Quantitative exploration of biological pathway networks must begin with a qualitative understanding of them. Often researchers aggregate and disseminate experimental data using regulatory diagrams with ad hoc notations leading to ambiguous interpretations of presented results. This thesis has two main aims. First, it develops software to allow researchers to aggregate pathway data diagrammatically using the Molecular Interaction Map (MIM) notation in order to gain a better qualitative understanding of biological systems. Secondly, it develops a quantitative biological model to study the effect of DNA damage on circadian rhythms. The second aim benefits from the first by making use of visual representations to identify potential system boundaries for the quantitative model. I focus first on software for the MIM notation - a notation to concisely visualize bioregulatory complexity and to reduce ambiguity for readers. The thesis provides a formalized MIM specification for software implementation along with a base layer of software components for the inclusion of the MIM notation in other software packages. It also provides an implementation of the specification as a user-friendly tool, PathVisio-MIM, for creating and editing MIM diagrams along with software to validate and overlay external data onto the diagrams. I focus secondly on the application of the MIM software to the quantitative exploration of the poorly understood role of SIRT1 and PARP1, two NAD+-dependent enzymes, in the regulation of circadian rhythms during DNA damage response. SIRT1 and PARP1 participate in the regulation of several key DNA damage-repair proteins and are the subjects of study as potential cancer therapeutic targets. In this part of the thesis, I present an ordinary differential equation (ODE) model that simulates the core circadian clock and the involvement of SIRT1 in both the positive and negative arms of circadian regulation. I then use this model is then used to predict a potential role for the competition for NAD+ supplies by SIRT1 and PARP1 leading to the observed behavior of primarily phase advancement of circadian oscillations during DNA damage response. The model further predicts a potential mechanism by which multiple forms of post-transcriptional modification may cooperate to produce a primarily phase advancement.