A computer simulation for the study of macromolecular adsorption with special applications to single-component protein adsorption

A computer simulation was created to solve the partial differential equation describing diffusion and adsorption in a one-component system given a boundary condition describing kinetic adsorbate behavior in the form of ordinary differential equations. Physical effects of a typical experimental system including diffusion and solution depletion are taken into account by the simulation so that the impact of hypothesized adsorption mechanisms on surface uptake may be tested independently. Simulation is especially useful when one considers mechanisms which are kinetically rather than thermodynamically limited. Protein adsorption, for example, exhibits highly “path dependent” and hysteretical behavior which cannot be adequately described using equations of state based on an assumption of thermodynamic equilibrium. A FORTRAN program was written to simulate an experimental system frequently employed in this laboratory involving protein adsorption in cylindrical geometry from a nonflowing, dilute solution. One advantage of the numerical methods employed is manifest in the ability of the simulation to deal with an infinite concentration gradient at the adsorbing surface when the two phases (protein solution and solid surface) are first brought together. This feature eliminates the need to assume the existence of a “diffusion layer” (i.e., concentration boundary layer) of finite thickness during the adsorption process. A number of simple adsorption mechanisms were incorporated into the simulation to show how experimental surface uptake data may be used to distinguish between simple reversible and irreversible molecular binding. The development at zero time of a concentration boundary layer due to the injection of a protein solution into a tube was shown to be capable of obscuring the nature of the true mechanism. The use of short adsorption time “isotherms” to determine the diffusion coefficient or protein—surface “affinity” was shown to be misleading in several circumstances. An example of a simple two-state adsorption model was simulated kinetically to demonstrate the ability of the simulation to be extended to more complex mechanisms.