Linear DNA is formed from various isoforms – superhelical coils, knots, and catenanes – of closed circular DNA at thermodynamic equilibrium.
Organic molecular folding is understood by applying the mathematical concepts of topology, specifically knot theory. Every molecule has an energy landscape: a set of possible conformations, with each potential spatial configuration having an associated energy level.
Atomic interactions in molecules dictate molecular conformations that take energy to maintain. The energy level ultimately relies upon hd quantum mechanical properties.
Topologically, an energy landscape has hills and valleys of energy levels for different configurations. Applying knot theory to mathematically figure an optimal conformation for a complex macromolecule is beyond daunting because the range of possible shapes is gigantic.
The chains found in biologically significant proteins are a tiny subset of those possible. Biology cohered to optimal efficiency of all things that could be considered, given inherent tradeoffs in the dynamics of folding and unfolding.
Because folding is essential to storing and retrieving the complex coding for cellular work and reproduction, geneticists first hypothesized, wrongly, that evolution favored formations with relatively simple energy landscapes. Instead, unfolding a carbon chain requires energy, whereas a folded shape is in relative energetic repose. As DNA strands spend much more time in folded stasis, it would be wasteful to use energy to maintain the folded state.