The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
The narrow escape problem for diffusion in cellular microdomains
Open accessAbstract
The study of the diffusive motion of ions or molecules in confined biological microdomains requires the derivation of the explicit dependence of quantities, such as the decay rate of the population or the forward chemical reaction rate constant on the geometry of the domain. Here, we obtain this explicit dependence for a model of a Brownian particle (ion, molecule, or protein) confined to a bounded domain (a compartment or a cell) by a reflecting boundary, except for a small window through which it can escape. We call the calculation of the mean escape time the narrow escape problem. This time diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. Here, we present asymptotic formulas for the mean escape time in several cases, including regular domains in two and three dimensions and in some singular domains in two dimensions. The mean escape time comes up in many applications, because it represents the mean time it takes for a molecule to hit a target binding site. We present several applications in cellular biology: calcium decay in dendritic spines, a Markov model of multicomponent chemical reactions in microdomains, dynamics of receptor diffusion on the surface of neurons, and vesicle trafficking inside a cell.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Reaction-rate theory: fifty years after Kramers
Hänggi, P., Talkner, P., & Borkovec, M. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.251 · Cited by 6,154
The molecular basis of CaMKII function in synaptic and behavioural memory
Lisman, J., Schulman, H., & Cline, H. (2002) · Nature Reviews Neuroscience · doi:10.1038/nrn753 · Cited by 1,860
Brownian motion in biological membranes
Saffman, P. G., & Delbrück, M. (1975) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.72.8.3111 · Cited by 1,773
AMPA receptor trafficking at excitatory synapses
Bredt, D. S., & Nicoll, R. A. (2003) · Neuron · doi:10.1016/s0896-6273(03)00640-8 · Cited by 1,150
Macromolecular Architecture in Eukaryotic Cells Visualized by Cryoelectron Tomography
Medalia, O., Weber, I., Frangakis, A. S., Nicastro, D., Gerisch, G., & Baumeister, W. (2002) · Science · doi:10.1126/science.1076184 · Cited by 837
Genesis of dendritic spines: insights from ultrastructural and imaging studies
Yuste, R., & Bonhoeffer, T. (2004) · Nature Reviews Neuroscience · doi:10.1038/nrn1300 · Cited by 639
Metabolic instability of plasmid DNA in the cytosol: a potential barrier to gene transfer
Lechardeur, D., Sohn, K.-J., Haardt, M., Joshi, P. B., Monck, M., Graham, R. W., Beatty, B., Squire, J., O’Brodovich, H., & Lukacs, G. L. (1999) · Gene Therapy · doi:10.1038/sj.gt.3300867 · Cited by 633
The CaM kinase II hypothesis for the storage of synaptic memory
Lisman, J. (1994) · Trends in Neurosciences · doi:10.1016/0166-2236(94)90014-0 · Cited by 501
Dendritic spines and long-term plasticity
Segal, M. (2005) · Nature Reviews Neuroscience · doi:10.1038/nrn1649 · Cited by 489
Direct measurement of coupling between dendritic spines and shafts
Svoboda, K., Tank, D. W., & Denk, W. (1996) · Science · doi:10.1126/science.272.5262.716 · Cited by 472
Cited by
Stochastic models of intracellular transport
Bressloff, P. C., & Newby, J. M. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.135 · Cited by 629
Bénichou, O., Chevalier, C., Klafter, J., Meyer, B., & Voituriez, R. (2010) · Nature Chemistry · doi:10.1038/nchem.622 · Cited by 351
Diffusion laws in dendritic spines
Holcman, D., & Schuss, Z. (2011) · The Journal of Mathematical Neuroscience · doi:10.1186/2190-8567-1-10 · Cited by 50
Self-citationGuerrier, C., & Holcman, D. (2016) · Scientific Reports · doi:10.1038/srep35506 · Cited by 16
Self-citation
Metadata
- Authors
- Schuss, Z., Singer, A., & Holcman, D.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2007-10-09
- Volume
- 104
- Issue
- 41
- Pages
- 16098-16103
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2048212809
- Cited by
- 332
- References
- 32
- FWCI
- 4.79
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The narrow escape problem for diffusion in cellular microdomains. https://app.cochat.ai/papers/10.1073/pnas.0706599104
- The paper
- Schuss, Z., Singer, A., & Holcman, D. (2007). The narrow escape problem for diffusion in cellular microdomains. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.0706599104
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
