The dynamics of ligand-protein interactions are necessary to understand for the design of novel therapeutic agents. In this paper, we establish the use of Stochastic Roadmap Simulation (SRS) for the study of ligand-protein interactions through two studies. In our first study, we measure the effects of mutations on the catalytic site of a protein, a process called computational mutagenesis. In our second study, we focus on distinguishing the catalytic site from other putative binding sites. SRS compactly represents many Monte Carlo (MC) simulation paths in a compact graph structure, or roadmap. Furthermore, SRS allows us to analyze all the paths in this roadmap simultaneously. In our application of SRS to the domain of ligand-protein interactions, we consider a new parameter called escape time, the expected number of MC simulation steps required for the ligand to escape from the ”funnel of attraction” of the binding site, as a metric for analyzing such interactions. Although compu...