RBS Calculator Free Energy Model

The RBS Calculator's free energy model quantifies the energetic (thermodynamic) interactions affecting the translation initiation rate of an individual start codon. These interactions are quantified in terms of Gibbs free energy changes, compared to a reference mRNA state in a system with constant temperature and pressure. The reference mRNA state is a fully unfolded mRNA that is not bound by the ribosome. Overall, the current equation for the RBS Calculator free energy model is:

$$\Delta G_{total} = \Delta G_{standby} + \Delta G_{mRNA-rRNA} +\Delta G_{spacing} + \Delta G_{start} + \Delta G_{stacking} - \Delta G_{mRNA}$$

From these calculations, the translation initiation rate $(r)$ of a start codon is then calculated according to Boltzmann's relationship:

$$r = exp(-\beta\Delta G_{total})$$

The constant$\beta$is a conversion factor from energy to probability under equilibrium conditions. In ideal (dilute) systems,$\beta=1/RT$ where R is the gas constant and T is temperature. However, based on empirical measurements, the value for$\beta$ is about $0.45 \pm 0.05$ mol/kcal inside the non-ideal (crowded) environment inside the cell.

The major interactions controlling translation initiation rate are:

1. Initial binding of the 30S small ribosomal subunit to upstream standby sites. Upstream standby sites with different geometric accessibilities and structural unfolding free energies will lead to different rates of initial ribosome binding. The Gibbs free energy term $\Delta G_{standby}$ quantifies how well the 30S ribosomal subunit can bind to upstream standby sites. It is either zero for a fully accessible site and becomes more positive as the site is less favorably bound. There are three components to this free energy term: $\Delta G_{distortion}$, $\Delta G_{unfolding}$, and $\Delta G_{sliding}$.

2. Unfolding of mRNA structures that overlap with the ribosomal footprint surrounding the start codon. mRNAs fold into structures. Before a ribosome can initiate translation, it must unfold any mRNA structures that overlap with its binding site. The ribosome's binding site (its physical footprint) extends from the 5' end of the 16S rRNA binding site to 13 nucleotides after the start codon. The Gibbs free energy term $-\Delta G_{mRNA}$ is the energy needed to unfold all mRNA structures within this region. More stable mRNA structures require more energy to unfold, leading to lower translation initiation rates.

3. Hybridization between mRNA and the 16S rRNA. The superstructure of the 30S ribosomal subunit is made up of the 16S rRNA. The last 9 nucleotides of the 16S rRNA are accessible (in most bacteria) and is used by the ribosome to stabilize binding to mRNAs. Hybridization between the mRNA and 16S rRNA occurs at a sequence commonly known as the Shine-Dalgarno. The Gibbs free energy term $\Delta G_{mRNA-rRNA}$ is the quantification of this hybridization energy together with other mRNA-mRNA interactions do not require unfolding during translation initiation. A more negative free energy indicates a more favorable interaction at the Shine-Dalgarno sequence.

4. Start codon-tRNA interactions. Inside the ribosome, the start codon base pairs to the tRNA-fMet. The canonical start codon AUG has perfect complimentary to the anti-codon loop of tRNA-fMet and therefore has the highest binding free energy. However, other non-canonical start codons (GUG, CUG, and UUG) can still base pair to tRNA-fMet, but with reduced binding free energies. The Gibbs free energy term $\Delta G_{start}$ is the free energy released when the start codon base pairs to tRNA-fMet. Translation initiation factors (IFs) can additionally alter these binding free energies.

5. Stretching or compression of the ribosome by the spacer region. The length of mRNA between the 16S rRNA binding site (Shine-Dalgarno sequence) and the start codon is called the spacer region. There is an optimal spacer length where the ribosome forms both contacts with distortion. However, if the spacer region is too long or too short, it causes the ribosome to stretch or compress, resulting in an energetic penalty. The Gibbs free energy term $\Delta G_{spacing}$ is the free energy penalty for stretching or compression of the 30S ribosomal subunit when bound. This term is zero when the spacer length is optimal and positive when the ribosome is either stretched or compressed.

6. Certain motifs form unusual mRNA structures that alter ribosome binding. Long stretches of homopolymer sequence in the spacer region cause stacking interactions (quantified by $\Delta G_{stacking}$). G-rich sequences may form unusually stable G-quadruplex structures. Pseudoknots may also form between long distance nucleotides that alter structure formation.

7. Ribosome Drafting is a non-equilibrium phenomenon that increases a mRNA's translation initiation rate. Ribosome Drafting takes place when a mRNA with slow-folding structures is successively bound by fast-binding ribosomes. Here, the mRNA structures do not have enough time to refold, eliminating the energetic penalty for unfolding these structures. The presence of Ribosome Drafting adds a kinetic component to determining the free energy needed to unfold mRNA structures,$\Delta G_{mRNA}$.

8. Certain motifs bind RNA-binding proteins that alter ribosome binding. Examples include CsrA and Hfq in Escherichia coli.