Solution (source code)

= Solution

At low <concentration>, the array with more and higher-affinity binding sites is preferentially occupied, giving one visible <protein> cluster on an otherwise extended <DNA> molecule. At higher <concentration> the weaker origin array also becomes occupied. \b[<homotypic protein interactions> between <proteins> at the two arrays can bridge them, trapping the intervening <DNA> through <DNA looping>.] This explains why the electron-dense <protein> cluster lies at the loop junction rather than uniformly coating the entire molecule.

The high-affinity array can stabilize weak-site occupancy through tethering: once one partner is anchored, the second site experiences a high effective local <concentration> and several contacts can contribute <avidity>. This reconciles stable looped assemblies with the vulnerability of the isolated weak site to <nonspecific competitor DNA>. The images support intramolecular <DNA bridging>, but selected micrographs do not measure its frequency or exclude some intermolecular associations. A high local density of <protein> need not imply <biomolecular phase separation>. The printed scale-bar unit appears implausible for a kilobase-scale <DNA> substrate; the mechanistic inference uses topology and site positions rather than that unit.