Mathematical modeling is a tool that enables the investigation of phenomena that may be hard to measure or emulate experimentally. Traditional biochemical network modeling approaches are often complex and nonlinear and require the estimation of a large number of unknown parameters. The power-law formalism - or biochemical systems theory (BST) – which is based on generic model descriptions and yields reduced systems of non-linear ordinary differential equations, has become an area of interest since it was proposed in the 1960s by Savageau. The development of accurate lower-order models of biochemical kinetics would potentially streamline the modeling process in many applications. Toward this goal, we developed dynamic power-law models in two overarching topics: coagulopathies and cell-free systems. In this work, our models describe coagulatory and fibrinolytic pathways in pregnant patients, quantifyinghypercoagulability at various stages of pregnancy. We then developed models of coagulation in hemophilia patients and were able to predict clotting dynamics. Finally, we developed a model of sequence-specific gene transcription in a cell-free system and successfully captured mRNA dynamics. Taken together, we have developed lower-order models that could be used in clinical, academic, and industrial applications.