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1.
The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.  相似文献   

2.
The impact of dendritic geometry on somatopetal transfer of the current generated by steady uniform activation of excitatory synaptic conductance distributed over passive, or active (Hodgkin-Huxley type), dendrites was studied in simulated neurons. Such tonic activation was delivered to the uniform dendrite and to the dendrites with symmetric or asymmetric branching with various ratios of branch diameters. Transfer effectiveness of the dendrites with distributed sources was estimated by the core current increment directly related to the total membrane current per unit path length. The effectiveness decreased with increasing path distance from the soma along uniform branches. The primary reason for this was the asymmetry of somatopetal vs somatofugal input core conductance met by synaptic current due to a greater leak conductance at the proximal end of the dendrite. Under these conditions, an increasing somatopetal core current and a corresponding drop of the depolarization membrane potential occurred. The voltage-dependent extrasynaptic conductances, if present, followed this depolarization. Consequently, the driving potential and membrane current densities decreased with increasing path distance from the soma. All path profiles were perturbed at bifurcations, being identical in symmetrical branches and diverging in asymmetrical ones. These perturbations were caused by voltage gradient breaks (abrupt change in the profile slope) occurring at the branching node due to coincident inhomogeneity of the dendritic core cross-section area and its conductance. The gradient was greater on the side of the smaller effective cross-section. Correspondingly, the path profiles of the somatopetal current transfer effectiveness were broken and/or diverged. The dendrites, their paths, and sites which were more effective in the current transfer from distributed sources were also more effective in the transfer from single-site inputs. The effectiveness of the active dendrite depended on the activation-inactivation kinetics of its voltage-gated conductances. In particular, dendrites with the same geometry were less effective with the Hodgkin-Huxley membrane than with the passive membrane, because of the effect of the noninactivating K+-conductance associated with the hyperpolarization equilibrium potential. Such electrogeometrical coupling may form a basis for path-dependent input-output conversion in the dendritic neurons, as the output discharge rate is defined by the net current delivered to the soma. Received: 18 December 1997 / Accepted in revised form: 12 June 1998  相似文献   

3.
The functional geometry of the reconstructed dendritic arborization of Purkinje neurons is the object of this work. The combined effects of the local geometry of the dendritic branches and of the membrane mechanisms are computed in passive configuration to obtain the electrotonic structure of the arborization. Steady-currents applied to the soma and expressed as a function of the path distance from the soma form different clusters of profiles in which dendritic branches are similar in voltages and current transfer effectiveness. The locations of the different clusters are mapped on the dendrograms and 3D representations of the arborization. It reveals the presence of different spatial dendritic sectors clearly separated in 3D space that shape the arborization in ordered electrical domains, each with similar passive charge transfer efficiencies. Further simulations are performed in active configuration with a realistic cocktail of conductances to find out whether similar spatial domains found in the passive model also characterize the active dendritic arborization. During tonic activation of excitatory synaptic inputs homogeneously distributed over the whole arborization, the Purkinje cell generates regular oscillatory potentials. The temporal patterns of the electrical oscillations induce similar spatial sectors in the arborization as those observed in the passive electrotonic structure. By taking a video of the dendritic maps of the membrane potentials during a single oscillation, we demonstrate that the functional dendritic field of a Purkinje neuron displays dynamic changes which occur in the spatial distribution of membrane potentials in the course of the oscillation. We conclude that the branching pattern of the arborization explains such continuous reconfiguration and discuss its functional implications.  相似文献   

4.
Geometry and membrane properties of the dendrites crucially determine input–output relations in neurons. Unlike geometry often available in detail from computer reconstruction, the membrane resistivity is fragmentarily known if at all. Moreover, it varies during ongoing activity. In this study we address the question: what is the impact of the variation in membrane resistivity on the transfer properties of dendrites? Following a standard approach of the control system theory, we derive and explore the sensitivity functions complementary to the transfer functions of the passive dendrites with arbitrary geometrical parameters (length and diameter) and boundary conditions. We use the location-dependent somatopetal current transfer ratio (the reciprocal of the somatofugal voltage) as the transfer function, and its membrane resistivity derivatives, as the sensitivity functions. In the dendrites, at every path distance from the origin, the sensitivity function in a common form relates the transfer function, membrane resistivity, characteristic input conductance of semi-infinite cable and directional somatofugal input conductances at the given internal site and origin, and the length. Plotted in membrane resistivity versus path distance coordinates, the sensitivity functions display common features: along any coordinate there are low and high ranges, in which the sensitivity, respectively, increases and decreases. The ranges and corresponding rates depend on morphology and boundary conditions in a characteristic manner. These features predict existence of the geometry-dependent range of membrane resistivity (the earlier unattended mid-conductance state), such that the dendrites with a given metrical asymmetry are most distinguished in their transfer properties and electrical states if membrane resistivity is within the range and are not otherwise.  相似文献   

5.
This simulation study aimed at assessing linkage between the membrane properties and the effectiveness of somatopetal current transfer from activated tonic excitatory inputs homogeneously distributed along uniform dendrites. It was shown that in the dendrites having anN-shaped steady current-voltage membrane characteristic due to the negative slope within a certain range of potentials, distal sites can be more effective than proximal sites in somatopetal current transfer from tonically activated excitatory synaptic inputs. Inhomogeneous dendritic depolarization produced by these inputs should be found everywhere within a range of the negative slope. In simulated dendrites receiving, as in rat abducens motoneurons, voltage-sensitive synaptic inputs of anN-methyl-D-aspartate (NMDA) type, such spatial effects occurred at low depolarization produced by subcritical excitation. At supercritical excitation, depolarization increased and left the range of the negative slope, and proximal sites became much more effective than distal ones. It is suggested that persistent inward currents (including other than of NMDA nature) can provide similar effects.  相似文献   

6.
Mathematical models of abducens motoneurons with reconstructed dendritic arborizations were investigated. The two types of models differed from each other in electrical properties of the dendrites, either passive (model group 1) or active and non-linear (model group 2). The relations between morphology of the dendrites, their electrical transfer characteristics, and formation of impulse patterns at the cell output were studied under conditions of tonic activation of glutamatergic (NMDA-type) excitatory synapses homogeneously distributed over the dendrites. For reconstructed dendritic arborizations, their morphometric characteristics (size, complexity, and metrical asymmetry) and electrical ones (somatopetal current transfer effectiveness function and sensitivity of the latter to variations of the homogeneous membrane conductivity) were computed. Changes in the membrane potential were also studied in different parts of the dendritic arborization during generation of various patterns of discharges of action potentials (APs) at the neuronal output under different intensities of synaptic activation; this allowed us to reveal “spatial signatures” of the above-mentioned temporal patterns. The output patterns and their “spatial signatures” changed in a certain manner with increase in the intensity of synaptic activation. A simple periodical discharge of low-frequency APs with constant interspike intervals was replaced by a complex periodical or nonperiodical (stochastic) bursting pattern, which then was replaced again by a simple rhythmic but high-frequency discharge. Simple periodical patterns were associated with generation of synchronous oscillatory dendritic depolarizations phase-shifted in metrically asymmetrical parts of the arborization. In the case of generation of complex periodical or stochastic patterns, depolarization processes in asymmetrical dendritic parts were asynchronous and differed from each other in their amplitude and duration. Such a structure-dependent repertoire of output discharge patterns was quite compatible with that observed earlier in examined simulated neocortical pyramidal and cerebellar Purkinje neurons. This fact is indicative of a possible similarity of the rules governing the formation of specific output patterns in neurons with active membrane properties of the dendrites based on intrinsic mophological/functional features of the dendritic arborization of a given neuron.  相似文献   

7.
In the mathematical model of a neuron, properties of the active membrane during action of tonically activated synaptic inputs of an N-methyl-D-aspartate (NMDA) type were studied. In the dendrites with these properties, the impact of geometry on the somatopetal current transfer was investigated. The conditions were considered when the distal sites are more effective, as compared with the proximal ones, in their contribution to the somatopetal current. Contributions of “sister” branches to the net current transferred to the soma were compared at different levels of depolarization caused by action of homogeneously distributed NMDA synaptic inputs.  相似文献   

8.
Altered dendritic arborization contributes to numerous physiological processes including synaptic plasticity, behavior, learning and memory, and is one of the most consistent neuropathologic conditions found in a number of mental retardation disorders, schizophrenia, and neurodegenerative disease. COP9 signalosome (CSN), an evolutionarily conserved regulator of the Cullin-based ubiquitin ligases that act in the proteasome pathway, has been found associated with diverse debilitating syndromes, suggesting that CSN may be involved in regulation of dendritic arborization. However, the mechanism of this control, if it exists, is unknown. To address whether the CSN pathway plays a role in dendrites, we used a simple and genetically tractable model, Drosophila larval peripheral nervous system. Our model study identified the COP9 signalosome as the key and multilayer regulator of dendritic arborization. CSN is responsible for shaping the entire dendritic tree through both stimulating and then repressing dendritic branching. We identified that CSN exerts its dualistic function via control of different Cullins. In particular, CSN stimulates dendritic branching through Cullin1, and inhibits it via control of Cullin3 function. We also identified that Cullin1 acts in neurons with the substrate-specific F-box protein Slimb to target the Cubitus interruptus protein for degradation.  相似文献   

9.
On mathematical models of pyramidal neurons localized in the neocortical layers 2/3, whose reconstructed dendritic arborization possessed passive linear or active nonlinear membrane properties, we studied the effect of morphology of the dendrites on their passive electrical transfer characteristics and also on the formation of patterns of spike discharges at the output of the cell under conditions of tonic activation via uniformly distributed excitatory synapses along the dendrites. For this purpose, we calculated morphometric characteristics of the size, complexity, metric asymmetry, and function of effectiveness of somatopetal transmission of the current (with estimation of the sensitivity of this efficacy to changes in the uniform membrane conductance) for the reconstructed dendritic arborization in general and also for its apical and basal subtrees. Spatial maps of the membrane potential and intracellular calcium concentration, which corresponded to certain temporal patterns of spike discharges generated by the neuron upon different intensities of synaptic activation, were superimposed on the 3D image and dendrograms of the neuron. These maps were considered “spatial autographs” of the above patterns. The main discharge pattern included periodic two-spike bursts (dublets) generated with relatively stable intraburst interspike intervals and interburst intervals decreasing with a rise in the intensity of activation. Under conditions of intense activation, the interburst intervals became close to the intraburst intervals, so the cell began to generate continuous trains of action potentials. Such a repertoire (consisting of two patterns of the activity, periodical dublets and continuous discharges) is considerably scantier than that described earlier in pyramidal neurons of the neocortical layer 5. Under analogous conditions of activation, we observed in the latter cells a variety of patterns of output discharges of different complexities, including stochastic ones. A relatively short length of the apical dendrite subtree of layer 2/3 neurons and, correspondingly, a smaller metric asymmetry (differences between the lengths of the apical and basal dendritic branches and paths), as compared with those in layer 5 pyramidal neurons, are morphological factors responsible for the predominance of periodic spike dublets. As a result, there were two combinations of different electrical states of the sites of dendritic arborization (“spatial autographs”). In the case of dublets, these were high depolarization of the apical dendrites vs. low depolarization of the basal dendrites and a reverse combination; only the latter (reverse) combination corresponded to the case of continuous discharges. The relative simplicity and uniformity of spike patterns in the cells, apparently, promotes the predominance of network interaction in the processes of formation of the activity of pyramidal neurons of layers 2/3 and, thereby, a higher efficiency of the processes of intracortical association.  相似文献   

10.
Development of appropriate dendritic arbors is crucial for neuronal information transfer. We show, using seizure-related gene 6 (sez-6) null mutant mice, that Sez-6 is required for normal dendritic arborization of cortical neurons. Deep-layer pyramidal neurons in the somatosensory cortex of sez-6 null mice exhibit an excess of short dendrites, and cultured cortical neurons lacking Sez-6 display excessive neurite branching. Overexpression of individual Sez-6 isoforms in knockout neurons reveals opposing actions of membrane-bound and secreted Sez-6 proteins, with membrane-bound Sez-6 exerting an antibranching effect under both basal and depolarizing conditions. Layer V pyramidal neurons in knockout brain slices show reduced excitatory postsynaptic responses and a reduced dendritic spine density, reflected by diminished punctate staining for postsynaptic density 95 (PSD-95). In behavioral tests, the sez-6 null mice display specific exploratory, motor, and cognitive deficits. In conclusion, cell-surface protein complexes involving Sez-6 help to sculpt the dendritic arbor, in turn enhancing synaptic connectivity.  相似文献   

11.
Ultrastructural studies on the synaptology of dendritic arborizations of motoneurones have been problematic because dendrites are very thin in relation to their great length, and most of the studies on this topic have therefore dealt with only small parts of the dendritic tree. Here we compared the ultrastructural characteristics of the axon terminals distributed along the various dendrites of a single motoneurone. For this purpose, the light microscopic 3D reconstruction of the dendritic arborization of an intracellularly labelled abducens motoneurone was combined with an electron microscopic analysis of its synaptic contacts. Dendritic profiles were randomly sampled along the various dendrites and the axon terminals they received were classified on the basis of their ultrastructural features and their GABA-immunoreactivity. It emerged that the various dendrites differed according to the type and local arrangement of their synaptic inputs. Our second aim was to incorporate the morphological data obtained into a model giving the charge transfer effectiveness T(x) of the dendritic sites. The sensitivity S(x) of T(x) to changes in the membrane resistivity (Rm) simulating various levels of tonic synaptic activity was calculated. It turned out that both the proximal and distal regions of the dendritic arborization have a dense synaptic covering and a weak sensitivity to changes in the Rm, whereas the intermediate dendrites have a sparse synaptic covering and a high sensitivity to changes in tonic synaptic activity. This pattern of organisation might mediate the “gating” of a population of synapses covering some dendritic regions in a state-dependent fashion.  相似文献   

12.
Dendrites allow neurons to integrate sensory or synaptic inputs, and the spatial disposition and local density of branches within the dendritic arbor limit the number and type of inputs. Drosophila melanogaster dendritic arborization (da) neurons provide a model system to study the genetic programs underlying such geometry in vivo. Here we report that mutations of motor-protein genes, including a dynein subunit gene (dlic) and kinesin heavy chain (khc), caused not only downsizing of the overall arbor, but also a marked shift of branching activity to the proximal area within the arbor. This phenotype was suppressed when dominant-negative Rab5 was expressed in the mutant neurons, which deposited early endosomes in the cell body. We also showed that 1) in dendritic branches of the wild-type neurons, Rab5-containing early endosomes were dynamically transported and 2) when Rab5 function alone was abrogated, terminal branches were almost totally deleted. These results reveal an important link between microtubule motors and endosomes in dendrite morphogenesis.  相似文献   

13.
14.
In the model of a cerebellar Purkinje neuron with reconstructed active dendrites, we investigated the impact of the ratio between volumes of the endoplasmic reticulum (organellar calcium store) and cytosol on the Ca2+ dynamics in asymmetrical parts of the dendritic arborization during generation of different structure-dependent patterns of bursting activity. Tonic synaptic excitation homogeneously distributed over the dendrites (a spatially homogeneous stationary input signal) caused spatially heterogeneous variations of the dendritic membrane potential (MP) accompanied by periodical or nonperiodical bursts of action potentials at the cell output. The MP waveforms recorded from the segments of asymmetrical dendrites were then applied to the membrane of selected dendrite segments as command voltages in a dynamic clamp mode. In these segments, the relative size of the stores was varied. This provided equal to each other local calcium currents and influxes into the cytosol of the segment differently filled with the organellar store. Regardless of the impulse pattern, microgeometry of the segment and the store modulated calcium transients exactly in the same way as in previous studies of electrical and concentration responses to local phasic synaptic excitation of the modeled neuron. Peak values of depolarization-induced elevations of the cytosolic Ca2+ concentration increased with the portion of the intracellular volume occupied by the store. The most important factor defining this dependence was the ratio of the membrane area vs the organelle-free cytosol volume of the dendritic segment. Concentrations of Са2+ deposited in equal-sized segments of asymmetrical parts of the dendritic arborization where asynchronous unequal variations of the MP were observed during generation of nonperiodical bursting at the output demonstrated considerable specificity. A greater amount of calcium was deposited in the segments staying, on average, in a high-depolarization state for a longer time (this intensified activation of calcium channels and amplified the corresponding Ca2+ influx into the cytosol). Hence, local dynamics of the Ca2+ concentration depend directly on local microgeometry and indirectly on global macrogeometry of the dendrite arborization, as the latter determines spatial asymmetry-related unequal transients in different parts of the dendritic arborization having active membrane properties.  相似文献   

15.
16.
The structure of local synaptic circuits is the key to understanding cortical function and how neuronal functional modules such as cortical columns are formed. The central problem in deciphering cortical microcircuits is the quantification of synaptic connectivity between neuron pairs. I present a theoretical model that accounts for the axon and dendrite morphologies of pre- and postsynaptic cells and provides the average number of synaptic contacts formed between them as a function of their relative locations in three-dimensional space. An important aspect of the current approach is the representation of a complex structure of an axonal/dendritic arbor as a superposition of basic structures—synaptic clouds. Each cloud has three structural parameters that can be directly estimated from two-dimensional drawings of the underlying arbor. Using empirical data available in literature, I applied this theory to three morphologically different types of cell pairs. I found that, within a wide range of cell separations, the theory is in very good agreement with empirical data on (i) axonal–dendritic contacts of pyramidal cells and (ii) somatic synapses formed by the axons of inhibitory interneurons. Since for many types of neurons plane arborization drawings are available from literature, this theory can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies. It can also have significant implications for computational models of cortical networks by making it possible to wire up simulated neural networks in a realistic fashion.  相似文献   

17.
Dendritic shaft (Zd) and spine (Zsp) input impedances were computed numerically for sites on hippocampal neurons, using a segmental format of cable calculations. The Zsp values for a typical spine appended onto a dendritic shaft averaged less than 2% higher than the Zd values for the adjacent dendritic shaft. Spine synaptic inputs were simulated by a brief conductance transient, which possessed a time integral of 12 X 10(-10)S X ms. This input resulted in an average peak spine response of 20 mV for both dentate granule neurons and CA1 pyramidal cells. The average spine transient was attenuated less than 2% in conduction across the spine neck, considering peak voltage, waveform parameters, and charge transfer. The spine conductance transient resulted in an average somatic response of 100 microV in the dentate granule neurons, because of passive electrotonic propagation. The same input transient was also applied to proximal and distal sites on CA1 pyramidal cells. The predicted responses at the soma demonstrated a clear difference between the proximal and distal inputs, in terms of both peak voltage and waveform parameters. Thus, the main determinant of the passive propagation of transient electrical signals in these neurons appears to be dendritic branching rather than signal attenuation through the spine neck.  相似文献   

18.
A theoretical method, developed in a previous paper, enables one to calculate analytical expressions for time-varying voltages at specific locations in branching dendritic systems in response to synaptic current inputs at other sites. Exact results were obtained for a number of dendritic trees that possessed certain symmetries: all branch lengths had to be integral multiples of one another, and all branch diameters had to be equal. Because the second of these conditions is unrealistic, the method has been generalized to treat dendritic trees whose branches differ in diameter. The method entails adding onto the symmetric results a sum of correction terms. It is found that the correction terms, as well as the symmetric results, can be expressed as combinations of two families of functions. These functions, generalizations of those found in our earlier paper, provide a precise formalism for analyzing how voltage transients depend on the geometrical structure of the dendritic tree. Examples are given that show how the correction terms affect the value of the voltage, and how variations in branch diameters alter the behavior of the propagated postsynaptic potential. The implications of these results for our understanding of neuronal functioning are discussed.  相似文献   

19.
This study examined Leonardo da Vinci''s rule (i.e., the sum of the cross-sectional area of all tree branches above a branching point at any height is equal to the cross-sectional area of the trunk or the branch immediately below the branching point) using simulations based on two biomechanical models: the uniform stress and elastic similarity models. Model calculations of the daughter/mother ratio (i.e., the ratio of the total cross-sectional area of the daughter branches to the cross-sectional area of the mother branch at the branching point) showed that both biomechanical models agreed with da Vinci''s rule when the branching angles of daughter branches and the weights of lateral daughter branches were small; however, the models deviated from da Vinci''s rule as the weights and/or the branching angles of lateral daughter branches increased. The calculated values of the two models were largely similar but differed in some ways. Field measurements of Fagus crenata and Abies homolepis also fit this trend, wherein models deviated from da Vinci''s rule with increasing relative weights of lateral daughter branches. However, this deviation was small for a branching pattern in nature, where empirical measurements were taken under realistic measurement conditions; thus, da Vinci''s rule did not critically contradict the biomechanical models in the case of real branching patterns, though the model calculations described the contradiction between da Vinci''s rule and the biomechanical models. The field data for Fagus crenata fit the uniform stress model best, indicating that stress uniformity is the key constraint of branch morphology in Fagus crenata rather than elastic similarity or da Vinci''s rule. On the other hand, mechanical constraints are not necessarily significant in the morphology of Abies homolepis branches, depending on the number of daughter branches. Rather, these branches were often in agreement with da Vinci''s rule.  相似文献   

20.
Neuronal network formation depends on properly timed and localized generation of presynaptic as well as postsynaptic structures. Although of utmost importance for understanding development and plasticity of the nervous system and neurodegenerative diseases, the molecular mechanisms that ensure the fine-control needed for coordinated establishment of pre- and postsynapses are still largely unknown. We show that the F-actin-binding protein Abp1 is prominently expressed in the Drosophila nervous system and reveal that Abp1 is an important regulator in shaping glutamatergic neuromuscular junctions (NMJs) of flies. STED microscopy shows that Abp1 accumulations can be found in close proximity of synaptic vesicles and at the cell cortex in nerve terminals. Abp1 knock-out larvae have locomotion defects and underdeveloped NMJs that are characterized by a reduced number of both type Ib synaptic boutons and branches of motornerve terminals. Abp1 is able to indirectly trigger Arp2/3 complex-mediated actin nucleation and interacts with both WASP and Scar. Consistently, Arp2 and Arp3 loss-of-function also resulted in impairments of bouton formation and arborization at NMJs, i.e. fully phenocopied abp1 knock-out. Interestingly, neuron- and muscle-specific rescue experiments revealed that synaptic bouton formation critically depends on presynaptic Abp1, whereas the NMJ branching defects can be compensated for by restoring Abp1 functions at either side. In line with this presynaptic importance of Abp1, also presynaptic Arp2 and Arp3 are crucial for the formation of type Ib synaptic boutons. Interestingly, presynaptic Abp1 functions in NMJ formation were fully dependent on the Arp2/3 complex, as revealed by suppression of Abp1-induced synaptic bouton formation and branching of axon terminals upon presynaptic Arp2 RNAi. These data reveal that Abp1 and Arp2/3 complex-mediated actin cytoskeletal dynamics drive both synaptic bouton formation and NMJ branching. Our data furthermore shed light on an intense bidirectional functional crosstalk between pre- and postsynapses during the development of synaptic contacts.  相似文献   

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