### RNAsc

is a web server that computes RNA
secondary structure with user-input chemical/enzymatic probing data,
especially Selective 2'-hydroxyl acylation analyzed by primer extension
(SHAPE) or inline-probing data. Unlike other methods, RNAsc computes
the partition function and minimum energy structure by applying Boltzmann
derived weights applied to every nucleotide position. See

Integrating chemical foot
printing data into RNA secondary structure prediction,
by K. Zarringhalam, M.M. Meyer, I. Dotu, J.H. Chuang, P.Clote.
PLoS One. 2012;7(10):e45160. doi: 10.1371/journal.pone.0045160.
Epub 2012 Oct 16.

### RNAiFold

is a web server that solves the RNA
inverse folding problem, using constraint programming.
Given a target RNA secondary structure, as well as optional
nucleotide constraints, RNAiFold determines all (or a large number of)
RNA sequences, whose minimum free energy structure is the target
structure. See

RNAiFold: A constraint programming algorithm for RNA inverse folding and
molecular design
J.A. Garcia Martin, Peter Clote, Ivan Dotu.
J Bioinform Comput Biol 11(2): 1350001, 2013

### Expected5to3distance

is a web server that computes
the expected distance between the 5' and 3' ends of the Boltzmann
ensemble of all secondary structures for a given RNA sequence. See

Expected distance between terminal nucleotides of RNA
secondary structures.
P. Clote, Y. Ponty, J.-M. Steyaert.
J Math Biol. 2012 Sep;65(3):581-99. Epub 2011 Oct 9.

### RNApagenumber

is a web server that computes the optimal
"page number" of an RNA pseudoknotted or tertiary structure,
input as a PDB file or .ct (mfold connect) file. See

On the Page Number of Secondary Structures with Pseudoknots.
Peter Clote, Stefan Dobrev, Ivan Dotu, Evangelos Kranakis,
Danny Krizanc, Jorge Urrutia.
J Math Biol. 2012 Dec;65(6-7):1337-57. doi: 10.1007/s00285-011-0493-6.

where we show that computing the page number is NP-complete, and describe
an approximation algorithm as well as an exact solution using constraint
programming (CP). The web server is an implementation of the CP algorithm,
which can compute the optimal page number for large RNAs within seconds --
for example the 23S chain PDB file 1FFK of length 2,922 for the

*Haloarcula marismortui* ribosome.

### RNAlocopt

is a web server that computes the partition function
and samples structures from the ensemble of

*locally optimal*
secondary structures of a given RNA sequence. Here, a locally optimal
secondary structure is one for which the free energy can

*not*
be lowered by the addition or removal of a single base pair (i.e. a
kinetic trap in unit resolution energetics).
The algorithm is described in
the paper

Computing the partition function for kinetically trapped RNA
secondary structures.
W.A. Lorenz, P. Clote.
Public Library of Science One (PLoS ONE), (2011)
PLoS ONE 6(1): e16178. doi:10.1371/journal.pone.0016178.

### RNAborMEA

computes the

*maximum expected accurate*
δ-neighbors of a given RNA secondary structure for a given RNA
sequence. Here, a structure T is a δ-neighbor of a given structure
S, if S can be transformed into T by a minimum number δ of edit
operations, where an edit operation consists of removing or adding a single
base pair (i.e. if the base pair distance between S and T is δ).
The algorithm is described in
the paper

Peter Clote, Feng Lou, William A. Lorenz.

Maximum expected accuracy structural neighbors of an RNA secondary structure.

BMC Bioinformatics BMC Bioinformatics. 2012 Apr 12;13 Suppl 5:S.

### RNA-WL

is an implementation of the Wang-Landau non-Boltzmannian
sampling algorithm to approximate the partition function for RNA secondary
structures. It is well-known that Monte-Carlo Boltzmannian sampling can be
used to compute an approximation to the minimum free energy
pseudoknotted structure for a given RNA sequence (allowing all possible
pseudoknots). Since it is also NP-complete to compute the
partition function for pseudoknotted RNA structures, Wang-Landau sampling
can be used to estimate the density of states (from which the partition
function can be computed).
The algorithm is described in the paper

"Thermodynamics of RNA structures by Wang-Landau sampling."
Feng Lou, Peter Clote.
*Bioinformatics* 2010 Jun 15;26(12):278-86.

### RNApathfinder

is a web server to compute near-optimal folding pathways between
two given secondary structures for a given RNA sequence. Since this
problem is known to be NP-complete, our main algorithm,

*RNAtabupath*
uses the TABU local search heuristic. The web server
includes both downloadable source code for several algorithms, as well
as a web engine to compute pathways. Intended applications concern
folding pathways for RNA conformational switches.

*RNApathfinder* and the

*RNAtabupath* algorithm are
described in the paper

I. Dotú, W.A. Lorenz, P. Van Hentenryck, P. Clote.

*Nucleic Acids Res.* 2010 Mar 1;38(5):1711-22.

### RNAmutants

is a web server to perform mutational analysis for a given RNA sequence.
Previous methods relied on exhaustively enumerating k-point mutant
sequences and subsequently applying mfold or RNAfold, a procedure with
run time exponential in k. In contrast, RNAmutants computes the
minimum free energy structure and Boltzmann partition function for all
k-point mutants, for 0 ≤ k ≤ K, with run time
O(K

^{2}n

^{3}). RNAmutants is described in the paper

Jerome Waldispühl, Srinivas Devadas, Bonnie Berger, Peter Clote.

Efficient algorithms for probing the RNA mutation landscape.

PLoS Comput Biol. 2008 Aug 8;4(8):e1000124.

###
LocalMove

is a web server to compute 3-dimensionals cubic and face-centered
cubic lattice fits for both RNA and protein. Various levels of granularity
are supported: backbone and several coarse grain models (CA, C1',P, etc.).
Since optimal on-lattice fit for the cubic lattice is NP-complete,
LocalMove implements the Monte-Carlo with simulated annealing, with a
variety of user-definable parameters. LocalMove web server produces
animated movies of the folding procedure, and stores job IDs for future
reference. The web server and algorithm are described in
Y. Ponty, R. Istrate, E. Porcelli, P. Clote.

LocalMove: Computing on-lattice fits for biopolymers.
Nucleic Acids Res. (Web Server Issue) (2008).

###
RNAbor

*RNAbor*
is a web server to compute secondary structural neighbors of a given RNA
structure. The algorithm is described in

Boltzmann probability of RNA structural neighbors and riboswitch detection.
,
Eva Freyhult; Vincent Moulton; Peter Clote,
Bioinformatics. 2007 Aug 15;23(16):2054-62. Epub 2007 Jun 14.

Abstract,

PDF
The web server is described in

RNAbor: A web server for RNA structural neighbors.
E. Freyhult, V. Moulton, P. Clote.
Nucleic Acids Res. 2007 Jul 1;35(Web Server issue):W305-9. Epub 2007 May 25.
###
DIAL

*DIAL* is a
web server for 3-dimensional RNA structural alignment (global and local)
and for motif detection. DIAL (DIhedral ALignment)
runs in time that is quadratic in input length by performing an alignment
which accounts for (i) pseudo-dihedral and/or dihedral angle similarity,
(ii) nucleotide sequence similarity,
(iii) nucleotide base-pairing similarity. The algorithm and web server are
described in

DIAL: a web server for the pairwise alignment of two RNA three-dimensional
structures using nucleotide, dihedral angle and base-pairing similarities
,
F. Ferre; Y. Ponty; W. A. Lorenz; Peter Clote
Nucleic Acids Res. 2007 Jul 1;35(Web Server issue):W659-68. Epub 2007 Jun 13.

Abstract ,

Full Text,

PDF.

###
transFold

*transFold* is a
web server for beta-barrel supersecondary structure prediction.
Unlike other software which employ machine learning methods,

*transFold* uses multi-tape S-attribute grammars to describe the
space of all possible supersecondary structures, then applies dynamic
programming to compute the global energy minimum structure.
The algorithm, due to J. Waldispühl, is described in

Predicting transmembrane beta-barrels and
interstrand residue interactions from sequence,
J. Waldispühl, B. Berger, P. Clote, J.-M. Steyaert,

*Proteins* 65(1):61-74 (2006).

BibTeX entry
The web server, implemented by J. Waldispühl, is described in

transFold: a Web Server for predicting the structure
and residue contacts of transmembrane beta-barrels,
J. Waldispühl, B. Berger, P. Clote, J.-M. Steyaert,

*Nucleic Acids Res.* 34(Web Server Issue):189-193 (2006).

BibTeX entry
###
Boltzmann Time Warping

*Boltzmann Time Warping* is software to compute the
(symmetric, pairwise, all-against-all) time warping distance for
gene expression time series values between two data sets.
The user uploads two tab-separated textfiles of gene expression time
series data, and the web server computes the time warping distance
as well as the Boltzmann pair probability in the optimal alignment.
Boltzmann pair probabilities provide a measure of potential

*biological significance* of aligned positions.
The new algorithms are due to P. Clote and described in

Symmetric time warping, Boltzmann pair probabilities and
functional genomics
,
P. Clote, J. Straubhaar,

* J Math Biol.* 53(1):135-61 (2006).

BibTeX entry
and the web server is described in

BTW: A web server for Boltzmann time warping of gene expression
time series,
F. Ferre, P. Clote,

*Nucleic Acids Res.* 34(Web Server issue):W482-5 (2006).

BibTeX entry
###
Energy of k-point mutants of RNA

RNAmutants is software to predict
the expected energy of k-point mutants of a given RNA sequence, and
as well to compute the k-superoptimal secondary
structure, or secondary structure whose free energy is a minimum over
all pointwise mutants of a given RNA involving at most k mutated sites.
The algorithms are described in

Energy landscape of k-point mutants of an RNA molecule by
P. Clote, J. Waldispuhl, B. Behzadi, J.-M. Steyaert,

*Bioinformatics*, Vol. 21, 4140-4147, 2005.

### DiANNA: Diresidue amino acid neural network for
cysteine oxidation state and disulfide bond connectivity

DiANNA is software to predict both
cysteine oxidation state and which half-cystines partner with which
other half-cystines in disulfide bonds. The neural net design and
implementation is due to F. Ferre and P. Clote, and is described in
the papers:

Disulfide connectivity prediction using secondary
structure information and diresidue frequencies ,
F. Ferre and P. Clote,

*Bioinformatics* 21(10):2336-2346 (2005),
and

DiANNA: a web server for disulfide connectivity prediction ,
F. Ferre, P. Clote,

*Nucleic Acids Research*,
Nucleic Acids Res. 2005 Jul 1;

**33**(Web Server issue):W230-232.
The extension to a ternary classifier using Support Vector Machines
(SVMs), due to F. Ferre, is described in

DiANNA1.1webServer.pdf
DiANNA 1.1: An extension of the DiANNA web server
for ternary cysteine classification,
F. Ferre, P. Clote,

*Nucleic Acids Res.* 34(Web Server issue):W182-5 (2006).

BibTeX entry
### RNA energy spectrum computation (density of states)

RNALOSS
is a web server to compute the number and relative density of states
of RNA Locally Optimal Secondary Structures. The underlying algorithm
runs in O(n

^{4}) time and O(n

^{3}) space, and computes
the (relative) density of states for the entire energy
spectrum for the Nussinov-Jacobson energy for RNA secondary structures
on an input RNA. The algorithm and webserver are described in

An efficient algorithm to compute the landscape of
locally optimal RNA secondary structures with respect to the
Nussinov-Jacobson energy model ,
P. Clote,

*Journal of
Computational Biology* * 12*(1) 2005 83--101, and

RNALOSS: A web server for RNA locally optimal secondary structures ,
P. Clote,

*Nucleic Acids Research*,
web server W1-W5 (2005).

### rna dinucleotide shuffle

*Dishuffle* is a web
interface to a local implementation of the Altschul-Erikson
dinucleotide shuffle algorithm, described in
"Significance of nucleotide sequence alignments: A method for random
sequence permutation that preserves dinucleotide and codon usage",
S.F. Altschul and B.W. Erikson,
Mol. Biol. Evol., 2(6):526--538, 1985. This algorithm was used
in the paper,

*Structural RNA has lower folding energy than random RNA of the
same dinucleotide frequency*, by
P. Clote, F. Ferre, E. Kranakis, D. Krizanc in

*RNA* 11(5):578-591 (2005).

### Refined global and local alignments

Boltzmann Alignment
performs a (local) Smith-Waterman alignment of two input proteins,
then calculates the Boltzmann probability of any two aligned residues,
or residue aligned with gap symbol. This idea was first published in
"Stochastic Pairwise Alignments",
U. Mueckstein, I. L. Hofacker, and P. F. Stadler,

*Bioinformatics* 18 (suppl) 2002,
though it was later independently discovered and implemented in
April 2003 by P. Clote.
See

"Biologically significant sequence alignments using
Boltzmann probabilities" by P. Clote.