Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length

Abstract

Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (especially multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive experimental data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helices. We quantitatively evaluate the effects of ion concentration, ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful analytical formulas for the thermodynamic parameters as functions of finite helix length, ion type, and ion concentration. We find that the helix stability is additive for high ion concentration and long helix and nonadditive for low ion concentration and short helix. All these results are tested against and supported by extensive experimental data.

FIGURE 1

The tightly bound regions around (a) a 13-bp dsDNA and (b) a 13-nt ssDNA in Mg²⁺ solutions at bulk concentration [MgCl₂] = 0.1 M. The red spheres represent the phosphate groups and the green dots represent the points on the boundaries of the tightly bound regions. The dsDNA and ssDNA are produced from the grooved primitive model (see Appendix A) (55,95).

FIGURE 2

(a,b) The electrostatic free energy for dsDNA (black lines) and the respective ssDNA (gray lines) as functions of (a) NaCl and (b) MgCl₂ 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 ΔG°₃₇ due to dsDNA helix formation for different sequences of various lengths in (c) NaCl and (d) MgCl₂ solutions. (Dotted lines) Poisson-Boltzmann theory; (solid lines) the TBI theory; (dashed lines) SantaLucia's salt extrapolation formula for NaCl (22,40). (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 (36); □ GGAATTCC (79); × GGAATTCC (80); ▵ GCCAGTTAA (37); ⋄ ATCGTCTGGA (82); ♦ are calculated from the nearest neighbor model with the thermodynamic parameters of SantaLucia at 1 M NaCl (22). (d) The sequences used for MgCl₂ are: GCATGC, GCCAGTTAA, and AGAAAGAGAAGA (from the top to bottom). The symbols are the experimental data: ▪ GCCAGTTAA in MgCl₂ (37); □ AGAAAGAGAAGA in MgCl₂ (84); ▴ AGAAAGAGAAGA in MgCl₂ (85); ♦ GCATGC in NaCl/MgCl₂ mixed solution with 0.012 M NaCl (36). The experimental data in NaCl/MgCl₂ mixed solutions for GCATGC are used for semiquantitative comparison because NaCl is at very low concentration (36). For the MgCl₂ solutions, the values of from the TBI theory are used in the calculations of ΔG₃₇°.

FIGURE 3

The temperature-dependence of the folding free energy ΔG°_T for (a) NaCl and (b) MgCl₂ solutions. (Solid lines) The TBI theory; (dotted lines) experimental data with the use of the equation ΔG_T° = ΔH° − TΔS°, where ΔH° and ΔS° are taken from experiments. (a) The upper three lines are for sequence GGAATTCC at 0.046, 0.1, and 0.267 M NaCl (from the top to bottom) (79,80), and the bottom three lines are for sequence ATCGTCTGGA at 0.069, 0.22, and 0.62 M NaCl (from the top to bottom) (82). (b) The three lines are for sequence GCCAGTTAA at 1, 10, and 100 mM MgCl₂ (from the top to bottom) (37).

FIGURE 4

The temperature-dependence of the electrostatic part of the free energy. (a,b) The electrostatic free energy of dsDNA (solid lines) and ssDNA (dashed lines) as functions of temperature: (a) for a 10-bp dsDNA and the respective ssDNA at 3 mM, 10 mM, 30 mM, 69 mM, 220 mM, and 1 M NaCl (from the top to bottom); (b) for a 9-bp dsDNA and the respective ssDNA at 0.1, 0.3, 1, 10, and 100 mM MgCl₂ (from the top to bottom). (c,d) The temperature-dependence of electrostatic contribution to folding free energy for dsDNA helix formation in (c) NaCl and (d) MgCl₂ solutions. (Dotted lines) Poisson-Boltzmann theory; (solid lines) the TBI theory. (c) Sequence ATCGTCTGGA at 3 mM, 10 mM, 30 mM, 69 mM, 220 mM, and 1 M NaCl (from the top to bottom); (d) sequence GCCAGTTAA at 0.1, 0.3, 1, 10, and 100 mM MgCl₂ (from the top to bottom).

FIGURE 5

The melting temperature T_m for dsDNA of different sequences in (a) NaCl and (b) MgCl₂ solutions. (Solid lines) The TBI theory; (dotted lines) Poisson-Boltzmann theory; (dashed lines) SantaLucia's salt extension for NaCl (22,40); (symbols) the experimental data. (a) The sequences and total strand concentrations C_S are (from the top to bottom): + GGAATTCC at C_S = 3 mM (79); ▪ CCATTGCTACC at C_S = 2 μM (35); ▵ ATCGTCTGGA at C_S = 2 μM (35); × GCCAGTTAA at C_S = 8 μM (37); and □ GGAATTCC at C_S = 18.8 μM (81). (b) The sequences and C_S are (from the top to bottom): □ AGAAAGAGAAGA at C_S = 6 μM (84); and ▪ GCCAGTTAA at C_S = 8 μM (37). Here, the data for AGAAAGAGAAGA are taken from the duplex melting in the study of the triplex melting in MgCl₂ and C_S = 6 μM is the total strand concentration for triplex formation. T_m is calculated from ΔG°_T − RTlnC_S/6 = 0 (84).

FIGURE 6

The length-dependence of the electrostatic part of the free energy. and are the electrostatic free energies per base stack. N − 1 is the number of base stacks for a N-bp helix. (a,b) The electrostatic free energy (per base stack) for dsDNA (solid lines) and the respective ssDNA (dashed lines) as functions of sequence length N in NaCl (a) and MgCl₂ (b) solutions. (a) [NaCl] = 3 mM, 10 mM, 30 mM, 100 mM, 300 mM, and 1 M (from the top to bottom); (b) [MgCl₂] = 0.1, 0.3, 1, 3, 10, and 30 mM (from the top to bottom). (c,d) The length N-dependence of electrostatic contribution (per base stack) to folding free energy for dsDNA helix formation in NaCl (c) and MgCl₂ (d) solutions. (Dotted lines) Poisson-Boltzmann theory; (solid lines) the TBI theory. [NaCl] = 3 mM, 10 mM, 30 mM, 100 mM, 300 mM, and 1 M (from the top to bottom); [MgCl₂] = 0.1, 0.3, 1, 3, 10, and 30 mM (from the top to bottom).

FIGURE 7

The folding free energies ΔG°₃₇ for dsDNA helix formation as functions of (a) 1:1 and (b) 2:1 salt concentrations for sequence ATCGTCTGGA. (Solid lines) The TBI theory; (dotted lines) Poisson-Boltzmann theory. (a) The radii of monovalent cations are: 3, 3.5, and 4 Å (from the bottom to top). (b) The radii of divalent cations are: 4, 4.5, and 5 Å (from the bottom to top), respectively.

FIGURE 8

The free energy change ΔG°₃₇ for dsDNA helix formation as functions of (a) NaCl and (b) MgCl₂ concentrations for the sequences: GCATGC, GGAATTCC, GCCAGTTAA, ATCGTCTGGA, CCATTGCTACC, and CCAAAGATTCCTC (from the top to bottom). (a) (Solid lines) The empirical relation Eq. 23; (symbols) calculated from the TBI theory. (b) (Solid lines) The empirical relation Eq. 28; (symbols) calculated from the TBI theory.

FIGURE 9

Comparisons between the empirical formulas (solid lines) for T_m (Eqs. 27 and 30) and experimental data (symbols) for (a) NaCl and (b) MgCl₂ solutions. (a) The DNA sequences for NaCl solutions are (5′-3′): GGAATTCC (81), GCCAGTTAA (37), ATCGTCTGGA (82), CCATTGCTACC (35), ATCGTCTCGGTATAA (35), CCATCATTGTGTCTACCTCA (35), AATATCTCTCATGCGCCAAGCTACA (35), GTTATTCCGCAGT-CCGATGGCAGCAGGCTC (35), and E. coli (33) (from the bottom to top). (b) The sequences for MgCl₂ solutions are (5′-3′): GCCAGTTAA (37), AGAAAGAGAAGA (84), TTTTTTTGTTTTTTT (38), TAATTTAAAATTTTTAAAAAA (88), TTTTTTTTTTATTAAAATTTATAAA (89), and AAAAAAAAAATAATTTTAAATATTT (89) (from the bottom to top). T_m(1 M Na⁺) is calculated from the nearest neighbor model with the thermodynamic parameters of SantaLucia (20) except for E. coli. For E. coli, T_m(1 M Na⁺) is taken as 96.5°C.