(

*a*,

*b*) The electrostatic free energy

for dsDNA (

*black lines*) and the respective ssDNA (

*gray lines*) as functions of (

*a*) NaCl and (

*b*) MgCl

_{2} concentrations. (

*Dotted lines*) Poisson-Boltzmann theory; (

*solid lines*) the TBI theory. (

*a*) DNA length

*N* are 10, 9, 8, and 6 bp (from the

*top to bottom*), respectively; (

*b*) DNA length

*N* are 12, 9, and 6 bp (from the

*top to bottom*), respectively. (

*c*,

*d*) The folding free energies Δ

*G*°

_{37} due to dsDNA helix formation for different sequences of various lengths in (

*c*) NaCl and (

*d*) MgCl

_{2} solutions. (

*Dotted lines*) Poisson-Boltzmann theory; (

*solid lines*) the TBI theory; (

*dashed lines*) SantaLucia's salt extrapolation formula for NaCl (,). (

*c*) The sequences used for NaCl solution are: GCATGC, GGAATTCC, GCCAGTTAA, and ATCGTCTGGA (from the

*top to bottom*). The symbols are the experimental data. + GCATGC (); □ GGAATTCC (); × GGAATTCC (); ▵ GCCAGTTAA (); ⋄ ATCGTCTGGA (); ♦ are calculated from the nearest neighbor model with the thermodynamic parameters of SantaLucia at 1 M NaCl (). (

*d*) The sequences used for MgCl

_{2} are: GCATGC, GCCAGTTAA, and AGAAAGAGAAGA (from the

*top to bottom*). The symbols are the experimental data: ▪ GCCAGTTAA in MgCl

_{2} (); □ AGAAAGAGAAGA in MgCl

_{2} (); ▴ AGAAAGAGAAGA in MgCl

_{2} (); ♦ GCATGC in NaCl/MgCl

_{2} mixed solution with 0.012 M NaCl (). The experimental data in NaCl/MgCl

_{2} mixed solutions for GCATGC are used for semiquantitative comparison because NaCl is at very low concentration (). For the MgCl

_{2} solutions, the values of

from the TBI theory are used in the calculations of Δ

*G*_{37}°.

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