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- General remarks
- Minimum free energy (MFE) structure
- Partition function folding and dot plots
- Ensemble free energy
- Centroid structure
- Circular folding
- Dangling ends
- Dot bracket notation
- Mountain plot
- Vienna RNA conservation coloring schema
- SVG files
- Postscript files
- Final Remarks

Once the computation is complete you will be redirected to the results page, or you'll receive an email with the URL of the page. Note that the results will be deleted on our server after a while (currently 2 days). Download any files you want to keep to your local computer. The servers provide little protection for confidential data. Anyone who manages to guess the URL of your results page can access the data. Consider installing the software locally if this is an issue for you.

The Vienna RNA WebServers are based on the latest ViennaRNA Package (Version 2.3.1)

The MFE structure of an RNA sequence is the secondary structure that contributes a
minimum of free energy. This structure is predicted using a loop-based energy model and
the dynamic programming algorithm introduced by Zuker et al. [1].
As an RNA secondary structure can be uniquely decomposed into loops and external bases
the loop-based energy model treats the free energy *F(s)* of an RNA secondary structure *s*
as the sum of the contributing free energies *F _{L}* of the loops

[1] Zuker, M. and Stiegler, P. Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information
*Nucleic Acid Res.* **9(1)**: 133-148, 1981

In several bioinformatical applications one is not only interested in a single
secondary structure with a special property like a minimum of free energy but in the
probability of the occurance of a secondary structure *s _{i}* contained
in the whole Boltzmann ensemble

This dot plot consists of an upper and a lower triangle of a quadratic matrix. In both
dimensions, each letter of the primary structure is assigned to a matrix index *i*
and *j*, respectively. Matrix entries at position *i,j* are filled by black
boxes indicating a base pair *(i,j)*. In the upper triangle, the size of the boxes
is proportinal to the base pairing probability where small boxes indicate low and large
boxes high probability to form a base pair (i, j). The lower triangle is filled by boxes
of equal size, depicting the secondary structure with minimal free energy. Considering
alignments of RNA sequences results in colored dot-plots where the color represents
sequence variation, as described in the Vienna RNA conservation coloring
schema.

[1] McCaskill, J.S. The equilibrium partition function and base pair binding probabilities for RNA secondary structure
*Biopolymers* **29(6-7)**: 1105-1119, 1990

If partition function folding was selected, an ensemble structure depicting the base pair
probabilities summarized by pseudo bracket notation with the additional symbols ',', '|',
'{', '}' is shown on the results page too. Here, the usual '(', ')', '.', represent
bases with a strong preference (more than 2/3) to pair upstream (with a partner
further 3'), pair down-stream, or not pair, respectively. '{', '}', and ',' are just
weaker version of the above and '|' represents a base that is mostly paired but has
pairing partners both upstream and downstream. In this case open and closed brackets
need not match up. This pseudo bracket notation is followed by the ensemble free
energy *F = -kT ln Q* in kcal/mol. Considering alignments of RNA sequences,
these energies include the covariance term (they're not physical energies).

The centroid structure of an RNA sequence is the secondary structure with minimal base pair distance to all other secondary structures in the Boltzmann ensemble.

Although most RNA molecules are linear, circular single stranded RNAs occur
in a few cases. To take such circular RNAs into account the Vienna RNA Package
implements additional memory efficient post- and pre-processing steps [1] for
almost all included programs since Version 1.7 . If you use the Vienna RNA
Webservers to treat circular RNAs check the option "*assume RNA molecule
to be circular*" which is located in *advanced options*.

[1] Hofacker IL, Stadler PF. Memory efficient folding algorithms for circular RNA secondary structures
*Bioinformatics* **22(10)**: 1172-1176, 2006

Additional stabilizing energies which arize if an unpaired nucleotide stacks
with an adjacent base pair are called *dangling-end contributions*. When
calculating the free energy of a loop, three possibilites for regarding dangling-end
contributions exist. Firstly they may be ignored and therefore do not play a role in
the algorithm. The second way is to take them into account for every combination of
adjacent bases and base pairs. And thirdly, a more complicated energy model can be
appliedletting unpaired bases stack with at most one base pair. The Vienna RNA
Package implements each of these three models plus an additional energy contribution
for coaxial stacking of helices. Using the Vienna RNA Webservers, you can switch
dangling-end handling in *advanced options*.

The bracket notation for RNA secondary structures
Pseudo-knot free secondary structures can be represented in the
space-efficient *bracket notation*, which is used throughout
the Vienna RNA package. A structure on a sequence of length n is
represented by a string of equal length consisting of matching
brackets and dots. A base pair between base i and j is represented by
a '(' at position i and a ')' at position j, unpaired bases are
represented by dots. Thus the secondary structure

(((..((((...)))).)))is equivalent to:

i.e. a stem-loop structure consisting of a an outer helix of 3 base pairs followed by an interior loop of size 3, a second helix of length 4, and a hairpin loop of size 3.

A mountain plot represents a secondary structure in a plot of height versus position, where the height m(k) is given by the number of base pairs enclosing the base at position k. I.e. loops correspond to plateaus (hairpin loops are peaks), helices to slopes.

Representations that are generated by RNAalifold use a
coloring scheme for highlighting the mutational pattern
with respect to the structure. If one predicted base-pair
is formed by several different combinations of nucleotides
consistent or compensatory mutations have taken place. This
is indicated by different colors (see below). Pale colors
indicate that a base-pair cannot be formed in some
sequences of the alignment.

A SVG output is produced by several severs, as this file format allows to easily generate interactive drawings. The web browser Firefox natively supports SVG without the need of installing additional plugins. If you are using the Internet Explorer please install the Adobe SVG plugin.

PostScript (PS) is a page description language (PDL) developed by Adobe. Each server will provide graphical output in form of PostScript files. These files can be used straight forward in professional type setting programs such as LaTeX. In addtion, we provide for each PS file a PDF file and a link to send the PS file to an online image converter that is able to export the file to several bitmap formats. Unfortunately, Microsoft Windows ships without a PostScript viewer. If your machine can't display postscript files install gsview.