The National Science Foundation (NSF) Division of Mathematical Sciences (DMS), in collaboration with the Division of Molecular and Cellular Biosciences (MCB), seeks to promote interdisciplinary research that enables novel mathematical and computational approaches that capture and explore the full range of mechanisms and biological variability needed to better understand complex and nonlinear behavior across multiple biological systems and scales. The development of replicative or descriptive models for complex biological systems remains a challenging task, yet models that move beyond replication into the realm of prediction and ultimately becoming indispensable tools for discovery-driven biology are severely lacking. A paradigm shift in the current approach to interdisciplinary mathematical biology is needed to promote the realization of modeling platforms that facilitate discovery of novel biological phenomena, rules, and theories. As part of the effort, funding opportunities are available in fiscal years FY2021 and FY2022 to provide support for proposals from interdisciplinary teams comprised of mathematical, computational, and biological scientists to develop MODels for Uncovering Rules and Unexpected Phenomena in Biological Systems (MODULUS). This Dear Colleague Letter (DCL) is to encourage researchers involved in the biosciences and the mathematical sciences to collaborate in a substantive manner in biological investigations using novel mechanistic mathematical models to guide biological exploration and discovery of new rules, phenomena, and theories in living systems.