We studied the optimal choice between feedforward and feedback control in the production of heat shock proteins. Heat shocks causes damage through denaturation of proteins in cells. Many organisms have mechanisms to protect themselves against damage through such deformed proteins, by production of so-called heat shock proteins. Such protective mechanisms play an important role in development of higher organisms, but also in unicellular organisms such as bacteria. In many cases, there are different pathways for protective mechanisms. For instance, in E. coli there are two such pathways. One is through feedforward control, i.e. a supply of heat shock proteins is present, that can be used immediately to reduce the damage, and the other one is through feedback control, i.e. heat shock proteins are produced in response to a shock. The latter mechanism obviously involves a delay. The question we examined is under which conditions the use of either one of the mechanisms (or both) is optimal. To do this, we adopted a model where the damage done by a heat shock depends partly on the intensity of the shock, but also contains a stochastic component. Thus, when a heat shock occurs, an organism cannot predict with certainty what will be the total amount of deformed proteins. We assume that the organism can chose the amount of investment in feedforward control, which is based on the heat shock intensity, and the amount of investment in feedback control, which is based on the already invested feedforward control plus the observed level of damage done by the heat shock. There is assumed to be a cost involved with the total amount of investment.
We are able to show that, irrespective of the form of the conditional distribution of damage done by the heat shock, feedforward control should always be used. In addition, feedback control should sometimes be used. This largely depends on the magnitude of the delay involved in production of proteins through feedback control. We are currently investigating this dependency for different forms of damage distributions.