nips nips2001 nips2001-42 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Giorgio A. Ascoli, Alexei V. Samsonovich
Abstract: Visual inspection of neurons suggests that dendritic orientation may be determined both by internal constraints (e.g. membrane tension) and by external vector fields (e.g. neurotrophic gradients). For example, basal dendrites of pyramidal cells appear nicely fan-out. This regular orientation is hard to justify completely with a general tendency to grow straight, given the zigzags observed experimentally. Instead, dendrites could (A) favor a fixed (“external”) direction, or (B) repel from their own soma. To investigate these possibilities quantitatively, reconstructed hippocampal cells were subjected to Bayesian analysis. The statistical model combined linearly factors A and B, as well as the tendency to grow straight. For all morphological classes, B was found to be significantly positive and consistently greater than A. In addition, when dendrites were artificially re-oriented according to this model, the resulting structures closely resembled real morphologies. These results suggest that somatodendritic repulsion may play a role in determining dendritic orientation. Since hippocampal cells are very densely packed and their dendritic trees highly overlap, the repulsion must be cellspecific. We discuss possible mechanisms underlying such specificity. 1 I n t r od uc t i on The study of brain dynamics and development at the cellular level would greatly benefit from a standardized, accurate and yet succinct statistical model characterizing the morphology of major neuronal classes. Such model could also provide a basis for simulation of anatomically realistic virtual neurons [1]. The model should accurately distinguish among different neuronal classes: a morphological difference between classes would be captured by a difference in model parameters and reproduced in generated virtual neurons. In addition, the model should be self-consistent: there should be no statistical difference in model parameters measured from real neurons of a given class and from virtual neurons of the same class. The assumption that a simple statistical model of this sort exists relies on the similarity of average environmental and homeostatic conditions encountered by individual neurons during development and on the limited amount of genetic information that underlies differentiation of neuronal classes. Previous research in computational neuroanatomy has mainly focused on the topology and internal geometry of dendrites (i.e., the properties described in “dendrograms”) [2,3]. Recently, we attempted to include spatial orientation in the models, thus generating 2 virtual neurons in 3D [4]. Dendritic growth was assumed to deviate from the straight direction both randomly and based on a constant bias in a given direction, or “tropism”. Different models of tropism (e.g. along a fixed axis, towards a plane, or away from the soma) had dramatic effects on the shape of virtual neurons [5]. Our current strategy is to split the problem of finding a statistical model describing neuronal morphology in two parts. First, we maintain that the topology and the internal geometry of a particular dendritic tree can be described independently of its 3D embedding (i.e., the set of local dendritic orientations). At the same time, one and the same internal geometry (e.g., the experimental dendrograms obtained from real neurons) may have many equally plausible 3D embeddings that are statistically consistent with the anatomical characteristics of that neuronal class. The present work aims at finding a minimal statistical model describing local dendritic orientation in experimentally reconstructed hippocampal principal cells. Hippocampal neurons have a polarized shape: their dendrites tend to grow from the soma as if enclosed in cones. In pyramidal cells, basal and apical dendrites invade opposite hemispaces (fig. 1A), while granule cell dendrites all invade the same hemispace. This behavior could be caused by a tendency to grow towards the layers of incoming fibers to establish synapses. Such tendency would correspond to a tropism in a direction roughly parallel to the cell main axis. Alternatively, dendrites could initially stem in the appropriate (possibly genetically determined) directions, and then continue to grow approximately in a radial direction from the soma. A close inspection of pyramidal (basal) trees suggests that dendrites may indeed be repelled from their soma (Fig. 1B). A typical dendrite may reorient itself (arrow) to grow nearly straight along a radius from the soma. Remarkably, this happens even after many turns, when the initial direction is lost. Such behavior may be hard to explain without tropism. If the deviations from straight growth were random, one should be able to “remodel”th e trees by measuring and reproducing the statistics of local turn angles, assuming its independence of dendritic orientation and location. Figure 1C shows the cell from 1A after such remodeling. In this case basal and apical dendrites retain only their initial (stemming) orientations from the original data. The resulting “cotton ball” uggests that dendritic turns are not in dependent s of dendritic orientation. In this paper, we use Bayesian analysis to quantify the dendritic tropism. 2 M e t h od s Digital files of fully reconstructed rat hippocampal pyramidal cells (24 CA3 and 23 CA1 neurons) were kindly provided by Dr. D. Amaral. The overall morphology of these cells, as well as the experimental acquisition methods, were extensively described [6]. In these files, dendrites are represented as (branching) chains of cylindrical sections. Each section is connected to one other section in the path to the soma, and may be connected on the other extremity to two other sections (bifurcation), one other section (continuation point), or no other section (terminal tip). Each section is described in the file by its ending point coordinates, its diameter and its
Reference: text
sentIndex sentText sentNum sentScore
1 1 Bayesian morphometry of hippocampal cells suggests same-cell somatodendritic repulsion Giorgio A. [sent-1, score-0.409]
2 edu Abstract Visual inspection of neurons suggests that dendritic orientation may be determined both by internal constraints (e. [sent-4, score-0.805]
3 For example, basal dendrites of pyramidal cells appear nicely fan-out. [sent-9, score-0.943]
4 This regular orientation is hard to justify completely with a general tendency to grow straight, given the zigzags observed experimentally. [sent-10, score-0.258]
5 Instead, dendrites could (A) favor a fixed (“external”) direction, or (B) repel from their own soma. [sent-11, score-0.47]
6 To investigate these possibilities quantitatively, reconstructed hippocampal cells were subjected to Bayesian analysis. [sent-12, score-0.306]
7 The statistical model combined linearly factors A and B, as well as the tendency to grow straight. [sent-13, score-0.203]
8 In addition, when dendrites were artificially re-oriented according to this model, the resulting structures closely resembled real morphologies. [sent-15, score-0.506]
9 These results suggest that somatodendritic repulsion may play a role in determining dendritic orientation. [sent-16, score-0.707]
10 Since hippocampal cells are very densely packed and their dendritic trees highly overlap, the repulsion must be cellspecific. [sent-17, score-1.038]
11 1 I n t r od uc t i on The study of brain dynamics and development at the cellular level would greatly benefit from a standardized, accurate and yet succinct statistical model characterizing the morphology of major neuronal classes. [sent-19, score-0.205]
12 Such model could also provide a basis for simulation of anatomically realistic virtual neurons [1]. [sent-20, score-0.131]
13 The model should accurately distinguish among different neuronal classes: a morphological difference between classes would be captured by a difference in model parameters and reproduced in generated virtual neurons. [sent-21, score-0.176]
14 In addition, the model should be self-consistent: there should be no statistical difference in model parameters measured from real neurons of a given class and from virtual neurons of the same class. [sent-22, score-0.229]
15 The assumption that a simple statistical model of this sort exists relies on the similarity of average environmental and homeostatic conditions encountered by individual neurons during development and on the limited amount of genetic information that underlies differentiation of neuronal classes. [sent-23, score-0.226]
16 Previous research in computational neuroanatomy has mainly focused on the topology and internal geometry of dendrites (i. [sent-24, score-0.569]
17 Recently, we attempted to include spatial orientation in the models, thus generating 2 virtual neurons in 3D [4]. [sent-27, score-0.219]
18 Dendritic growth was assumed to deviate from the straight direction both randomly and based on a constant bias in a given direction, or “tropism”. [sent-28, score-0.23]
19 along a fixed axis, towards a plane, or away from the soma) had dramatic effects on the shape of virtual neurons [5]. [sent-31, score-0.131]
20 Our current strategy is to split the problem of finding a statistical model describing neuronal morphology in two parts. [sent-32, score-0.184]
21 First, we maintain that the topology and the internal geometry of a particular dendritic tree can be described independently of its 3D embedding (i. [sent-33, score-0.728]
22 , the experimental dendrograms obtained from real neurons) may have many equally plausible 3D embeddings that are statistically consistent with the anatomical characteristics of that neuronal class. [sent-38, score-0.174]
23 The present work aims at finding a minimal statistical model describing local dendritic orientation in experimentally reconstructed hippocampal principal cells. [sent-39, score-0.893]
24 Hippocampal neurons have a polarized shape: their dendrites tend to grow from the soma as if enclosed in cones. [sent-40, score-0.775]
25 In pyramidal cells, basal and apical dendrites invade opposite hemispaces (fig. [sent-41, score-0.911]
26 1A), while granule cell dendrites all invade the same hemispace. [sent-42, score-0.759]
27 This behavior could be caused by a tendency to grow towards the layers of incoming fibers to establish synapses. [sent-43, score-0.17]
28 Such tendency would correspond to a tropism in a direction roughly parallel to the cell main axis. [sent-44, score-0.446]
29 Alternatively, dendrites could initially stem in the appropriate (possibly genetically determined) directions, and then continue to grow approximately in a radial direction from the soma. [sent-45, score-0.713]
30 A close inspection of pyramidal (basal) trees suggests that dendrites may indeed be repelled from their soma (Fig. [sent-46, score-0.965]
31 A typical dendrite may reorient itself (arrow) to grow nearly straight along a radius from the soma. [sent-48, score-0.238]
32 If the deviations from straight growth were random, one should be able to “remodel”th e trees by measuring and reproducing the statistics of local turn angles, assuming its independence of dendritic orientation and location. [sent-51, score-0.873]
33 In this case basal and apical dendrites retain only their initial (stemming) orientations from the original data. [sent-53, score-0.779]
34 The resulting “cotton ball” uggests that dendritic turns are not in dependent s of dendritic orientation. [sent-54, score-1.126]
35 In this paper, we use Bayesian analysis to quantify the dendritic tropism. [sent-55, score-0.563]
36 2 M e t h od s Digital files of fully reconstructed rat hippocampal pyramidal cells (24 CA3 and 23 CA1 neurons) were kindly provided by Dr. [sent-56, score-0.612]
37 In these files, dendrites are represented as (branching) chains of cylindrical sections. [sent-60, score-0.47]
38 , the attached section in the path to the soma [5,7]. [sent-64, score-0.143]
39 In CA3 cells, basal dendrites had an average of 687(±216) continuation points and 72(±17) bifurcations per cell, while apical dendrites had 717(±156) continuation points and 80(±21) bifurcations per cell. [sent-65, score-1.6]
40 CA1 cells had 462(±138) continuation points and 52(±12) bifurcations (basal), 860(±188) continuation points and 120(±22) bifurcations (apical). [sent-66, score-0.59]
41 In the present work, basal and apical trees of CA3 and CA1 pyramidal cells were treated as 4 different classes. [sent-67, score-0.64]
42 Digital data of rat dentate granule cells [8] are kindly made available by Dr. [sent-68, score-0.428]
43 Only 36 of the 42 cells in this archive were used: in 6 cases numerical processing was not accomplished due to minor inconsistencies in the data files. [sent-73, score-0.212]
44 The “ rejected” cells were 1208875, 3319201, 411883, 411884A, 411884B, 803887B. [sent-74, score-0.176]
45 Granule dendrites had 3 549(±186) continuation points and 30(±6) bifurcations per cell. [sent-75, score-0.677]
46 Figure 1: A: A pyramidal cell (c53063) from Amaral’s archive. [sent-81, score-0.271]
47 B: A zoom-in from panel A (arrows point to the same basal tree location). [sent-82, score-0.177]
48 C: Same cell (c53063) with its dendritic orientation remodeled assuming zero tropism and same statistics of all turn angles (see Results). [sent-84, score-0.979]
49 In agreement with the available format of morphological data (described above), the process of dendritic growth1 can be represented as a discrete stochastic process consisting of sequential attachment of new sections to each growing dendrite. [sent-85, score-0.635]
50 Here we keep the given internal geometry of the experimental data while remodeling the 3D embedding geometry (dendritic orientation). [sent-86, score-0.293]
51 Specifically, we assume that (i) each step in dendritic outgrowth only depends on the preceding step and on current local conditions; and (ii) dendrites do not undergo geometrical or topological modification after their formation (see, however, Discussion). [sent-89, score-1.058]
52 In this Markov approximation, a plausible 3D embedding can be found by sequentially orienting individual sections, starting from the soma and moving toward the terminals. [sent-90, score-0.206]
53 For a continuation point, the most likely direction n'i+1 is computed as the direction of the vector sum ni + vi. [sent-93, score-0.372]
54 The first term is the direction of the parent section ni , and reflects the tendency dendrites exhibit to grow relatively straight due to membrane tension, mechanical properties of the cytoskeleton, etc. [sent-94, score-0.903]
55 The second term is a local value of a vector field: vi = v(ri ), which comprises the influence of external local conditions on the direction of growth (as specified below). [sent-95, score-0.237]
56 Finally, we generate a perturbation of the most likely direction n'i+1 to produce a particular plausible instance of a new direction. [sent-96, score-0.158]
57 A more accurate and plausible description of dendritic orientation at bifurcations might require a more complex model. [sent-103, score-0.781]
58 In this case one would first need to generate the internal geometry of the dendrites [1-5]. [sent-106, score-0.569]
59 Most importantly, model (1), (2) can be used to quantitatively assess the significance of the somatocentric (radial) tropism of real dendrites. [sent-107, score-0.333]
60 Assuming that there is a significant preferential directionality of growth in hippocampal dendrites, the two main alternatives are (see Introduction): HA: The dominating tropic factor is independent of the location of the soma. [sent-108, score-0.343]
61 nri is the unit vector in the direction connecting the soma to node i, thus representing a somatocentric tropic factor. [sent-113, score-0.397]
62 The most likely direction of a varied significantly among cells, i. [sent-127, score-0.152]
63 The slightly higher coefficient of variation obtained for granule cells could be due to a larger experimental error in the z coordinate (orthogonal to the slice). [sent-193, score-0.374]
64 In several granule cells (but in none of the pyramidal cells) the greater noise in z was apparent upon visual inspection of the rendered structures. [sent-194, score-0.543]
65 Results changed only minimally for pyramidal cells, and the granule cell parameters became more consistent with the pyramidal cells. [sent-196, score-0.571]
66 The measured average values of the model parameters were used for remodeling of experimental neuronal shapes, as described above. [sent-197, score-0.206]
67 We kept the internal geometry and the initial stemming direction of each tree from the experimental data, and simulated dendritic orientation at all nodes separated by more than 2 steps from the soma. [sent-200, score-0.944]
68 Generally, the artificially re-oriented dendrites looked better than one could expect for a model as simple as (1) – (3). [sent-202, score-0.506]
69 This result may be compared with figure 1C, which shows an example of remodeling based on the same model in the absence of tropism (a = b = 0). [sent-203, score-0.24]
70 Thus, although the tendency to grow straight represents the dominant component of the model (i. [sent-206, score-0.24]
71 , b<1), somatocentric tropism may exert a dramatic effect on dendritic shape. [sent-208, score-0.833]
72 Surprisingly, even the asymmetry of the dendritic spread (compare front and side views) is preserved after remodeling. [sent-209, score-0.563]
73 However, two details are difficult to reproduce with this model: the uniform distribution of dendrites in space and other subtle medium-distance correlations among dendritic deflections. [sent-210, score-1.033]
74 6 4 D i s c us s i on The key results of this work is that, according to Bayesian analysis, dendrites of hippocampal principal cells display a significant radial tropism. [sent-212, score-0.792]
75 This means that the spatial orientation of these neuronal trees can be statistically described as if dendrites were repelled from their own soma. [sent-213, score-0.781]
76 This preferential direction is stronger than any tendency to grow along a fixed direction independent of the location of the soma. [sent-214, score-0.419]
77 These results apply to all dendritic classes, but in general pyramidal cell basal trees (and granule cell dendrites) display a bigger somatocentric tropism than apical trees. [sent-215, score-1.662]
78 A, B: front and side views of cell 10861 from Amaral' s archive. [sent-217, score-0.142]
79 © ¥ £ ¡ Assuming that dendrites are indeed repelled from their soma during development, what could be a plausible mechanism? [sent-222, score-0.743]
80 Principal cells are very densely packed in the hippocampus, and their dendrites highly overlap. [sent-223, score-0.707]
81 If repulsion were mediated by a diffusible chemical factor, in order for dendrites to be repelled radially from their own soma, each neuron should have its own specific chemical marker (a fairly unlikely possibility). [sent-224, score-0.81]
82 If the same repulsive factor were released by all neurons, each dendrite would be repelled by hundreds of somata, and not just by their own. [sent-225, score-0.172]
83 The resulting tropism would be perpendicular to the principal cell layer, i. [sent-226, score-0.299]
84 The philopodia of dendritic growth 7 cones could possess voltage-gated receptors to sense transient chemical gradients (e. [sent-233, score-0.803]
85 Only dendrites that are depolarized during the transient chemical gradient (i. [sent-236, score-0.603]
86 However, it is important to note that any observed deviation of dendritic path from a straight line, including that due to measurement errors, causes an increase in the most likely values of parameters a and b. [sent-243, score-0.688]
87 Another possibility is that dendrites do grow almost precisely in straight lines, and the measured values of a and b reflect distortions of dendritic shapes after development. [sent-244, score-1.266]
88 In order to assess the effect of these factors on a and b, we pre-processed the experimental data by adding a gradually increasing noise to all coordinates of dendritic sections. [sent-245, score-0.628]
89 For basal trees of CA3 pyramidal cells, this analysis yielded an estimated “corrected” value of b between 0. [sent-248, score-0.356]
90 Interestingly, our analysis based on extrapolation shows that, regardless of the assumed amount of distortion present in the experimental data, given the numbers measured for CA3 basal trees, positive initial <α> implies positive initial b. [sent-251, score-0.196]
91 In other words, not only measurement errors, but also possible biological distortions of the dendritic tree may not be capable of accounting for the observed positivity of the parameter b. [sent-252, score-0.674]
92 Nevertheless, artificially reoriented dendrites according to our simple model appear almost as realistic as the original structures, and we could not achieve the same result with any choice of parameters in models of distortion without a somatocentric tropism. [sent-255, score-0.614]
93 In conclusion, whether the present Bayesian analysis reveals a phenomenon of somatodendritic repulsion remains an (experimentally testable) open question. [sent-256, score-0.144]
94 What is unquestionable is that the presented model is a significant step forward in the formulation of an accurate statistical description of dendritic morphology. [sent-257, score-0.563]
95 Ulfhake (1992) A parsimonious description of motoneurons dendritic morphology using computer simulation. [sent-275, score-0.641]
96 Krichmar (2000) L-Neuron: a modeling tool for the efficient generation and parsimonious description of dendritic morphology. [sent-282, score-0.563]
97 Senft (2001) Generation, description and storage of dendritic morphology data. [sent-289, score-0.641]
98 Amaral (1995) A quantitative analysis of the dendritic organization of pyramidal cells in the rat hippocampus. [sent-298, score-0.944]
99 Wheal (1998) An on-line archive of reconstructed hippocampal neurons. [sent-308, score-0.166]
100 Claiborne (1990) Dendritic growth and regression in rat dentate granule cells during late postnatal development. [sent-315, score-0.467]
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simIndex simValue paperId paperTitle
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Author: Giorgio A. Ascoli, Alexei V. Samsonovich
Abstract: Visual inspection of neurons suggests that dendritic orientation may be determined both by internal constraints (e.g. membrane tension) and by external vector fields (e.g. neurotrophic gradients). For example, basal dendrites of pyramidal cells appear nicely fan-out. This regular orientation is hard to justify completely with a general tendency to grow straight, given the zigzags observed experimentally. Instead, dendrites could (A) favor a fixed (“external”) direction, or (B) repel from their own soma. To investigate these possibilities quantitatively, reconstructed hippocampal cells were subjected to Bayesian analysis. The statistical model combined linearly factors A and B, as well as the tendency to grow straight. For all morphological classes, B was found to be significantly positive and consistently greater than A. In addition, when dendrites were artificially re-oriented according to this model, the resulting structures closely resembled real morphologies. These results suggest that somatodendritic repulsion may play a role in determining dendritic orientation. Since hippocampal cells are very densely packed and their dendritic trees highly overlap, the repulsion must be cellspecific. We discuss possible mechanisms underlying such specificity. 1 I n t r od uc t i on The study of brain dynamics and development at the cellular level would greatly benefit from a standardized, accurate and yet succinct statistical model characterizing the morphology of major neuronal classes. Such model could also provide a basis for simulation of anatomically realistic virtual neurons [1]. The model should accurately distinguish among different neuronal classes: a morphological difference between classes would be captured by a difference in model parameters and reproduced in generated virtual neurons. In addition, the model should be self-consistent: there should be no statistical difference in model parameters measured from real neurons of a given class and from virtual neurons of the same class. The assumption that a simple statistical model of this sort exists relies on the similarity of average environmental and homeostatic conditions encountered by individual neurons during development and on the limited amount of genetic information that underlies differentiation of neuronal classes. Previous research in computational neuroanatomy has mainly focused on the topology and internal geometry of dendrites (i.e., the properties described in “dendrograms”) [2,3]. Recently, we attempted to include spatial orientation in the models, thus generating 2 virtual neurons in 3D [4]. Dendritic growth was assumed to deviate from the straight direction both randomly and based on a constant bias in a given direction, or “tropism”. 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In pyramidal cells, basal and apical dendrites invade opposite hemispaces (fig. 1A), while granule cell dendrites all invade the same hemispace. This behavior could be caused by a tendency to grow towards the layers of incoming fibers to establish synapses. Such tendency would correspond to a tropism in a direction roughly parallel to the cell main axis. Alternatively, dendrites could initially stem in the appropriate (possibly genetically determined) directions, and then continue to grow approximately in a radial direction from the soma. A close inspection of pyramidal (basal) trees suggests that dendrites may indeed be repelled from their soma (Fig. 1B). A typical dendrite may reorient itself (arrow) to grow nearly straight along a radius from the soma. Remarkably, this happens even after many turns, when the initial direction is lost. Such behavior may be hard to explain without tropism. 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Each section is connected to one other section in the path to the soma, and may be connected on the other extremity to two other sections (bifurcation), one other section (continuation point), or no other section (terminal tip). Each section is described in the file by its ending point coordinates, its diameter and its
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