Nonequilibrium thermodynamics of the RNA-RNA interaction underlying a genetic transposition program

Thermodynamic descriptions are powerful tools to formally study complex gene expression programs evolved in living cells on the basis of macromolecular interactions. While transcriptional regulations are often modeled in the equilibrium, other interactions that occur in the cell follow a more complex pattern. Here, we adopt a nonequilibrium thermodynamic scheme to explain the RNA-RNA interaction underlying IS10 transposition. We determine the energy landscape associated with such an interaction at the base-pair resolution, and we present an original scaling law for expression prediction that depends on different free energies characterizing that landscape. Then, we show that massive experimental data of the IS10 RNA-controlled expression are better explained by this thermodynamic description in nonequilibrium. Overall, these results contribute to better comprehend the kinetics of post-transcriptional regulations and, more broadly, the functional consequences of processes out of the equilibrium in biology.

Figure 1

(a) Energy landscape of the sRNA-mRNA interaction in the IS10 system at the base-pair resolution. The intramolecular folding state is labeled as 1, the just-the-seed-paired intermolecular folding state as 2, and the final intermolecular folding state as 3. Vertical arrows (in blue) mark the different free energies that characterize the interaction. (b) Intramolecular RNA secondary structures in state 1. (c) RNA secondary structure in the state 2 with intra- and intermolecular contacts. (d) Intermolecular RNA secondary structure in state 3. The Shine-Dalgarno box and the start codon are shaded (in blue).

Figure 2

Abstracted energy landscape of the sRNA-mRNA interaction in the IS10 system. There are two transition states and three stable states (labeled as 1, 2, and 3). Vertical arrows (in blue) mark the different free energies that characterize the interaction. Oblique arrows over the landscape (in black) designate the kinetic constants.

Figure 3

Numerical simulations of the RNA-based regulated response with a kinetic model. (a) Time-dependent concentrations ($x_i$) of the different RNA species that correspond to the three stable states (labeled as 1, 2, and 3). The initial condition corresponds to a scenario of absence of sRNA. The kinetic parameters are $n=1$, $\alpha =10\mathrm{nM}/\min$, $\delta =0.1\mathrm{mi}{\mathrm{n}}^{\text{–}1}$, $k_{12}=0.06n{\mathrm{M}}^{\text{–}1}\mathrm{mi}{\mathrm{n}}^{\text{–}1}$, $k_{21}=6\mathrm{mi}{\mathrm{n}}^{\text{–}1}$, and $k_{32}=0.01\mathrm{mi}{\mathrm{n}}^{\text{–}1}$, and the initial condition is $x_1=100$ nM and $x_2=x_3=0$. (b)–(d) Dynamic regulatory range ($r$) as a function of distinct kinetic parameters. $k_{12}$ varies from $0.01$ to $0.1\mathrm{n}{\mathrm{M}}^{\text{–}1}\mathrm{mi}{\mathrm{n}}^{\text{–}1}$ in (b) and (c), and $\delta$ varies from $0.1$ to $0.3\mathrm{mi}{\mathrm{n}}^{\text{–}1}$ in (d).

Figure 4

Correlation of experimentally measured dynamic range ($r$) against a computationally predicted free energy for different mutants of the IS10 system (529 data points). (a) Nonequilibrium thermodynamic model ($r$ vs $\varphi$), fitted with $\beta =0.545$ mol/Kcal, $\mu =-26.6$ Kcal/mol, and ${\mu }^{\prime }=20.7$ Kcal/mol. (b) Equilibrium thermodynamic model ($r$ vs $\mathrm{\Delta }{G}_{\mathrm{inter}}$, this corresponds to the null model), fitted with $\beta =0.514$ mol/Kcal and $\mu =-27.6$ Kcal/mol. (c) Variance of experimental data vs model predictions for data with a maximal dynamic range ($r_{\max }$). $r_{\max }=1$ means that all data are considered, while $r_{\max }=0.25$ means that only those systems with substantial regulatory activity are considered.