Charting a new frontier of science by integrating mathematical modeling to understand and predict complex biological systems

Biological systems are staggeringly complex. To untangle this complexity and make predictions about biological systems is a continuous goal of biological research. One approach to achieve these goals is to emphasize the use of quantitative measures of biological processes. Advances in quantitative biology data collection and analysis across scales (molecular, cellular, organismal, ecological) has transformed how we understand, categorize, and predict complex biological systems. Simultaneously, thanks to increased computational power, mathematicians, engineers and physical scientists -- collectively termed theoreticians -- have developed sophisticated models of biological systems at different scales. But there is still a disconnect between the two fields. This surge of quantitative data creates an opportunity to apply, develop, and evaluate mathematical models of biological systems and explore novel methods of analysis. The novel modeling schemes can also offer deeper understanding of principles in biology. In the context of this paper, we use “models” to refer to mathematical representations of biological systems. This data revolution puts scientists in a unique position to leverage information-rich datasets to improve descriptive modeling. Moreover, advances in technology allow inclusion of heterogeneity and variability within these datasets and mathematical models. This inclusion may lead to identifying previously undetermined variables driving or maintaining heterogeneity and diversity. Improved inclusion of variation may even improve biologically meaningful predictions about how systems will respond to perturbations. Although some of these practices are mainstream in specific sub-fields of biology, such practices are not widespread across all fields of biological sciences. With resources dedicated to better integrating biology and mathematical modeling, we envision a transformational improvement in the ability to describe and predict complex biological systems