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Topological characterization of neuronal arbor morphology via sequence representation: I--motif analysis.

Gillette TA, Ascoli GA - BMC Bioinformatics (2015)

Bottom Line: Numerous reports have focused on metrics at the level of individual branches or whole arbors; however, no studies have attempted to quantify repeated morphological patterns within neuronal trees.In addition, pyramidal apical dendrites reveal a distinct motif profile.The quantitative characterization of topological motifs in neuronal arbors provides a thorough description of local features and detailed boundaries for growth mechanisms and hypothesized computational functions.

View Article: PubMed Central - PubMed

Affiliation: Department of Molecular Neuroscience, Center for Neural Informatics, Structures, and Plasticity, Krasnow Institute for Advanced Study (MS2A1), George Mason University, Fairfax, VA, USA. todd.gillette@gmail.com.

ABSTRACT

Background: The morphology of neurons offers many insights into developmental processes and signal processing. Numerous reports have focused on metrics at the level of individual branches or whole arbors; however, no studies have attempted to quantify repeated morphological patterns within neuronal trees. We introduce a novel sequential encoding of neurite branching suitable to explore topological patterns.

Results: Using all possible branching topologies for comparison we show that the relative abundance of short patterns of up to three bifurcations, together with overall tree size, effectively capture the local branching patterns of neurons. Dendrites and axons display broadly similar topological motifs (over-represented patterns) and anti-motifs (under-represented patterns), differing most in their proportions of bifurcations with one terminal branch and in select sub-sequences of three bifurcations. In addition, pyramidal apical dendrites reveal a distinct motif profile.

Conclusions: The quantitative characterization of topological motifs in neuronal arbors provides a thorough description of local features and detailed boundaries for growth mechanisms and hypothesized computational functions.

No MeSH data available.


Measuring k-mers. a. Highlighted dimers in a portion of a fly tangential cell [64] and its associated sequence. b. Dimer schematics displaying the possible configurations. Triangles represent subtrees of unspecified size and shape. Bold segments indicate branches leading to the larger side subtree of the parent A node. Given the (Smaller then Larger) traversal method, the TT dimer must be preceded by an A. TA and TC schematics are examples, as additional bifurcations could be found between the parent A and small-side T nodes. c. Number of k-mers (with examples) by k shows an approximately exponential rise. d. Calculating the percentile rank of a k-mer given the distribution of k-mer counts in the source sequence’s surrogate population. An example apical dendrite (NMO_02582 from [65]), dendrogram, and sequence are shown along with cumulative distribution of k-mer counts for k-mers AT (red) and AC (green). Below: Six out of 100 node-type-constrained surrogates are shown. The example k-mers are highlighted and their counts compose the distributions. Colored dots show the respective percentile ranks of the apical dendrite k-mer counts, with AT being above nearly the entire surrogate distribution (thus constituting a motif) and AC being “captured” inside the middle 95% of its surrogate distribution.
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Fig2: Measuring k-mers. a. Highlighted dimers in a portion of a fly tangential cell [64] and its associated sequence. b. Dimer schematics displaying the possible configurations. Triangles represent subtrees of unspecified size and shape. Bold segments indicate branches leading to the larger side subtree of the parent A node. Given the (Smaller then Larger) traversal method, the TT dimer must be preceded by an A. TA and TC schematics are examples, as additional bifurcations could be found between the parent A and small-side T nodes. c. Number of k-mers (with examples) by k shows an approximately exponential rise. d. Calculating the percentile rank of a k-mer given the distribution of k-mer counts in the source sequence’s surrogate population. An example apical dendrite (NMO_02582 from [65]), dendrogram, and sequence are shown along with cumulative distribution of k-mer counts for k-mers AT (red) and AC (green). Below: Six out of 100 node-type-constrained surrogates are shown. The example k-mers are highlighted and their counts compose the distributions. Colored dots show the respective percentile ranks of the apical dendrite k-mer counts, with AT being above nearly the entire surrogate distribution (thus constituting a motif) and AC being “captured” inside the middle 95% of its surrogate distribution.

Mentions: To determine what patterns neurites exhibit among all tree shapes, a motif analysis was carried out for bifurcation subsequences of (increasing) length k, termed k-mers. Besides the three monomers A, C, and T, there are nine dimers (Figure 2a,b), and the number of k-mers grows approximately exponentially with k (Figure 2c). There are 27 permutations of trimer sequences, but not all exist due to tree constraints, while some LtS trimers are included as they capture different structures than StL trimers (the same applies to tetrametrs and pentamers). The StL trimers CTT and TTT do not occur as the latter T is a complete subtree that is smaller than its preceding sibling subtree. Any LtS k-mer with an A or T in the middle (of which there are 14 trimers), such as AAT or CCTC, describes a sequence of bifurcations not captured by any StL k-mer. In contrast, the ACStL dimer represents a pattern equivalent to that of the TCLtS dimer as in both cases the C is the smaller-side child of an A. The same relationship holds between the ACTStL and TCTLtS trimers, in which the CT is the smaller-side child of an A. Indeed, some LtS trimers do differ from their corresponding StL trimers (e.g. CTC and L-CTC or ATA and L-TTA: see Additional file 1: Figure S3).Figure 2


Topological characterization of neuronal arbor morphology via sequence representation: I--motif analysis.

Gillette TA, Ascoli GA - BMC Bioinformatics (2015)

Measuring k-mers. a. Highlighted dimers in a portion of a fly tangential cell [64] and its associated sequence. b. Dimer schematics displaying the possible configurations. Triangles represent subtrees of unspecified size and shape. Bold segments indicate branches leading to the larger side subtree of the parent A node. Given the (Smaller then Larger) traversal method, the TT dimer must be preceded by an A. TA and TC schematics are examples, as additional bifurcations could be found between the parent A and small-side T nodes. c. Number of k-mers (with examples) by k shows an approximately exponential rise. d. Calculating the percentile rank of a k-mer given the distribution of k-mer counts in the source sequence’s surrogate population. An example apical dendrite (NMO_02582 from [65]), dendrogram, and sequence are shown along with cumulative distribution of k-mer counts for k-mers AT (red) and AC (green). Below: Six out of 100 node-type-constrained surrogates are shown. The example k-mers are highlighted and their counts compose the distributions. Colored dots show the respective percentile ranks of the apical dendrite k-mer counts, with AT being above nearly the entire surrogate distribution (thus constituting a motif) and AC being “captured” inside the middle 95% of its surrogate distribution.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4496917&req=5

Fig2: Measuring k-mers. a. Highlighted dimers in a portion of a fly tangential cell [64] and its associated sequence. b. Dimer schematics displaying the possible configurations. Triangles represent subtrees of unspecified size and shape. Bold segments indicate branches leading to the larger side subtree of the parent A node. Given the (Smaller then Larger) traversal method, the TT dimer must be preceded by an A. TA and TC schematics are examples, as additional bifurcations could be found between the parent A and small-side T nodes. c. Number of k-mers (with examples) by k shows an approximately exponential rise. d. Calculating the percentile rank of a k-mer given the distribution of k-mer counts in the source sequence’s surrogate population. An example apical dendrite (NMO_02582 from [65]), dendrogram, and sequence are shown along with cumulative distribution of k-mer counts for k-mers AT (red) and AC (green). Below: Six out of 100 node-type-constrained surrogates are shown. The example k-mers are highlighted and their counts compose the distributions. Colored dots show the respective percentile ranks of the apical dendrite k-mer counts, with AT being above nearly the entire surrogate distribution (thus constituting a motif) and AC being “captured” inside the middle 95% of its surrogate distribution.
Mentions: To determine what patterns neurites exhibit among all tree shapes, a motif analysis was carried out for bifurcation subsequences of (increasing) length k, termed k-mers. Besides the three monomers A, C, and T, there are nine dimers (Figure 2a,b), and the number of k-mers grows approximately exponentially with k (Figure 2c). There are 27 permutations of trimer sequences, but not all exist due to tree constraints, while some LtS trimers are included as they capture different structures than StL trimers (the same applies to tetrametrs and pentamers). The StL trimers CTT and TTT do not occur as the latter T is a complete subtree that is smaller than its preceding sibling subtree. Any LtS k-mer with an A or T in the middle (of which there are 14 trimers), such as AAT or CCTC, describes a sequence of bifurcations not captured by any StL k-mer. In contrast, the ACStL dimer represents a pattern equivalent to that of the TCLtS dimer as in both cases the C is the smaller-side child of an A. The same relationship holds between the ACTStL and TCTLtS trimers, in which the CT is the smaller-side child of an A. Indeed, some LtS trimers do differ from their corresponding StL trimers (e.g. CTC and L-CTC or ATA and L-TTA: see Additional file 1: Figure S3).Figure 2

Bottom Line: Numerous reports have focused on metrics at the level of individual branches or whole arbors; however, no studies have attempted to quantify repeated morphological patterns within neuronal trees.In addition, pyramidal apical dendrites reveal a distinct motif profile.The quantitative characterization of topological motifs in neuronal arbors provides a thorough description of local features and detailed boundaries for growth mechanisms and hypothesized computational functions.

View Article: PubMed Central - PubMed

Affiliation: Department of Molecular Neuroscience, Center for Neural Informatics, Structures, and Plasticity, Krasnow Institute for Advanced Study (MS2A1), George Mason University, Fairfax, VA, USA. todd.gillette@gmail.com.

ABSTRACT

Background: The morphology of neurons offers many insights into developmental processes and signal processing. Numerous reports have focused on metrics at the level of individual branches or whole arbors; however, no studies have attempted to quantify repeated morphological patterns within neuronal trees. We introduce a novel sequential encoding of neurite branching suitable to explore topological patterns.

Results: Using all possible branching topologies for comparison we show that the relative abundance of short patterns of up to three bifurcations, together with overall tree size, effectively capture the local branching patterns of neurons. Dendrites and axons display broadly similar topological motifs (over-represented patterns) and anti-motifs (under-represented patterns), differing most in their proportions of bifurcations with one terminal branch and in select sub-sequences of three bifurcations. In addition, pyramidal apical dendrites reveal a distinct motif profile.

Conclusions: The quantitative characterization of topological motifs in neuronal arbors provides a thorough description of local features and detailed boundaries for growth mechanisms and hypothesized computational functions.

No MeSH data available.