the intrinsic dynamics crucial to memory management during continual learning, spotlighting their role in "spine dysgenesis" associated with mental disorders. P5: Mechanics - Exploring how synaptic mechanics influence both sides of synapses to establish structural traces of short- and long-term memory, thereby aiding the integration of mental functions. We also delve into the historical background and foresee impending challenges.
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Affiliation(s)
- Haruo KASAI
- International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
- Laboratory of Structural Physiology, Center for Disease Biology and Integrative Medicine, Faculty of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
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Hagihara H, Shoji H, Kuroiwa M, Graef IA, Crabtree GR, Nishi A, Miyakawa T. Forebrain-specific conditional calcineurin deficiency induces dentate gyrus immaturity and hyper-dopaminergic signaling in mice. Mol Brain 2022; 15:94. [PMID: 36414974 PMCID: PMC9682671 DOI: 10.1186/s13041-022-00981-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2022] [Accepted: 11/12/2022] [Indexed: 11/24/2022] Open
Abstract
Calcineurin (Cn), a phosphatase important for synaptic plasticity and neuronal development, has been implicated in the etiology and pathophysiology of neuropsychiatric disorders, including schizophrenia, intellectual disability, autism spectrum disorders, epilepsy, and Alzheimer's disease. Forebrain-specific conditional Cn knockout mice have been known to exhibit multiple behavioral phenotypes related to these disorders. In this study, we investigated whether Cn mutant mice show pseudo-immaturity of the dentate gyrus (iDG) in the hippocampus, which we have proposed as an endophenotype shared by these disorders. Expression of calbindin and GluA1, typical markers for mature DG granule cells (GCs), was decreased and that of doublecortin, calretinin, phospho-CREB, and dopamine D1 receptor (Drd1), markers for immature GC, was increased in Cn mutants. Phosphorylation of cAMP-dependent protein kinase (PKA) substrates (GluA1, ERK2, DARPP-32, PDE4) was increased and showed higher sensitivity to SKF81297, a Drd1-like agonist, in Cn mutants than in controls. While cAMP/PKA signaling is increased in the iDG of Cn mutants, chronic treatment with rolipram, a selective PDE4 inhibitor that increases intracellular cAMP, ameliorated the iDG phenotype significantly and nesting behavior deficits with nominal significance. Chronic rolipram administration also decreased the phosphorylation of CREB, but not the other four PKA substrates examined, in Cn mutants. These results suggest that Cn deficiency induces pseudo-immaturity of GCs and that cAMP signaling increases to compensate for this maturation abnormality. This study further supports the idea that iDG is an endophenotype shared by certain neuropsychiatric disorders.
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Affiliation(s)
- Hideo Hagihara
- Division of Systems Medical Science, Center for Medical Science, Fujita Health University, Toyoake, Aichi 470-1192 Japan
| | - Hirotaka Shoji
- Division of Systems Medical Science, Center for Medical Science, Fujita Health University, Toyoake, Aichi 470-1192 Japan
| | - Mahomi Kuroiwa
- Department of Pharmacology, Kurume University School of Medicine, Kurume, Fukuoka 830-0011 Japan
| | - Isabella A. Graef
- Department of Pathology, Stanford University of Medicine, Stanford, CA 94305 USA
| | - Gerald R. Crabtree
- Department of Pathology, Stanford University of Medicine, Stanford, CA 94305 USA
| | - Akinori Nishi
- Department of Pharmacology, Kurume University School of Medicine, Kurume, Fukuoka 830-0011 Japan
| | - Tsuyoshi Miyakawa
- Division of Systems Medical Science, Center for Medical Science, Fujita Health University, Toyoake, Aichi 470-1192 Japan
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5
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Computational roles of intrinsic synaptic dynamics. Curr Opin Neurobiol 2021; 70:34-42. [PMID: 34303124 DOI: 10.1016/j.conb.2021.06.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Revised: 05/14/2021] [Accepted: 06/15/2021] [Indexed: 12/26/2022]
Abstract
Conventional theories assume that long-term information storage in the brain is implemented by modifying synaptic efficacy. Recent experimental findings challenge this view by demonstrating that dendritic spine sizes, or their corresponding synaptic weights, are highly volatile even in the absence of neural activity. Here, we review previous computational works on the roles of these intrinsic synaptic dynamics. We first present the possibility for neuronal networks to sustain stable performance in their presence, and we then hypothesize that intrinsic dynamics could be more than mere noise to withstand, but they may improve information processing in the brain.
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Kasai H, Ziv NE, Okazaki H, Yagishita S, Toyoizumi T. Spine dynamics in the brain, mental disorders and artificial neural networks. Nat Rev Neurosci 2021; 22:407-422. [PMID: 34050339 DOI: 10.1038/s41583-021-00467-3] [Citation(s) in RCA: 77] [Impact Index Per Article: 25.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/14/2021] [Indexed: 12/15/2022]
Abstract
In the brain, most synapses are formed on minute protrusions known as dendritic spines. Unlike their artificial intelligence counterparts, spines are not merely tuneable memory elements: they also embody algorithms that implement the brain's ability to learn from experience and cope with new challenges. Importantly, they exhibit structural dynamics that depend on activity, excitatory input and inhibitory input (synaptic plasticity or 'extrinsic' dynamics) and dynamics independent of activity ('intrinsic' dynamics), both of which are subject to neuromodulatory influences and reinforcers such as dopamine. Here we succinctly review extrinsic and intrinsic dynamics, compare these with parallels in machine learning where they exist, describe the importance of intrinsic dynamics for memory management and adaptation, and speculate on how disruption of extrinsic and intrinsic dynamics may give rise to mental disorders. Throughout, we also highlight algorithmic features of spine dynamics that may be relevant to future artificial intelligence developments.
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Affiliation(s)
- Haruo Kasai
- Laboratory of Structural Physiology, Center for Disease Biology and Integrative Medicine, Faculty of Medicine, The University of Tokyo, Tokyo, Japan. .,International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Bunkyo-ku, Tokyo, Japan.
| | - Noam E Ziv
- Technion Faculty of Medicine and Network Biology Research Labs, Technion City, Haifa, Israel
| | - Hitoshi Okazaki
- Laboratory of Structural Physiology, Center for Disease Biology and Integrative Medicine, Faculty of Medicine, The University of Tokyo, Tokyo, Japan.,International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Sho Yagishita
- Laboratory of Structural Physiology, Center for Disease Biology and Integrative Medicine, Faculty of Medicine, The University of Tokyo, Tokyo, Japan.,International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Taro Toyoizumi
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Saitama, Japan.,Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan
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Hyun JS, Inoue T, Hayashi-Takagi A. Multi-Scale Understanding of NMDA Receptor Function in Schizophrenia. Biomolecules 2020; 10:biom10081172. [PMID: 32796766 PMCID: PMC7465114 DOI: 10.3390/biom10081172] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2020] [Revised: 08/06/2020] [Accepted: 08/07/2020] [Indexed: 01/19/2023] Open
Abstract
Schizophrenia is a chronic and disabling psychiatric disorder characterized by disturbances of thought, cognition, and behavior. Despite massive research efforts to date, the etiology and pathophysiology of schizophrenia remain largely unknown. The difficulty of brain research is largely a result of complex interactions between contributory factors at different scales: susceptible gene variants (molecular scale), synaptopathies (synaptic, dendritic, and cell scales), and alterations in neuronal circuits (circuit scale), which together result in behavioral manifestations (individual scale). It is likely that each scale affects the others, from the microscale to the mesoscale to the macroscale, and vice versa. Thus, to consider the intricate complexity of schizophrenia across multiple layers, we introduce a multi-scale, hierarchical view of the nature of this disorder, focusing especially on N-methyl-D-aspartate-type glutamate receptors (NMDARs). The reason for placing emphasis on NMDAR is its clinical relevance to schizophrenia, as well as its diverse functions in neurons, including the robust supralinear synaptic integration provided by N-methyl-D-aspartate-type glutamate (NMDA) spikes and the Ca2+ permeability of the NMDAR, which facilitates synaptic plasticity via various calcium-dependent proteins. Here, we review recent evidence implicating NMDARs in the pathophysiology of schizophrenia from the multi-scale perspective. We also discuss recent advances from optical techniques, which provide a powerful tool for uncovering the mechanisms of NMDAR synaptic pathology and their relationships, with subsequent behavioral manifestations.
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Affiliation(s)
- Jo Soo Hyun
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama Prefecture 351-0106, Japan;
- Department of Life Science and Medical Bioscience, School of Advanced Science and Engineering, Waseda University, Tokyo 162-8480, Japan;
| | - Takafumi Inoue
- Department of Life Science and Medical Bioscience, School of Advanced Science and Engineering, Waseda University, Tokyo 162-8480, Japan;
| | - Akiko Hayashi-Takagi
- Laboratory for Multi-scale Biological Psychiatry, Center for Brain Science, RIKEN, 2-1 Hirosawa, Wako City, Saitama Prefecture 351-0106, Japan;
- Correspondence: ; Tel.: +81-48-467-5156
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8
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Kuśmierz Ł, Ogawa S, Toyoizumi T. Edge of Chaos and Avalanches in Neural Networks with Heavy-Tailed Synaptic Weight Distribution. PHYSICAL REVIEW LETTERS 2020; 125:028101. [PMID: 32701351 DOI: 10.1103/physrevlett.125.028101] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Revised: 03/03/2020] [Accepted: 05/26/2020] [Indexed: 06/11/2023]
Abstract
We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous transition to chaos and can reproduce biologically relevant low activity levels and scale-free avalanches, i.e., bursts of activity with power-law distributions of sizes and lifetimes. In contrast, the Gaussian counterpart exhibits a discontinuous transition to chaos and thus cannot be poised near the edge of chaos. We validate our predictions in simulations of networks of binary as well as leaky integrate-and-fire neurons. Our results suggest that heavy-tailed synaptic distribution may form a weakly informative sparse-connectivity prior that can be useful in biological and artificial adaptive systems.
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Affiliation(s)
- Łukasz Kuśmierz
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Shun Ogawa
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Taro Toyoizumi
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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Humble J, Hiratsuka K, Kasai H, Toyoizumi T. Intrinsic Spine Dynamics Are Critical for Recurrent Network Learning in Models With and Without Autism Spectrum Disorder. Front Comput Neurosci 2019; 13:38. [PMID: 31263407 PMCID: PMC6585147 DOI: 10.3389/fncom.2019.00038] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2019] [Accepted: 05/28/2019] [Indexed: 11/13/2022] Open
Abstract
It is often assumed that Hebbian synaptic plasticity forms a cell assembly, a mutually interacting group of neurons that encodes memory. However, in recurrently connected networks with pure Hebbian plasticity, cell assemblies typically diverge or fade under ongoing changes of synaptic strength. Previously assumed mechanisms that stabilize cell assemblies do not robustly reproduce the experimentally reported unimodal and long-tailed distribution of synaptic strengths. Here, we show that augmenting Hebbian plasticity with experimentally observed intrinsic spine dynamics can stabilize cell assemblies and reproduce the distribution of synaptic strengths. Moreover, we posit that strong intrinsic spine dynamics impair learning performance. Our theory explains how excessively strong spine dynamics, experimentally observed in several animal models of autism spectrum disorder, impair learning associations in the brain.
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Affiliation(s)
- James Humble
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Saitama, Japan
| | - Kazuhiro Hiratsuka
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Saitama, Japan
| | - Haruo Kasai
- Laboratory of Structural Physiology, Faculty of Medicine, Center for Disease Biology and Integrative Medicine, University of Tokyo, Tokyo, Japan
| | - Taro Toyoizumi
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Saitama, Japan
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In Vivo Volume Dynamics of Dendritic Spines in the Neocortex of Wild-Type and Fmr1 KO Mice. eNeuro 2018; 5:eN-NWR-0282-18. [PMID: 30417082 PMCID: PMC6223115 DOI: 10.1523/eneuro.0282-18.2018] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Revised: 09/30/2018] [Accepted: 10/03/2018] [Indexed: 02/06/2023] Open
Abstract
Excitatory synapses are often formed at small protrusions of dendrite, called dendritic spines, in most projection neurons, and the spine-head volumes show strong correlations with synaptic connectivity. We examined the dynamics of spine volume in the adult mouse visual cortex using time-lapse in vivo two-photon imaging with a resonant Galvano scanner. Contrary to expectations, we found that the spines in the adult neocortex showed fluctuations to a similar degree as that observed in young hippocampal preparations, but there were systematic differences in how the dynamics were dependent on spine volumes, thus allowing for fewer fluctuations in small spines, which could account for the relatively low turnover rates of neocortical spines in vivo. We found that spine volumes fluctuated to a greater extent in a mouse model (Fmr1 knockout) of fragile X mental retardation than in wild-type mice, and the spine turnover rates were also higher in Fmr1 knock-out mice. Such features of spine dynamics in Fmr1 knock-out mice could be represented by a single slope factor in our model. Our data and model indicate a small but significant change in the average spine volume and more eminent differences in the statistical distribution in Fmr1 knock-out mice even in adulthood, which reflects the abnormal in vivo dynamics of spine volumes.
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