  DNA looping is important in DNA condensation and regulation. One method for
forming a DNA loop, thought to be used by the condensing agent protamine, is
bind-and-bend. In bind-and-bend, molecules bind all along the DNA, each
creating a bend in the DNA. Eventually, enough bending leads to the formation
of a loop. Here, we adapt theory for DNA bending by cations to create a simple
bind-and-bend model. To test the model, we simulate bending and looping by the
condensing agent protamine and compare the output of the simulation to
experimental data. The model captures several interesting features of the data
including: the curvature of the DNA due to both protamine-induced bending and
thermal fluctuations, the small circumference of the loops (200-300 bp), the
bias in the location where the loop forms, and the emergence of multi-looped
flower structures. The model leads to insight into where protamine binds, how
it bends DNA, and how it creates one or more DNA loops. More broadly, the model
could be useful in understanding the compaction of nucleic acids or
polyelectrolytes.
