The adaptive immune system is a dynamical, self-organized multiscale system that protects vertebrates from both pathogens and internal irregularities, such as tumours. For these reason it fascinates physicists, yet the multitude of different cells, molecules and sub-systems is often also petrifying. Despite this complexity, as experiments on different scales of the adaptive immune system become more quantitative, many physicists have made both theoretical and experimental contributions that help predict the behaviour of ensembles of cells and molecules that participate in an immune response. Here we review some recent contributions with an emphasis on quantitative questions and methodologies. We also provide a more general methods section that presents some of the wide array of theoretical tools used in the field.
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Dissociation ratesAs discussed below, immunological interactions span the range of very short lived interactions, k off > 10 s −1 or τ off = (k off ) −1 < 0.1 s for antibody binding to its target in the initial phase of an immune response, to extremely long-lived interactions, k off < 10 −4 s −1 or τ off > 3 hours for cytokines interacting with their receptors. These estimates set a huge range of time scales the immune system must deal with, even before taking into consideration delays in cellular responses and how these affect the ligand environment on time scales ranging from hours to days. These considerations form the crux of the matter for quantitative immunology at the cellular scale: while the physical chemistry of ligand-receptor interactions is straightforward, the immune system builds a response of devilish complexity from such elementary interactions.
Numbers of receptors per cellIn some situations, such as in T cell antigen recognition, where both the T cell receptor and the antigen exist in a membrane-bound form. All dynamics of interactions must be estimated taking into account the surface concentrations of molecules, with proper adjustment for slower diffusion in the association rates.