An Algorithm for Finding Candidate Synaptic Sites in Computer Generated Networks of Neurons with Realistic Morphologies

Pelt, Jaap van; Carnell, Andrew; Ridder, Sander de; Mansvelder, Huibert D.; Ooyen, Arjen van

doi:10.3389/fncom.2010.00148

Cited by 11 publications

(20 citation statements)

References 28 publications

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“…With arborizations approximated by series of line pieces, one needs to test all combinations of axonal and dendritic line pieces. An algorithm for such a search has recently been developed by van Pelt et al ( 2010 ). The algorithm is based on the requirement that pairs of axonal and dendritic line pieces cross with a crossing distance smaller than a given criterion distance.…”

Section: Methodsmentioning

confidence: 99%

“…When we use the word synapse in the following, it is meant to mean candidate synapse. The method is based on proximity and crossing of axonal and dendritic line pieces (van Pelt et al, 2010 ). By varying the positions of the somata of the pre- and post-synaptic neurons, one can obtain the number of synaptic contacts as a function of neuron positions.…”

Section: Introductionmentioning

confidence: 99%

“…The objectives of this paper are (i) to derive connectivity from overlapping density fields using our recently developed criterion for the formation of synaptic contacts (van Pelt et al, 2010 ); (ii) to develop a method that is also applicable for highly irregular density fields (such as those of individual neurons) and that is thus not dependent on any smoothness requirement of the density fields; (iii) to validate the neuronal connectivity estimates from the overlapping density fields with the actual connectivity derived from mutually innervating axonal and dendritic arborizations.…”

Section: Introductionmentioning

confidence: 99%

“…These densities are then used to calculate the probabilities of finding axonal and dendritic line pieces in the voxels. Assuming uniform random orientations of these line pieces in each voxel, we then apply the above mentioned proximity/crossing criterion to axonal and dendritic line pieces (van Pelt et al, 2010 ) in the same or within different voxels. The connectivity measures between two neurons at given positions are obtained by evaluating all voxel pairs of the axonal and dendritic density fields.…”

Section: Introductionmentioning

confidence: 99%

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Estimating neuronal connectivity from axonal and dendritic density fields

Pelt

Ooyen

2013

Front. Comput. Neurosci.

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Neurons innervate space by extending axonal and dendritic arborizations. When axons and dendrites come in close proximity of each other, synapses between neurons can be formed. Neurons vary greatly in their morphologies and synaptic connections with other neurons. The size and shape of the arborizations determine the way neurons innervate space. A neuron may therefore be characterized by the spatial distribution of its axonal and dendritic “mass.” A population mean “mass” density field of a particular neuron type can be obtained by averaging over the individual variations in neuron geometries. Connectivity in terms of candidate synaptic contacts between neurons can be determined directly on the basis of their arborizations but also indirectly on the basis of their density fields. To decide when a candidate synapse can be formed, we previously developed a criterion defining that axonal and dendritic line pieces should cross in 3D and have an orthogonal distance less than a threshold value. In this paper, we developed new methodology for applying this criterion to density fields. We show that estimates of the number of contacts between neuron pairs calculated from their density fields are fully consistent with the number of contacts calculated from the actual arborizations. However, the estimation of the connection probability and the expected number of contacts per connection cannot be calculated directly from density fields, because density fields do not carry anymore the correlative structure in the spatial distribution of synaptic contacts. Alternatively, these two connectivity measures can be estimated from the expected number of contacts by using empirical mapping functions. The neurons used for the validation studies were generated by our neuron simulator NETMORPH. An example is given of the estimation of average connectivity and Euclidean pre- and postsynaptic distance distributions in a network of neurons represented by their population mean density fields.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating neuronal connectivity from axonal and dendritic density fields

Pelt

Ooyen

2013

Front. Comput. Neurosci.

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“…O ne of the main roles of dendrites is to connect a neuron to its synaptic inputs. To interpret neural connectivity from morphological data, it is important to understand the relationship between dendrite shape and synaptic input distribution (1)(2)(3)(4). As early as the end of the 19th century (5), it was suggested that dendrites optimize connectivity in terms of cable length and conduction time costs, and a number of recent studies have supported the idea that optimal wiring explains dendritic branching patterns using simulations (6)(7)(8) or by reasoning from first principles (1, 2, 9, 10).…”

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confidence: 99%

A scaling law derived from optimal dendritic wiring

Cuntz

Mathy

Häusser

2012

Proc. Natl. Acad. Sci. U.S.A.

111

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The wide diversity of dendritic trees is one of the most striking features of neural circuits. Here we develop a general quantitative theory relating the total length of dendritic wiring to the number of branch points and synapses. We show that optimal wiring predicts a 2/3 power law between these measures. We demonstrate that the theory is consistent with data from a wide variety of neurons across many different species and helps define the computational compartments in dendritic trees. Our results imply fundamentally distinct design principles for dendritic arbors compared with vascular, bronchial, and botanical trees.computational neuroscience | branching | dendrite | morphology | minimum spanning tree O ne of the main roles of dendrites is to connect a neuron to its synaptic inputs. To interpret neural connectivity from morphological data, it is important to understand the relationship between dendrite shape and synaptic input distribution (1-4). As early as the end of the 19th century (5), it was suggested that dendrites optimize connectivity in terms of cable length and conduction time costs, and a number of recent studies have supported the idea that optimal wiring explains dendritic branching patterns using simulations (6-8) or by reasoning from first principles (1, 2, 9, 10). However, although dendrite length is the most common measure for molecular studies of dendritic growth (11), its relationship to dendritic branching and the number of synaptic contacts has not been elucidated. Understanding this relationship should provide crucial constraints for circuit structure and function. Here we directly test the hypothesis that neurons wire up a space in an optimal way by studying the consequences for dendrite length and branching complexity. We derive a simple equation that directly relates dendrite length with the number of branch points, dendrite spanning volume, and number of synapses. ResultsRelating Total Dendritic Length to Optimal Wiring. We assume that a dendritic tree of total length L connects n target points distributed over a volume V (Fig. 1A). Each target point occupies an average volume V =n. A tree that optimizes wiring will tend to connect points to their nearest neighbors, which are on average located at distances proportional to ðV =nÞ 1=3 . We need at least n such dendritic sections to make up the tree. The total length L of these sections sums up toThis result shows that a 2/3 power law relationship between L and n (12) provides a lower bound for the total dendritic length, where c is a proportionality constant. Approximating the volume around each target point by a sphere, then c ¼ ð3=4πÞ 1=3 , and each dendritic section corresponds to the radius of a sphere, giving(SI Text and Fig. S1). Importantly, assuming a constant ratio between the number of branch points, bp and the number of target points (which is addressed later), this assumption also results in a 2/3 power law between wiring length and the number of branch points. Supporting these intuitive derivations of power laws, there ...

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