External optimal control of self-organisation dynamics in a chemotaxis reaction diffusion system.
Detailed quantitative understanding and specific external control of cellular behaviour are general long-term goals of modem bioscience research activities in systems biology. Pattern formation and self-organisation processes both in single cells and in distributed cell populations are phenomena which are highly significant for the functionality of life, because life requires to maintain a highly organised spatiotemporal system structure. In particular chemotaxis is crucial for various biological aspects of intercellular signalling and cell aggregation. As an example for model based control of self-organising biological systems, we describe numerical optimal control of E. coli bacterial chemotaxis based on a 1-D two-component partial differential equation (PDE) model of reaction diffusion type. We present a numerical scheme to force cell aggregation patterns to particular desired results by applying a boundary influx control of chemoattractant without interfering with the system itself. Optimal controls are numerically computed by using a specially tailored interior point optimisation technique applied to a direct collocation discretisation of the control function and the PDE constraint. The objective to be minimised is the deviation of a desired cell distribution from the cell density, which results from the dynamics of the controlled system.
Lebiedz
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D
Interdisciplinary Center for Scientific Computing, Heidelberg, Germany. lebiedz@iwr.uni-heidelberg.de
Maurer
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H
D001426:Bacterial Proteins; D002449:Cell Aggregation / Q000187:drug effects / Q000502:physiology; D002628:Chemoreceptor Cells / Q000187:drug effects / Q000502:physiology*; D002630:Chemotactic Factors / Q000494:pharmacology*; D002633:Chemotaxis / Q000187:drug effects / Q000502:physiology*; D004058:Diffusion; D004926:Escherichia coli / Q000737:chemistry / Q000187:drug effects / Q000502:physiology*; D029968:Escherichia coli Proteins / Q000737:chemistry / Q000378:metabolism*; D005246:Feedback / Q000187:drug effects / Q000502:physiology; D008954:Models, Biological; D015398:Signal Transduction / Q000187:drug effects / Q000502:physiology*
D001426:Bacterial Proteins; D002630:Chemotactic Factors; D029968:Escherichia coli Proteins