Time dependent adhesion of cells on nanorough surfaces

Understanding and controlling the mechanisms of cell adhesion to nanomaterials is essential in tissue engineering, regenerative medicine, the development of experimental models for the study of neurodegenerative diseases. Nonetheless, despite the great many of studies that have examined how cells interact with nanoscale surfaces, little is known about the temporal dimension of the process of adhesion. In a previous work, Decuzzi and Ferrari, by examining how the energy of a cell changes while binding to a nanoscale surface, determined a criterion to decide whether nanoroughness can either enhance or retard cell adhesion. While accurate, however their model template disregards the time variable. Here, starting from the work of Decuzzi and Ferrari, we have developed a mathematical model based on chemotaxis that describes how cells adhere to a nanorough surface over time. Relaxing the originating constraint of a fixed density of ligand molecules expressed by the cell membrane, we show that the strength of adhesion depends on time and that, for certain values of the model parameters, a cell can arrive to establish a stable adhesion to a substrate even if the process of binding is initially energetically unfavourable. We show that, for a cell-membrane stiffness of 10kPa, an initial density of receptors of 500bonds/μm², a specific and non-specific energy density of adhesion of 10^-5J/m² and 10^-7J/m², and roughness in the low nanometer range, cell adhesion forces can be completely activated from few seconds to some tens of minutes from the initial contact with the surface.