= Solution
The bare packed-sphere estimate exceeds $2.1\times10^5\,\mathrm{pN\,nm}$ by approximately $659$; subtracting the estimated extended-rod self-energy still leaves a factor of about $629$. The dominant missing effect is <electrostatic screening>: mobile positive <counterions> accompany the negatively charged <DNA>, greatly reducing long-range repulsion. <Counterion condensation> can further reduce its effective <electric charge>. Treating the genome's bare charge as uncompensated throughout and outside a $20\,\mathrm{nm}$ sphere therefore grossly overestimates its long-range <electrostatic energy>.
An <optical tweezers> measurement integrates an imposed <force> over a displacement. A reversible extraction or packaging comparison concerns a <free energy> difference relative to the unconfined <DNA> and ionic reservoirs. It can include <entropy>, bending and hydration contributions; dissipative pulling can add further <work>. Extraction can also be assisted by stored internal <free energy>, so the sign of externally supplied <work> requires the experimental convention. Here the supplied positive value is compared as an energy magnitude.
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