Chemistry and Biology of Non-canonical Nucleic Acids. Naoki Sugimoto

Chemistry and Biology of Non-canonical Nucleic Acids

duplexes and 4 for non-self-complementary duplexes, and α is the fraction of strands in a duplex:

(3.5) upper C Subscript normal t Baseline equals left-bracket normal upper A right-bracket plus 2 left-bracket normal upper A right-bracket left-parenthesis self minus complementary duplex right-parenthesis

(3.6) upper C Subscript normal t Baseline equals left-bracket normal upper B right-bracket plus left-bracket normal upper C right-bracket plus left-bracket normal upper B dot normal upper C right-bracket left-parenthesis non minus self minus complementary duplex right-parenthesis

For a unimolecular transition,

(3.7) upper K Subscript o b s Baseline equals alpha slash left-parenthesis 1 minus alpha right-parenthesis equals left-bracket normal upper D Subscript normal f Baseline right-bracket slash left-bracket normal upper D Subscript s s Baseline right-bracket

where

(3.8) alpha equals left-bracket normal upper D Subscript normal f Baseline right-bracket slash left-parenthesis left-bracket normal upper D Subscript s s Baseline right-bracket plus left-bracket normal upper D Subscript normal f Baseline right-bracket right-parenthesis

Figure 3.4 shows a UV melting curve for the self-complementary duplex (5′-ATGCGCAT-3′). At low temperatures, the strands are in duplex form and the absorbance is low. As the temperature is increased, the duplex dissociates into single strands. The UV absorbance of the duplex is increased by dissociation of the duplex, and the increment of absorbance is referred to as hyperchromicity. (The opposite, a decrement of absorbance, is called hypochromicity.) For self-complementary or non-self-complementary duplexes with equal concentrations of each strand, the melting temperature, T_m (in degrees Kelvin), is the point at which the concentrations of strands in duplex and in single strands are equal (Figure 3.4a). The steepness of the transition indicates the cooperativity of the transition. The width and maximum of the first derivative of the melting curve can also indicate the cooperativity and melting temperature, although the peak of the derivative curve only occurs at the T_m only when the transition is unimolecular [5]. T_m is most accurately measured by fitting the lower and upper baselines. The melting temperature is measured at several concentrations over a 100-fold range and then plotted versus the concentration in a van't Hoff plot. The van't Hoff equation relates the T_m (in degrees Kelvin), C_t, ΔH^°, and ΔS^°:

(3.9) upper T Subscript normal m Superscript negative 1 Baseline equals upper R ln left-parenthesis upper C Subscript normal t Baseline slash s right-parenthesis slash upper Delta upper H Superscript degree Baseline plus upper Delta upper S Superscript degree Baseline slash upper Delta upper H Superscript degree

where R is the ideal gas constant, 1.987 cal K⁻¹ mol⁻¹ or 8.314 J K⁻¹ mol⁻¹. The slope of the van't Hoff plot gives the ΔH^°, and the y-intercept gives the ratio of ΔH^° to ΔS^°. The free energy and equilibrium constant at any temperature can then be calculated using Gibb's relation:

(3.10) upper Delta upper G Subscript normal upper T Superscript degree Baseline equals upper Delta upper H Superscript degree Baseline minus upper T dot upper Delta upper S Superscript degree Baseline comma upper K Subscript o b s Baseline equals normal e Superscript negative upper Delta Baseline upper G Subscript normal upper T Superscript degree Superscript slash italic upper R upper T

To increase the accuracy of these parameters, data analysis can be performed by curve fitting as shown below. When the ratio of the double-stranded DNA is represented by α, absorbance (A) at a temperature (T) is calculated as

(3.11) epsilon left-parenthesis upper T right-parenthesis equals upper A left-parenthesis upper T right-parenthesis slash left-parenthesis l dot upper C Subscript normal t Baseline right-parenthesis equals epsilon Subscript d s Baseline plus 2 left-parenthesis 1 minus alpha right-parenthesis epsilon Subscript s s

where ε_ds and ε_ss indicate the absorbance for the single-stranded and double-stranded DNA, respectively, and l and C_t represent the length of the light pass (or the path length of the cuvette used) and the total concentration of DNA strands, respectively. The ε_ds, ε_ss, and observed equilibrium constant (K_obs) for the duplex formation can be represented as follows with the assumption that absorbance is directly proportional to temperature:

(3.12) epsilon Subscript d s Baseline equals m Subscript d s Baseline upper T plus b Subscript d s

(3.13) epsilon Subscript s s Baseline equals m Subscript s s Baseline upper T plus b Subscript s s

(3.14) upper K Subscript o b s Baseline equals exp left-parenthesis minus upper Delta upper H Superscript degree Baseline slash italic upper R upper T plus upper Delta upper S Superscript degree Baseline slash upper R right-parenthesis

where R is the gas constant and m_ds and b_ds or m_ss and b_ss represent the slope and intercept of the upper baseline or lower baseline for the melting curve of a duplex dissociation (Figure 3.4b), respectively. The six variables (ε_ds, ε_ss, b_ds, b_ss, ΔH^°, and ΔS^°) can be calculated by the curve fitting using Eqs. (3.11, 3.12, 3.13, 3.14). These calculations, which are performed using a PC equipped with the curve fitting software such as IGOR Pro, KaleidaGraph, or ORIGIN, derive the thermodynamic parameters from the shape of the melting curve.

Estimated errors in the thermodynamic values (σ_ΔH°, σ_ΔS°, and sigma Subscript upper Delta upper G Sub Subscript normal upper T Sub Superscript ring ) derived from the curve fitting procedure are calculated from the standard deviations among data points of each melting curve at different C_t values. Estimated errors in ΔH^°(σ_ΔH°) and ΔS^°(σ_ΔS°) obtained from the Скачать книгу