A nonlinear dynamic model of DNA with a sequence-dependent stacking term

Abstract

No simple model exists that accurately describes the melting behavior and breathing dynamics of double-stranded DNA as a function of nucleotide sequence. This is especially true for homogenous and periodic DNA sequences, which exhibit large deviations in melting temperature from predictions made by additive thermodynamic contributions. Currently, no method exists for analysis of the DNA breathing dynamics of repeats and of highly G/C- or A/T-rich regions, even though such sequences are widespread in vertebrate genomes. Here, we extend the nonlinear Peyrard-Bishop-Dauxois (PBD) model of DNA to include a sequence-dependent stacking term, resulting in a model that can accurately describe the melting behavior of homogenous and periodic sequences. We collect melting data for several DNA oligos, and apply Monte Carlo simulations to establish force constants for the 10 dinucleotide steps (CG, CA, GC, AT, AG, AA, AC, TA, GG, TC). The experiments and numerical simulations confirm that the GG/CC dinucleotide stacking is remarkably unstable, compared with the stacking in GC/CG and CG/GC dinucleotide steps. The extended PBD model will facilitate thermodynamic and dynamic simulations of important genomic regions such as CpG islands and disease-related repeats.

Figure 1.

Normalized UV absorption melting curves for the (dG)₃₆.(dC)₃₆ (squares) and (dGdC)₁₈.(dGdC)₁₈ (circles) oligos.

Figure 2.

Values of the obtained PBD base stacking force constants in eV/Ų. The identity of the 10 dinucleotide steps is shown below the bars. The stacking force constants are shown as vertical bars. The dashed lines indicate the stacking constant of the average stacking PBD model (black) and the average of the 10 stacking constants of the sequence-dependent PBD model (red).

Figure 3.

Experimentally determined and calculated melting temperatures of periodic and homogeneous dsDNA sequences. The calculated melting temperatures [T_m (°C), on the vertical axis] are identified as follows: experimentally determined, green bar; sequence-dependent PBD (sdPBD), red; average stacking PBD (asPBD), brown; NN thermodynamic model (NN1, http://www.promega.com/biomath/calc11.htm (16), dark blue; NN thermodynamic model (NN2, http://www.basic.northwestern.edu/biotools/oligocalc.html) (14,31), light blue; salt adjusted model calculated with a regression (http://www.promega.com/biomath/calc11.htm) (32), dark grey; basic regression model (http://www.promega.com/biomath/calc11.htm) (33), light grey. The identity of the sequences is shown bellow the bars.

Figure 4.

Average strand displacements for the sequence L60B36, calculated by MC PBD simulations with an average (dashed line) and a sequence-dependent (solid line) stacking term. Strand displacements are presented on the vertical axis in Å. The base pare position is shown on the horizontal where base pair 1 is the first base at the 5′ end of the sequence.

Figure 5.

Average bubble times (color scales) for (A) P5-wild type and (B) P5-mutant promoters. The bubble times are given in picoseconds on the color scale. The bubble length is shown on the vertical axis in units of base pairs. The positions of the base pairs are shown relative to the transcription start site (+1) on the horizontal axis.