Statistical and thermodynamic analysis of the binding of trans-activation response–binding proteins to HIV-1 TAR RNA

In a recent article (1), the authors examine the binding of lab-evolved trans-activation response (TAR)–binding proteins (TBPs) to HIV-1 TAR RNA. Here, we show our analysis of the thermodynamic data of the binding that identifies three quantitative features of the binding, which may provide further insight into the interactions.

• (1)The binding of TBPs to HIV-1 TAR RNA exhibits enthalpy–entropy compensation (2, 3), which suggests that the bindings of the six TBPs follow a common mechanism in the binding (Fig. 1A).
• (2)Two other variants of TBPs do not fit the linear regression (Fig. 1A), according to a regression diagnostic test using studentized deleted residuals (4). This suggests that the rest structure of TBPs other than the TAR-binding β2-β3 loop, which is absent in the two outliers, contributes to the binding.
• (3)The ΔG° values of the six TBPs at 310.15 K calculated using Equation 1 are normally distributed, according to the Shapiro–Wilk normality test (W = 0.933, p = 0.607):

$$\Delta G°=\Delta H°-T\Delta S°$$ (1)

where ΔH° and ΔS° are experimentally measured values reported in the original paper (1). Based on the statistical parameters, probability density of the ΔG° can be generated using Equation 2:

$$p\left(\Delta G°\right)=\frac{1}{\sigma \sqrt{2\pi }}\times \exp \left(-\frac{1}{2}\times {\left(\frac{\Delta G°-\Delta G{°}_{\text{mean}}}{\sigma }\right)}^2\right)$$ (2)

where σ = 1.9407 kJ/mol and ΔG°_mean = –41.3 kJ/mol. The distribution allows one to relate the probability to find a TBP variant to its binding affinity. For example, statistically expected maximum ΔG° of the highest-affinity variant of TBPs (Fig. 1B) is obtained by solving Equation 3 for x to be –46.8 kJ/mol:

$$1-\underset{x}{\overset{\infty }{\int }}p\left(\Delta G°\right)d\Delta G°=\frac{1}{400}$$ (3)

Figure 1.

Statistical and thermodynamic analysis of the binding of TBPs to HIV-1 TAR RNA.A, enthalpy–entropy compensation in the binding. The solid line is the best fit to the data without two outliers (Tat ARM and TB-CP-6.9a), ΔH° = 343.3 × ΔS° – 36.6 (R² = 0.9972), and the dotted line is its extrapolation. B, the β2-β3 loop sequence of the lab-evolved TBPs. X indicates two positions of mutation, leading to 400 possible variations of the sequence. All statistical analyses were conducted using SigmaPlot (version 11; Systat Software). TAR, trans-activation response; TBP, TAR-binding protein.

Conflict of interest

The authors declare that they have no conflicts of interest with the contents of this article.

Edited by F. Peter Guengerich