Fig 1.
(a): Solutions of random-sequence DNA (rsDNA) oligomers of length L are mixtures made of 4L distinct molecules, obtained by all the combinations of the four nucleobases, which are present at any position in the sequence with equal probability. (b): Each rsDNA oligomer can interact with 4L different rsDNA oligomers, leading to a 4L × 4L interaction matrix. Each dot in the matrix represents the most energetically favorable pairing between the two selected rsDNA oligomers, among all the possible mutual shifts. (c) Each position in the interaction matrix corresponds to a specific duplex motif, characterized by pairing errors which are here described by the parameters in α. The most probable duplex in the matrix is highly defected, as the last example in the panel.
Fig 2.
Double strand vs. random sequence DNA melting.
Ensemble melting curve as a function of temperature. Green dots: measured ensemble melting of 12N at crsDNA = 0.04 g/l. Shading marks experimental uncertainty resulting from the average over 8 experimental replicas. Dashed lines: theoretical melting predicted for equimolar solutions of two complementary 12mers at cDNA = 0.02 g/l each (dashed blue line) and cDNA = 0.04/412 ≈ 2.4 10−9 g/l each (dashed red line). 12N θe(T) exhibits a behavior intermediate between the two. Dashed lines are obtained by averaging many melting curves of complementary 12mers. cNaCl = 1M in all curves.
Fig 3.
Measured ensemble melting curves of rsDNA at crsDNA = 0.04 g/L for 12N (panel a, open circles), 20N (panel a, full diamonds) and 8N at crsDNA = 25 g/L (panel b, open squares), at various salt concentrations: cNaCl = 0.15M (blue), cNaCl = 0.45M (green) and cNaCl = 1M (red). Shading marks experimental uncertainty resulting from the average over 6–8 experimental replicas for 8N and 12N, whereas, for 20N, just one experiment is shown as described in the text. Dashed lines, with same color code, are the theoretical predictions of Eq (7).
Fig 4.
Probability of defectless duplexes in rsDNA.
θA*B* Fraction of paired 8A*8B* in 8N measured with CQ experiments, at cNaCl = 0.15M. Colors correspond to different values of the stoichiometric ratio ϕ between the probes A* / B* and rsDNA strands. Black data is the melting curve of a neat A* B* solution (without rsDNA). In all experiments cfluo = 100nM. Each data point is obtained as an average over 5–10 replications of the experiment. The corresponding standard deviation is reported as shaded regions.
Fig 5.
Theoretical predictions of melting curves, computed for DNA 8mers at 25g/L and 1M NaCl.
The green solid line stands for the melting curve predicted for a pair of complementary strands when using the energy obtained from our parametrization, with α = 0 and fCG = 0.5. The purple dashed-line and related shading are, respectively, the mean value and the standard deviation computed using the NN model over a set of 40 melting curves of distinct DNA sequences with fixed fCG = 0.5. The dotted lines are the melting curve of 8N with different values of fCG (Eq (6)), as specified in the colorbar. The solid dark red line is the ensemble melting curve θe, obtained by the average of
over the possible values of fCG (as given by Eq (7)).
Fig 6.
Theoretical predictions of the fraction of perfect and defected rsDNA duplexes (as given by Eq (9)), parametrized by α. (a): the six most probable duplex motifs in 12N. (b): fraction of duplexes with a total number of unpaired bases |α|, in 8N (dotted lines), 12N (continuous lines), 20N (dashed lines). cNaCl = 1M and crsDNA = 25g/l.
Fig 7.
Melting temperatures for rsDNA: Theory vs experiment.
Comparison of measured and predicted Tm for rsDNA solutions. Symbols: experimental Tm obtained from the melting curves of 8N, 12N and 20N (Fig 3), as function of salt, cNaCl. Conditions are specified in the legend. Dashed lines: theoretical predictions of Eq (7).
Fig 8.
Probability of defectless duplexes in rsDNA: Theory vs experiment.
Fraction of paired 8A*8B* in 8N, θA*B*, as determined via CQ experiments (dots and light shading, as in Fig 4) and from the model (dashed lines and dark shading), at cNaCl = 0.15M and for several ϕ values (colors, see legend). Black data, lines and shadings: melting in 8A*+8B* solutions, in the absence of rsDNA. Shaded regions of the theoretical predictions are obtained from the experimental uncertainty on the pairing energy between A* and B** (see S2 Text).
Fig 9.
Probability of defectless duplexes in rsDNA: Salt dependence.
Fraction of paired 8A*8B* as a function of ϕ, expressing their dilution in 8N, at T = 15°C for cNaCl = 0.15M (blue dots) and cNaCl = 1.0M (red dots). Dashed lines: theoretical predictions, with the shaded regions obtained from the experimental uncertainty on the pairing energy between A*B*, (see S2 Text).