Parameter estimation for a model of fibronectin adsorption onto hydroxylapatite, oxidised polystyrene and nanostructured silica

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. References M. A. Brusatori and P. R. van Tassel. A kinetic model of protein adsorption/surface-induced transition kinetics evaluated by the scaled particle theory. J. Colloid Interface Sci., 219(2):333--338, 1999. doi:10.1006/jcis.1999.6496 D. E. MacDonald, B. Markovic, M. Allen, P. Somasundaran, A. L. Boskey. Surface analysis of human plasma fibronectin adsorbed to commercially pure titanium materials. J. Biomed. Mater. Res., 41:120--130, 1998. http://www.ncbi.nlm.nih.gov/pubmed/9641632 E. Helfand, H. Reiss, H. L. Frisch, J. L. Lebowitz. Scaled particle theory of fluids. J. Chem. Phys., 33(5):1379--1385, 1960. doi:10.1063/1.1731417 H. P. Erikson and N. A. Carrell. Fibronectin in extended and compact conformations: Electron microscopy and sedimentation analysis. J. Biol. Chem., 258(23):14539--14544, 1983. http://www.jbc.org/content/258/23/14539 H. Reiss, H. L. Frisch and J. L. Lebowitz. Statistical mechanics of rigid spheres. J. Chem. Phys., 31(2):369--380, 1959. doi:10.1063/1.1730361 I. Langmuir. The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc., 40(9):1361--1403, 1918. doi:10.1021/ja02242a004 P. R. van Tassel, L. Guemouri, J. J. Ramsden, G. Tarjus, P. Viot and J. Talbot. A particle--level model of irreversible protein adsorption with a postadsorption transition. J. Colloid Interface Sci., 207(2):317--323, 1998. doi:10.1006/jcis.1998.5781 P. Schaaf and J. Talbot. Surface exclusion effects in adsorption processes. J. Chem. Phys., 91(7):4401--4409, 1989. doi:10.1063/1.456768 B. Widom. Random sequential addition of hard spheres to a volume. J. Chem. Phys., 44(10):3888--3894, 1966. doi:10.1063/1.172654