Predicting and Explaining with Models: A Few Remarks on Mathematical Immunology

Abstract

In this work, we discuss the limitations of mathematical models to provide explanations and make useful predictions in Biology. As a benchmark to assess the utility of models, we first create two toy systems that mimic the individual behavior of T cells during immune responses. We use these microscopic toy systems to simulate the process that is usually followed in mathematical immunology. We formulate macroscopic models that simulate the dynamics of the toy systems and analyze their explicative power. The rationale for our approach is that: (i) the microscopic causes of the observed behavior are (by definition) perfectly known, which allows evaluating the performance of the macroscopic models; and (ii) the predictions made by these models can easily be tested by comparing them with numerical simulations of the toy systems they intend to simulate. By using this strategy, we show that models can reproduce an observed behavior while being incompatible with the biological rules that produce that behavior. Therefore, the ability of a mathematical model to describe a given dynamics does not imply that it can explain the causes underlying it. We also show that a mechanistic approach is unnecessary to provide valuable insight into immunological problems. Macroscopic models of an utterly phenomenological nature can be used to predict important aspects of immune responses using virtually no information about the microscopic details of the interactions between effector immune cells and pathogens.