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.

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