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This research uses visual analytics to better understand genome dynamics, through a novel application of topological data analysis (TDA) to time series gene expression data. TDA is a model-free approach in which relations are obtained directly from the data. We build the dynamics of the system into the topology, then calculate the influence of potential regulatory genes over the expression of other genes. An interactive 3D visualization is provided to aid in the discovery of functional relationships. These capabilities are contained in a new R package. We apply our technique to synthetic data from the DREAM4 gene regulatory network inference challenge and compare our results to both the challenge submissions and those produced by networkBMA, a Bioconductor package designed to work with time series gene expression data. A case study is presented detailing the use of the visual analytics tool.