Modeling and Model Simplification to Facilitate Biological Insights and Predictions

Abstract

Mathematical dynamical models of intracellular signaling networks are continuously increasing in size and model complexity due in large part to the data explosion in biology. However, the sheer complexity of the relationship between state-variables through numerous parameters constitutes a significant barrier against obtaining insight into which parts of a model govern a certain read-out, and the uncertainty in model structure and especially model parameters is here a further complicating factor. To meet these two challenges of complexity and uncertainty, systematic construction of simplified models from complex models is a central area of investigation within systems biology as well as for personalized medicine. Model complexity makes the task of deriving predictions difficult in general and in particular when different read-outs depend on combinations of parameters, since exhaustive computer simulations are not sufficient for understanding nor feasible in practice. Construction of simplified models is therefore an important complementary approach to this end, while also facilitating the identifiability of over-parameterized models. Within this chapter we discuss different methods for model simplification, and we specifically summarize a recently developed simplification method based on an iterative “tearing, zooming and simplifying” approach. We also look into the modeling process in general. In the “tearing, zooming and simplifying” approach the original model is divided into modules (tearing), the modules are considered as input-output systems (zooming), which then are replaced by simplified transfer functions (simplifying). The idea behind the simplification is to utilize biological features such as modularity and robustness as well as abundance of typical dynamical behaviors in biology such as switch-like responses. The methodology is illustrated using a relatively complex model of the cell division cycle, where the resulting simplification corresponds to a piecewise linear system with delay, facilitating an understanding of the underlying core dynamics and enabling the prediction of combinations of parameters that can change different model features like the size of the cell. Hence, the existence of biological organization principles enables a simplified description of intracellular dynamics.