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For soft nonhomologous helices, one can also expect a slight increase in the concentration of single-stranded domains, which can lower the (nonlinear) interaction energy of such fragments; see eq 1c. Note also that since the interaction energy of very short rigid, soft, and homologous DNA fragments is the same, Figure 2, above the melting transition, when the helical domains become short, the electrostatic interactions is expected to modify the melting curves in a similar manner for all three cases.
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To account for this repulsion, one can use the energy (eq A1) without the second term in curly brackets that corresponds to the interaction of the image charges, since the single-stranded DNAs loose the low-dielectric core considered for the interaction of the double-stranded DNA.
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p is the persistence length of single-stranded DNA (∼20 Å). If this entropic repulsion occurs in reality, then such scaling can be extracted from experimental data. Below the melting transition, however, when the melted domains are very short, this entropie repulsion in the aggregates can be neglected.
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For DNA in solution, the length of the helical fragments and the concentration of single-stranded breaks/defects in DNA structure can be measured experimentally and treated theoretically, see ref 15. [The measurement of the intrinsic viscosity of partially melted DNA together with the degree of DNA helicity provides the mean length of the helical domains (flexible single-stranded fragments decrease the DNA persistence length). The number of melted fragments has been obtained by measuring the initial velocity of stimulated DNA unwinding under the action of formaldehyde.] In dense DNA assembly, however, different methods have to be used.
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