Diffusion laws in dendritic spines
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Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically consist of a relatively large head connected to the dendritic shaft by a narrow cylindrical neck. The surface of the head is connected smoothly by a funnel or non-smoothly to the narrow neck, whose end absorbs the particles at the dendrite. We demonstrate here how the geometry of the neuronal spine can control diffusion and ultimately synaptic processes. We show that the mean residence time of a Brownian particle, such as an ion or molecule inside the spine, and of a receptor on its membrane, prior to absorption at the dendritic shaft depends strongly on the curvature of the connection of the spine head to the neck and on the neck's length. The analytical results solve the narrow escape problem for domains with long narrow necks.
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Modeling studies have often emphasized the interesting effects that shape can have on the diffusion of proteins, calcium ions and other signaling molecules.
“Nevertheless, modeling studies have often emphasized the interesting effects that shape can have on the diffusion of proteins, calcium ions and other signaling molecules (Holcman and Schuss, 2011).”
From Barriers in the brain: resolving dendritic spine morphology and compartmentalization (2014) · cites this paper as Holcman and Schuss, 2011
Modeling studies show that typical mushroom-like morphology strongly alters lateral diffusion of AMPA receptors, with pronounced suppression of receptor exit rate out of spines with decreasing neck radius and increasing neck length.
“These observations have been rationalized by several modeling studies, which showed that the typical mushroom-like morphology of dendritic spines strongly alters the lateral diffusion of AMPA receptors, demonstrating a pronounced suppression of the receptor exit rate out of spines with decreasing neck radius as well as increasing neck length (Holcman and Schuss, 2011; Kusters et al., 2013; Kusters”
From Barriers in the brain: resolving dendritic spine morphology and compartmentalization (2014) · cites this paper as Holcman and Schuss, 2011
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Lee, H., Li, X., & Wang, Y. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1702.07301
Resting-state dynamics in epilepsy : mechanistic insights from large-scale brain network modeling
Courtiol, J. (2020) · theses.fr (ABES) · doi:10.70675/0e102279zeb19z4f46zbf0ezbf7bdf9dd296
- Authors
- Holcman, D., & Schuss, Z.
- Affiliations
- École Normale Supérieure - PSL (FR)
- Tel Aviv University (IL)
- Corresponding author
- Holcman, David
- ORCID
- Holcman, David
- Venue
- The Journal of Mathematical Neuroscience
- Published
- 2011
- Volume
- 1
- Issue
- 1
- Pages
- 10
- ISSN
- 2190-8567 (ISSN-L)
- PMC
- PMC3365919
- OpenAlex
- W2140435774
- Cited by
- 50
- References
- 64
- Citations by year
- 2025: 2 · 2023: 1 · 2022: 4 · 2021: 3 · 2020: 2 · 2019: 1 · 2018: 2 · 2017: 5 · 2016: 3 · 2015: 5 · 2014: 10 · 2013: 7 · 2012: 5
- FWCI
- 7.71
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by
- Locations
- The Journal of Mathematical Neuroscience (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Modeling and Simulation › Fractional Differential Equations Solutions
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neuroscience and Neuropharmacology Research
- Keywords
- dendritic spines, diffusion, narrow escape problem, mean residence time, Brownian particles, spine geometry, synaptic transmission, ion channels, neck length, curvature, dendritic shafts
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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