Stochastic Processes for Anomalous Diffusion in Biological Systems

DATES: 18 - 22 November 2019 (5 sessions)
TIME: 09:00 - 11:00 (a total of 10 hours)
LOCATION: BCAM Seminar room

PROGRAMME:
Day 1: Introduction to stochastic processes
Day 2: Anomalous diffusion in biological systems
Day 3: The continuous time random walk
Day 4: The diffusing diffusivity approach
Day 5: The generalized grey Brownian motion

ABSTRACT:
Particles spreading in classical diffusion is characterized by a Gaussian distribution function for particle displacement and its variance grows linearly in time. This motion is the celebrated Brownian motion and its formulation dates back to Einstein in 1905. On the contrary, diffusion in biological systems can display non-Gaussian distribution of particle displacements as well as a non-linear growth of its variance, namely anomalous diffusion, because diffusion takes place in a crowded, heterogeneous and fluctuating environment. Hence, modelling diffusion in living systems requires the development of stochastic processes within complex environments. The aim of the course is to provide a survey of the state-of-the-science in modelling anomalous diffusion with applications to biological systems. The selection of the discussed modelling approaches reflects the research developed at BCAM.

BIBLIOGRAPHY:
Day 1:
Pavliotis G.A., Stochastic Processes and Applications. Diffusion Processes, the Fokker- Planck and Langevin Equations. Springer Science+Business Media New York, 2014.
Day 2:
Golding I., Cox E.C., Physical nature of bacterial cytoplasm. Phys. Rev. Lett., 2006, 96, 098102.
Barkai E. Garini Y. Metzler R. Strange kinetics of single molecules in living cells. Phys. Today, 2012, 65(8), 29-35.
Hofling F., Franosch T., Anomalous transport in the crowded world of biological cells. Rep. Prog. Phys., 2013, 76, 046602.
Day 3:
Scalas E. Gorenflo R. Mainardi F., Uncoupled continuous-time random walks: Solution and limiting behaviour of the master equation. Phys. Rev. E, 2004, 69, 011107.
Metzler R., Jeon J.-H., Cherstvy A.G., Barkai E., Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys. Chem. Chem. Phys., 2014,16, 24128.
Pagnini G., Short note on the emergence of fractional kinetics. Physica A, 2014, 409, 29- 34.
Day 4:
Chubynsky M., Slater G., Diffusing diffusivity: A model for anomalous, yet Brownian, diffusion. Phys. Rev. Lett., 2014, 113, 098302.
Chechkin A.V., Seno F., Metzler R., Sokolov I.M., Brownian yet non-Gaussian diffusion: From superstatistics to subordination of diffusing diffusivities. Phys. Rev. X, 2017, 7, 021002.
Sposini V., Chechkin A.V., Seno F., Pagnini G., Metzler R., Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion. New J. Phys., 2018, 20, 043044.
Day 5:
Mura A., Pagnini G., Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A: Math. Theor., 2008, 41, 285003. Molina-García D., Pham T. Minh, Paradisi P., Manzo C., Pagnini G. Fractional kinetics emerging from ergodicity breaking in random media. Phys. Rev. E, 2016, 94, 052147. Mackala A., Magdziarz M., Statistical analysis of superstatistical fractional Brownian motion and applications. Phys. Rev. E, 2019, 99, 012143.


*Registration is free, but mandatory before November 14th.
To sign-up go to https://forms.gle/2TR2ca5WFCvW9a7JA and fill the registration form.

Student grants are available. Please, let us know if you need support for travel and accommodation expenses in the previous form before October 13th.

• BCAM_UPV_Course_2019_11_18