The optimization of peptide-MHC class I complexes at the surface of antigen presenting cells is one of the key factors that determines the hierarchy of the T-cell response to a complex antigen 
. Peptide optimization is also important for vaccine design, where vaccine peptides compete with endogenous peptides for presentation 
. In this paper we propose a dynamical systems model of MHC class I peptide optimization, which takes into account the supply of peptides in the cytosol, the affinity of peptides to MHC and the interactions between peptide and MHC at the different stages of the optimization process, both within the ER and at the cell surface. The model also incorporates the effects of tapasin, which is known to increase peptide optimization 
and to affect different MHC class I alleles to different extents 
. This variation in tapasin dependence may protect from viral immune evasion strategies such as tapasin inhibition by an adenovirus 
The dynamical systems model is firmly grounded in experimental data, and techniques already exist to measure many of the model parameters 
. The model therefore allows a multitude of experimental results to be unified within a common framework, so that a range of mechanistic hypotheses can be formulated and tested. We derive a peptide filtering relation which, for the first time, provides a mechanistic explanation for experimental data on MHC class I peptide optimization, both over time 
and at steady state 
. Specifically, it suggests that tapasin enhances peptide off-rate in order to improve peptide optimization without significantly delaying the transit of MHC to the cell surface.
We have also shown that an allele-specific peptide on-rate is the most likely mechanistic explanation for differences in peptide optimization across HLA–B alleles. A possible interpretation is that differences in peptide on-rate are due to allelic differences in molecular conformation. For example, alleles such as B4402 could adopt a closed conformation, reducing the ability of peptides to bind MHC, while alleles such as B2705 could adopt a more open conformation, allowing peptides to readily bind MHC, as suggested in 
. When tapasin binds to MHC the peptide binding groove may then adopt a peptide receptive conformation, allowing MHC to bind peptides more readily, as suggested in 
. Although allelic differences in the conformation of MHC class I are largely peptide-independent, variations in the on-rates of different peptides have nevertheless been observed. These variations can be incorporated in future versions of the model by allowing a separate on-rate for each peptide. However, published estimates indicate that variations in the affinity of peptide-MHC interactions are mostly governed by variations in peptide off-rate 
, supporting our assumption that the on-rate is allele-specific and largely peptide-independent.
Although the current model makes a number of simplifying assumptions on the antigen presentation process, the model can be readily extended to incorporate additional details as more data are acquired. These details could include the explicit contribution of TAP transport, proteasomal cleavage and cytosolic protein abundance to ER peptide supply 
. At present these mechanisms are only implicitly represented in the model via peptide-specific supply rates
. Further extensions could also include conformational changes in MHC 
, and chaperones such as ERp57 and calreticulin which are known to influence total cell-surface presentation 
. Since the mechanisms by which additional chaperones interact with MHC class I are only partially known, we can investigate a variety of hypotheses by using our Information Theoretic framework to assess allele-specific chaperone-dependency. In the future, coupling model analysis with additional experimental measurements will enable quantitative predictions of peptide optimization for a wide range of MHC class I genotypes. Having a robust model, known to make accurate predictions, will improve our ability to assess the efficacy of vaccines involving multiple peptides, and will provide a quantitative means to prioritize different vaccination strategies.
The current work is part of a broader research programme to use experimental data to build credible mathematical models of immunological processes, ranging from relatively simple examples to complex systems such as organ-specific autoimmunity. The resulting models can then be used to make specific and testable predictions that relate directly to immunological function. Subsequent iterations offer an opportunity to refine or develop the models from the simple to the complex, or from the static to the time-resolved, at the molecular, cellular or organ level.