To understand the mechanism of action of the chaperone protein tapasin, which mediates loading of high-affinity peptides onto major histocompatibility complex (MHC) class I molecules in the antiviral immune response, we have performed numerical simulations of the class I-peptide binding process with four different mechanistic hypotheses from the literature, and tested our predictions by laboratory experiments. We find - in agreement of experimental and theoretical studies - that class I-peptide binding in cells is generally under kinetic control, and that tapasin introduces partial thermodynamic control to the process by competing with peptide for binding to class I. Based on our results, we suggest further experimental directions.