Thermodynamic modeling of donor splice site recognition in pre-mRNA

When eukaryotic genes are edited by the spliceosome, the first step in intron recognition is the binding of a U1 small nuclear RNA with the donor $\left(5^{\prime }\right)$ splice site. We model this interaction thermodynamically to identify splice sites. Applied to a set of 65 annotated genes, our “finding with binding” method achieves a significant separation between real and false sites. Analyzing binding patterns allows us to discard a large number of decoy sites. Our results improve statistics-based methods for donor site recognition, demonstrating the promise of physical modeling to find functional elements in the genome.

Figure 1

A schematic for the “finding with binding” method. We model the association of a conserved 13 base region of the U1 snRNA $\left(AUACUUACCUGGC\right)$ to possible precursor mRNA sites and compute the base-pairing conformation and free energy. Each possible pre-mRNA donor site includes the consensus $GU$ plus the $n$ bases after it, the $m$ bases prior to it, and a three base contribution to the artificial linker region [shown is $(m,n)=(3,4)$]. The U1 and pre-mRNA sequences are concatenated into a single strand. Prohibiting base pairing (x) in the five-base artificial linker region, we find the optimal fold and its free energy. Note that bulges can shift the alignment of U1-mRNA pairing and that $GU$ wobble base pairing $(•)$ is included.

Figure 2

Histograms of the free energy of U1-mRNA binding. Binding energies for all 338 real and 16 961 decoy sites are given, as well as the select subset whose $GU$ consensus pairs with the corresponding $AC$ in the U1 snRNA. Notice that the selection process rejects $64\%$ of the decoy sequences, while rejecting only $2\%$ of real sequences. The data shown are for $(m,n)=(2,6)$.

Figure 3

Comparing $-RT\ln \left(p_{\text{wmm}}\right)$ and $\Delta G$ at $T=\mathrm{37\hspace{0.17em}}°\mathrm{C}$ allows us to evaluate the claim that biases in sequences represent a free energy. The log of the WMM’s “Boltzmann weight” shows significant scatter when plotted against the binding free energy. The best-fit slopes are inconsistent with the hypothesis that $p_{\text{wmm}}$ can effectively estimate binding free energies. The data shown are for all 338 real and 16 961 decoy sequences.

Figure 4

The receiver operating curves for the weight matrix method (WMM), the finding with binding free energy method $\left(\Delta G\right)$, and the combined method [Eq. (2)] are shown for all data, and after selecting for pairing at the $GU$. Interestingly, the accuracy of the combo method did not improve with selection so we do not present values for the combo-select method.

Figure 5

The probability of base pairing is position dependent for real (circles) and decoy (box) sequences (filled, all; open, after selecting). Selecting for proper base pairing at the $GU$ decreases the number of decoy sequences at a cost of relatively few real sites. The physical selection procedure improves the results of statistics-based approaches (see Fig. 4). Data are given for $(m,n)=(2,6)$.