  To characterize the thermodynamical equilibrium of DNA chains interacting
with a solution of non-specific binding proteins, a Flory-Huggins free energy
model was implemented. We explored the dependence on DNA and protein
concentrations of the DNA collapse. For physiologically relevant values of the
DNA-protein affinity, this collapse gives rise to a biphasic regime with a
dense and a dilute phase; the corresponding phase diagram was computed. Using
an approach based on Hamiltonian paths, we show that the dense phase has either
a molten globule or a crystalline structure, depending on the DNA bending
rigidity, which is influenced by the ionic strength. These results are valid at
the thermodynamical equilibrium and should therefore be consistent with many
biological processes, whose characteristic timescales range typically from 1 ms
to 10 s. Our model may thus be applied to biological phenomena that involve
DNA-binding proteins, such as DNA condensation with crystalline order, which
occurs in some bacteria to protect their chromosome from detrimental factors;
or transcription initiation, which occurs in clusters called transcription
factories that are reminiscent of the dense phase characterized in this study.
