The applicability of mathematics in computational systems biology and its experimental relations

Abstract

In 1966 Richard Levins argued that applications of mathematics to population biology faced various constraints which forced mathematical modelers to trade-off at least one of realism, precision, or generality in their approach. Much traditional mathematical modeling in biology has prioritized generality and precision in the place of realism through strategies of idealization and simplification. This has at times created tensions with experimental biologists. The past 20 years however has seen an explosion in mathematical modeling of biological systems with the rise of modern computational systems biology and many new collaborations between modelers and experimenters. In this paper I argue that many of these collaborations revolve around detail-driven modeling practices which in Levins’ terms trade-off generality for realism and precision. These practices apply mathematics by working from detailed accounts of biological systems, rather than from initially idealized or simplified representations. This is possible by virtue of modern computation. The form these practices take today suggest however Levins’ constraints on mathematical application no longer apply, transforming our understanding of what is possible with mathematics in biology. Further the engagement with realism and the ability to push realistic models in new directions aligns well with the epistemological and methodological views of experimenters, which helps explain their increased enthusiasm for biological modeling.

Perspective: Systems biology beyond biology

“…They had to be able to deal with change and complicated nonlinearities and thereby facilitate the functional integration of small models ("modules") into increasingly larger, well-organized ensembles of models in complex contexts. It was beyond doubt that these approaches required the use of mathematics and computation (Melham, 2013;Motta and Pappalardo, 2013;Cvijovic et al, 2016;MacLeod, 2021). Initially, the scientific community at large was reluctant to accept the proposal to use computational methods and control theory to understand living systems, because "biology was too complicated to use math."…”