We develop mathematical models to connect molecular events to dynamic physiological outcomes. Of particular interest is the challenge of using numerical simulations to bridge length-scales in integrated computational and experimental investigations – with the aim of accelerating the translation of molecular and cellular level findings to medical applications. The models we develop involve mechanistic representations of biophysical, biochemical, and physiological events thought to underlie medical outcomes. Integrated with experimental data, they become valuable tools in hypothesis testing, identification of experimentally inaccessible causal mechanisms, and experimental design. Current areas of interest include cardiovascular systems pharmacology, molecular and systems toxicology, and host-pathogen interactions.