Full design automation of multi-state RNA devices to program gene expression using energy-based optimization

Abstract

Small RNAs (sRNAs) can operate as regulatory agents to control protein expression by interaction with the 5' untranslated region of the mRNA. We have developed a physicochemical framework, relying on base pair interaction energies, to design multi-state sRNA devices by solving an optimization problem with an objective function accounting for the stability of the transition and final intermolecular states. Contrary to the analysis of the reaction kinetics of an ensemble of sRNAs, we solve the inverse problem of finding sequences satisfying targeted reactions. We show here that our objective function correlates well with measured riboregulatory activity of a set of mutants. This has enabled the application of the methodology for an extended design of RNA devices with specified behavior, assuming different molecular interaction models based on Watson-Crick interaction. We designed several YES, NOT, AND, and OR logic gates, including the design of combinatorial riboregulators. In sum, our de novo approach provides a new paradigm in synthetic biology to design molecular interaction mechanisms facilitating future high-throughput functional sRNA design.

Figure 1. Schemes of different sRNA-based mechanisms to control protein expression.

Riboregulation is based on conformational changes in the secondary structures of RNA molecules that allow controlling protein expression. The annealing mechanism between two sRNAs starts by the nucleotides in the seed to form an intermediate complex and then follows to reach the structure of minimal energy. (A) Scheme of a NOT logic gate, which consists in an sRNA able to bind to the RBS sequence to block translation. (B) Scheme of a YES logic gate, where the sRNA is designed to release the RBS that is cis-repressed. (C) Scheme of a further NOT logic gate, where the sRNA is able to induce cis-repression (exploiting the mechanism shown in B). (D) Scheme of a further YES logic gate, where the sRNA interacts with a transcription terminator placed upstream of the RBS, allowing or preventing the formation of the mRNA. (E) Scheme of an AND logic gate, where two sRNAs are designed to interact among them and form a complex that can release the RBS.

Figure 2. Experimental validation of the objective function.

(A) Representation of the log of the experimental activation folds for a set of RNA devices constructed in this work (mutational variants of the RAJ11 system [11]) versus ΔG _kin (Eq. 13). This system implements a YES logic gate, which was designed with the algorithm presented here (see also Table S4). (B) Representation of the log of the experimental repression folds recently reported for a set of mutational variants of the IS10 antisense RNA system versus ΔG _kin. This system implements a NOT logic gate, and it serves to test the predictability of the method against independent experimental data (see also Table S2). Here, we do not consider ΔG _str as we are only analyzing the interaction ability. The lines correspond to linear regressions, and the coefficients R ² are shown, assuming a model where the fold change scales exponentially with the free energy.

Figure 3. Designs of sRNA-based NOT logic gates.

We show four designs (A to D) using different structures for the trans-repressing sRNAs (mechanism shown in Fig. 1A). (A.1) Detail of a design, showing the RBS in blue, start codon in green, and seed region in red. The secondary structures of the intramolecular and intermolecular folding states are presented. (A.2, B.1, C.1 and D.1) Helical plot of the complex, where the RBS is blocked. ΔG, ΔG _kin and ΔG _str are in Kcal/mol. Z is the partition function. (A.3, B.2, C.2 and D.2) Base pairing probability matrix, encircling the pairs of intermolecular interaction with high probability. RNA sequences shown in Table S1. Secondary structures imposed for all species shown in Fig. S1.

Figure 4. Designs of sRNA-based YES logic gates.

We show four designs (A to D) using different structures for the trans-activating sRNAs (mechanism shown in Fig. 1B). (A.1) Detail of a design, showing the RBS in blue, start codon in green, and seed region in red. The secondary structures of the intramolecular and intermolecular folding states are presented. (A.2, B.1, C.1 and D.1) Helical plot of the complex, where the RBS is released. ΔG, ΔG _kin and ΔG _str are in Kcal/mol. Z is the partition function. (A.3, B.2, C.2 and D.2) Base pairing probability matrix, encircling the pairs of intermolecular interaction with high probability. RNA sequences shown in Table S1. Secondary structures imposed for all species shown in Fig. S1.

Figure 5. Further designs of sRNA-based NOT and YES logic gates.

We show two designs (A and B) using the mechanisms shown in Figs. 1C and 1D. For the NOT gate, helical plots showing (A.1) the RBS exposed, and (A.2) the RBS blocked after sRNA interaction. For the YES gate, helical plots showing (B.1) a transcription terminator, and (B.2) that the hairpin before the poly(U) tail is destabilized after sRNA interaction. ΔG is in Kcal/mol. Z is the partition function. (A.3 and B.3) Base pairing probability matrix, encircling the pairs of intermolecular interaction with high probability. RNA sequences shown in Table S1. Secondary structures imposed for all species shown in Fig. S1.

Figure 6. Design of a multi-input, multi-output sRNA-based logic circuit.

We show a design of a circuit that assembles different riboregulators. Here, sRNA tR13 is able to both repress and activate the expression of two different cis-repressed genes, by cR31 and cR19 respectively, resulting in a coupled YES/NOT logic gate. In addition, sRNA tR19 is able to activate cR19, implementing together with tR13 an OR logic gate. RNA sequences shown in Table S1. Secondary structures imposed for all species shown in Fig. S1.

Figure 7. Designs of sRNA-based AND logic gates.

We show two designs (A and B) using different structures for the trans-activating sRNAs (mechanism shown in Fig. 1E). (A.1) Detail of a design, showing the RBS in blue, start codon in green, and seed regions in red and magenta. The secondary structures of the intramolecular and intermolecular folding states are presented. (A.2 and B.1) Helical plot of the complex, where the RBS is released. ΔG, ΔG _kin and ΔG _str are in Kcal/mol. Z is the partition function. (A.3 and B.2) Base pairing probability matrix, encircling the pairs of intermolecular interactions with high probability. RNA sequences shown in Table S1. Secondary structures imposed for all species shown in Fig. S1.