Table 1.
The cost function F(m) measures the harm caused to an organism by the time that immune receptors have had m encounters with a pathogen. The optimal receptor distribution is determined by minimizing this cost, given a pathogen distribution Q and a cross-reactivity function specifying the probability that receptor r binds to antigen a. The second column gives the form of over scales larger than the cross-reactivity. The optimal can be reached as a steady state resulting from competitive binding between receptors and antigens (last section of Results) quantified by an “availability function” A. represents the coverage of antigen a by the repertoire; is the total steady-state population; and are positive constants.