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Bacterial movement by run and tumble: models, patterns, pathways, scales
Virtualconference
Authors : Perthame, Benoît (Author of the conference)
CIRM (Publisher )
35B25 - Singular perturbations
35Q20 - Boltzmann equations
92C17 - Cell movement (chemotaxis, etc.)
35Q84 - Fokker-Planck equations
35Q92 - PDEs in connection with biology and other natural sciences
Additional resources :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Benoit_PERTHAME.pdf
CIRM (Publisher )
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Abstract :
At the individual scale, bacteria as E. coli move by performing so-called run-and-tumble movements. This means that they alternate a jump (run phase) followed by fast re-organization phase (tumble) in which they decide of a new direction for run. For this reason, the population is described by a kinetic-Botlzmann equation of scattering type. Nonlinearity occurs when one takes into account chemotaxis, the release by the individual cells of a chemical in the environment and response by the population.
These models can explain experimental observations, fit precise measurements and sustain various scales. They also allow to derive, in the diffusion limit, macroscopic models (at the population scale), as the Flux-Limited Keller-Segel system, in opposition to the traditional Keller-Segel system, this model can sustain robust traveling bands as observed in Adler's famous experiment.
Furthermore, the modulation of the tumbles, can be understood using intracellular molecular pathways. Then, the kinetic-Boltzmann equation can be derived with a fast reaction scale. Long runs at the individual scale and abnormal diffusion at the population scale, can also be derived mathematically.
Keywords : flux limited Keller-Segel system; chemotaxis; drift-diffusion equation; asymptotic analysis; kinetic transport
MSC Codes : These models can explain experimental observations, fit precise measurements and sustain various scales. They also allow to derive, in the diffusion limit, macroscopic models (at the population scale), as the Flux-Limited Keller-Segel system, in opposition to the traditional Keller-Segel system, this model can sustain robust traveling bands as observed in Adler's famous experiment.
Furthermore, the modulation of the tumbles, can be understood using intracellular molecular pathways. Then, the kinetic-Boltzmann equation can be derived with a fast reaction scale. Long runs at the individual scale and abnormal diffusion at the population scale, can also be derived mathematically.
Keywords : flux limited Keller-Segel system; chemotaxis; drift-diffusion equation; asymptotic analysis; kinetic transport
35B25 - Singular perturbations
35Q20 - Boltzmann equations
92C17 - Cell movement (chemotaxis, etc.)
35Q84 - Fokker-Planck equations
35Q92 - PDEs in connection with biology and other natural sciences
Additional resources :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Benoit_PERTHAME.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/04/2021 Conference Date : 25/03/2021 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : Mathematics in Science & Technology Format : MP4 (.mp4) - HD Video Time : 00:41:48 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-25_Perthame.mp4 
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Information on the Event
Event Title : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et AnalyseEvent Organizers : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine Dates : 22/03/2021 - 26/03/2021 Event Year : 2021 Event URL : https://www.chairejeanmorlet.com/2355.html
Citation Data
DOI : 10.24350/CIRM.V.19735403Cite this video as: Perthame, Benoît (2021). Bacterial movement by run and tumble: models, patterns, pathways, scales. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19735403 URI : http://dx.doi.org/10.24350/CIRM.V.19735403 |
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Bibliography
- CALVEZ, Vincent, PERTHAME, Benoȋt, et YASUDA, Shugo. Traveling wave and aggregation in a flux-limited Keller-Segel model. Kinetic & Related Models, 2018, vol. 11, no 4, p. 891 - http://dx.doi.org/10.3934/krm.2018035
- PERTHAME, Benoît, TANG, Min, et VAUCHELET, Nicolas. Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway. Journal of mathematical biology, 2016, vol. 73, no 5, p. 1161-1178. - https://doi.org/10.1007/s00285-016-0985-5
