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A Hybrid Control Model of Fractone-Dependent Morphogenesis

It has been hypothesized that the generation of new neural cells (neurogenesis) in the developing and adult brain is guided by the extracellular matrix. The extracellular matrix of the neurogenic niches features specialized structures termed fractones, which are scattered in between stem/progenitor cells and bind and activate growth factors at the surface of stem/progenitor cells to influence their proliferation. We present a mathematical control model that considers the role of fractones as captors and activators of growth factors, controlling the rate of proliferation and directing the location of the newly generated neuroepithelial cells in the forming brain. The model is a hybrid control system that incorporates both continuous and discrete mechanics. The fractones in the model are represented by controls that allow for their dynamic placement in and removal from the evolving cell mass. We conclude with a discussion on controllability and optimization of the model.

Type of Seminar:
IfA Seminar
Prof. Monique Chyba
University of Hawaii
Jan 18, 2016   14.15

Contact Person:

John Lygeros
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Biographical Sketch:
Professor Monique Chyba, University of Hawaii-Manoa, Honolulu, USA, received her Phd thesis in Mathematics from the University of Geneva. Her expertise lies in the development of geometric optimal control methods and its application to real problems especially from physics, biology and engineering. Her contribution varies from robotics, especially optimal guidance and navigation of autonomous underwater vehicles, to applications in the medical field. Her most recent work focuses on designing efficient spacecraft rendezvous mission with temporarily captured orbiters, mathematical modeling of brain morphogenesis based on the distribution of the extracellular matrix structures fractones and the optimization of the protein misfolding cyclic amplification procedure.