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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Space-time fractional diffusion equations in chemo
 taxis and immunology - Gissell Estrada-Rodriguez (
 Universitat Politècnica de Catalunya)
DTSTART;TZID=Europe/London:20231108T113000
DTEND;TZID=Europe/London:20231108T123000
UID:TALK203260AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/203260
DESCRIPTION:In the presence of sparse attractants\, the moveme
 nt of both cells and large organisms has been show
 n to be governed by long distance runs\, according
  to an approximate L&acute\;evy distribution. In t
 his talk we clarify theform of biologically releva
 nt PDE descriptions for such movements. Motivated 
 by experiments we consider a microscopic velocity-
 jump model in which an individual performs occasio
 nal long jumps according to an approximate L&acute
 \;evy distribution. We derive the appropriate kine
 tic-transport equation\, where the collision term 
 describes the nonlocal motion. Under a perturbatio
 n argument and an appropriate parabolic scaling in
  space and time\, we derive fractional Patlak-Kell
 er-Segel equations [2].\nFurther\, we consider the
  implications of such biological diffusion in the 
 context of T cell movement in the brain [3]. In re
 sponse to Toxoplasma gondii infections\, these cel
 ls have been shown to exhibit a mixed L&acute\;evy
  walk in which an additional resting time occurs b
 etween directional changes. The resulting equation
  generates a time-fractional term and allows us to
  formally interpret the results of [1]. Consequent
 ly\, we shed light on the extent to which L&acute\
 ;evy flight behaviour impacts on the average time 
 taken for T cells to locate the sparsely distribut
 ed infected targets. We use the PDE description to
  present numerical results. This work is in collab
 oration with H. Gimperlein\, K. Painter and J. Sto
 cek.\nReferences[1] T. Harris\, et al. Generalized
  L&acute\;evy walks and the role of chemokines in 
 migration of effector CD8+ T cells\, Nature 486\, 
 545&ndash\;548\, 2012.[2] G. Estrada\, H. Gimperle
 in\, K.J. Painter. Fractional Patlak-Keller-Segel 
 equations for chemotactic superdiffusion\, SIAP\, 
 78(2): 1155-1177\, 2018.[3] G. Estrada\, H. Gimper
 lein\, K.J. Painter\, J. Stocek. Space-time fracti
 onal diffusion in immune cell models with delay\, 
 M3AS\, 29\, 65-88\, 2019.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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