Fig. 4.

Impact of antigen kinetics on T cell proliferation. (A) Antigen input schedules: single pulse, constant input, and exponentially increasing input (increase each day by fivefold as in ref. 7). (B) Dynamics of pMHCs. (C) Dynamics of T cells. (D) The optimal schedule is close to the experimentally used exponential schedule. The antigen input schedule over 4 d that optimizes fold expansion at day 6 was computed numerically using a projected gradient algorithm (16). (E) Fold expansion for exponential schedules as a function of the fold increase per day, with the experimental schedule indicated by the dot. Parameters: $\alpha$, $\mu$, and $\delta$ as in Fig. 2; $K=10$; $C\left(0\right)=0,T\left(0\right)=100$; and total administered antigen is $2\cdot 10^6$.