Physical Model
NUPACK algorithms are formulated in terms of nucleic acid secondary structure. The secondary structure of one or more interacting nucleic acid strands is defined by a list of base pairs (Dirks et al., 2007). A polymer graph representation of a secondary structure is constructed by ordering the strands around a circle, drawing the backbones in succession from 5’ to 3’ around the circumference with a nick between each strand, and drawing straight lines connecting paired bases. A secondary structure is unpseudoknotted if there exists a strand ordering for which the polymer graph has no crossing lines. A secondary structure is connected if no subset of the strands is free of the others. A complex of interacting strands has a structural ensemble containing all connected polymer graphs with no crossing lines for a particular ordering of a set of strands (Wolfe & Pierce, 2015). Note that we dispense with our prior convention (Dirks et al., 2007) of calling this entity an ordered complex. A test tube may contain an arbitrary number of strand species interacting to form an arbitrary number of complex species in a dilute solution. The free energy of a given sequence in a given secondary structure is calculated using nearest-neighbor empirical parameters for RNA (Serra and Turner, 1995; Mathews et al., 1999; Zuker, 2003) in 1M Na+ or DNA (SantaLucia, 1998; Zuker, 2003) in user-specified concentrations of Na+ and Mg++ (SantaLucia and Hicks, 2004; Koehler and Peyret, 2005). Additional parameters are employed for pseudoknotted secondary structures (Dirks and Pierce, 2003), which may be included in the structural ensemble only when analyzing a single RNA strand. |
References
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