Optimal defense strategy: storage vs. new production.

If hosts produce defense proteins after they are infected by pathogens, it may take hours to days before defense becomes fully active. By producing defense proteins beforehand, and storing them until infection, the host can cope with pathogens with a short time delay. However, producing and storing defense proteins require energy, and the activated defense proteins often cause harm to the host's body as well as to pathogens. Here, we study the optimal strategy for a host who chooses the amount of stored defense proteins, the activation of the stored proteins upon infection, and the new production of the proteins. The optimal strategy is the one that minimizes the sum of the harm by pathogens and the cost of defense. The host chooses the storage size of defense proteins based on the probability distribution of the magnitude of pathogen infection. When the infection size is predictable, all the stored proteins are to be activated upon infection. The optimal strategy is to have no storage and to rely entirely on new production if the expected infection size n(0) is small, but to have a big storage without new production if n(0) is large. The transition from the "new production" phase to "storage" phase occurs at a smaller n(0) when storage cost is small, activation cost is large, pathogen toxicity is large, pathogen growth is fast, the defense is effective, the delay is long, and the infection is more likely. On the other hand, the storage size to produce for a large n(0) decreases with three cost parameters and the defense effectiveness, increases with the likelihood of infection, the toxicity and the growth rate of pathogens, and it is independent of the time delay. When infection size is much smaller than the expected size, some of the stored proteins may stay unused.