English
Bacterial movement by run and tumble: models, patterns, pathways, scales
Virtualconference
Auteurs : Perthame, Benoît (Auteur de la Conférence)
CIRM (Editeur )
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
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Benoit_PERTHAME.pdf
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Benoit_PERTHAME.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 09/04/2021 Date de captation : 25/03/2021 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : Mathematics in Science & Technology Format : MP4 (.mp4) - HD Durée : 00:41:48 Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-25_Perthame.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et AnalyseOrganisateurs de la rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine Dates : 22/03/2021 - 26/03/2021 Année de la rencontre : 2021 URL Congrès : https://www.chairejeanmorlet.com/2355.html
Données de citation
DOI : 10.24350/CIRM.V.19735403Citer cette vidéo: 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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Bibliographie
- 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
