Universal proximity effect in target search kinetics in the few-encounter limit

Physical Review X

Volumn 6, Issue 4, 2016, Pages

  Godec, Aljaž ^a,b   Metzler, Ralf ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

^b NATIONAL INSTITUTE OF CHEMISTRY   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR BIOLOGY; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

DIFFUSING PARTICLES; FIRST PASSAGE TIME; INITIAL DISTANCE; LONG-TIME ASYMPTOTICS; MOLECULAR REACTIONS; PROXIMITY EFFECTS; TIME SCALE SEPARATION; TRANSPORT PROCESS;

ELECTRON TRANSITIONS;

EID: 85008214403     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.6.041037     Document Type: Article

References (82)

1. M. von Smoluchowski, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Phys. Z. 17, 557 (1916).
2. P. Hänggi, P. Talkner, and M. Borkovec, Reaction-Rate Theory: Fifty Years after Kramers, Rev. Mod. Phys. 62, 251 (1990).
3. S. Redner, A Guide to First Passage Processes. (Cambridge University Press, New York, 2001).
4. M. Shlesinger, Mathematical Physics: Search Research, Nature (London) 443, 281 (2006).
5. First-Passage Phenomena and Their Applications, edited by R. Metzler, G. Oshanin, and S. Redner (World Scientific, Singapore, 2014).
6. R. Kopelman, Fractal Reaction Kinetics, Science 241, 1620 (1988).
7. A. Szabo, K. Schulten, and Z. Schulten, First Passage Time Approach to Diffusion Controlled Reactions, J. Chem. Phys. 72, 4350 (1980).
8. O. Bénichou, C. Chevalier, J. Klafter, B. Meyer, and R. Voituriez, Geometry-Controlled Kinetics, Nat. Chem. 2, 472 (2010).
9. Z. Schuss, Theory and Applications of Stochastic Processes: An Analytical Approach (Springer, New York, 2010).
10. E. Ben-Naim, S. Redner, and F. Leyvraz, Decay Kinetics of Ballistic Annihilation, Phys. Rev. Lett. 70, 1890 (1993).
11. G. Oshanin, A. Stemmer, S. Luding, and A. Blumen, Smoluchowski Approach for Three-Body Reactions in One Dimension, Phys. Rev. E 52, 5800 (1995).
12. B. Meyer, C. Chevalier, R. Voituriez, and O. Bénichou, Universality Classes of First-Passage-Time Distribution in Confined Media, Phys. Rev. E 83, 051116 (2011).
13. O. Bénichou and R. Voituriez, From First-Passage Times of Random Walks in Confinement to Geometry-Controlled Kinetics, Phys. Rep. 539, 225 (2014).
14. Z. Schuss, A. Singer, and D. Holcman, The Narrow Escape Problem for Diffusion in Cellular Microdomains, Proc. Natl. Acad. Sci. U.S.A. 104, 16098 (2007).
15. O. Pulkkinen and R. Metzler, Distance Matters: The Impact of Gene Proximity in Bacterial Gene Regulation, Phys. Rev. Lett. 110, 198101 (2013).
16. Z.Wunderlich and L. A. Mirny, Spatial Effects on the Speed and Reliability of Protein-DNA Search, Nucleic Acids Res. 36, 3570 (2008).
17. D. Holcman and Z. Schuss, Time Scale of Diffusion in Molecular and Cellular Biology, J. Phys. A 47, 173001 (2014).
18. A. Godec and R. Metzler, First Passage Time Distribution in Heterogeneity Controlled Kinetics: Going Beyond the Mean First Passage Time, Sci. Rep. 6, 20349 (2016).
19. A. Godec and R. Metzler, Optimization and Universality of Brownian Search in a Basic Model of Quenched Heterogeneous Media, Phys. Rev. E 91, 052134 (2015).
20. M. Kurzynski, K. Palacz, and P. Chelminiak, Time Course of Reactions Controlled and Gated by Intramolecular Dynamics of Proteins: Predictions of the Model of Random Walk on Fractal Lattices, Proc. Natl. Acad. Sci. U.S.A. 95, 11685 (1998).
21. G. Kolesov, Z. Wunderlich, O. N. Laikova, M. S. Gelfand, and L. A. Mirny, How Gene Order Is Influenced by the Biophysics of Transcription Regulation, Proc. Natl. Acad. Sci. U.S.A. 104, 13948 (2007).
22. W. Bialek and S. Setayeshgar, Physical Limits to Biochemical Signaling, Proc. Natl. Acad. Sci. U.S.A. 102, 10040 (2005).
23. G.W. Li and X. S. Xie, Central Dogma at the Single-Molecule Level in Living Cells, Nature (London) 475, 308 (2011).
24. J. C. M. Gebhardt, D.M Suter, R. Roy, Z.W Zhao, A. R. Chapman, S. Basu, T. Maniatis, and X. S. Xie, Single-Molecule Imaging of Transcription Factor Binding to DNA in Live Mammalian Cells, Nat. Methods 10, 421 (2013).
25. C. Mejía-Monasterio, G. Oshanin, and G. Schehr, First Passages for a Search by a Swarm of Independent Random Searchers, J. Stat. Mech. (2011) P06022.
26. A. Godec and R. Metzler, Signal Focusing through Active Transport, Phys. Rev. E 92, 010701(R) (2015).
27. C. Di Rienzo, V. Piazza, E. Gratton, F. Beltram, and F. Cardarelli, Probing Short-Range Protein Brownian Motion in the Cytoplasm of Living Cells, Nat. Commun. 5, 5891 (2014).
28. S. A. Gorski, M. Dundr, and T. Misteli, The Road Much Traveled: Trafficking in the Cell Nucleus, Curr. Opin. Cell Biol. 18, 284 (2006).
29. F. Höfling and T. Franosch, Anomalous Transport in the Crowded World of Biological Cells, Rep. Prog. Phys. 76, 046602 (2013).
30. W. Bialek, Biophysics: Searching for Principles (Princeton University Press, New Jersey, 2012).
31. P. Fraser and W. Bickmore, Nuclear Organization of the Genome and the Potential for Gene Regulation, Nature (London) 447, 413 (2007).
32. J. J. Liou, Recurrence and Transience of Gaussian Diffusion Processes, Kodai Math. J. 13, 210 (1990).
33. A. Bancaud, S. Huet, N. Daigle, J. Mozziconacci, J. Beaudouin, and J. Ellenberg, Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatin and reveals the fractal organization of chromatin, EMBO J. 28, 3785 (2009).
34. C. Lanctót, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, Dynamic Genome Architecture in the Nuclear Space: Regulation of Gene Expression in Three Dimensions, Nat. Rev. Genet. 8, 104 (2007).
35. E. Toro and L. Shapiro, Bacterial Chromosome Organization and Segregation, Cold Spring Harbor Persp. Biol. 2, a000349 (2010).
36. J. Zlatanova and K. E. van Holde, Molecular Biology: Structure and Dynamics of Genomes and Proteomes (Garland Science, New York, 2015).
37. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Intermittent Search Strategies, Rev. Mod. Phys. 83, 81 (2011).
38. G. E. Viswanathan, M. G. E. da Luz, E. P. Raposo, and H. E. Stanley, The Physics of Foraging: An Introduction to Random Searches and Biological Encounters (Cambridge University Press, New York, 2011).
39. A. L. Lloyd and R. M. May, How Viruses Spread Among Computers and People, Science 292, 1316 (2001).
40. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, M. G. E. da Luz, E. P. Raposo, and H. Eugene Stanley, Optimizing the Success of Random Searches, Nature (London) 401, 911 (1999).
41. V. V. Playulin, A. V. Chechkin, and R. Metzler, Lévy Flights Do Not Always Optimize Random Blind Search for Sparse Targets, Proc. Natl. Acad. Sci. U.S.A. 111, 2931 (2014).
42. D.W. Sims, M. J. Witt, A. J. Richardson, E. J. Southall, and J. D. Metcalfe, Encounter Success of Free-Ranging Marine Predator Movements Across a Dynamic Prey Landscape, Proc. Biol. Sci. 273, 1195 (2006).
43. J. D. Houghton, T. K. Doyle, M.W. Wilson, J. Davenport, and G. C. Hays, Jellyfish Aggregations and Leatherback Turtle Foraging Patterns in a Temperate Coastal Environment, Ecology 87, 1967 (2006).
44. C. J. A. Bradshaw, M. A. Hindell, M. D. Sumner, and K. J. Michael, Loyalty Pays: Potential Life History Consequences of Fidelity to Marine Foraging Regions by Southern Elephant Seals, Animal Behaviour 68, 1349 (2004).
45. C. T. Harbison et al., Transcriptional Regulatory Code of a Eukaryotic Genome, Nature (London) 431, 99 (2004).
46. S. Redner and B. Meerson, First Invader Dynamics in Diffusion-Controlled Absorption, J. Stat. Mech. (2014) P06019.
47. K. Lindenberg, V. Seshadri, K. E. Shuler, and G. H. Weiss, Lattice Random Walks for Sets of Random Walkers. First Passage Times, J. Stat. Phys. 23, 11 (1980).
48. Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevX.6.041037 for detailed proofs of the general results (2)-(6) as well as for explicit calculations and exact results for all the model systems considered in the main text.
49. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968), Vol. II.
50. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin-Heidelberg, 1985).
51. A. Godec and R. Metzler, Linear Response, Fluctuation-Dissipation, and Finite-System-Size Effects in Superdiffusion, Phys. Rev. E 88, 012116 (2013).
52. T. Guérin, N. Levernier, O. Bénichou, and R. Voituriez, Mean First-Passage Times of Non-Markovian Random Walkers in Confinement, Nature (London) 534, 356 (2016).
53. T. Verechtchaguina, I. M. Sokolov, and L. Schimansky-Geier, First Passage Time Densities in Non-Markovian Models with Subthreshold Oscillations, Europhys. Lett. 73, 691 (2006).
54. B. O'Shaughnessy and I. Procaccia, Analytical Solutions for Diffusion on Fractal Objects, Phys. Rev. Lett. 54, 455 (1985).
55. D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, England, 2002).
56. J. Koplik, S. Redner, and E. J. Hinch, Universal and Nonuniversal First-Passage Properties of Planar Multipole Flows, Phys. Rev. Lett. 74, 82 (1995).
57. H. A. Kramers, Brownian Motion in a Field of Force and the Diffusion Model of Chemical Reactions, Physica (Amsterdam) 7, 284 (1940).
58. A. J. F. Siegert, On the First Passage Time Probability Problem, Phys. Rev. 81, 617 (1951).
59. K. Schulten, Z. Schulten, and A. Szabo, Dynamics of Reactions Involving Diffusive Barrier Crossing, J. Chem. Phys. 74, 4426 (1981).
60. G. Margolin and E. Barkai, Single-Molecule Chemical Reactions: Reexamination of the Kramers Approach, Phys. Rev. E 72, 025101 (2005).
61. D. Grebenkov, First Exit Times of Harmonically Trapped Particles: A Didactic Review, J. Phys. A 48, 013001 (2015).
62. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion (Springer-Verlag, Berlin-Heidelberg, 1999).
63. D.W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes (Springer, Berlin-Heidelberg, 2006).
64. E. Sparre Andersen, On the Fluctuations of Sums of Random Variables, Math. Scand. 1, 263 (1953)
65. On the Fluctuations of Sums of Random Variables. II., Math. Scand. 2, 195 (1954).
66. T. Koren, M. A. Lomholt, A. V. Chechkin, J. Klafter, and R. Metzler, Leapover Lengths and First Passage Time Statistics for Lévy Flights, Phys. Rev. Lett. 99, 160602 (2007).
67. S. N. Majumdar, G. Schehr, and G. Wergen, Record Statistics and Persistence for a Random Walk with a Drift, J. Phys. A 45, 355002 (2012).
68. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
69. B. Alberts et al., Molecular Biology of the Cell (Garland, New York, NY, 2002).
70. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Enhanced Reaction Kinetics in Biological Cells, Nat. Phys. 9, 134 2008.
71. K. Chen, B. Wang, and S. Granick, Memoryless Self-Reinforcing Directionality in Endosomal Active Transport within Living Cells, Nat. Mater. 14, 589 (2015).
72. A. Godec and R. Metzler, Active Transport Improves the Precision of Linear Long Distance Molecular Signalling, J. Phys. A 49, 364001 (2016).
73. T. Cavalier-Smith, Nuclear Volume Control by Nucleoskeletal DNA, Selection for Cell Volume and Cell Growth Rate, and the Solution of the DNA C-Value Paradox, J. Cell Sci. 34, 247 (1987).
74. T. G. Mattos, C. Mejìa-Monasterio, R. Metzler, and G. Oshanin, First Passages in Bounded Domains: When Is the Mean First Passage Time Meaningful?, Phys. Rev. E 86, 031143 (2012).
75. J. Yu, J. Xiao, X. Ren, K. Lao, and X. S. Xie, Probing Gene Expression in Live Cells, One Protein Molecule at a Time, Science 311, 1600 (2006).
76. L. Cai, N. Friedman, and X. S. Xie, Stochastic Protein Expression in Individual Cells at the Single Molecule Level, Nature (London) 440, 358 (2006).
77. A. Honigmann, V. Mueller, H. Ta, A. Schoenle, E. Sezgin, S.W. Hell, and C. Eggeling, Scanning STED-FCS Reveals Spatiotemporal Heterogeneity of Lipid Interaction in the Plasma Membrane of Living Cells, Nat. Commun. 5, 5412 (2014).
78. A. V.Weigel, M. M. Tamkun, and D. Krapf, Quantifying the Dynamic Interactions Between a Clathrin-Coated Pit and Cargo Molecules, Proc. Natl. Acad. Sci. U.S.A. 110, E4591 (2013).
79. P. H. Hippel and O. G. Berg, Facilitated Target Location in Biological Systems, J. Biol. Chem. 264, 675 (1989).
80. A. Mahmutovic, D. Fange, O. Berg, and J. Elf, Lost in Presumption: Stochastic Reactions in Spatial Models, Nat. Methods 9, 1163 (2012).
81. C. Di Rienzo, E. Gratton, F. Beltram, and F. Cardarelli, Spatiotemporal Fluctuation Analysis: A Powerful Tool for the Future Nanoscopy of Molecular Processes, Biophys. J. 111, 679 (2016).
82. T. Lu, T. Shen, C. Zhong, J. Hastym, and P. Wolynes, Statistics of Cellular Signal Transduction as a Race to the Nucleus by Multiple Random Walkers in Compartment/ Phosphorylation Space, Proc. Natl. Acad. Sci. U.S.A. 103, 16752 (2006).