Brownian motion in dire straits

Multiscale Modeling and Simulation

Volumn 10, Issue 4, 2012, Pages 1204-1231

  Holcman, D ^a   Schuss, Z ^b  

^a PSL RESEARCH UNIVERSITY   (France)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Asymptotic analysis; Boundary layer; Brownian motion; Conformal mapping; Diffusion; First eigenvalue; Laplace equation; Mean first passage time; Mixed Dirichlet Neumann boundary value problem; Narrow escape; Small hole; Stochastic processes

Indexed keywords

BOUNDED DOMAIN; CELLULAR BIOLOGY; EIGEN-VALUE; ESCAPE TIME; MEAN FIRST PASSAGE TIME; NARROW ESCAPE; SMALL HOLE; SPATIAL DOMAINS;

ASYMPTOTIC ANALYSIS; BOUNDARY LAYERS; CONFORMAL MAPPING; CYTOLOGY; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; LAPLACE EQUATION; RANDOM PROCESSES;

BROWNIAN MOVEMENT;

EID: 84871838974     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/110857519     Document Type: Article

References (46)

1. J. W. S. Baron Rayleigh, The Theory of Sound, vol. 2, 2nd ed., Dover, New York, 1945.
2. V. I. Fabrikant, Applications of Potential Theory in Mechanics, Kluwer, Dodrecht, 1989.
3. V. I. Fabrikant, Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering, Kluwer, Dodrecht, 1991.
4. K. M. Harris and J. K. Stevens, Dendritic spines of rat cerebellar Purkinje cells: Serial electron microscopy with reference to their biophysical characteristics, J. Neurosci., 12 (1988), pp. 4455-4469.
5. J. N. Bourne and K. M. Harris, Balancing structure and function at hippocampal dendritic spines, Ann. Rev. Neurosci., 31 (2008), pp. 47-67.
6. E. Korkotian, D. Holcman, and M. Segal, Dynamic regulation of spine-dendrite coupling in cultured hippocampal neurons, Eur. J. Neurosci., 20 (2004), pp. 2649-2663.
7. P. Hotulainen and C. C. Hoogenraad, Actin in dendritic spines: Connecting dynamics to function, J. Cell Biol., 189 (2010), pp. 619-629.
8. T. M. Newpher and M. D. Ehlers, Spine microdomains for postsynaptic signaling and plasticity, Trends Cell Biol., 5 (2009), pp. 218-227.
9. R. Yuste, A. Majewska, and K. Holthoff, From form to function: Calcium compartmentalization in dendritic spines, Nat. Neurosci., 7 (2000), pp. 653-659.
10. K. Svoboda, D. W. Tank, and W. Denk, Direct measurement of coupling between dendritic spines and shafts, Science, 272 (1996), pp. 716-719.
11. A. Biess, E. Korkotian, and D. Holcman, Diffusion in a dendritic spine: The role of geometry, Phys. Rev. E, 76 (2007), 021922.
12. D. Holcman and I. Kupka, Some questions in computational cellular biology, J. Fixed Point Theory Appl., 7 (2010), pp. 67-83.
13. A. J. Borgdorff and D. Choquet, Regulation of AMPA receptor lateral movements, Nature, 417 (2002), pp. 649-653.
14. D. Choquet and A. Triller, The role of receptor diffusion in the organization of the postsynaptic membrane, Nat. Rev. Neurosci., 4 (2003), pp. 251-265.
15. D. Holcman and A. Triller, Modeling synaptic dynamics and receptor trafficking, Biophys. J., 91 (2006), pp. 2405-2415.
16. D. Holcman, E. Korkotian, and M. Segal, Calcium dynamics in dendritic spines, modeling and experiments, Cell Calcium, 37 (2005), pp. 467-475.
17. P. Macheboeuf, A. M. Di Guilmi, V. Job, T. Vernet, O. Dideberg, and A. Dessen, Active site restructuring regulates ligand recognition in class A penicillin-binding proteins, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 577-582.
18. A. Lieber, A. Leis, A. Kushmaro, A. Minsky, and O. Medalia, Chromatin organization and radio resistance in the bacterium Gemmata obscuriglobus, J. Bacteriol., 191 (2009), pp. 1439-1445.
19. M. J. Ward and J. B. Keller, Strong localized perturbations of eigenvalue problems, SIAM J. Appl. Math., 53 (1993), pp. 770-798.
20. M. J. Ward, W. D. Henshaw, and J. B. Keller, Summing logarithmic expansions for singularly perturbed eigenvalue problems, SIAM J. Appl. Math., 53 (1993), pp. 799-828.
21. M. J. Ward and E. Van De Velde, The onset of thermal runaway in partially insulated or cooled reactors, IMA J. Appl. Math., 48 (1992), pp. 53-85.
22. T. Kolokolnikov, M. Titcombe, and M. J. Ward, Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps, European J. Appl. Math., 16 (2005), pp. 161-200.
23. D. Holcman and Z. Schuss, Escape through a small opening: Receptor trafficking in a synaptic membrane, J. Statist. Phys., 117 (2004), pp. 191-230.
24. A. Singer, Z. Schuss, D. Holcman, and B. Eisenberg, Narrow escape I, J. Statist. Phys., 122 (2006), pp. 437-463.
25. A. Singer, Z. Schuss, and D. Holcman, Narrow escape II, J. Statist. Phys., 122 (2006), pp. 465-489.
26. A. Singer, Z. Schuss, and D. Holcman, Narrow escape III, J. Statist. Phys., 122 (2006), pp. 491-509.
27. A. Gandolfi, A. Gerardi, and F. Marchetti, Diffusion-controlled reactions in two dimensions, Acta Appl. Math., 4 (1985), pp. 139-159.
28. J. Linderman and D. Laufengerger, Analysis of intracellular receptor/ligand sorting: Calculation of mean surface and bulk diffusion times within a sphere, Biophys. J., 50 (1986), pp. 295-305.
29. D. Coombs, R. Straube, and M. Ward, Diffusion on a sphere with localized traps: Mean first passage time, eigenvalue asymptotics, and Fekete points, SIAM J. Appl. Math., 70 (2009), pp. 302-332.
30. Z. Schuss, A. Singer, and D. Holcman, The narrow escape problem for diffusion in cellular microdomains, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 16098-16103.
31. I. V. Grigoriev, Y. A. Makhnovskii, A. M. Berezhkovskii, and V. Y. Zitserman, Kinetics of escape through a small hole, J. Chem. Phys., 116 (2002), pp. 9574-9577.
32. A. M. Berezhkovskii, A. V. Barzykin, and V. Yu. Zitserman, Escape from cavity through narrow tunnel, J. Chem. Phys., 130 (2009), 245104.
33. D. Holcman and Z. Schuss, Diffusion laws in dendritic spines, J. Math. Neurosci., 1 (2011), 10.
34. D. Holcman, N. Hoze, and Z. Schuss, Narrow escape through a funnel and effective diffusion on a crowded membrane, Phys. Rev. E, 84 (2011), 021906.
35. A. Singer, Z. Schuss, and D. Holcman, Narrow escape and leakage of Brownian particles, Phys. Rev. E, 78 (2008), 051111.
36. A. F. Cheviakov, M. J. Ward, and R. Straube, An asymptotic analysis of the mean first passage time for narrow escape problems: Part II: The sphere, Multiscale Model. Simul., 8 (2010), pp. 836-870.
37. J. Jackson, Classical Electrodynamics, 3rd ed., John Wiley, New York, 1998, pp. 27-35.
38. Z. Schuss, Equilibrium and recrossings of the transition state: What can be learned from diffusion?, J. Phys. Chem. C, 114 (2010), pp. 20320-20334.
39. B. J. Matkowsky and Z. Schuss, Eigenvalues of the Fokker-Planck operator and the approach to equilibrium for diffusions in potential fields, SIAM J. Appl. Math., 40 (1981), pp. 242-254.
40. P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory: Fifty years after Kramers, Rev. Mod. Phys., 62 (1990), pp. 251-332.
41. Z. Schuss, Diffusion and Stochastic Processes: An Analytical Approach, Springer, New York, 2010.
42. J. M. Arrieta, Rates of eigenvalues on a dumbbell domain. Simple eigenvalue case, Trans. Amer. Math. Soc., 347 (1995), pp. 3503-3531.
43. M. J. Ward and D. Stafford, Metastable dynamics and spatially inhomogeneous equilibria in dumbbell-shaped domains, Stud. Appl. Math., 103 (1999), pp. 51-73.
44. S. Jimbo and S. Kosugi, Spectra of domains with partial degeneration, J. Math. Sci. Univ. Tokyo, 16 (2009), pp. 269-414.
45. L. Dagdug, A. M. Berezhkovskii, S. Y. Shvartsman, and G. Weiss, Equilibration in two chambers connected by a capillary, J. Chem. Phys., 119 (2003), 12473.
46. Z. Schuss, Theory and Applications of Stochastic Differential Equations, John Wiley, New York, 1980.