Mathematical Models of Bacteria Polarity and Fibrin Network Mechanics

Two novel mathematical models are described and used in this thesis to study important biological problems of blood clot formation and cell polarity during division. These two models are clearly distinguished with respect to mathematical and computational methods as well as models calibration using experiential data.

First, a model of Myxococcus xanthus internal protein dynamics is presented and its relation with the motility based bacterial polarity is discussed. The model is compared with experimental data on Myxococcus xanthus and the protein RomR to simulate oscillations of protein inside a bacteria cell.

Second, an extension of the model for studying the mechanical deformation of fibrin networks in a blood clot is presented for studying compression and shear stress. Lastly, Numerical Algebraic Geometry methods are used to improve the computational efficiency and accuracy of this model.