Complete RNA inverse folding: computational design of functional hammerhead ribozymes

Abstract

Nanotechnology and synthetic biology currently constitute one of the most innovative, interdisciplinary fields of research, poised to radically transform society in the 21st century. This paper concerns the synthetic design of ribonucleic acid molecules, using our recent algorithm, , which can determine all RNA sequences whose minimum free energy secondary structure is a user-specified target structure. Using , we design ten cis-cleaving hammerhead ribozymes, all of which are shown to be functional by a cleavage assay. We additionally use to design a functional cis-cleaving hammerhead as a modular unit of a synthetic larger RNA. Analysis of kinetics on this small set of hammerheads suggests that cleavage rate of computationally designed ribozymes may be correlated with positional entropy, ensemble defect, structural flexibility/rigidity and related measures. Artificial ribozymes have been designed in the past either manually or by SELEX (Systematic Evolution of Ligands by Exponential Enrichment); however, this appears to be the first purely computational design and experimental validation of novel functional ribozymes. is available at http://bioinformatics.bc.edu/clotelab/RNAiFold/.

RNA folding kinetics using Monte Carlo and Gillespie algorithms

“…We argue that the Gillespie algorithm should be used for RNA secondary structure folding kinetics, and that specifically one should compute the population occupancy vector p(t) determined by solution of the matrix differential equation dp(t) dt = p(t) · Q, for rate matrix Q as in [58,56], rather than the mean first passage time by use of the fundamental matrix or by matrix inversion [35] as done for Markov state models in [7,25]. For synthetic design of RNA molecules [57,13], we advocate fast MFPT computation using coarse-grained models [52,43] to select design candidates for subsequent scrutiny by more accurate methods such as KFOLD. for all y ∈ Nx do 6.…”

“…On the other hand, we prove that asymptotically, the expected time for a K-transition Monte Carlo trajectory is equal to that for a K-transition Gillespie trajectory multiplied by N . A rapidly emerging area of synthetic biology concerns the computational design of synthetic RNA [9,13] by using inverse folding software [48,57,19,15]. It seems clear that the next step in synthetic RNA design will be to control the kinetics of RNA folding.…”

Fast, Approximate Kinetics of RNA Folding

“…The rate equation R for is usually defined as in (5) for Markov processes which model macromolecular folding, hence it is easy to see that such Markov processes satisfy detailed balance and moreover that the equilibrium distribution is the Boltzmann distribution; i.e. p * x = exp(−E(x)/RT ) for all 1 ≤ x ≤ n. Since detailed balance ensures that the eigenvalues of the rate matrix R are real, one can solve the matrix differential equation (7) by diagonalizing the rate matrix, and thus obtain the solution…”

“…(Right) Minimum free energy structure of the 54 nt Peach Latent Mosaic Viroid (PLMVd) AJ005312.1/282-335, which is identical to the consensus structure from Rfam 11.0 [20]. RNAfold from Vienna RNA Package 2.1.7 with energy parameters from the Turner 1999 model were used, since the minimum free energy structure determined by the more recent Turner 2004 energy parameters does not agree with the Rfam consensus structure -see [7]. Positional entropy, a measure of divergence in the base pairing status at each positions for the low energy ensemble of structures, is indicated by color, using the RNA Vienna Package utility script relplot.pl.…”

“…In [25], small conditional RNAs have been engineered to silence a gene Y by using the RNA interference machinery, only if a gene X is transcribed. In [43] a novel theophylline riboswitch has been computationally designed to transcriptionally regulate a gene in E. coli, and in [7] a purely computational approach was used to design functionally active hammerhead ribozymes. Computational design of synthetic RNA molecules invariably uses some form of thermodynamics-based algorithm; indeed, NUPACK-Design [49] was used to design small conditional RNAs [25], Vienna RNA Package [23] was used in the design of the synthetic theophylline riboswitch, and the RNAiFold inverse folding software [19,18] was used to design the synthetic hammerhead ribozymes.…”