Predictive models in tumor immunology.

The role of the immune system in tumor surveillance is clearly established, and tumor immunologists are actively working to devise preventive and therapeutical vaccines against cancer; however, the growth of biological knowledge is still too slow to win the war against cancer as soon as possible. Mathematical models are quantitative representations of phenomena developed in the framework of a theory using the language of mathematics. Living organisms are natural complex systems and their modeling may play a crucial role since models can also be built with approximate and imperfect knowledge of a phenomenon, and model parameters (initial data, entities, relations between entities) can be adjusted to fit modeling results to experimental measurements. Such models can then be used to understand the general behavior of the phenomenon in different situations, to perform model experiments or simulations to study the role of single constituents and relations, to plan new experiments, and to test theoretical assumptions and suggest theory modifications. In this chapter we present a success story of scientific cooperation between tumor immunologists and applied mathematicians. We developed a model of the effects of a vaccine designed to prevent mammary carcinoma in transgenic mice. This model faithfully summarizes not only the outcome of the vaccination experiments, but also the dynamics of the immune responses elicited by the vaccine. We then used a genetic algorithm to search for an optimal vaccination schedule. The predicted schedules are currently being tested in vivo. The model plays the role of a virtual laboratory, performing in a few minutes in silico experiments that would take years in vivo.