Sfold
Table of Contents
Sfold predicts probable RNA secondary structures, assesses target accessibility, and provides tools for the rational design of RNA-targeting nucleic acids.
Sfold is based on patent-pending algorithms developed by Ding and Lawrence (2001, 2002, 2003) for RNA folding, prediction of target accessibility, and rational design of RNA-targeting nucleic acids. The RNA folding algorithm generates a statistical sample of secondary structures from the Boltzmann ensemble of RNA secondary structures. From a statistical mechanics perspective, an RNA molecule can have a population of structures distributed according to a Boltzmann distribution, which gives the probability of a secondary structure I at equilibrium as (1/U)exp[-E(I)/RT], where E(I) is the free energy of the structure, R is the gas constant, T is the absolute temperature, and U is the partition function for all admissible secondary structures of the RNA sequence. The algorithm samples secondary structures exactly and rigorously according to the Boltzmann distribution, using recent Turner free energy rules.
A focus of Sfold is on applications of prediction of target accessibility, and rational design of
RNA-targeting nucleic acids. Three modules, Sirna, Soligo and Sribo, provide application tools
for the design of short-interfering RNAs (siRNAs), antisense oligonucleotides (oligos), and
trans-cleaving ribozymes, respectively. General folding features and output are available from
the fourth module, Srna.
Rules for siRNA design and Sfold design methodology
A note to all users: please do not design siRNAs or other RNA-targeting nucleic acids based on
a single structure from module Srna. We believe that there may be an ensemble of structures for mRNAs and viral RNAs. Please refer to FAQ # 3 on Sfold front page.
Sfold is available through web server at two sites: http://sfold.wadsworth.org/ and http://www.bioinfo.rpi.edu/applications/sfold/. On the server home page, a user can select the application module of primary interest. From the output page for the selected module, links for output are provided for the other modules, with default input settings as described below.
Common information for all modules
Folding conditions. Folding temperature is 37 o C. Ionic conditions are 1M NaCl, with no divalent ions.
Job mode and limits. A job can run in either interactive mode or batch mode. Current limits are 200 bases for an interactive job, and 5,000 bases for a batch job. For a batch job, a correct e-mail address is required, for notification of job completion.
For a sequence exceeding the length limit, the user needs to truncate the sequence for folding. It is quite possible that some portions of the secondary structure of a truncated sequence will be different from the structure of the full sequence. This in turn can change the predicted accessibility of some sites on the target. To computationally address this issue, we suggest two strategies:
(1) Centering. For a decision on where to truncate the sequence, we suggest that the region of primary interest be located far way from the sites of the truncation, e.g., near the center of the truncated sequence. Our computational experience suggests that the accessibility of a site is more likely to be maintained when the site is located near the center of the truncated sequence. This can be explained by the fact that, to a great extent, RNA secondary structure is determined by nearest-neighbor interactions. The regions near the 5' and 3' ends of the shortened sequence, i.e., the sites of truncation, are most likely to have different predictions for local structures and accessibility.
(2) Folding of two overlapping sequences. For a region X of primary interest, the user selects two truncated sequences 5'-A-X-B-3', and 5'-C-X-D-3', such that both contain X and both are within the length limit. After folding both sequences, the user selects common accessible sites in X that are predicted by the sequences. This process takes more work, however, the reward is increased confidence in accessible sites, because the location of truncation has little effect on the predicted accessibility.
Sequence input format. Sequences in raw format, in FASTA format, or in GenBank format are accepted. A sequence can be entered in the input window; alternatively, a sequence file can be uploaded from your computer directory (folder). Note that any character other than A, C, G, T, or U will be edited out. An option is provided if the RNA sequence to be folded is the reverse complement of the input sequence.
Module-specific input information
Sirna. The length of siRNAs with 3' TT overhangs is fixed at 21 nt.
Soligo. The user has the option to set the length of the oligos. The default length is 20 nt.
Sribo. The user can specify an NUH cleavage triplet for hammerhead ribozymes. The default triplet is GUC.
Srna. None.
Graphical output
Probability profiling for visual display of accessibility prediction. For prediction of target accessibility, a complete probability profile of single-stranded regions is generated for the entire target RNA. Sites with high probabilities of being single-stranded are predicted to be accessible. At nucleotide position i, the profile shows the probability that nucleotides i, i+1, i+2, and i+3 are all unpaired. In other words, the profile is for consecutive fragments with a width W of 4 bases. Although the profile can be generated for any W, W=4 has been found to be particularly useful (Ding & Lawrence 2001). Currently, colored or black and white profile plots are available in PDF and PostScript formats.
For RNA sequences longer than 200 bases, the regional probability profile allows the user to examine either any region of 200 bases, by specifying the starting position, or an adjacent region of 200 bases, by clicking << or >>.
Loop profiling. Probability profiles for all types of loops (loop probability profiles) are also produced. The user
can select among hairpin, bulge, interior, multi-branched, or exterior loops, for generation of
Hplot, Bplot, Iplot, Mplot and Extplot, respectively. The probability that nucleotide i is in a loop
of selected type is plotted at position i (here we are interested in individual bases with W=1,
not
fragments of several bases). For RNA sequences longer than 400 bases,
the loop profile is
displayed for any region of 400 bases, with the starting position
specified by the user. At the present, we do not know whether a certain
type of loop is more favorable than other types for binding by
complementary nucleic acids.
Text output files
Implementation of target accessibility rule. The probability profile displays predicted accessible sites on the target RNA. Because an
accessible site can be targeted by a number of siRNAs, selection of the "optimal" one can be
based on binding energy of the antisense strand, together with other design rules. Stronger
binding is indicated by smaller binding energy (stacking energies are negatively valued). For
example, an antisense siRNA with a binding energy of -15 kcal/mol is predicted to be more effective than an
antisense siRNA with a binding energy of -10 kcal/mol. The antisense siRNA binding energy is a
weighted sum of the RNA/RNA stacking energies (Xia et al. 1998)
for the hybrid formed by the
antisense siRNA and the targeted sequence. For a base-pair stack, the
weight for the
sum is calculated by the probability of the unpaired dinucleotide in
the target sequence that is involved in the stack. In addition, A-U
terminal penalty is included and is weighted by the probability of the
unpaired terminal base. This weighting scheme accounts for the
structural variation at the target site. The target accessibility rule
is implemented by requiring the siRNA binding energy to be below a
threshold value. The current default of the threshold is -10 kcal/mol.
|
File filtered.out gives output for siRNAs that meet all filter criteria: | |
| Line 1: | |
| Column 1: |
target position (starting-ending) |
| Column 2: |
sense siRNA (5' → 3') |
| Column 3: |
antisense siRNA (5' → 3') |
| Column 4: |
dinucleotide leader preceding the target sequence |
| Line 2: | |
| Column 1: | total score for siRNA duplex |
| Column 2: | target accessibility score |
| Column 3: | duplex feature score |
| Column 4: | duplex thermodynamics score |
| Column 5: | siRNA GC content |
| Column 6: | antisense siRNA binding energy (kcal/mol) |
| Column 7: | differential stability of siRNA duplex ends (DSSE, in kcal/mol) |
| Column 8: | average internal stability at the cleavage site (AIS, in kcal/mol) |
| Column 9: | total stability of siRNA duplex (kcal/mol) |
| Column 10: | sum of probabilities of unpaired target bases (column 4 of output file sstrand.out) |
Filter criteria:
| A) |
Antisense siRNA binding energy ≤ -10 kcal/mol (target accessibility rule); |
| B) |
Duplex feature score of 6 or higher; |
| C) |
DSSE > 0 kcal/mol (asymmetry rule); |
| D) |
AIS > -8.6 kcal/mol (cleavage site instability rule); |
| E) |
30% ≤ GC % ≤ 60%; |
| F) |
Exclusion of target sequence with at least one of AAAA, CCCC, GGGG, or UUUU. |
Notes:
| 1) |
The
starting (ending) position of the target sequence corresponds to
position 19 (1) of the antisense siRNA (i.e., dinucleotide leader and
nt 22 and nt 23 in Tuschl patterns are not considered by us to be part of the target sequence); |
| 2) |
Sense siRNA = target sequence + 3' dTdT overhang; dTdT for both sense and antisense siRNAs can be replaced by UU; |
| 3) |
GC % = GC count in siRNA (excluding overhangs) / 19 x 100%; |
| 4) |
DSSE = stability of 5'-antisense end of 4 base pairs - stability of 5'-sense end of 4 base pairs; the asymmetry rule is enforced by DSSE > 0 (see Schwartz et al. Cell, 115, 199-208, 2003). |
| 5) |
AIS = average of internal
stability values for positions 9-14 of the antisense strand; starting
at a position, the internal stability is for 4 BP stacks; the rule of
relative instability at the cleavage site is enforced by AIS > -8.6
kcal/mol, the midpoint between the minimum of -3.6 and the maximum of -13.6 (see Khvorova et al. Cell, 115, 209-216, 2003). |
| 6) |
Total siRNA duplex score is the
sum of target accessibility score, duplex feature score and duplex
thermodynamics score, with a maximum of 20 points; the accessibility
score is based on antisense siRNA binding energy and has a range of [0,
8]; the duplex feature score is computed with the algorithm by Reynolds
et al. (Nature Biotech., 22,
326-330, 2004), and has a range of [-2, 10]; the duplex thermodynamics
score has a range of [0, 2], with contribution of 1 point for DSSE > 0, and 1 point for AIS > -8.6 kcal/mol. |
|
File sirna_s.out
provides output information for siRNAs with total score greater or
equal to a preset threshold. The current threshold is 12 points.
| ||
| Line 1: | target position |
antisense siRNA (5' → 3') |
| |
5'-antisense stability (AntiS, in kcal/mol) |
|
| 5'-sense stability (SS, in kcal/mol) |
||
| differential stability of siRNA duplex ends (DSSE, in kcal/mol) |
||
| average internal stability at the cleavage site (AIS, in kcal/mol) |
||
| Line 2: | internal stability for antisense positions 1-10 |
|
| Line 3: | internal stability for antisense positions 11-19 |
|
Notes:
| 1) |
AntiS
is computed by a sum of energies for 4 base pair stacks and the 3'
dangling T for the 5' end of the antisense siRNA strand; SS is the sum
for the 5' end of the sense strand; |
| 2) |
DSSE = AntiS - SS; the symmetry rule is enforced by DSSE > 0 (see Schwartz et al. 2003); |
| 3) |
AIS
= average of internal stability values for positions 9-14 of the
antisense strand; starting at a position, the internal stability is for
4 BP stacks; the rule of relative instability at the cleavage site is
enforced by AIS > -8.6 kcal/mol, the midpoint between the minimum of
-3.6 and the maximum of -13.6 (see Khvorova et al. 2003). |
File sstrand.out contains information for probability profiling and for probability-weighted calculations for antisense siRNA binding energy and antisense oligo binding energy:
| Column 1: | nucleotide position i |
| Column 2: | nucleotide |
| Column 3: | complementary nucleotide |
| Column 4: | the probability that nucleotide i is unpaired (i.e., W=1) |
| Column 5: | probability that dinucleotide i and i+1 are both unpaired (i.e., W=2) |
| Column 6: | the probability that nucleotide i, i+1, i+2, and i+3 are all unpaired (i.e., W=4) |
Note:
Column 4 is used for making profile plot for individual bases for ribozyme application.
Column 5 is used for probability weighted calculations of antisense siRNA binding energy and antisense oligo binding energy.
Column 6 is used for probability profiling for single-stranded fragments of 4 bases.
File loopr.out contains information for probability profiling of loops:
| Column 1: | nucleotide position |
| Column 2: | nucleotide |
| Column 3: | the probability that this nucleotide is in a hairpin loop (for Hplot) |
| Column 4: | the probability that this nucleotide is in a bulge loop (for Bplot) |
| Column 5: | the probability that this nucleotide is in an interior loop (for Iplot) |
| Column 6: | the probability that this nucleotide is in a multi-branched loop (for Mplot) |
| Column 7: | the probability that this nucleotide is in the exterior loop (for Extplot) |
| Column 8: | sum of columns 3 through 7 (this is the same as column 4 of file sstrand.out) |
Other output
Links to output from other modules with default input settings are provided.
Output downloading
With the exception of siRNA internal stability profiles, all of the output and sampled structures in Zip or compressed tar (tar.gz) format are available for downloading. After the compressed file has been uncompressed, a directory with the job ID as the name is created under the current directory. Under the job ID directory, there are seven subdirectories and a file readme.txt to describe the files in the seven subdirectories.
Job and system information
Links to information on the job and system usage are provided.
Graphical output
Same as the output for Sirna, except for internal stability profiling for siRNAs.
Text output files
The probability profile displays predicted accessible sites on the target RNA. Because an accessible site can be targeted by a number of antisense oligos, selection of the "optimal" one can be based on binding energy, together with other empirical rules such as GC content, avoidance of GGGG (or more stringent GGG) motifs, etc. Stronger binding is indicated by smaller binding energy (stacking energies are negatively valued). For example, an antisense oligo with a binding energy of -10 kcal/mol is more effective than an oligo with a binding energy of -5 kcal/mol. The antisense oligo binding energy is a weighted sum of the DNA/RNA stacking energies (Sugimoto et al. 1995) for the hybrid formed by the antisense oligo and the targeted sequence. For a base-pair stack, the weight for the sum is calculated by the probability of the unpaired dinucleotide in the target sequence that is involved in the stack. This weighting scheme accounts for the structural variation at the target site among the structures in the sample.
File oligo_f.out gives filtered output for design of antisense oligos:
| Column 1: | target position (starting - ending) |
| Column 2: | target sequence (5' → 3') |
| Column 3: | antisense oligo (5' → 3') |
| Column 4: | GC content |
| Column 5: | oligo binding energy (kcal/mol) |
Filter criteria:
| A) |
40% ≤ GC % ≤ 60%; |
| B) |
Antisense oligo binding energy ≤ -8 kcal/mol; |
| C) |
No GGGG in the target sequence. |
File oligo.out gives complete output for design of antisense oligos:
| Column 1: | target position (starting - ending) |
| Column 2: | target sequence (5' → 3') |
| Column 3: | antisense oligo (5' → 3') |
| Column 4: | GC content |
| Column 5: | oligo binding energy (kcal/mol) |
| Column 6: |
GGGG indicator |
Note:
GGGG indicator=1 for at least one GGGG in the target sequence; indicator=0 otherwise.
Files sstrand.out and loopr.out are the same as described for Sirna.
Graphical output
For every site of the selected cleavage triplet (e.g., GUC) on the target RNA, the probability profile for individual bases (W= 1) is produced for the region that includes the triplet and the two flanking sequences of 15 bases each. Thus, column 4 (not column 5 or 6) of file sstrand.out is used as input data for profiling in ribozyme applications. Sfold does not address the issue of optimal length for flanking sequences (hammerhead's binding arms); the length of 15 bases was selected for the purpose of covering the normal range of length with some cushion. We recommend selection of cleavage sites for which both flanking sequences are at least partially accessible, because antisense hybridization is believed to start with nucleation at a location of several unpaired bases, and then elongation occurs by "unzipping" the adjacent helix on the target (Milner et al. 1997). It is unclear if accessibility of the cleavage triplet is important for cleavage. We note that profiling of the target RNA only addresses the accessibility of the target. It is also important to assess the folding of a designed ribozyme whose binding arms are determined by the cleavage triplet and its flanking sequences. To address the issue of ribozyme folding, the user can run module Srna to fold the ribozyme. Output from this module is helpful for a confidence assessment about the degree of correct ribozyme folding.
Loop profiling is the same as described for Sirna.
Text output files
Files sstrand.out and loopr.out are the same as described for Sirna. The user can examine column 4 of sstrand.out for prediction of other cleavage triplets.
This module provides tools and statistics to statistically characterize the Boltzmann ensemble through the sampled structures.
Representation of the structure sample
A two-dimensional histogram (2Dhist) displays base pair probabilities computed from a statistical sample of structures. In the 2Dhist, base pair probabilities are shown by solid squares in the upper left triangle, with the nucleotide positions on both axes. The areas of the solid squares are proportional to the frequencies of the base pairs in the sampled structures. The current sample size is 1,000 structures, which is sufficiently large for producing stable estimates for 2Dhist and probability profiles (Ding & Lawrence 2001). Of course, the user can experiment with this, by folding the same sequence twice and comparing results to assess the power of statistical sampling.
2Dhist has an option for the display of base pair probabilities. When this is option is selected, the probability and positions of the base pair for a solid square can be shown through mouse pointing. For long RNA sequences, the base pair probabilities take some time to load after the 2Dhist is displayed, we thus have set "no base pair probabilities" as the default display. The lower right triangle could be used to plot the minimum free energy (MFE) structure or any single structure of particular interest. However, particularly for long sequences, a single structure is of little significance from the Boltzmann ensemble perspective. For example, for E. coli RNAase P, which has a moderate length of 377 nt, the MFE structure from mfold 3.1 has a free energy of -173.6 kcal/mol, and its Boltzmann probability is merely 0.000037. For E.coli lacZ, 3113 nt, the MFE is -1234 kcal/mol, and the MFE structure has a Boltzmann probability of 2.84E-49!
The cumulative free energy distribution of sampled structures is similar to the cumulative distribution function (CDF) in probability theory. The MFE in the sample (SMFE) is computed. We note that the SMFE is not necessarily the global MFE for long sequences, because of the MFE structure's small Boltzmann probability and the many competing structures with similar free energies. However, the chance of observing the MFE structure in the sample increases with the size of the sample. For an integer 0 ≤ P ≤ 100, the free energy CDF plots the probability that a structure in the sample has a free energy within P% of the SMFE.
An ad hoc representation of the structure sample is given by a table. First, LFE, the largest free energy of structures in the sample is computed. The free energy range covering all structures in the sample, i.e., [SMFE, LFE], is then divided into ten equally spaced intervals. For each free energy interval, the structure with the lowest free energy is selected as the representative. For the representative, the table presents its associated free energy interval, the frequency with which structures in the sample fall into the energy interval (the frequencies for the ten intervals add up to 1.0), the free energy of the structure, and the secondary structural diagram. The structural diagram is currently available in PNG, PDF, and PostScript formats. The PNG format has the capabilities for enlargement and local display. The structural diagrams are produced with further modifications of the modified naview program (Zuker, Mathews & Turner 1999; Bruccoleri & Heinrich 1988; http://www.bioinfo.rpi.edu/~zukerm/rna/node3.html#SECTION00033). The GCG connect file is also provided. We note that this is a rather crude representation of the structure sample and the Boltzmann ensemble, mainly because structures in a common free energy interval can have substantially different structural features. An appealing method for an efficient statistical presentation of the Boltzmann ensemble is to classify the structures in the sample (Ding & Lawrence 2003). A classification algorithm based on a suitable distance measure is under development.
Text output files
File 2dhist.out contains base pair frequencies for constructing 2Dhist. The first and second column are positions of a base pair; the third column is the number of occurrences in the sample; the last column is the size of the sample (i.e., number of structures generated).
File fe.out gives free energies (in kcal/mol, column 2) for all sampled structures.
File cdf.out is used for constructing the free energy CDF plot.
File pdf.out is a density version of cdf.out. It gives the probability with which structures in the sample will fall into an interval of width 5% with respect to the SMFE. The intervals are, (0%, 5%], ..., (90%, 95%], and (95%, 100%]. The probability of structures with SMFE is computed and is listed in column 2 in line 1 of pdf.out. Starting from line 2, the first column is the upper bound percentage of each interval, and the second column is the associated probability.
The software is based on a statistical sampling algorithm for prediction of RNA secondary structure. The details of the algorithm and its unique capabilities are presented in Ding & Lawrence (2003). The recent Turner free energies (Xia et al. 1998; Mathews et al. 1999) are used in the algorithm, with the exception of co-axial stacking. The extension of the algorithm to a probability profiling algorithm for prediction of target accessibility is reported in Ding & Lawrence (2001). A much simpler sampling algorithm for the stacking energy model is presented in Ding (2002). Bayesian inferences on energy parameters and loop numbers for the stacking energy model are described in Ding & Lawrence (1999).
In research publications, the users of Sfold
are requested to cite the articles describing the algorithms and the
web server (Ding & Lawrence 2003, 2001; Ding, Chan, Lawrence 2004),
in addition to including the web server site http://sfold.wadsworth.org.
RNA structure sampling algorithms and applications
Ding, Y., and Lawrence, C.E. (2003) A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res. 31, 7280-7301.
Ding, Y., and Lawrence, C.E. (2002) Statistical algorithms for folding and target accessibility prediction and design of nucleic acids. Pending U.S. Patent, Wadsworth Center, New York State Department of Health; filed on January 28, 2003 by Frommer Lawrence & Haug LLP, 745 Fifth Avenue, New York, NY 10151, (212) 588-0800. (U.S. Provisional Patent Application 60/352,643, filed on January 29, 2002; law office case # 454311-2230.1 WO)
Ding, Y. (2002) Rational statistical design of antisense oligonucleotides for high throughput functional genomics and drug target validation. Statistica Sinica 12, 273-296.
Ding, Y., and Lawrence, C.E. (2001) Statistical prediction of single-stranded regions in
RNA secondary structure and application to predicting effective antisense target sites an
beyond, Nucleic Acids Res. 29, 1034-1046.
Ding, Y., and Lawrence, C.E. (1999) A Bayesian statistical algorithm for RNA secondary
structure prediction. Computers and Chemistry 23, 387-400.
Target RNA secondary structure/accessibility and potency of siRNAs
Far, R.K. and Sczakiel, G. (2003). The activity of siRNA in mammalian cells is related to structural target accessibility: a comparison with antisense oligonucleotides. Nucleic Acids Research, 31, 4417-4424.
Vickers, T.A., Koo, S., Bennett, C.F., Crooke, S.T., Dean, N.M., Baker, B. (2003) Efficient reduction of target RNAs by small interfering RNA and RNase H-dependent antisense agents. A comparative analysis. J. Biol. Chem. 278, 7108-18.
Bohula, E.A., Salisbury, A.J., Sohail, M., Playford, M.P., Riedemann, J., Southern, E.M.,
Macaulay, V.M. (2003) The efficacy of small interfering RNAs targeted to the type 1 Insulin-like
growth factor receptor (IGF1R) is influenced by secondary structure in the IGF1R transcript. J. Biol. Chem. 278, 15991-7.
Lee, N.S., Dohjima, T., Bauer, G., Li, H., Li, M.J., Ehsani, A., Salvaterra, P., Rossi, J. (2002) Expression of small interfering RNAs targeted against HIV-1 rev transcripts in human cells. Nat. Biotechnol. 20, 500-5.
siRNA duplex thermodynamics and features and rational design of siRNAs
Schwarz, D.S., Hutvagner, G., Du, T., Xu, Z., Aronin, N., Zamore, P.D. (2003) Asymmetry in
the assembly of the RNAi enzyme complex. Cell. 115, 199-208.
Khvorova, A., Reynolds, A., Jayasena, S.D. (2003) Functional siRNAs and miRNAs exhibit
strand bias. Cell. 115, 209-216.
Reynolds, A., Leake, D., Boese, Q., Scaringe, S., Marshall, W.S.,
Khvorova, A. (2004) Rational siRNA design for RNA interference. Nat Biotechnol. 22, 326-30.
Ui-Tei, K., Naito, Y., Takahashi, F., Haraguchi, T., Ohki-Hamazaki, H.,
Juni, A., Ueda, R., Saigo, K. (2004) Guidelines for the selection of
highly effective siRNA sequences for mammalian and chick RNA
interference. Nucleic Acids Res. 32, 936-48.
Amarzguioui, M., Prydz, H. (2004) An algorithm for selection of functional siRNA sequences. Biochem Biophys Res Commun. 316, 1050-8.
Ding, Y. and Lawrence, C.E. (2004) Rational design of siRNAs with the Sfold software. In RNA Interference: from Basic Science to Drug Development, ed. Krishnarao Appasani, Cambridge University Press (PDF available from Sfold Web site).
Turner thermodynamic parameters
Mathews, D.H., Sabina, J., Zuker, M. and Turner, D.H. (1999) Expanded sequence
dependence of thermodynamic parameters provides robust prediction of RNA secondary
structure. J. Mol. Biol. 288, 911-940.
Xia, T., SantaLucia, J. Jr, Burkard, M.E., Kierzek, R., Schroeder, S.J., Jiao, X., Cox, C.,
Turner, D.H. (1998) Thermodynamic parameters for an expanded nearest-neighbor model
for formation of RNA duplexes with Watson-Crick base pairs. Biochemistry 37, 14719-35.
DNA/RNA stacking energy parameters
Sugimoto, N., Nakano, S., Katoh, M., Matsumura, A., Nakamuta, H., Ohmichi, T.,
Yoneyama, M., Sasaki, M. (1995) Thermodynamic parameters to predict stability of
RNA/DNA hybrid duplexes. Biochemistry 34, 11211-6.
Other references
Bruccoleri RE; Heinrich G (1988). An improved algorithm for nucleic acid secondary structure display. Comput. Appl. Biosci. 4, 167-73.
Milner, N., Mir, K.U. and Southern, E.M. (1997). Selecting effective antisense reagents on combinatorial oligonucleotide arrays. Nat. Biotechnol. 15, 537-541.
Zuker, M., Mathews, D.H. and Turner, D.H. (1999). Algorithms and thermodynamics for RNA secondary structure prediction: a practical guide. In, RNA Biochemistry and Biotechnology, 11-43, J. Barciszewski & B.F.C. Clark, eds., NATO ASI Series, Kluwer Academic Publishers, Dordrecht, the Netherlands.