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Ribonucleic acid (RNA) molecules play important roles in many biological processes including gene expression and regulation. An RNA molecule is a linear polymer which folds back on itself to form a three dimensional (3D) functional structure. In this paper we briefly address mathematical problems associated with the grid computing approach to RNA structure prediction. In particular, we introduce models to partition a large RNA molecule into smaller segments to be assigned to different computers on the grid. Based on these models, we formulate a sampling strategy to select RNA segments for computational prediction to maximize prediction consistency. This strategy is under construction as part of RNAVLab, our unified environment for computational RNA structure analysis, i.e., prediction, alignment, comparison, and classification. A first prototype of RNAVLab is presented and used to investigate the possible association of secondary structure types with RNA functions by analyzing secondary structures for a family of nodavirus genomes.