Parameter estimation for a model of fibronectin adsorption onto hydroxylapatite, oxidised polystyrene and nanostructured silica
- Austral.Mathematical Society
- Publication Type:
- Journal Article
- Langtry, Timothy et al. 2013, 'Parameter estimation for a model of fibronectin adsorption onto hydroxylapatite, oxidised polystyrene and nanostructured silica', ANZIAM, vol. 54, no. CTAC2012, pp. C429-C445.
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Fibronectin is a protein present in blood and the extracellular matrix which has important roles in cell adhesion and migration, wound healing and blood clotting. Three models of fibronectin adsorption, on various substrates of interest to biochemists, are compared. The first model (of Langmuir) is expressed explicitly as a time dependent function for the mass of protein adsorbed. The second model is a modification of the scaled particle theory of Reiss et al. [J. Chem. Phys., 31:369--380, 1959] and takes into account the probability of a molecule finding a sufficiently large vacant area on the adsorbing substrate surface. The third model extends the second model to the case in which molecules may expand the radius of their contact with the substrate upon adsorption. We used datasets obtained from experiments to compare the models. The Langmuir model is straightforward to fit to a dataset. The remaining models are fitted using a steepest descent method to minimise least squares error. We describe initial estimates for parameters for this procedure and compare the quality of fit of the models.
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