Narrow escape problem

For the Fargo episode, see The Narrow Escape Problem.

The narrow escape problem[1][2] is a ubiquitous problem in biology, biophysics and cellular biology.

The mathematical formulation is the following: a Brownian particle (ion, molecule, or protein) is confined to a bounded domain (a compartment or a cell) by a reflecting boundary, except for a small window through which it can escape. The narrow escape problem is that of calculating the mean escape time. This time diverges as the window shrinks, thus rendering the calculation a singular perturbation problem.[3][4][5][6][7][8][9]

When escape is even more stringent due to severe geometrical restrictions at the place of escape, the narrow escape problem becomes the dire strait problem.[10][11]

The narrow escape problem was proposed in the context of biology and biophysics by D. Holcman and Z. Schuss,[12] and later on with A.Singer and led to the narrow escape theory in applied mathematics and computational biology.[13][14][15]

  1. ^ Schuss, Z.; Singer, A.; Holcman, D. (2007-09-27). "The narrow escape problem for diffusion in cellular microdomains". Proceedings of the National Academy of Sciences. 104 (41). Proceedings of the National Academy of Sciences USA: 16098–16103. Bibcode:2007PNAS..10416098S. doi:10.1073/pnas.0706599104. ISSN 0027-8424. PMC 1994903. PMID 17901203.
  2. ^ D Holcman, Z Schuss, The narrow escape problem SIAM Review 56 (2), 213-257 (2014)
  3. ^ Singer, A.; Schuss, Z.; Holcman, D. (2008-11-14). "Narrow escape and leakage of Brownian particles". Physical Review E. 78 (5). American Physical Society (APS): 051111. arXiv:0808.2288. Bibcode:2008PhRvE..78e1111S. doi:10.1103/physreve.78.051111. ISSN 1539-3755. PMID 19113099. S2CID 8739640.
  4. ^ M. J. Ward, S. Pillay, A. Peirce, and T. Kolokolnikov An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains
  5. ^ Holcman, D; Schuss, Z (2008-04-02). "Diffusion escape through a cluster of small absorbing windows". Journal of Physics A: Mathematical and Theoretical. 41 (15). IOP Publishing: 155001. Bibcode:2008JPhA...41o5001H. doi:10.1088/1751-8113/41/15/155001. ISSN 1751-8113. S2CID 4179599.
  6. ^ Holcman, D., & Schuss, Z. (2015). Stochastic Narrow Escape in Molecular and Cellular Biology: Analysis and Applications. Springer.
  7. ^ Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny (2010). "An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere". Multiscale Modeling & Simulation. 8 (3). Society for Industrial & Applied Mathematics (SIAM): 836–870. doi:10.1137/100782620. hdl:11858/00-001M-0000-0013-908F-6. ISSN 1540-3459.
  8. ^ Cheviakov, Alexei F.; Zawada, Daniel (2013-04-22). "Narrow-escape problem for the unit sphere: Homogenization limit, optimal arrangements of large numbers of traps, and the N2 conjecture". Physical Review E. 87 (4). American Physical Society (APS): 042118. Bibcode:2013PhRvE..87d2118C. doi:10.1103/physreve.87.042118. ISSN 1539-3755. PMID 23679384.
  9. ^ Coombs, Daniel; Straube, Ronny; Ward, Michael (2009). "Diffusion on a Sphere with Localized Traps: Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points". SIAM Journal on Applied Mathematics. 70 (1). Society for Industrial & Applied Mathematics (SIAM): 302–332. doi:10.1137/080733280. hdl:11858/00-001M-0000-0013-9335-3. ISSN 0036-1399.
  10. ^ D. Holcman Z. Schuss, The dire strait time, SIAM Multiscale Modeling and simulations, 10(4), 1204–1231.
  11. ^ Holcman, D; Schuss, Z (2013-06-20). "Control of flux by narrow passages and hidden targets in cellular biology". Reports on Progress in Physics. 76 (7). IOP Publishing: 074601. Bibcode:2013RPPh...76g4601H. doi:10.1088/0034-4885/76/7/074601. ISSN 0034-4885. PMID 23787818. S2CID 2102724.
  12. ^ Holcman, D.; Schuss, Z. (2004). "Escape Through a Small Opening: Receptor Trafficking in a Synaptic Membrane". Journal of Statistical Physics. 117 (5–6). Springer Science and Business Media LLC: 975–1014. Bibcode:2004JSP...117..975H. doi:10.1007/s10955-004-5712-8. ISSN 0022-4715. S2CID 6324415.
  13. ^ Singer, A.; Schuss, Z.; Holcman, D.; Eisenberg, R. S. (2006-01-20). "Narrow Escape, Part I". Journal of Statistical Physics. 122 (3). Springer Science and Business Media LLC: 437–463. arXiv:math-ph/0412048. Bibcode:2006JSP...122..437S. doi:10.1007/s10955-005-8026-6. ISSN 0022-4715. S2CID 14014727.
  14. ^ Singer, A.; Schuss, Z.; Holcman, D. (2006-01-20). "Narrow Escape, Part II: The Circular Disk". Journal of Statistical Physics. 122 (3). Springer Science and Business Media LLC: 465–489. arXiv:math-ph/0412050. Bibcode:2006JSP...122..465S. doi:10.1007/s10955-005-8027-5. ISSN 0022-4715. S2CID 15765954.
  15. ^ Singer, A.; Schuss, Z.; Holcman, D. (2006-01-20). "Narrow Escape, Part III: Non-Smooth Domains and Riemann Surfaces". Journal of Statistical Physics. 122 (3). Springer Science and Business Media LLC: 491–509. Bibcode:2006JSP...122..491S. doi:10.1007/s10955-005-8028-4. ISSN 0022-4715. S2CID 12317568.