Thermoelectric effect and its dependence on molecular length and sequence in single DNA molecules

Studying the thermoelectric effect in DNA is important for unravelling charge transport mechanisms and for developing relevant applications of DNA molecules. Here we report a study of the thermoelectric effect in single DNA molecules. By varying the molecular length and sequence, we tune the charge transport in DNA to either a hopping- or tunnelling-dominated regimes. The thermoelectric effect is small and insensitive to the molecular length in the hopping regime. In contrast, the thermoelectric effect is large and sensitive to the length in the tunnelling regime. These findings indicate that one may control the thermoelectric effect in DNA by varying its sequence and length. We describe the experimental results in terms of hopping and tunnelling charge transport models.


Supplementary
. Seebeck coefficient and its dependence on DNA sequence and length. The Seebeck coefficients are for the inserted part in the middle of sequence.
AT, (AT) 2 , (AT) 3 , CG and none means calculation for one, two, three alternating AT units, one CG alternating unit, and no molecule. * From FWHM1 to FWHM5, the data is acquired from increasing temperature gradient.

Supplementary Discussion 1 Stretching length of dsDNA in the air and in solution
The stretching length is the distance over which a DNA junction can be stretched before breakdown in the STM break junction experiment, which reflects the breakdown of the hydrogen bonds at the very end of the dsDNA. Supplementary Fig.4 shows the stretching length histograms of A(CG) 3 T in the air and in solution, and Gaussian fittings to the histograms. From the fittings, the average stretching lengths were found to be 0.11 nm and 0.12 nm, respectively. The similarity in the stretching length measured in air and in solution confirms that the dsDNA retained its native structure in humidified air.

Molecular length dependence of DNA resistance
The resistance of A(CG) n T sequences is weakly length dependent, which can be fitted with a linear relation (Supplementary Figure 7a). Plotting the same data in a logarithmic scale shows a roughly linear behavior with the reception of the first data point (Supplementary Figure 7b). This is not surprising because an exponential function, R=R 0 exp(-βL), can be expressed as linear as R~R0(1-βL), for small βL. However, forcing the fit of data with the exponential function leads to β=0.29±0.02 nm -1 , which is small. This result is consistent with the previously reported STM break-junction 1 and photochemistry data 2,3 .
Compared to A(CG) n T, the resistance of ACGC(AT) m GCGT and ACGC(AT) m-1 AGCGT is more strongly length dependent (see Fig. 2b in main text).

Thermoelectricity measurements
Thermoelectric voltage histograms measured at different temperature gradients for all the sequences are presented in Supplementary Fig. 8. The peak positions determined from Gaussian fitting (with the error bars determined from the fitting errors) were plotted against the temperature gradient and fitted with a linear relation ( Supplementary Fig. 9).
From the slope of the fitted line, the Seebeck coefficient of the DNA molecule was obtained based on Eq. 2. The variations in U TE are originated from the variations in single molecular conductance, rather from experimental errors 9,10 . We have listed the fwhms for all the sequences in the supporting information, which shows 10-15% standard deviations (Supplementary table 1). Despite the variability in fwhm, we cannot identify a systematic dependence of the fwhm on DNA sequence.

Derivations of Eq. 4 in the main text
If we assume that the energy dependent resistance function, R(E), of A(CG) n T, is the sum of contact (R c ) and hopping (R h ) contributions, we can express the Seebeck coefficients of A(CG) n T sequences as . (1) Supplementary Eq. 1 can be simplified as, (Eq. 4 in main text) , leading to Eq. 4 in the main text. Eq. 6 in the main text can also be derived from this.
Alternatively, we may assume that the total thermal voltage as a sum of the contact and hopping thermal voltages, given by 11 If we further assume that total temperature difference is a sum of the contact and hopping  15 , indicating that the Wiedeman-Franz law might be applicable also in the hopping regime, although a complete theory is still lacking.

Tight binding theory of DNA thermoelectricity
A theory that treats electron-phonon coupling in the strong coupling regime has been developed to calculate DNA conductance 16 . The theory has been recently extended to determine the Seebeck coefficient in conducting polymers 17 . While the strong coupling theory is useful in predicting qualitative trends of molecular conductance and thermoelectric effect, it cannot include chemical details in the calculations easily. In this respect, the weak coupling theory is more suitable. Previously, the weak coupling theory has been used to explain the tunneling-hopping transition in single oligomers, 18 and to determine other charge transport properties, such as the electric current noise in molecular junctions 19 . In this work, we applied the weak coupling theory to examine the length and sequence dependence of the DNA Seebeck coefficient. We

Circular dichroism (CD) measurements
CD measurements were carried out on Jasco (Easton, MD) J-1710 Spectropolarimeter for 10 uM dsDNA in phosphate buffer (5 mM phosphate buffer, pH=7). Data shown in Supplementary Fig. 2 were average over five scans, collected from 320 nm to 200 nm or 220 nm with a scanning rate of 100 nm min -1 . The positive band at around 275 nm and negative band at around 245 nm indicate a typical B-form structure for all the DNA sequences.

Melting temperature
Melting temperature experiment was carried out in a Varian Cary 300 Bio UV spectrophotometer with a Peltier thermal controller to determine melting temperature. 5-μM dsDNA samples were prepared by annealing in 5 mM sodium phosphate buffer, and then heated at a rate of 0.2 K min -1 from 283 K (10 o C) to 353 K (80 o C) with the absorbance at 260 nm recorded in 60 s intervals. A(CG) 3 T ( Supplementary Fig. 3) is the shortest sequence measured in this work, which has the lowest melting temperature. The melting curve (black curve) was fitted to a two-state thermodynamic model (red curve), giving a melting temperature of 311±6 K (38 o C), well above the experimental temperature of 295 K (22 o C) for the shortest sequence.