Mathematical modeling approaches to describe the dynamics of protein adsorption at solid interfaces

Protein adsorption on solid surfaces play a crucial role in many biological applications. While extensive experimental studies have revealed the dynamics of protein adsorption in detail using newly developed experimental techniques, mathematical modeling approaches provide illustrative insight of such complex processes, which are often difficult to describe experimentally. To advance our understanding of dynamic protein behaviors at interfaces between proteins and solid surfaces, there are needs for additional information about such complex phenomena, especially conformational changes in protein mixture system. In this review, we will briefly describe competitive protein adsorption process (known as 'Vroman effect') and provide a brief overview of some important mathematical modeling approaches to advance our knowledge of the dynamic adsorption/desorption processes and highlight the need for experimental methods to determine the extent of conformational changes and the rate of conformational change of adsorbed proteins at the surfaces.