Biological researchers increasingly rely on computational models to integrate biological systems knowledge, test hypotheses, and forecast system behavior. The expanding size of these models requires solutions for managing their complexity. Modularity, a time-tested design principle for managing complexity, can be applied within the biological modeling field to parallelize work, automate composition, and promote effective model sharing. As modelers of complex biological systems, we aim to apply modular production to accelerate our efforts and have therefore investigated several currently available approaches for modular modeling. We argue that some traditional features of modularity, in particular the isolation of a module's contents from the rest of the system, can impede model sharing and composition when applied within the context of biological simulation. Alternative approaches that can automatically interface model components based on the biological meaning of their contents (their semantics) avoid these limitations. Our conclusions have strategic implications for the design of systems biology, synthetic biology, and integrated physiological modeling technologies, as well as community-level model curation efforts.