Surface pressure of protein adsorption layers: application to molecular mass and molecular area measurements

Abstract

In the study of protein adsorption at fluid interfaces, the relation between the surface concentration and the surface pressure is of general interest and is usually quantitated by state equations. In the dilute range, the ideal gas law is a good approximation which allows the calculation of the molecular mass of the molecule. It may be extended on the increasing concentration side by the two-dimensional solution (2D solution) approximation which allows the calculation of both the molecular mass and the molecular area of the protein at the interface. When the surface concentration increases beyond a critical value, the interfacial layer enters a semi-dilute regime where a scaling law approach gives a good approximation of the structure and of the properties of the layer but which only allows a “rough” calculation of either the molecular area or the molecular mass from the other parameter. Moreover, in the scaling law approach, the semi-dilute regime is connected to the gas-like regime by an angulous transition which is not observed in the experimental isotherms. In this communication, a mixed approach is proposed in which the state equation is the 2D solution law below the critical surface concentration and the scaling law beyond this value where both the surface pressure and its derivative with respect to the surface concentration are equal when expressed from one law or from the other. Simple relations are found between the critical surface concentrations calculated from either the 2D solution, the scaling law or the mixed approaches. Within that framework, it is possible to define precisely the range of data belonging to the 2D solution regime and to know whether the molecular mass and molecular area calculations are performed by fitting the right equation to the right data or not.