The Combinatorics of Neurite Self-Avoidance

Forbes, Elizabeth M.; Hunt, Jonathan J.; Goodhill, Geoffrey J.

doi:10.1162/neco_a_00186

Cited by 8 publications

(7 citation statements)

References 26 publications

(47 reference statements)

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“…To consider this model in detail and to evaluate the implications of the high level of common-isoform tolerance identified in our study, we carried out an independent analysis of the factors that may contribute to Pcdh-mediated neuronal identity. Our analysis is based in part on earlier studies on Dscam1 by (Hattori et al, 2009) and by (Forbes et al, 2011), but focuses on the issue of isoform tolerance and introduces a factor not addressed previously; specifically how do neurites of the same neuron recognize that they are “the same”? We believe that the cis -tetramer model fails to answer this question.…”

Section: Discussionmentioning

confidence: 99%

“…Given the total number of possible isoforms, the number of isoforms expressed per cell (the x-axis in the figure), and a common-isoform tolerance, analytical expressions (Forbes, 2011) or Monte-Carlo simulations (Hattori et al, 2009) can be used to calculate these probabilities (See Supplemental Information). Results for Dscam1 were reported for a 5000-member isoform pool with a 15% tolerance (Hattori et al, 2009).…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Single-Cell Identity Generated by Combinatorial Homophilic Interactions between α, β, and γ Protocadherins

Thu

Chen

Rubinstein

et al. 2014

Cell

198

447

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Summary Individual mammalian neurons express distinct repertoires of protocadherin (Pcdh) -α, -β and -γ proteins that function in neural circuit assembly. Here we show that all three types of Pcdhs can engage in specific homophilic interactions, that cell surface delivery of alternate Pcdhα isoforms requires cis interactions with other Pcdh isoforms, and that the extracellular cadherin domain EC6 plays a critical role in this process. Analysis of specific combinations of up to five Pcdh isoforms showed that Pcdh homophilic recognition specificities strictly depend on the identity of all of the expressed isoforms, such that mismatched isoforms interfere with cell-cell interactions. We present a theoretical analysis showing that the assembly of Pcdh-α, –β and –γ isoforms into multimeric recognition units, and the observed tolerance for mismatched isoforms can generate the cell surface diversity necessary for single-cell identity. However, competing demands of non-self discrimination and self-recognition place limitations on the mechanisms by which recognition units can function.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Single-Cell Identity Generated by Combinatorial Homophilic Interactions between α, β, and γ Protocadherins

Thu

Chen

Rubinstein

et al. 2014

Cell

198

447

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“…Previous studies using RT-PCR analysis on single MB neurons also indicated that each neuron expresses multiple variants of exon 9 (Zhan et al, 2004). Monte Carlo simulations and mathematical modeling suggest that expression of multiple isoforms in a neuron through probabilistic splicing can provide a robust mechanism to endow each neuron with a unique cell surface identity (Forbes et al, 2011; Hattori et al, 2009). Indeed, this robustness is supported by the observation that the differential Dscam1 expression in L1 and L2 neurons arises from probabilistic splicing in these neurons.…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively, the pattern of isoform expression may not be regulated in a deterministic fashion, but rather may result from lack of regulation. A probabilistic choice of isoforms, in theory, provides a robust and efficient means by which neurons acquire unique identities (Forbes et al, 2011; Hattori et al, 2009). Furthermore, different strategies may be employed in different systems.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Splicing of Dscam1 Establishes Identity at the Level of Single Neurons

Miura

Martins

Zhang

et al. 2013

Cell

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The Drosophila Dscam1 gene encodes a vast number of cell recognition molecules through alternative splicing. These exhibit isoform-specific homophilic binding and regulate self-avoidance, the tendency of neurites from the same cell to repel one another. Genetic experiments indicate that different cells must express different isoforms. How this is achieved is not known, as the expression of alternative exons in vivo has not been shown. Here, we modified the endogenous Dscam1 locus to generate splicing reporters for all variants of exon 4. We demonstrate that splicing does not occur in a cell-type specific fashion, that cells identified by their unique locations express different exon 4 variants in different animals, and that splicing in identified neurons can change over time. Probabilistic expression is compatible with a widespread role in neural circuit assembly through self-avoidance and is incompatible with models in which specific isoforms of Dscam1 mediate recognition between processes of different cells.

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“…The Dscam1 protein isoforms have homophilic activity at the single isoform level. Calculation using a Monte Carlo simulation (Hattori et al, 2009) and combinatorics by closed-form solutions (Forbes et al, 2011) indicated a 4.4% chance that a pair of neurons shares at least one isoform, from 30 random expressions of 20,000 isoforms. Similar probabilities are estimated for Dscam1 in insects and clustered Pcdhs in vertebrates, even though the mechanism for randomness is different; that is, alternative splicing of Dscam1 or promoter choice and cis -tetramers for clustered Pcdh.…”

Section: Heteromultimeric Protein Complexmentioning

confidence: 99%

Molecular codes for neuronal individuality and cell assembly in the brain

Yagi¹

2012

Front. Mol. Neurosci.

118

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The brain contains an enormous, but finite, number of neurons. The ability of this limited number of neurons to produce nearly limitless neural information over a lifetime is typically explained by combinatorial explosion; that is, by the exponential amplification of each neuron's contribution through its incorporation into “cell assemblies” and neural networks. In development, each neuron expresses diverse cellular recognition molecules that permit the formation of the appropriate neural cell assemblies to elicit various brain functions. The mechanism for generating neuronal assemblies and networks must involve molecular codes that give neurons individuality and allow them to recognize one another and join appropriate networks. The extensive molecular diversity of cell-surface proteins on neurons is likely to contribute to their individual identities. The clustered protocadherins (Pcdh) is a large subfamily within the diverse cadherin superfamily. The clustered Pcdh genes are encoded in tandem by three gene clusters, and are present in all known vertebrate genomes. The set of clustered Pcdh genes is expressed in a random and combinatorial manner in each neuron. In addition, cis-tetramers composed of heteromultimeric clustered Pcdh isoforms represent selective binding units for cell-cell interactions. Here I present the mathematical probabilities for neuronal individuality based on the random and combinatorial expression of clustered Pcdh isoforms and their formation of cis-tetramers in each neuron. Notably, clustered Pcdh gene products are known to play crucial roles in correct axonal projections, synaptic formation, and neuronal survival. Their molecular and biological features induce a hypothesis that the diverse clustered Pcdh molecules provide the molecular code by which neuronal individuality and cell assembly permit the combinatorial explosion of networks that supports enormous processing capability and plasticity of the brain.

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The Combinatorics of Neurite Self-Avoidance

Cited by 8 publications

References 26 publications

Single-Cell Identity Generated by Combinatorial Homophilic Interactions between α, β, and γ Protocadherins

Single-Cell Identity Generated by Combinatorial Homophilic Interactions between α, β, and γ Protocadherins

Probabilistic Splicing of Dscam1 Establishes Identity at the Level of Single Neurons

Molecular codes for neuronal individuality and cell assembly in the brain

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