Nucleic Acids Research 2005 33(Web Server Issue):W573-W576; doi:10.1093/nar/gki424
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Stitchprofiles.uio.no: analysis of partly melted DNA conformations using stitch profiles
Eivind Tøstesen*,
Geir Ivar Jerstad1 and
Eivind Hovig
The Norwegian Radium Hospital N-0310 Oslo, Norway
1Department of Informatics, University of Oslo N–0316 Oslo, Norway
*To whom correspondence should be addressed. Tel: +47 22935392; Fax: +47 22522421; Email: eivind.tostesen{at}medisin.uio.no
Received February 14, 2005. Revised March 23, 2005. Accepted March 23, 2005.
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ABSTRACT
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In this study, we describe a web server that performs computations
on DNA melting, thus predicting the localized separation of
the two strands for sequences provided by the users. The output
types are stitch profiles, melting curves, probability profiles,
etc. Stitch profile diagrams visualize the ensemble of alternative
conformations that DNA can adopt with different probabilities.
For example, a stitch profile shows the possible loop openings
in terms of their locations, sizes, probabilities and fluctuations
at a given temperature. Sequences with lengths up to several
tens or hundreds of kilobase pairs can be analysed. The tools
are freely available at
http://stitchprofiles.uio.no.
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INTRODUCTION
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Many software and web tools exist for computing various aspects
of melting of double-stranded DNA (
1–
7). The repertoire
of output that they provide is limited to a few categories.
For example, in category comprises the plots of some quantity
along the chain describing the base-pair stabilities or states.
We report a web server that adds to the repertoire a recently
developed type of diagram called stitch profiles. A DNA stitch
profile indicates the multitude of possible conformations that
a partly melted DNA may adopt, and it shows what regions can
be base-paired or melted more specifically than the traditional
plots. The web server provides a new type of information that
may be useful in genomics (
8,
9), in studying the relationship
between the structure and the biological functions of DNA, in
comparison with the single-molecule techniques, and as a part
of the experimental techniques that utilize the melting and
the hybridization properties of DNA (
3,
5).
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INPUT
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When using the web server, a user must specify a DNA sequence
by either (i) uploading a text file with the sequence, or (ii)
retrieving the sequence from the NCBI GenBank using its GI number,
or (iii) typing the sequence (or copy/paste) into a text box.
In addition, the user has the option of specifying a start position
and a stop position in the sequence, which allows for an analysis
of the specified fragment only. In order to reduce the load
on the server, certain restrictions on the sequence length are
imposed, which is explained on the website.
The following sections describe the four presently available types of calculation on the server and their required input besides the sequence. In addition to stitch profile calculations, the three ‘usual’ types of melting profile can be performed: melting curves, probability profiles and temperature profiles. (They are sometimes known under different terms, such as melting maps, melting profiles, stability maps and denaturation maps.)
Stitch profiles
Stitch profile diagrams were introduced by Tøstesen et al. (10) and a complete description of the methodology is given by E. Tøstesen (submitted for publication). A stitch profile is a set of ‘stitches’, where each stitch spans a region of the sequence and characterizes a possible conformation of that region. Figure 1 shows an example of how a stitch profile diagram can represent three alternative DNA conformations. Each conformation corresponds to a row of stitches that are divided into the upper and lower sides, where the upper-side stitches indicate single-stranded (melted) regions and the lower-side stitches indicate double-stranded (not melted) regions. The three rows of stitches are then merged into the same stitch profile. The regions spanned by the stitches can overlap each other, indicating alternative conformations of a region. The horizontal direction in a stitch profile diagram corresponds to sequence position, while the vertical direction is being used for separating the overlapping stitches and for dividing the stitches into the upper and lower sides. The upper-side stitches are further distinguished as either ‘tails’ or ‘loops’, according to whether they reach the end of the molecule or not, respectively. For each stitch, the probability pv of that region of the molecule being in that state is calculated (loop, tail or helical) while leaving the rest of the molecule unspecified. These probabilities can be shown in the diagram by labelling or colouring the stitches.
View larger version (9K):
[in this window]
[in a new window]
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Figure 1 (a) Three possible conformations of a 15 kb DNA. (b) Each conformation corresponds to a row of stitches. (c) The three rows of stitches are merged in a single stitch profile diagram.
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In order to calculate a stitch profile, three parameters are
required as input: the temperature
T, a maximum depth
Dmax and
a probability cut-off
pc. Instead of the temperature, however,
a helicity
can be specified, whereupon the corresponding temperature
is calculated. The probability cut-off determines how many stitches
are included in the profile, as stitches having probabilities
below
pc are excluded. The maximum depth
Dmax determines the
level of uncertainty in locating the positions of each stitch.
This uncertainty is indicated in the diagram by horizontal ‘fluctuation
bars’ at both ends of each stitch. A more detailed introduction
to the concepts and the methods of stitch profiles is given
by E. Tøstesen (submitted for publication).
Melting curves
A ‘melting curve’ is a plot of the helicity as a function of T. The helicity is the average total fraction of closed base pairs, and it decreases from 1 to 0 over the melting range of temperatures. For intermediate length sequences (103–104 bp), the curve declines in a stepwise manner reflecting the domain subtransitions (2,11). Experimentally, melting curves can be measured using ultraviolet (UV) spectroscopy where the absorption is related to the helicity. Plots of the derivative –d/dT as a function of T are also referred to as melting curves, and they usually show a series of peaks located at the temperatures where the different domains melt. A melting curve can be calculated as a first step in a sequence analysis to find the range of temperatures where interesting melting events take place. The server calculates as the average of the base-pairing probabilities, 
and plots it versus T. The user must specify either a temperature interval (on the x-axis) or the corresponding helicity interval (on the y-axis). The temperature step size can be chosen specifically (default 1°C) or it can be determined automatically to limit the computation time.
Probability profiles
A ‘probability profile’ depends on the temperature and is a plot of the base-pairing probability pbp(i) versus sequence position i. Plots of 1 – pbp(i) are also called probability profiles. A probability profile indicates on average the regions that are base-paired and the regions that are melted at a specific temperature T. This information can be used for identifying the structural changes behind each peak in a melting curve. The server can plot several probability profiles pbp(i) at different temperatures in the same diagram, which can provide an overview of the melting process. The required input is either (i) a list of one or more temperatures, or (ii) a list of helicities, from which the corresponding temperatures are calculated.
Temperature profiles
For a given value p between 0 and 1, the corresponding ‘temperature profile’ is a plot of the temperature Tp(i) at which the i-th base-pairing probability pbp(i) equals p versus sequence position i. As a special case, a ‘Tm profile’ is a temperature profile with p = 0.5, i.e. a plot of the base-pair melting temperatures Tm(i) versus i. Usually, a temperature profile has plateaus for regions of the sequence that melt cooperatively. A Tm profile provides the different melting temperatures of these domains. Whereas a probability profile describes the molecule at a single temperature only, a Tm profile summarizes the behaviour over a range of temperatures. The server can plot a temperature profile Tp(i) of the sequence at any p-value chosen by the user (0.5 is default). The Tp(i)-values are calculated by interpolation between a set of probability profiles.
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OUTPUT
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The result of each of the four kinds of calculation is shown
on a results page as a PNG picture produced by using Gnuplot.
For those plots having sequence position on the horizontal axis,
the width of the picture increases with increasing sequence
length
N, so as to keep a constant scale (pixels per kb). A
link leads the user to a text file with the numerical data behind
the graphics. From the results page of a stitch profile, it
is possible to submit a new
pc-value that is greater than the
original value, which produces a new diagram containing fewer
stitches.
This paper should be cited when using the results and the data from the server. Refs [(10) and E. Tøstesen, submitted for publication] can also be cited as appropriate.
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ALGORITHMS
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All the results are based on the Poland–Scheraga model
of DNA melting (
12) that considers two possible states of each
base pair. However, instead of Poland's 1974 algorithm (
13),
we use our more recent DNA melting algorithm (
10). The algorithm
builds on the partition function approach of Yeramian
et al.
(
14), to which we added two main characteristics: all types
of probabilities are calculated by multiplying left-hand side
and right-hand side partition functions, which is faster (
10);
and instead of using an approximation that was originally introduced
by Gotoh and Tagashira (
15), we implement an exact scheme for
adding the nearest neighbour quantities (
10). The DNA melting
algorithm calculates base-pairing probabilities and certain
block probabilities. The base-pairing probabilities are used
for obtaining the usual melting profiles using standard methods.
The block probabilities are used in a second algorithm that
calculates stitch profiles: it is a probability peak finding
algorithm (E. Tøstesen, submitted for publication), which
basically finds and groups the conformations that give rise
to the same probability peak, and distinguishes those conformations
that belong to different probability peaks. The peak finding
algorithm is demanding for long sequences: the computation time
depends on both the sequence length
N and the temperature, and
is believed to be
O(
N2), but this has not been confirmed. However,
typical examples of stitch profile calculations on the server
are 10 s for 3000 bp, 1 min for 10 kb and 17 min for 48 kb.
Under the heading ‘Advanced options’, the user can change some thermodynamic and algorithmic settings. Several sets of empirical thermodynamic parameters can be used (11,15–18). Currently, the recommended default is Blake and Delcourt's parameters (16) with Blossey and Carlon's modified loop entropy (11). For some parameter sets, it is possible to choose the salt concentration (11,16,18). For the usual melting profiles, two versions of the DNA melting algorithm (10) can be chosen: a slower version using the exact loop entropy factor and a faster version using instead a multiexponential approximation. For stitch profile calculations, only the faster version is implemented.
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THE MULTIEXPONENTIAL APPROXIMATION
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It is established how a multiexponential approximation of the
loop entropy factor can reduce the computation time of melting
algorithms (
14,
17). The exact loop entropy factor (
11,
12) has
a power law dependence on loop size:
(
x)
x–
. In the approximation,
x– is substituted by a sum of
I exponential functions:
 | (1) |
It is a curve-fitting problem to find the parameters An, Bn and I and the obtained accuracy depends on the method (19). We have devised a simple method in which the An, Bn and I depend on the sequence length N and the exponent through the following formulas: I 
2 + ln 2N, Bn = en–I and
 | (2) |
Using this approximation, the computation time of a probability profile on the server is of the order O(I x N). Note that this is not strictly ‘linear’, as has previously been stated (10), but rather of the order O(Nlog N) because the number I grows logarithmically with N.
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FUTURE DEVELOPMENTS
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The web server has been launched recently and the future developments
are expected. For example, a user will be able to provide an
email address in order to be notified automatically when the
results are ready. This will make computations on longer sequences
possible. Another development could be plots that highlight
the difference between the melting behaviours of two different
sequences or at different temperatures, which would be useful
in analysing mutations and other perturbations. All the developments
will be documented on a ‘News’ page on the website.
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ACKNOWLEDGEMENTS
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We thank Fang Liu and Vegard Nygaard for testing the website.
Funding to pay the Open Access publication charges for this
article was provided by FUGE—The national programme for
research in functional genomics in Norway.
Conflict of interest statement. None declared.
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INTRODUCTION