Mean escape time for randomly switching narrow gates in a steady flow. (English) Zbl 1446.76153
Summary: The escape of particles through a narrow absorbing gate in confined domains is a rich phenomenon in various systems in physics, chemistry and molecular biophysics. We consider the narrow escape problem in a bounded annular when the two gates randomly switch between different states with a switching rate \(k\) between the two gates. After briefly deriving the coupled partial differential equations for the escape time through two gates, we compute the mean escape time for particles escaping from the gates with different initial states. By numerical simulation under nonuniform boundary conditions, we quantify how narrow escape time is affected by the switching rate \(k\) between the two gates, arc length \(s\) between two gates, angular velocity \(w\) of the steady flow and diffusion coefficient \(D\). We reveal that the mean escape time decreases with the switching rate \(k\) between the two gates, angular velocity \(w\) and diffusion coefficient \(D\) for fixed arc length, but takes the minimum when the two gates are evenly separated on the boundary for any given switching rate \(k\) between the two gates. In particular, we find that when the arc length size \(s\) for the gates is sufficiently small, the average narrow escape time is approximately independent of the gate arc length size. We further indicate combinations of system parameters (regions located in the parameter space) such that the mean escape time is the longest or shortest. Our findings provide mathematical understanding for phenomena such as how ions select ion channels and how chemicals leak in annulus ring containers, when drift vector fields are present.
MSC:
| 76R50 | Diffusion |
| 76U05 | General theory of rotating fluids |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
References:
| [1] | Holcman, D.; Schuss, Z., Stochastic Narrow Escape in Molecular and Cellular Biology: Analysis and Applications (2015), Springer: Springer New York · Zbl 1321.92008 |
| [2] | Bressloff, P. C., Stochastic Processes in Cell Biology (2014), Springer: Springer New York · Zbl 1402.92001 |
| [3] | Bressloff, P. C.; Newby, J. M., Stochastic models of intracellular transport, Rev. Modern Phys., 85, 1, 135-196 (2013) |
| [4] | Holcman, D.; Schuss, Z., 100 years after Smoluchowski: stochastic processes in cell biology, J. Phys. A, 50, Article 093002 pp. (2017) · Zbl 1360.92037 |
| [5] | Holcman, D.; Schuss, Z., Brownian motion in dire straits, SIAM J. Multiscale Model. Simul., 10, 4, 1204-1231 (2012) · Zbl 1266.60144 |
| [6] | Reingruber, J.; Holcman, D., Diffusion in narrow domains and application to phototransduction, Phys. Rev. E, 79, Article 030904 pp. (2009) |
| [7] | Bénichou, O.; Voituriez, R., Narrow-escape time problem: time needed for a particle to exit a confining domain through a small window, Phys. Rev. Lett., 100, Article 168105 pp. (2008) |
| [8] | Schuss, Z.; Singer, A.; Holcman, D., The narrow escape problem for diffusion in cellular microdomains, Proc. Natl. Acad. Sci. USA, 104, 41, 16098-16103 (2007) |
| [9] | Holcman, D.; Schuss, Z., Escape through a small opening: Receptor trafficking in a synaptic membrane, J. Stat. Phys., 117, 975-1014 (2004) · Zbl 1087.82018 |
| [10] | Lagache, T.; Holcman, D., Extended narrow escape with many windows for analyzing viral entry into the cell nucleus, J. Stat. Phys., 166, 244-266 (2017) · Zbl 1364.82044 |
| [11] | Ammari, H.; Garnier, J.; Kang, H.; Lee, H.; Sølna, K., The mean escape time for a narrow escape problem with multiple switching gates, Multiscale Model. Simul., 9, 2, 817-833 (2011) · Zbl 1231.82048 |
| [12] | Grebenkov, D. S., Universal formula for the mean first passage time in planar domains, Phys. Rev. Lett., 117, 26, Article 260201 pp. (2016) |
| [13] | Li, X., Matched asymptotic analysis to solve the narrow escape problem in a domain with a long neck, J. Phys. A, 47, Article 505202 pp. (2014) · Zbl 1308.35057 |
| [14] | Lindsay, A. E.; Kolokolnikov, T.; Tzou, J. C., Narrow escape problem with a mixed trap and the effect of orientation, Phys. Rev. E, 91, Article 032111 pp. (2015) |
| [15] | Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T., An asymptotic analysis of the mean first passage time for narrow escape problems: Part I: Two-dimensional domains, Multiscale Model. Simul., 8, 803-835 (2010) · Zbl 1203.35023 |
| [16] | Reingruber, J.; Holcman, D., Narrow escape for a stochastically gated Brownian ligand, J. Phys. Condens. Matter., 22, Article 065103 pp. (2010) |
| [17] | Reingruber, J.; Holcman, D., Gated narrow escape time for molecular signaling, Phys. Rev. Lett., 103, Article 148102 pp. (2009) |
| [18] | Gomez, D.; Cheviakov, A. F., Asymptotic analysis of narrow escape problems in nonspherical three-dimensional domains, Phys. Rev. E, 91, Article 012137 pp. (2015) |
| [19] | Li, X.; Lee, H.; Wang, Y., Asymptotic analysis of the narrow escape problem in dendritic spine shaped domain: Three dimension, J. Phys. A, 50, Article 325203 pp. (2017) · Zbl 1370.92052 |
| [20] | Chevalier, C.; Bénichou, O.; Meyer, B.; Voituriez, R., First-passage quantities of brownian motion in a bounded domain with multiple targets: a unified approach, J. Phys. A, 44, Article 025002 pp. (2011) · Zbl 1207.82020 |
| [21] | Singer, A.; Schuss, Z.; Holcman, D., Narrow escape and leakage of Brownian particles, Phys. Rev. E, 78, Article 051111 pp. (2008) |
| [22] | Agranov, T.; Meerson, B., Narrow escape of interacting diffusing particles, Phys. Rev. Lett., 12, Article 120601 pp. (2018) |
| [23] | Cheviakov, A. F.; Reimer, A. S.; Ward, M. J., Mathematical modeling and numerical computation of narrow escape problems, Phys. Rev. E, 85, Article 021131 pp. (2012) |
| [24] | Holcman, D.; Schuss, Z., Control of flux by narrow passages and hidden targets in cellular biology, Rep. Prog. Phys. Phys. Soc., 76, Article 074601 pp. (2013) |
| [25] | Holcman, D.; Schuss, Z., Diffusion escape through a cluster of small absorbing windows, J. Phys. A, 41, Article 155001 pp. (2008) · Zbl 1138.35379 |
| [26] | Grebenkov, D. S.; Rupprecht, J.-F., The escape problem for mortal walkers, J. Chem. Phys., 146, Article 084106 pp. (2017) |
| [27] | Bénichou, O.; Grebenkov, D. S.; Hillairet, L.; Phun, L.; Voituriez, R.; Zinsmeister, M., Mean exit time for surface-mediated diffusion: spectral analysis and asymptotic behavior, Anal. Math. Phys., 5, 321-362 (2015) · Zbl 1330.35454 |
| [28] | Bressloff, P. C.; Lawley, S. D., Escape from subcellular domains with randomly switching boundaries, Multiscale Model. Simul., 13, 4, 1420-1445 (2015) · Zbl 1329.82092 |
| [29] | Piazza, F.; Traytak, S. D., Diffusion-influenced reactions in a hollow nano-reactor with a circular hole, Phys. Chem. Chem. Phys., 17, 10417-10425 (2015) |
| [30] | Singer, A.; Schuss, Z., Activation through a narrow opening, SIAM J. Appl. Math., 68, 1, 98-108 (2007) · Zbl 1147.60040 |
| [31] | Berezhkovskii, A. M.; Barzykin, A. V., Extended narrow escape problem: boundary homogenization-based analysis, Phys. Rev. E, 82, Article 011114 pp. (2010) |
| [32] | Levernier, N.; Bénichou, O.; Voituriez, R., Mean first-passage time of an anisotropic diffusive searcher, J. Phys. A, 50, Article 024001 pp. (2017) · Zbl 1357.82058 |
| [33] | Rojo, F.; Wio, H. S.; Budde, C. E., Narrow-escape-time problem: the imperfect trapping case, Phys. Rev. E, 86, Article 031105 pp. (2012) |
| [34] | Lions, P. L.; Sznitman, A. S., Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37, 511-537 (1984) · Zbl 0598.60060 |
| [35] | Acheson, D. J., Elementary Fluid Dynamics (1990), Clarendon Press: Clarendon Press Oxford · Zbl 0719.76001 |
| [36] | Bardet, J. B.; Guérin, H.; Malrieu, F., Long time behavior of diffusions with Markov switching latin, Am. J. Probab. Math. Stat., 7, 151-170 (2009) · Zbl 1276.60084 |
| [37] | Duan, J., An Introduction to Stochastic Dynamics (2015), Cambridge University Press · Zbl 1359.60003 |
| [38] | Cheviakov, A. F.; Ward, M. J.; Straube, R., An asymptotic analysis of the mean first passage time for narrow escape problems: Part II: The sphere, Multiscale Model. Simul., 8, 3, 836-870 (2010) · Zbl 1204.35030 |
| [39] | Chen, X.; Friedman, A., Asymptotic analysis for the narrow escape problem, SIAM J. Math. Anal., 43, 6, 2542-2563 (2011) · Zbl 1252.35030 |
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