[1] |
Bunde, A.; Caro, J.; Kaerger, J.; Vogl, G., Diffusive spreading in nature, technology and society (2018), Springer · Zbl 1405.00009 |
[2] |
Chen, L.; Painter, K.; Surulescu, C.; Zhigun, A., Mathematical models for cell migration: a non-local perspective, Philos Trans R Soc B, 375, 1807, 20190379 (2020) |
[3] |
rsos.201536 |
[4] |
Yu, C.; Guan, J.; Chen, K.; Bae, S. C.; Granick, S., Single-molecule observation of long jumps in polymer adsorption, ACS Nano, 7, 11, 9735-9742 (2013) |
[5] |
Metzler, R.; Klafter, J., The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys Rep, 339, 1, 1-77 (2000) · Zbl 0984.82032 |
[6] |
Sokolov, I. M., Models of anomalous diffusion in crowded environments, Soft Matter, 8, 35, 9043-9052 (2012) |
[7] |
Li, B.; Wang, J., Anomalous heat conduction and anomalous diffusion in one-dimensional systems, Phys Rev Lett, 91, 4, 044301 (2003) |
[8] |
Kong, M.; Van Houten, B., Rad4 recognition-at-a-distance: physical basis of conformation-specific anomalous diffusion of DNA repair proteins, Prog Biophys Mol Biol, 127, 93-104 (2017) |
[9] |
Barbi, M.; Place, C.; Popkov, V.; Salerno, M., A model of sequence-dependent protein diffusion along DNA, J Biol Phys, 30, 3, 203-226 (2004) |
[10] |
Liu, L.; Cherstvy, A. G.; Metzler, R., Facilitated diffusion of transcription factor proteins with anomalous bulk diffusion, J Phys Chem B, 121, 6, 1284-1289 (2017) |
[11] |
Weiss, M.; Elsner, M.; Kartberg, F.; Nilsson, T., Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells, Biophys J, 87, 5, 3518-3524 (2004) |
[12] |
Banks, D. S.; Fradin, C., Anomalous diffusion of proteins due to molecular crowding, Biophys J, 89, 5, 2960-2971 (2005) |
[13] |
Golding, I.; Cox, E. C., Physical nature of bacterial cytoplasm, Phys Rev Lett, 96, 9, 098102 (2006) |
[14] |
Gupta, S.; Biehl, R.; Sill, C.; Allgaier, J.; Sharp, M.; Ohl, M., Protein entrapment in polymeric mesh: diffusion in crowded environment with fast process on short scales, Macromolecules, 49, 5, 1941-1949 (2016) |
[15] |
Tan, P.; Liang, Y.; Xu, Q.; Mamontov, E.; Li, J.; Xing, X., Gradual crossover from subdiffusion to normal diffusion: a many-body effect in protein surface water, Phys Rev Lett, 120, 24, 248101 (2018) |
[16] |
Jiang, C.; Cui, C.; Li, L.; Shao, Y., The anomalous diffusion of a tumor invading with different surrounding tissues, PLoS One, 9, 10, e109784 (2014) |
[17] |
Bursac, P.; Lenormand, G.; Fabry, B.; Oliver, M.; Weitz, D. A.; Viasnoff, V., Cytoskeletal remodelling and slow dynamics in the living cell, Nat Mater, 4, 7, 557-561 (2005) |
[18] |
Shimamoto, N., One-dimensional diffusion of proteins along DNA: its biological and chemical significance revealed by single-molecule measurements, J Biol Chem, 274, 22, 15293-15296 (1999) |
[19] |
Gorman, J.; Greene, E. C., Visualizing one-dimensional diffusion of proteins along DNA, Nat Struct Mol Biol, 15, 8, 768-774 (2008) |
[20] |
Song, J.-J.; Bhattacharya, R.; Kim, H.; Chang, J.; Tang, T.-Y.; Guo, H., One-dimensional anomalous diffusion of gold nanoparticles in a polymer melt, Phys Rev Lett, 122, 10, 107802 (2019) |
[21] |
Sagi, Y.; Brook, M.; Almog, I.; Davidson, N., Observation of anomalous diffusion and fractional self-similarity in one dimension, Phys Rev Lett, 108, 9, 093002 (2012) |
[22] |
Stauffer, D.; Schulze, C.; Heermann, D. W., Superdiffusion in a model for diffusion in a molecularly crowded environment, J Biol Phys, 33, 4, 305 (2007) |
[23] |
Livshits, G. I.; Stern, A.; Rotem, D.; Borovok, N.; Eidelshtein, G.; Migliore, A., Long-range charge transport in single G-quadruplex DNA molecules, Nat Nanotechnol, 9, 12, 1040-1046 (2014) |
[24] |
Schmidt, H. G.; Sewitz, S.; Andrews, S. S.; Lipkow, K., An integrated model of transcription factor diffusion shows the importance of intersegmental transfer and quaternary protein structure for target site finding, PLoS One, 9, 10, e108575 (2014) |
[25] |
Sheinman, M.; Kafri, Y., The effects of intersegmental transfers on target location by proteins, Phys Biol, 6, 1, 016003 (2009) |
[26] |
Krepel, D.; Levy, Y., Intersegmental transfer of proteins between DNAregions in the presence of crowding, Phys Chem Chem Phys, 19, 45, 30562-30569 (2017) |
[27] |
Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D., Complex networks: structure and dynamics, Phys Rep, 424, 4-5, 175-308 (2006) · Zbl 1371.82002 |
[28] |
Estrada, E., The structure of complex networks: theory and applications (2011), Oxford University Press: Oxford University Press Oxford |
[29] |
Tarasov, V. E., No nonlocality. No fractional derivative, Commun Nonlinear Sci Numer Simul, 62, 157-163 (2018) · Zbl 1470.26014 |
[30] |
Du, M.; Wang, Z.; Hu, H., Measuring memory with the order of fractional derivative, Sci Rep, 3, 1, 1-3 (2013) |
[31] |
Estrada, E., Path Laplacian matrices: introduction and application to the analysis of consensus in networks, Linear Algebra Appl, 436, 9, 3373-3391 (2012) · Zbl 1241.05077 |
[32] |
Estrada, E.; Hameed, E.; Hatano, N.; Langer, M., Path Laplacian operators and superdiffusive processes on graphs. I. One-dimensional case, Linear Algebra Appl, 523, 307-334 (2017) · Zbl 06766348 |
[33] |
Estrada, E.; Hameed, E.; Langer, M.; Puchalska, A., Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice, Linear Algebra Appl, 555, 373-397 (2018) · Zbl 06914735 |
[34] |
Estrada, E., Path Laplacians versus fractional Laplacians as nonlocal operators on networks, New J Phys, 23, 7, 073049 (2021) |
[35] |
Balakrishnan, V., Anomalous diffusion in one dimension, Phys A, 132, 2-3, 569-580 (1985) · Zbl 0654.60065 |
[36] |
Anguige, K.; Schmeiser, C., A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion, J Math Biol, 58, 3, 395-427 (2009) · Zbl 1162.92009 |
[37] |
Villamaina, D.; Sarracino, A.; Gradenigo, G.; Puglisi, A.; Vulpiani, A., On anomalous diffusion and the out of equilibrium response function in one-dimensional models, J Stat Mech, 2011, 01, L01002 (2011) |
[38] |
Padgett, J.; Kostadinova, E.; Liaw, C.; Busse, K.; Matthews, L.; Hyde, T., Anomalous diffusion in one-dimensional disordered systems: a discrete fractional Laplacian method, J Phys A, 53, 13, 135205 (2020) · Zbl 1514.60113 |
[39] |
Nakade, S.; Kanki, K.; Tanaka, S.; Petrosky, T., Anomalous diffusion of a quantum Brownian particle in a one-dimensional molecular chain, Phys Rev E, 102, 3, 032137 (2020) |
[40] |
Jespersen, S.; Metzler, R.; Fogedby, H. C., Levy flights in external force fields: Langevin and fractional Fokker-Planck equations and their solutions, Phys Rev E, 59, 3, 2736-2745 (1999) |
[41] |
Dybiec, B.; Gudowska-Nowak, E.; Barkai, E.; Dubkov, A. A., Levy flights versus Levy walks in bounded domains, Phys Rev E, 95, 5, 052102 (2017) |
[42] |
Klafter, J.; Blumen, A.; Shlesinger, M. F., Stochastic pathway to anomalous diffusion, Phys Rev A, 35, 7, 3081-3085 (1987) |
[43] |
Allen-Perkins, A.; Serrano, A. B.; de Assis, T. A.; Andrade, R. F.S., Approach to the inverse problem of superdiffusion on finite systems based on time-dependent long-range navigation, Phys Rev E, 100, 3, 030101 (2019) |
[44] |
Murugan, R., Generalized theory of site-specific DNA-protein interactions, Phys Rev E, 76, 1, 011901 (2007) |
[45] |
Koslover, E. F.; de la Rosa, M. D.; Spakowitz, A. J., Crowding and hopping in a protein’s diffusive transport on DNA, J Phys A, 50, 7, 074005 (2017) · Zbl 1358.92042 |
[46] |
Reynolds, A., On the anomalous diffusion characteristics of membrane-bound proteins, Phys Lett A, 342, 5-6, 439-442 (2005) |
[47] |
Garrappa, R.; Popolizio, M., Computing the matrix Mittag-Leffler function with applications to fractional calculus, J Sci Comput, 77, 1, 129-153 (2018) · Zbl 1406.65031 |
[48] |
Alves, S. B.; de Oliveira, G. F.; de Oliveira, L. C.; Passerat de Silans, T.; Chevrollier, M.; Oriá, M., Characterization of diffusion processes: normal and anomalous regimes, Phys A, 447, 392-401 (2016) |