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March 12, 2010:
Venue: Auditorium Room 301, Building A5
Time: 14:00
Speaker: Prof. Dr. Karl-Heinz Hoffmann, Technical University of Munich
Title: Convection-Diffusion-Equations With Absorption-Boundary-Conditions: Modelling a Biosensor
Abstract:
We consider a problem which appears when developing sensors
which serve for detecting of certain proteins in solutions. An important
part of such a sensor is a wet cell, say a cube, filled with a liquid into
which a solution containing the protein to be detected is injected.
Special molecules called aptameres are immobilized on the bottom of the
wet cell. The aptameres can selectively bind the desired protein from the
solution. The change of the surface mass loading can be analyzed using
acoustic waves propagating along the aptamere-layer. Thus, the
concentration of the protein in the solution will be estimated.
In this presentation, a model that describes the propagation of the
protein in the wet cell and its adhering to the aptameres is proposed. It
is assumed for simplicity that the propagation of the injected protein in
the wet cell is governed by a diffusion equation. A special boundary
condition on the bottom provides the monotone grows of the deposited layer
with saturation which means the exhaustion of free aptamere-molecules.
Speaker: Prof. Dr. Willi Jäger, University of Heidelberg
Title: Mathematical Modelling and Simulation of Complex, Nonlinear Systems in Biosciences
Abstract:
Modelling and simulations of biological structures and
functions are challenges to Mathematics and Computational Sciences. Due to
the rapid increase of information about processes and structures on the
molecular and cellular level, it is necessary to couple model equations
for macroscopic state variables to the equations describing the processes
on the micro-scale. In this lecture two examples will be discussed to
illustrate the challenges and the potential for analysis and numerical
mathematics in investigating bio systems:
(1) Coupling reactive flow and biomechanics in tissues and membranes In
joint research with M. Neuss-Radu and A. Mikelic, we derived
effective equations for processes in tissues and membranes, using
multi-scale techniques to determine the limit with respect to a
characteristic scale. The resulting model equations are generalization of
model equations known as Biot-laws in case of porous media.
(2) Interaction of biomechanics and biochemistry of cell walls
Models for the mechanics of cell walls lead to flows involving
mean and Gaussian curvatures. In case of interactions with internal fiber
networks or under the influence of chemical reactions on
the cell wall, the dynamical equations have to be adjusted. Here
the penetration of virus through a cell wall and the dynamics of
blood cell will be discussed. Results obtained in PhD thesis of
D. Hartmann und in a running project jointly with M. Mercker
will be presented.
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