chemotaxis models
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2020 ◽  
Vol 171 (1) ◽  
Author(s):  
Gurusamy Arumugam ◽  
Jagmohan Tyagi
Keyword(s):  

Author(s):  
Martin Burger ◽  
Philippe Laurençot ◽  
Ariane Trescases
Keyword(s):  
Blow Up ◽  

Cells ◽  
2019 ◽  
Vol 8 (10) ◽  
pp. 1301 ◽  
Author(s):  
Pena ◽  
Zhang ◽  
Majeska ◽  
Venkatesh ◽  
Vazquez

Regenerative retinal therapies have introduced progenitor cells to replace dysfunctional or injured neurons and regain visual function. While contemporary cell replacement therapies have delivered retinal progenitor cells (RPCs) within customized biomaterials to promote viability and enable transplantation, outcomes have been severely limited by the misdirected and/or insufficient migration of transplanted cells. RPCs must achieve appropriate spatial and functional positioning in host retina, collectively, to restore vision, whereas movement of clustered cells differs substantially from the single cell migration studied in classical chemotaxis models. Defining how RPCs interact with each other, neighboring cell types and surrounding extracellular matrixes are critical to our understanding of retinogenesis and the development of effective, cell-based approaches to retinal replacement. The current article describes a new bio-engineering approach to investigate the migratory responses of innate collections of RPCs upon extracellular substrates by combining microfluidics with the well-established invertebrate model of Drosophila melanogaster. Experiments utilized microfluidics to investigate how the composition, size, and adhesion of RPC clusters on defined extracellular substrates affected migration to exogenous chemotactic signaling. Results demonstrated that retinal cluster size and composition influenced RPC clustering upon extracellular substrates of concanavalin (Con-A), Laminin (LM), and poly-L-lysine (PLL), and that RPC cluster size greatly altered collective migratory responses to signaling from Fibroblast Growth Factor (FGF), a primary chemotactic agent in Drosophila. These results highlight the significance of examining collective cell-biomaterial interactions on bio-substrates of emerging biomaterials to aid directional migration of transplanted cells. Our approach further introduces the benefits of pairing genetically controlled models with experimentally controlled microenvironments to advance cell replacement therapies.


2019 ◽  
Vol 29 (11) ◽  
pp. 2033-2062 ◽  
Author(s):  
Marcel Braukhoff ◽  
Johannes Lankeit

Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed. Following the suggestions that the main reason for that is the usage of inappropriate boundary conditions, in this paper we study the solutions to the stationary chemotaxis system [Formula: see text] in bounded domains [Formula: see text], [Formula: see text], under the no-flux boundary conditions for [Formula: see text] and the physically meaningful condition [Formula: see text] on [Formula: see text], with the given parameter [Formula: see text] and [Formula: see text], [Formula: see text], satisfying [Formula: see text], [Formula: see text] on [Formula: see text]. We prove the existence and uniqueness of solutions for any given mass [Formula: see text]. These solutions are nonconstant.


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