arXiv subjects

Peter Clote

Publications and source records attributed to Peter Clote.

14 recordsLinked to original sources

arXiv2018

RNAmountAlign: efficient software for local, global, semiglobal pairwise and multiple RNA sequence/structure alignment

Alignment of structural RNAs is an important problem with a wide range of applications. Since function is often determined by molecular structure, RNA alignment programs should take into account both sequence and base-pairing information for structural homology identi^Lcation. A number of successful alignment programs are heuristic versions of Sanko^K's optimal algorithm. Most of them require O(n4) run time. This paper describes C++ software, RNAmountAlign, for RNA sequence/structure alignment that runs in O(n3) time and O(n2) space; moreover, our software returns a p-value (transformable to expect value E) based on Karlin-Altschul statistics for local alignment, as well as parameter ^Ltting for local and global alignment. Using incremental mountain height, a representation of structural information computable in cubic time, RNAmountAlign implements quadratic time pairwise local, global and global/semiglobal (query search) alignment using a weighted combination of sequence and structural similarity. RNAmountAlign is capable of performing progressive multiple alignment as well. Benchmarking of RNAmountAlign against LocARNA, LARA, FOLDALIGN, DYNALIGN and STRAL shows that RNAmountAlign has reasonably good accuracy and much faster run time supporting all alignment types.

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arXiv2018

Small-world networks and RNA secondary structures

Let Sn denote the network of all RNA secondary structures of length n, in which undirected edges exist between structures s, t such that t is obtained from s by the addition, removal or shift of a single base pair. Using context-free grammars, generating functions and complex analysis, we show that the asymptotic average degree is O(n) and that the asymptotic clustering coeffcient is O(1/n), from which it follows that the family Sn, n = 1,2,3,... of secondary structure networks is not small-world.

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arXiv2018

On the scale-free nature of RNA secondary structure networks

A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small- degree nodes may provide alternate paths between any two nodes on average -- such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why biological networks are often found to be scale-free may lie in the well-known fact that expanding networks in which new nodes are preferentially attached to highly connected nodes tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all secondary structures of a user-specified length, and show both by computational and theoretical arguments that preferential attachment holds when expanding the network from length n to length n + 1 structures. Since existent power-law fitting software, such as powerlaw, cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov-Smirnov p-value. Statistical goodness-of-fit tests indicate that one must reject the hypothesis that RNA connectivity data follows a power-law distribution. Nevertheless, the power-law fit is visually a good approximation for the tail of connectivity data, and provides a rationale for investigation of preferential attachment in the context of macromolecular folding.

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arXiv2018

Minimum length RNA folding trajectories

The Kinfold and KFOLD programs for RNA folding kinetics implement the Gillespie algorithm to generate stochastic folding trajectories from an initial structure s to a target structure t, in which each intermediate secondary structure is obtained from its predecessor by the addition, removal or shift of a single base pair. Define MS2 distance between secondary structures s and t to be the minimum path length to refold s to t, where a move from MS2 is applied in each step. We describe algorithms to compute the shortest MS2 folding trajectory between any two given RNA secondary structures. These algorithms include an optimal integer programming (IP) algorithm, an accurate and efficient near-optimal algorithm, a greedy algorithm, a branch-and-bound algorithm, and an optimal algorithm if one allows intermediate structures to contain pseudoknots. Our optimal IP [resp. near-optimal IP] algorithm maximizes [resp. approximately maximizes] the number of shifts and minimizes [resp. approximately minimizes] the number of base pair additions and removals by applying integer programming to (essentially) solve the minimum feedback vertex set (FVS) problem for the RNA conflict digraph, then applies topological sort to tether subtrajectories into the final optimal folding trajectory. We prove NP-hardness of the problem to determine the minimum barrier energy over all possible MS2 folding pathways, and conjecture that computing the MS2 distance between arbitrary secondary structures is NP-hard. Since our optimal IP algorithm relies on the FVS, known to be NP-complete for arbitrary digraphs, we compare the family of RNA conflict digraphs with the following classes of digraphs (planar, reducible flow graph, Eulerian, and tournament) for which FVS is known to be either polynomial time computable or NP-hard. Source code available at http://bioinformatics.bc.edu/clotelab/MS2distance/.

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arXiv2017

RNA folding kinetics using Monte Carlo and Gillespie algorithms?

RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny (~ 20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm. Here we investigate the relation between the Monte Carlo algorithm and the Gillespie algorithm. We prove that asymptotically, the expected time for a K-step trajectory of the Monte Carlo algorithm is equal to times that of the Gillespie algorithm, where denotes the Boltzmann expected network degree. If the network is regular (i.e. every node has the same degree), then the mean first passage time (MFPT) computed by the Monte Carlo algorithm is equal to MFPT computed by the Gillespie algorithm multiplied by ; however, this is not true for non-regular networks. In particular, RNA secondary structure folding kinetics, as computed by the Monte Carlo algorithm, is not equal to the folding kinetics, as computed by the Gillespie algorithm, although the mean first passage times are roughly correlated. Simulation software for RNA secondary structure folding according to the Monte Carlo and Gille- spie algorithms is publicly available, as is our software to compute the expected degree of the net- work of secondary structures of a given RNA sequence { see http://bioinformatics.bc.edu/clote/ RNAexpNumNbors.

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arXiv2016

RNAiFold2T: Constraint Programming design of thermo-IRES switches

Motivation: RNA thermometers (RNATs) are cis-regulatory ele- ments that change secondary structure upon temperature shift. Often involved in the regulation of heat shock, cold shock and virulence genes, RNATs constitute an interesting potential resource in synthetic biology, where engineered RNATs could prove to be useful tools in biosensors and conditional gene regulation. Results: Solving the 2-temperature inverse folding problem is critical for RNAT engineering. Here we introduce RNAiFold2T, the first Constraint Programming (CP) and Large Neighborhood Search (LNS) algorithms to solve this problem. Benchmarking tests of RNAiFold2T against existent programs (adaptive walk and genetic algorithm) inverse folding show that our software generates two orders of magnitude more solutions, thus allow- ing ample exploration of the space of solutions. Subsequently, solutions can be prioritized by computing various measures, including probability of target structure in the ensemble, melting temperature, etc. Using this strategy, we rationally designed two thermosensor internal ribosome entry site (thermo-IRES) elements, whose normalized cap-independent transla- tion efficiency is approximately 50% greater at 42?C than 30?C, when tested in reticulocyte lysates. Translation efficiency is lower than that of the wild-type IRES element, which on the other hand is fully resistant to temperature shift-up. This appears to be the first purely computational design of functional RNA thermoswitches, and certainly the first purely computational design of functional thermo-IRES elements. Availability: RNAiFold2T is publicly available as as part of the new re- lease RNAiFold3.0 at https://github.com/clotelab/RNAiFold and http: //bioinformatics.bc.edu/clotelab/RNAiFold, which latter has a web server as well. The software is written in C++ and uses OR-Tools CP search engine.

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arXiv2015

RNA thermodynamic structural entropy

Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV aborption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. The software is available at http://bioinformatics.bc.edu/clotelab/RNAentropy.

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arXiv2015

Asymptotic connectivity for the network of RNA secondary structures

Given an RNA sequence a, consider the network G = (V;E), where the set V of nodes consists of all secondary structures of a, and whose edge set E consists of all edges connecting two secondary structures whose base pair distance is 1. Define the network connectivity, or expected network degree, as the average number of edges incident to vertices of G. Using algebraic combinatorial methods, we prove that the asymptotic connectivity of length n homopolymer sequences is 0:473418 ? n. This raises the question of what other network properties are characteristic of the network of RNA secondary structures. Programs in Python, C and Mathematica are available at the web site http://bioinformatics.bc.edu/clotelab/ RNAexpNumNbors.

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arXiv2015

RNAiFold 2.0: A web server and software to design custom and Rfam-based RNA molecules

Several algorithms for RNA inverse folding have been used to design synthetic riboswitches, ribozymes and thermoswitches, whose activity has been experimentally validated. The RNAiFold software is unique among approaches for inverse folding in that (exhaustive) constraint programming is used instead of heuristic methods. For that reason, RNAiFold can generate all sequences that fold into the target structure, or determine that there is no solution. RNAiFold 2.0 is a complete overhaul of RNAiFold 1.0, rewritten from the now defunct COMET language to C++. The new code properly extends the capabilities of its predecessor by providing a user-friendly pipeline to design synthetic constructs having the functionality of given Rfam families. In addition, the new software supports amino acid constraints, even for proteins translated in different reading frames from overlapping coding sequences; moreover, structure compatibility/incompatibility constraints have been expanded. With these features, RNAiFold 2.0 allows the user to design single RNA molecules as well as hybridization complexes of two RNA molecules. The web server, source code and linux binaries are publicly accessible at http://bioinformatics.bc.edu/clotelab/RNAiFold2.0

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arXiv2015

Fast, approximate kinetics of RNA folding

In this paper, we introduce the software suite, Hermes, which provides fast, novel algorithms for RNA secondary structure kinetics. Using the fast Fourier transform to efficiently compute the Boltzmann probability that a secondary structure S of a given RNA sequence has base pair distance x [resp. y] from reference structure A [resp. B], Hermes computes the exact kinetics of folding from A to B in this coarse-grained model. In particular, Hermes computes the mean first passage time from the transition probability matrix by using matrix inversion, and also computes the equilibrium time from the rate matrix by using spectral decomposition. Due to the model granularity and the speed of Hermes, it is capable of determining secondary structure refolding kinetics for large RNA sequences, beyond the range of other methods. Comparative benchmarking of Hermes with other methods indicates that Hermes provides refolding kinetics of accuracy suitable for use in computational design of RNA, an important area of synthetic biology. Source code and documentation for Hermes are available at http://bioinformatics. bc.edu/clotelab/Hermes/.

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arXiv2014

Expected degree for RNA secondary structure networks

Consider the network of all secondary structures of a given RNA sequence, where nodes are connected when the corresponding structures have base pair distance one. The expected degree of the network is the average number of neighbors, where average may be computed with respect to the either the uniform or Boltzmann probability. Here we describe the first algorithm, RNAexpNumNbors, that can compute the expected number of neighbors, or expected network degree, of an input sequence. For RNA sequences from the Rfam database, the expected degree is significantly less than the CMFE structure, defined to have minimum free energy over all structures consistent with the Rfam consensus structure. The expected degree of structural RNAs, such as purine riboswitches, paradoxically appears to be smaller than that of random RNA, yet the difference between the degree of the MFE structure and the expected degree is larger than that of random RNA. Expected degree does not seem to correlate with standard structural diversity measures of RNA, such as positional entropy, ensemble defect, etc. The program {\tt RNAexpNumNbors} is written in C, runs in cubic time and quadratic space, and is publicly available at http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.

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arXiv2014

Complete RNA inverse folding: computational design of functional hammerhead ribozymes

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, RNAiFold, which can determine all RNA sequences whose minimum free energy secondary structure is a user-specified target structure. Using RNAiFold, we design ten cis-cleaving hammerhead ribozymes, all of which are shown to be functional by a cleavage assay. We additionally use RNAiFold 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. RNAiFold is available at http://bioinformatics.bc.edu/clotelab/RNAiFold/.

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arXiv2012

Combinatorics of locally optimal RNA secondary structures

It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 \cdot n^{-3/2} \cdot 2.618034^n$. Motivated by the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are locally optimal, with respect to a particular energy model. In the Nussinov energy model, where each base pair contributes -1 towards the energy of the structure, locally optimal structures are exactly the saturated structures, for which we have previously shown that asymptotically, there are $1.07427\cdot n^{-3/2} \cdot 2.35467^n$ many saturated structures for a sequence of length $n$. In this paper, we consider the base stacking energy model, a mild variant of the Nussinov model, where each stacked base pair contributes -1 toward the energy of the structure. Locally optimal structures with respect to the base stacking energy model are exactly those secondary structures, whose stems cannot be extended. Such structures were first considered by Evers and Giegerich, who described a dynamic programming algorithm to enumerate all locally optimal structures. In this paper, we apply methods from enumerative combinatorics to compute the asymptotic number of such structures. Additionally, we consider analogous combinatorial problems for secondary structures with annotated single-stranded, stacking nucleotides (dangles).

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arXiv2009

Asymptotics of Canonical and Saturated RNA Secondary Structures

It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 n^{-3/2} 2.618034^n$. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures - canonical and saturated structures. Canonical secondary structures were introduced by Bompfünewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up. Saturated secondary structures have the property that no base pairs can be added without violating the definition of secondary structure (i.e. introducing a pseudoknot or base triple). Here we compute the asymptotic number of saturated structures, we show that the asymptotic expected number of base pairs is $0.337361 n$, and the asymptotic number of saturated stem-loop structures is $0.323954 1.69562^n$, in contrast to the number $2^{n-2}$ of (arbitrary) stem-loop structures as classically computed by Stein and Waterman. Finally, we show that the density of states for [all resp. canonical resp. saturated] secondary structures is asymptotically Gaussian. We introduce a stochastic greedy method to sample random saturated structures, called quasi-random saturated structures, and show that the expected number of base pairs of is $0.340633 n$.

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