This study focuses on the analysis of dynamic computational models capable of explaining bio-chemical and evolutionary systems. First, we mathematically modeled the intrinsic apoptosis pathway by using a system of ordinary differential equations (an ODE model) generated by a systems biology tool, Simpathica, which is a simulation and reasoning system developed to study biological pathways. Caspase-9 is the protease that mediates the intrinsic pathway of apoptosis, a type of cell death. Activation of caspase-9 is a multi-step process that requires dATP or ATP and involves at least two proteins, cytochrome c and Apaf-1. "Model checking" based on comparing simulation data with that obtained from a recombinant system of caspase-9 activation provided several new insights into regulation of this protease. Our model predicts that the activation begins with binding of dATP to Apaf-1, which initiates the interaction between Apaf-1 and cytochrome c, thus forming a complex that oligomerizes into an active caspase-9 holoenzyme via a linear binding model with bpositive cooperative interaction rather than through network formation. bSecond, we proposed a model that explains the low conservation of rDNA intergenic spacer (IGS). The rDNA IGS subrepeats play an important role in enhancing RNA Polymerase I transcription, and yet, despite this functional role and presumed selective constraint, they show surprisingly few similarities. We observed and modeled that fast insertion-deletion rates of short mononucleotide microsatellite (or Poly(N) runs) can explain this paradox. We mathematically calculated the ideal frequencies of the Poly(N) runs in random sequence and found their relative abundance in rDNA IGS subrepeats. Furthermore, by aligning sequences after modifying them by the drop-out method, i.e. by disregarding Poly(N) runs during the sequence aligning step, we uncovered evolutionarily shared similarities that fail to be recognized by current alignment programs. Our analysis led us to conclude that most diverse kinds of rDNA IGS subrepeats in one species must have been derived from a common ancestral subrepeat, and that it is possible to infer the evolutionary relationships among the rDNA IGS subrepeats of different species.