experimental data acquisition
A solution of a self-complementary DNA oligonucleotide is made with known concentration in a buffer containing NaCl. This solution is transferred to a quartz cuvette and inserted in a temperature-controlled holder inside a UV spectrophotometer set to 260 nm, the characteristic UV maximum extinction coefficient of DNA. The zero absorbance is previously set with the buffer solution. A typical classroom experiment starts by heating the sample to the maximum convenient temperature and registering the absorbance after stabilization. Temperature is decreased in steps of 2 or 3 ºC to the desired final value. After each temperature change, stabilization of absorbance is graphically monitored using a kinetics method. Do two experiments with different NaCl concentrations.
The melting, or denaturation, of double stranded DNA is a chemical equilibrium shift towards strand separation caused by an increase in temperature . For self-complementary DNA this can be written as equation 1. Symbol C designates single stranded DNA (unpaired) and C2 double stranded DNA (paired); Ctotal is the total concentration of strands, paired or unpaired. This is a simple two-state, all-or-nothing model that does not consider other possibilities besides the complete Watson-Crick pairing between self-complementary strands, which is a reasonable assumption if the oligonucleotide is relatively short. The equilibrium constant and material balance corresponding to chemical equation 1 are expressed in equations 2 and 3, respectively. Substitutions between these two equations enable to express [C]eq and [C2]eq as functions of Ctotal and K, equations 4 and 5. The signs of the square roots in the quadratic formulas were chosen so that [C]eq and [C2]eq are always real, positive numbers such that [C]eq ≤ Ctotal and 2[C2]eq ≤ Ctotal.
The DNA strands pairing/unpairing process caused by temperature changes is easily followed by UV spectrophotometry at 260 nm  because single strands are characterized by a higher extinction coefficient at that wavelength than double strands. This is known as a hyperchromic effect . The goal is therefore to deduce an equation that relates absorbance with temperature. Since, generally, absorbance A is a function of each solute concentration ci and is additive (equation 6) then the absorbance observed for a oligonucleotide solution may be written as equation 7, where L is the light path length through the sample, εds, is the molar extinction coefficient of paired strands and εss is the molar extinction coefficient of unpaired strands. These extinction coefficients (and thus A) also change with temperature, often represented as a linear function. Equations 8 and 9 do just that for εds and εss, respectively, with parameters for zero temperature, ε0, and the rate of change, r. The equilibrium constant is also a thermodynamic function of temperature, equation 10, where R is the ideal gas constant. The parameter K is replaced by the standard enthalpy and entropy change of equation 1, ΔH0 and ΔS0, respectively. The substitution of equation 10 into equations 4 and 5, and of equations 4, 5, 8 and 9 into equation 7 gives the sought for relation, equation 11, valid at equilibrium. The parameters are ε0,ds, ε0,ss, rds, rss, ΔH0, ΔS0, L and Ctotal. Of these, only L and Ctotal are usually known which makes for six adjustable parameters. Nonlinear regression of equation 11 over a data set (A, T) enables to estimate the melting parameters, corresponding to equation 1, for a self-complimentary oligonucleotide. It is assumed that the thermodynamic parameters ΔH0 and ΔS0 do not change significantly with temperature.
Matlab files can be downloaded using the links at the bottom of this page. Function melt.m is a simple implementation of the Matlab function nlinfit.m which estimates the parameters of equation 11 by nonlinear least squares fitting. Also, the Matlab functions nlparci.m and ttest.m are used to calculate, respectively, the uncertainty associated with the estimated parameter values and the Student-t statistic for the residue sample against a normal distribution of samples with mean zero. The code can be inspected with any word processor and run in the Matlab console window.
The function melt.m plots the experimental points and a line representation of the best fit of equation 10. The code can be inspected with any word processor and run in the Matlab console window with a command like:
melt(datavariablename, [ΔH0,ΔS0,rds,ε0,ds,rss,ε0,ss], 'namestring', o);
where datavariablename is the name of a variable in the Matlab workspace containing melting data (A, T) and the constant parameter values (see sample file below). The second argument of melt.m is a vector of initial values for the adjustable parameters (example: [-230000 -650 40 90000 23 115000]), and the last argument, o, is set to 0 to just plot the data points and the function curve using the initial parameters or to 1 to perform regression. This last option is useful to manually adjust the initial parameter values and see the effects on the theoretical function. After a good initial parameter vector is found by trial and error the nonlinear fitting process is much more likely to converge.
example and discussion
Figure 1 shows two plots of melting data for micromolar solutions of the oligonucleotide 5'-ATATCGATAT-3' with two different NaCl concentrations. Data is approximately centred on the melting temperatures, Tm. These are the temperatures at which equation 12 is valid, that is, where half of the strands are paired. Substitutions between equations 2, 3, 10 and 12 yield equation 13 for the melting temperature of a self-complementary oligonucleotide. Students are invited to deduce it.
Some procedures are discussed with the students. Since the absorbance interval between experimental temperature boundaries is not very large (less than 0.1 absorbance units), the use of a kinetic graphical method to register absorbance stabilization when temperature is changed enables the students with a visual way to follow reaction re-equilibration and, at equilibrium, to take a time average of absorbance, therefore reducing experimental errors. The procedural option of starting the DNA melting experiment with the highest temperature is explained as a means to make sure the oligonucleotide population is completely unpaired at the start, independently of whatever was its (unknown) situation at freezing or at room temperature. The experimental process follows the direction of equation 1, that is, it is in the annealing direction rather than in the melting direction. However, it is noted that this is in fact an experiment where data is acquired at equilibrium, it is not a kinetics experiment. Hence, the direction of temperature change is irrelevant.
Discussion is focused on the physical interpretation of signs and values of regression estimated thermodynamic parameters, taking into account what is known about the molecular structure of the oligonucleotide and the interactions involved in strand pairing, namely the number of, and enthalpy change associated with, hydrogen bond formation in water. The effect of NaCl concentration is also discussed. Since different values for Tm and for the thermodynamic parameters, ΔH0 and ΔS0, are obtained for different NaCl concentrations, hypothesis for the action mechanism of NaCl are proposed and discussed, namely the formation of ionic pairs between Na+ and the negative phosphates of DNA at pH 7.4. The relation between the number of data points and the uncertainties estimates are also debated because these are quite large (Figure 1) and therefore data size should be much larger so as to reduce regression uncertainties. Comparison between results obtained from different [NaCl] experiments is problematic when uncertainties are that high. These propagate to Tm through equation 13 as well.
Other ways of obtaining the oligonucleotide melting parameters [2,4] are reviewed and compared.
Figure 1 – Results from two melting
experiments done in classroom with the oligonucleotide
5'-ATATCGATAT-3' (synthesis by Stab Vida). The
solvents are pH 7.4 aqueous solution buffer of sodium phosphate with
 D’Abramo, M., Lara, Castellazzi, C.L., Orozco, M., Amadei, A., On the Nature of DNA Hyperchromic Effect, J. Phys. Chem. B 2013, 117, 8697−8704 (DOI: 10.1021/jp403369k)
 Hull, C., Szewcyk, C., St. John, P.M., Effects of Locked Nucleic Acid Substitutions on the Stability of Oligonucleotide Hairpins, Nucleosides, Nucleotides and Nucleic Acids 2012, 31:28–41 (DOI: 10.1080/15257770.2011.639826)