Mathematical and statistical modeling in cancer systems biology

Abstract

Cancer is a major health problem with high mortality rates. In the post-genome era, investigators have access to massive amounts of rapidly accumulating high-throughput data in publicly available databases, some of which are exclusively devoted to housing Cancer data. However, data interpretation efforts have not kept pace with data collection, and gained knowledge is not necessarily translating into better diagnoses and treatments. A fundamental problem is to integrate and interpret data to further our understanding in Cancer Systems Biology. Viewing cancer as a network provides insights into the complex mechanisms underlying the disease. Mathematical and statistical models provide an avenue for cancer network modeling. In this article, we review two widely used modeling paradigms: deterministic metabolic models and statistical graphical models. The strength of these approaches lies in their flexibility and predictive power. Once a model has been validated, it can be used to make predictions and generate hypotheses. We describe a number of diverse applications to Cancer Biology, including, the system-wide effects of drug-treatments, disease prognosis, tumor classification, forecasting treatment outcomes, and survival predictions.

Keywords: ODEs; cancer; dynamic; graphical models; high-throughput data; metabolism; steady-state.

Figure 1

Simplified schematic describing mathematical modeling of cellular systems with ODEs. (A) The cellular system is translated into a mathematical model with system of ODEs reflecting the mass balance of the system. (B) Dynamic analysis of the system requires specification of fluxes as non-linear functions, which depend on a number of unknown parameters. Solving the ODE system results in the time course of concentration values as output. (C) Steady-state analysis of the system requires the specification of an objective function and constraints, but the ODE system reduces to a simple linear system. The output of the analysis is optimal flux values.

Figure 2

Probabilistic graphical models can be (A) undirected, or (B) directed. Relationships between variables can be expressed using conditional independencies, allowing compact representation of the joint distribution.

Figure 3

Understanding how molecular traits from different biological domains connect in networks is critical to progressing Cancer Biology.