MELTING - nearest-neighbor computation of nucleic acid hybridation

Marine Dumousseau, William John Gowers

Nicolas Le Novère
n.lenovere@gmail.com

Date: February 2014

Contents

• Synopsis
• Description
• Usage
  • Information about MELTING
  • Mandatory options
  • General options
  • Set of thermodynamic parameters and methods (models)
  
  
• Algorithm
  • Thermodynamics of helix-coil transition of nucleic acid
  • The melting temperature
  • Correction for the concentration of nucleic acid
  • Correction for the concentration of cations
  • Correction for the concentration of denaturing agents
  • Long sequences
  
  
• Bibliography
• See Also
• Copyright
• Acknowledgements
• Authors
• History

Synopsis

The nearest-neighbor approach is based on the fact that the helix-coil transition works as a zipper. After an initial attachment, the hybridisation propagates laterally. The hybridization process depends on the adjacent nucleotides on each strand (the Crick's pairs). Two duplexes with the same base pairs could have different stabilities, and on the contrary, two duplexes with different sequences but identical sets of Crick's pairs will have the same thermodynamics properties (see Sugimoto et al. 1994). See Wetmur J.G (1991) and Santalucia (1998) for deep reviews on the nucleic acid hybridization and on the different set of nearest-neighbor parameters.

Description

MELTING computes, for a nucleic acid duplex, the enthalpy and the entropy of the helix-coil transition, and then its melting temperature. Four types of hybridisation are possible: DNA/DNA, DNA/RNA, RNA/RNA and 2-O-Methyl RNA/RNA. The program uses the method of nearest-neighbors. The set of thermodynamic parameters can be easely changed, for instance following an experimental breakthrough. Melting is a free program in both sense of the term. It comes with no cost and it is open-source. In addition it is coded in Java (1.5) and can be compiled on any operating system.

If you use MELTING, please quote

Le Novère. MELTING, a free tool to compute the melting temperature of nucleic acid duplex. Bioinformatics, 17: 1226-1227.

Dumousseau M, Rodriguez N, Juty N, Le Novère N. MELTING, a flexible platform to predict the melting temperatures of nucleic acids. BMC Bioinformatics, 16;13:101, PMID: 22591039.

Usage

The options are treated sequentially. If there is a conflict between the value of two options, the latter normally erases the former.

BE AWARE : The option syntax of MELTING 5 is different from the one of MELTING 4. There is a space between the option name and the option value. New option names are available in MELTING 5 to change the default thermodynamic models and default corrections.
There is no interactive mode in MELTING 5 therefore the option '-q' doesn't exist anymore.
You can use the MELTING 4 option syntax, but it doesn't allow the user to change some of the thermodynamic models and corrections. In addition to that, the user can't enter a formamide or DMSO See the README file to choose the adapted executable.
The MELTING 4 option name '-x' is equivalent to the MELTING 5 option name '-am'.
There is no input file option in MELTING 5 (option '-I') but you can use this option for the compatible executable of MELTING 5.
The MELTING 4 option names '-N', '-t', '-k', 'G' are replaced by the single option '-E' in MELTING 5.
The MELTING 4 option names '-A', '-D', '-M' are respectively equivalent to '-nn', '-sinDE', '-sinMM' in MELTING 5.
The file names to write with the precedent option are replaced by thermodynamic model names (see below).
The MELTING 4 option name '-K' is replaced by '-ion' in MELTING 5.

Information about MELTING

-h

Displays a short help and quit.

-L

Prints the legal informations and quit.

-V

Displays the version number and quit.

-p

Return the directory supposed to contain the sets of calorimetric parameters and quit. If the environment variable NN_PATH is set, it is returned. Otherwise, the value defined by default during the compilation is returned.

Mandatory options

-S sequence

Sequence of one strand of the nucleic acid duplex, entered 5' to 3'. Important: Uridine and thymidine are not considered as identical. The bases can be upper or lowercase.

-C complementary_sequence

Enters the complementary sequence, from 3' to 5'. This option is mandatory if there are mismatches, inosine(s) or hydroxyadenine(s) between the two strands. If it is not used, the program will compute it as the complement of the sequence entered with the option -S. In case of self complementary sequences, The program can automatically detect the symmetry and deduce the complementary even though there is (are) dangling end(s) and it is not necessary to write the complementary sequence with the option -C. Uridine and thymidine are not considered as identical. The bases can be upper or lowercase.

-E ion1_name=x.xxe-xx:ion2_name=x.xxe-xx:agent1_name=x.xxe-xx...

Enters the different ion (Na, Mg, Tris, K) or agent (dNTP, DMSO, formamide) concentrations. The effect of ions and denaturing agents on thermodynamic stability of nucleic acid duplexes is complex, and the correcting functions are at best rough approximations. All the concentrations must be positive numeric values and in M. There are some exceptions for the DMSO concentrations (in %) and the formamide concentrations (in % or M depending on the used correction method). Be aware, the $[$Tris$^+]$ is about half of the total tris buffer concentration. At least one cation concentration is mandatory, the other agents are optional. See the documentation for the concentration limits. It depends on the used correction.

-P x.xxe-xx

Concentration of the nucleic acid strand in excess. It must be a strict positive numeric value and it is mandatory. The oligomer concentration is in mol/L.

-H hybridisation_type

Specifies the hybridisation type. Moreover this parameter determines the nature of the sequences entered by the user. Possible values are :

dnadna

: DNA sequence (option -S) and DNA complementary sequence (option -C)

rnarna

: RNA sequence (option -S) and RNA complementary sequence (option -C)

dnarna

: DNA sequence (option -S) and RNA complementary sequence (option -C)

rnadna

: RNA sequence (option -S) and DNA complementary sequence (option -C)

mrnarna

: 2-o-methyl RNA sequence (option -S) and RNA complementary sequence (option -C)

mrnarna

: RNA sequence (option -S) and 2-o-methyl RNA complementary sequence (option -C)

This option is mandatory to select the default equations and methods to use.

General options

-T xxx

Size threshold before approximative computation. The nearest-neighbour approach will be used by default if the length of the sequence is inferior to this threshold, otherwise it is the approximative approach which will be used by default.

-v

Activates the verbose mode, issuing a lot more information about the current run (try it once to see if you can get something interesting).

-nnpath folder_pathway

Change the default pathway (Data) where to find the default calorimetric tables (thermodynamic parameters). The program will look for the file in a directory specified during the installation. However, if an environment variable NN_PATH is defined, melting will search in this one first.

-O output_file

The output is directed to this file instead of the standard output. The name of the file must be specified.

-self

To precise that the sequence entered with the option -S is self complementary. No complementary sequence is mandatory. The program automatically can detect a self complementary sequence for perfect matching sequences or sequences with dangling ends. In these cases, the option -self is not necessary. Otherwise we need to precise that the sequences are self complementary with this option. examples:

  Situation 1 : The sequence ATCGCGAT is self 
                complementary.

The option -self is not necessary because the program can automatically detect it.

  Situation 2 : The sequence -TCGCGAT is self 
                complementary with a single 
		dangling end.

The option -self is not necessary because the program can automatically detect it.

  
  Situation 3 :  If the sequence ATCCCGAT is self 
                 complementary with a single mismatch 
		(C/C)

The option -self is necessary to precise the self complementarity because the program can't detect it.

-F factor

This is the correction factor used to modulate the effect of the nucleic acid concentration in the computation of the melting temperature. See section ALGORITHM for details. If the sequences are automatically recognized as self complementary sequences or if the option -self is used, the factor correction is automatically 1. Otherwise F is 4 if the both strands are present in equivalent amount and 1 if one strand is in excess. The default factor value is 4.

Set of thermodynamic parameters and methods (models)

By default, the approximative mode is used for oligonucleotides longer than 60 bases (the default threshold value), otherwise the nearest neighbor model is used.

-am method_name

Forces to use a specific approximative formula, based on G+C content. You can use one of the following :

DNA DUPLEXES

ahs01

(from von Ahsen et al. 2001)

che93

(from Marmur 1962,, Chester and al. 1993)

che93corr

(from von Ahsen et al. 2001, Marmur 1962, Chester and al. 1993)

schdot

(Marmur-Schildkraut-Doty formula)

owe69

(from Owen et al. 1969)

san98

(from Allawi and Santalucia. 1998)

wetdna91

(from Wetmur 1991) (by default)

RNA DUPLEXES

wetrna91

(from Wetmur 1991) (by default)

DNA/RNA DUPLEXES

wetdnarna91

(from Wetmur 1991) (by default)

If there is no formula name after the option -am, we will compute the melting temperature with the default approximative formula. This option has to be used with caution. Note that such a calcul is increasingly incorrect when the length of the duplex decreases. Moreover, it does not take into account nucleic acid concentration, which is a strong mistake. examples :

   command line 1 : "-am"

if you want to force the approximative approach with the default formula.

   command line 2 : "-am ahs01"

if you want to use the approximative formula from Ahsen et al. 2001.

-nn method_name

Forces to use a specific nearest neighbor model. You can use one of the following :

DNA DUPLEXES

all97

(from Allawi and Santalucia 1997) (by default)

bre86

(from Breslauer et al. 1986)

san04

(from Hicks and Santalucia 2004)

san96

(from Santalucia et al. 1996)

sug96

(from Sugimoto et al 1996)

tan04

(from Tanaka et al. 2004)

RNA DUPLEXES

fre86

(from Freier al. 1986)

xia98

(from Xia et al. 1998) (by default)

DNA/RNA DUPLEXES

sug95

(from Sugimoto et al. 1995) (by default)

MRNA/RNA DUPLEXES

tur06

(from Kierzek et al. 2006) (by default)

If there is no formula name after the option -nn, we will compute the melting temperature with the default nearest neighbor model. Each nearest neighbor model uses a specific xml file containing the thermodynamic values. If you want to use another file, write the file name or the file pathway preceded by ':' (-nn [optionalname:optionalfile]). examples:

  Command line 1 : "-nn"

if you want to force the nearest neighbor computation with the default model.

  Command line 2 : "-nn tan04"

if you want to use the nearest neighbor model from Tanaka et al. 2004 with the thermodynamic parameters in the default xml file.

  Command line 3 : "-nn tan04:fileName"

if you want to use the nearest neighbor model from Tanaka et al. 2004 with the thermodynamic parameters in the file fileName.

  Command line 4 : "-nn :fileName"

if you want to use the default nearest neighbor model with the thermodynamic parameters in the file fileName.

-sinMM method_name

Forces to use a specific nearest neighbor model to compute the contribution of single mismatch to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

allsanpey

(from Allawi, Santalucia and Peyret 1997, 1998 and 1999) (by default)

DNA/RNA DUPLEXES

wat10

(from Watkins et al. 2011) (by default)

RNA DUPLEXES

tur06

(from Lu et al. 2006)

zno07

(from Davis et al. 2007) (by default)

zno08

(from Davis et al. 2008)

To change the file containing the thermodynamic parameters for single mismatch computation, the same syntax as the one for the -nn option is used. Single mismatches are not taken into account by the approximative mode.

-GU method_name

Forces to use a specific nearest neighbor model to compute the contribution of GU base pairs to the thermodynamic of helix-coil transition. You can use one of the following :

RNA DUPLEXES

tur99

(from Mathews et al. 1999)

ser12

(from Serra et al. 2012) (by default)

To change the file containing the thermodynamic parameters for GU base pair computation, the same syntax as the one for the -nn option is used. GU base pairs are not taken into account by the approximative mode.

-tanMM method_name

Forces to use a specific nearest neighbor model to compute the contribution of tandem mismatches to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

allsanpey

(from Allawi, Santalucia and Peyret 1997, 1998 and 1999) (by default)

RNA DUPLEXES

tur99

(from Mathews et al. 1999) (by default)

To change the file containing the thermodynamic parameters for tandem mismatch computation, the same syntax as the one for the -nn option is used. Tandem mismatches are not taken into account by the approximative mode. Note that not all the mismatched Crick's pairs have been investigated.

-intLP method_name

Forces to use a specific nearest neighbor model to compute the contribution of internal loop to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

san04

(from Hicks and Santalucia 2004) (by default)

RNA DUPLEXES

tur06

(from Lu et al. 2006) (by default)

zno07

(from Badhwar et al. 2007, only for 1x2 loop)

To change the file containing the thermodynamic parameters for internal loop computation, the same syntax as the one for the -nn option is used. Internal loops are not taken into account by the approximative mode.

-sinDE method_name

Forces to use a specific nearest neighbor model to compute the contribution of single dangling end to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

bom00

(from Bommarito et al. 2000) (by default)

sugdna02

(from Ohmichi et al. 2002, only for polyA dangling ends)

RNA DUPLEXES

sugrna02

(from Ohmichi et al. 2002, only for polyA dangling ends)

ser08

(from Miller et al. 2008) (by default)

To change the file containing the thermodynamic parameters for single dangling end computation, the same syntax as the one for the -nn option is used. Single dangling ends are not taken into account by the approximative mode.

-secDE method_name

Forces to use a specific nearest neighbor model to compute the contribution of double dangling end to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

sugdna02

(from Ohmichi et al. 2002, only for polyA dangling ends) (by default)

RNA DUPLEXES

sugrna02

(from Ohmichi et al. 2002, only for polyA dangling ends)

ser05

(from O'toole et al. 2005)

ser06

(from O'toole et al. 2006) (by default)

To change the file containing the thermodynamic parameters for double dangling end computation, the same syntax as the one for the -nn option is used. Double dangling ends are not taken into account by the approximative mode.

-longDE method_name

Forces to use a specific nearest neighbor model to compute the contribution of long dangling end to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

sugdna02

(from Ohmichi et al. 2002, only for polyA dangling ends) (by default)

RNA DUPLEXES

sugrna02

(from Ohmichi et al. 2002, only for polyA dangling ends)

To change the file containing the thermodynamic parameters for long dangling end computation, the same syntax as the one for the -nn option is used. Long dangling ends are not taken into account by the approximative mode.

-sinBU method_name

Forces to use a specific nearest neighbor model to compute the contribution of single bulge loop to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

san04

(from Santalucia 2004)

tan04

(from Tanaka et al. 2004) (by default)

RNA DUPLEXES

ser07

(from Blose et al. 2007)

tur06

(from Lu et al. 1999 and 2006) (by default)

To change the file containing the thermodynamic parameters for single bulge loop computation, the same syntax as the one for the -nn option is used. Single bulge loops are not taken into account by the approximative mode.

-lonBU method_name

Forces to use a specific nearest neighbor model to compute the contribution of long bulge loop to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

san04

(from Hicks and Santalucia 2004) (by default)

RNA DUPLEXES

tur06

(from Mathews et al. 1999 and Lu et al 2006) (by default)

To change the file containing the thermodynamic parameters for long bulge loop computation, the same syntax as the one for the -nn option is used. Long bulge loops are not taken into account by the approximative mode.

-CNG method_name

Forces to use a specific nearest neighbor model to compute the contribution of CNG repeats to the thermodynamic of helix-coil transition. N represents a single mismatch of type N/N. You can use one of the following :

RNA DUPLEXES

bro05

(from Magdalena et al. 2005) (by default)

To change the file containing the thermodynamic parameters for CNG repeats computation, the same syntax as the one for the -nn option is used. CNG repeats are not taken into account by the approximative mode. Be aware : Melting can compute the contribution of CNG repeats to the thermodynamic of helix-coil transition for only 2 to 7 CNG repeats.

-ino method_name

Forces to use a specific nearest neighbor model to compute the contribution of inosine bases (I) to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

san05

(from Watkins and Santalucia 2005) (by default)

RNA DUPLEXES

zno07

(from Wright et al. 2007, only IU base pairs) (by default)

To change the file containing the thermodynamic parameters for inosine bases computation, the same syntax as the one for the -nn option is used. Inosine bases (I) are not taken into account by the approximative mode.

-ha method_name

Forces to use a specific nearest neighbor model to compute the contribution of hydroxyadenine bases (A*) to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

sug01

(from Kawakami et al. 2001) (by default)

To change the file containing the thermodynamic parameters for hydroxyadenine bases computation, the same syntax as the one for the -nn option is used. Hydroxyadenine bases (A*) are not taken into account by the approximative mode.

-azo method_name

Forces to use a specific nearest neighbor model to compute the contribution of azobenzenes (X_T for trans azobenzenes and X_C for cis azobenzenes) to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

asa05

(from Asanuma et al. 2005)(by default)

To change the file containing the thermodynamic parameters for azobenzene computation, the same syntax as the one for the -nn option is used. Azobenzenes (X_T for trans azobenzenes and X_C for cis azobenzenes) are not taken into account by the approximative mode.

-lck method_name

Forces to use a specific nearest neighbor model to compute the contribution of single locked nucleic acids (AL, GL, TL and CL) to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

mct04

(from McTigue et al. 2004)

owc11

(from Owczarzy et al. 2011) (by default)

To change the file containing the thermodynamic parameters for single locked nucleic acids computation, the same syntax as the one for the -nn option is used. Locked nucleic acids (AL, GL, TL and CL) are not taken into account by the approximative mode.

-tanLck method_name

Forces to use a specific nearest neighbor model to compute the contribution of consecutive locked nucleic acids (AL, GL, TL and CL) to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

owc11

(from Owczarzy et al. 2011) (by default)

To change the file containing the thermodynamic parameters for consecutive locked nucleic acids computation, the same syntax as the one for the -nn option is used. Locked nucleic acids (AL, GL, TL and CL) are not taken into account by the approximative mode.

-sinMMLck method_name

Forces to use a specific nearest neighbor model to compute the contribution of single mismatch in consecutive locked nucleic acids (AL, GL, TL and CL) to the thermodynamic of helix-coil transition. You can use one of the following :

DNA DUPLEXES

owc11

(from Owczarzy et al. 2011) (by default)

To change the file containing the thermodynamic parameters for single mismatch in consecutive locked nucleic acids computation, the same syntax as the one for the -nn option is used. Locked nucleic acids (AL, GL, TL and CL) are not taken into account by the approximative mode.

-ion method_name

Forces to use a specific ion correction. You can use one of the following corrections :

Sodium corrections

DNA DUPLEXES

ahs01

(from von Ahsen et al. 2001)

kam71

(from Frank-Kamenetskii 2001)

owc1904

(equation 19 from Owczarzy et al. 2004)

owc2004

(equation 20 from Owczarzy et al. 2004)

owc2104

(equation 21 from Owczarzy et al. 2004)

owc2204

(equation 21 from Owczarzy et al. 2004) (by default)

san96

(from Santalucia et al. 1996)

san04

(from Santalucia et al. 1998, 2004)

schlif

(from Schildkraut and Lifson 1965)

tanna06

(from Tan et al. 2006)

wetdna91

(from wetmur 1991)

RNA DUPLEXES OR MRNA/RNA DUPLEXES

tanna07

(from Tan et al. 2007) (by default)

wetrna91

(from wetmur 1991)

DNA/RNA DUPLEXES

wetdnarna91

(from wetmur 1991)

Magnesium corrections

DNA DUPLEXES

owcmg08

(from Owczarzy et al. 2008) (by default)

tanmg06

(from Tan et al. 2006)

RNA DUPLEXES OR MRNA/RNA DUPLEXES

tanmg07

(from Tan et al. 2007) (by default)

Mixed Na Mg corrections

DNA DUPLEXES

owcmix08

(from Owczarzy et al. 2008) (by default)

tanmix07

(from Tan et al. 2007)

RNA DUPLEXES OR MRNA/RNA DUPLEXES

tanmix07

(from Tan et al. 2007) (by default)

The effect of ions on thermodynamic stability of nucleic acid duplexes is complex, and the correcting functions are at best rough approximations. By default, the program use the algorithm from Owczarzy et al 2008 : ratio = $[$Mg$^{0.5}]$ and monovalent = Na + Tris + K

if monovalent = 0, a magnesium correction is used.

if ratio < 0.22, a sodium correction is used.

if 0.22 <= ratio < 6, a mixed Na Mg correction is used.

if ratio >= 6, a magnesium correction is used.

example :

  Command line : "-ion owcmg08"

if you want to force the use of the magnesium correction from Owczarzy et al 2008. This correction will be used independently of the cations present in the solution.

-naeq method_name

Forces to use a specific ion correction which gives a sodium equivalent concentration if other cations are present. You can use one of the following :

DNA DUPLEXES

ahs01

(from von Ahsen et al 2001) (by default)

mit96

(from Mitsuhashi et al. 1996)

pey00

(from Peyret 2000)

For the other types of hybridization, the DNA default correction is used but there is no guaranty of accuracy. If there are other cations when an approximative approach is used, a sodium equivalence is automatically computed. The correcting functions are at best rough approximations. example :

  Command line 1 : "-naeq ahs01"

if you want to force the use of the sodium equivalence from Ahsen et al 2001. This sodium equivalence will be used in case of approximative approach. In case of nearest neighbor approach, the sodium equivalence will be used only if a sodium correction is selected by the user.

  Command line 2 : "-naeq ahs01 -ion san04"

it means that the sodium equivalence computed by the method ahs01 (from Ahsen et al 2001) will be combined with the sodium correction san04 (from Santalucia 2004).

-DMSO method_name

Forces to use a specific DMSO correction (DMSO is always in %). You can use one of the following :

DNA DUPLEXES

ahs01

(from von Ahsen et al 2001) (by default)

mus81

(from Musielski et al. 1981)

cul76

(from Cullen et al. 1976)

esc80

(from Escara et al. 1980)

For the other types of hybridization, the DNA default correction is used but there is no guaranty of accuracy. If there are DMSO when an approximative approach is used, a DMSO correction is automatically computed. The correcting functions are at best rough approximations. example :

  Command line : "-DMSO ahs01"

if you want to force the use of the DMSO correction from Ahsen et al 2001. This DMSO correction will be used if there is DMSO present in the solutions in case of nearest neighbor approach and approximative approach.

-for method_name

Forces to use a specific formamide correction. You can use one of the following :

DNA DUPLEXES

bla96

(from Blake 1996) with formamide concentration in mol/L (by default)

lincorr

(linear correction) with a % of formamide volume

For the other types of hybridization, the DNA default correction is used but there is no guaranty of accuracy. If there are formamide when an approximative approach is used, a formamide correction is automatically computed. The correcting functions are at best rough approximations. example :

  Command line : "-for lincorr"

if you want to force the use of the linear formamide correction. This formamide correction will be used if there is formamide present in the solutions in case of nearest neighbor approach and approximative approach.

Algorithm

Thermodynamics of helix-coil transition of nucleic acid

The nearest-neighbor approach is based on the fact that the helix-coil transition works as a zipper. After an initial attachment, the hybridisation propagates laterally. This program first computes the hybridisation enthalpy and entropy for each structure in the duplex. (see later for the different possible structures recognized by Melting). If the sequences are self complementary, a symmetry correction will be added to the initiation energy.

$$\begin{array}[t]{ccc} \Delta{}H&=&\delta{}h_\mathrm{initiation}+... ...&=&\delta{}s_\mathrm{initiation}+\sum \delta{}s_\mathrm{structure} \end{array}$$

Example :

Sequence with a single mismatch

ATCGGCTA
TAGACGAT

$$\begin{array}[t]{ccc} \Delta{}H&=&\delta{}h_\mathrm{initiation}+... ...ture1}+\delta{}s_\mathrm{structure2}+\delta{}s_\mathrm{structure3} \end{array}$$

where :

structure1 = perfectly matching sequences ATC/TAG

structure2 = single mismatch G/A

structure 3 = perfectly matching sequences GCTA/CGAT

Perfectly matching sequences

The hybridization process depends on the adjacent nucleotides on each strand (the Crick's pairs). Two duplexes with the same base pairs could have different stabilities, and on the contrary, two duplexes with different sequences but identical sets of Crick's pairs will have the same thermodynamics properties. This program first computes the hybridisation enthalpy and entropy from the elementary parameters of each Crick's pair.

$$\begin{array}[t]{ccc} \Delta{}h_\mathrm{perfectly-matching}&=&\s... ...\mathrm{perfectly-matching}&=&\sum \delta{}s_\mathrm{Crick's pair} \end{array}$$

The initiation computation is not the same for each following model.

model	limits	Article
all97	DNA	Allawi and SantaLucia (1997)
		Biochemistry 36 : 10581-10594
bre86	DNA	Breslauer et al. (1986)
		Proc Natl Acad Sci USA 83 : 3746-3750
san04	DNA	Santalucia and Hicks (2004)
		Annu. Rev. Biophys. Biomol. Struct 33 : 415-440
san96	DNA	SantaLucia et al.(1996)
		Biochemistry 35 : 3555-3562
sug96	DNA	Sugimoto et al. (1996)
		Nuc Acids Res 24 : 4501-4505
tan04	DNA	Tanaka et al (2004)
		Biochemistry 43 : 7143-7150
fre86	RNA	Freier et al (1986)
		Proc Natl Acad Sci USA 83: 9373-9377
xia98	RNA	Xia et al (1998)
		Biochemistry 37: 14719-14735
sug95	DNA/RNA	SantaLucia et al.(1996)
		Biochemistry 35 : 3555-3562
tur06	mRNA/RNA	Kierzeck et al (2006)
	A sodium	Nucleic acids research 34: 3609-3614
	correction (san04)
	is automatically
	applied to
	the computed
	entropy to
	convert the
	entropy (Na = 0.1M)
	into the
	entropy (Na=1M)

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{AGCGA}} \choose \mbox{\texttt{TCGCT}}}... ...}} } + \Delta H {\mbox{\texttt{GA}} \choose \mbox{\texttt{CT}} } \end{multline*}$$

(The same computation is performed for $\Delta S$)

Figure: Comparison of experimental and computed Tm for various sets of DNA nearest-neighbor parameters. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 4\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA nearest-neighbor parameters. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 2\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of DNA/RNA nearest-neighbor parameters. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of 2-O-methyl RNA nearest-neighbor parameters. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Sequences composed of CNG repeats

If the sequence (sens 5'3') is a sequence of type G(CNG)xC where x is the number of CNG repeats in the sequence and N a unique nucleic acid which will get bound to itself, we can use specific experimental parameters to compute the enthalpy and entropy of the duplex formation. These parameters can be used only for sequences composed from 2 to 7 CNG repeats and the initiation is already included.

$$\begin{array}[t]{ccc} \Delta{}H&=&\Delta{}h_\mathrm{sequence-of-type-\texttt{G(CNG)xC}}\\ \end{array}$$

For further information, see the referenced article.

model	limits	Article
bro05	RNA	Magdalena et al (2005)
	Self complementary sequences	Biochemistry 44: 10873-10882
	2 to 7 CNG repeats

Example :

GCAGCAGCAGC
CGACGACGACG

$$\begin{multline*} \Delta H {\mbox{\texttt{GCAGCAGCAGC}} \choose \mbox{\texttt{CGACGACGACG}}} = \Delta H {(\mbox{3-CAG-repeats})} \end{multline*}$$

(The same computation is performed for $\Delta S$)

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences composed of CNG repeats. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Be aware : The results for sequences composed of 4 or 5 CCG repeats is not reliable. (the figure shows two values far from the expected temperature). This might be due to a majority of hairpin loop formation. See the article above for further informations.

Single mismatch effect

The single mismatches are taken into account but the two first and positions cannot be mismatched. in such a case, the result is unpredictable, and all cases are possible. for instance (see Allawi and SanLucia 1997), the duplex

A          T  
 GTGAGCTCAT  
 TACTCGAGTG  
T          A   

is more stable than

AGTGAGCTCATT
TTACTCGAGTGA

For DNA duplexes, this program computes the hybridisation enthalpy and entropy from the elementary parameters of each Crick's pair containing the single mismatch.

$$\begin{array}[t]{ccc} \Delta{}h_\mathrm{single-mismatch}&=&\sum \delta{}h_\mathrm{Crick's-pair-containing-the-mismatch}\\ \end{array}$$

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{ATC}} \choose \mbox{\texttt{TCG}}} = ... ...+ \Delta H {\mbox{\texttt{TC}} \choose \mbox{\texttt{CG}} } \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing one single mismatch. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 4\cdot{}10^{-4}$ M

For DNA/RNA duplexes, the same model is used, taking parameters from Watkins et al. (2011). The only mismatches permitted are dA/rA, dT/rU, dC/rC and dG/rG.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{CAT}} \choose \mbox{\texttt{GAU}}} = ... ... + \Delta H {\mbox{\texttt{AT}} \choose \mbox{\texttt{AU}} } \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

Figure: Comparison of experimental and computed Tm for various sets of DNA/RNA sequences containing one single mismatch. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 4\cdot{}10^{-4}$ M

For RNA duplexes, the different models to computes the thermodynamic contribution of single mismatch to the helix coil stability are more complex.

Model from Amber R. Davis and Brent M Znosco, 2007-2008

$$\begin{multline*} \Delta h {(\mbox{single-mismatch})} = \delta{}h_\mathrm{misma... ..._\mathrm{mismatch-NN-interaction} + \delta{}h_\mathrm{AU/GU} \\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{mismatch-nucleotides}$ accounts for the identity of the single mismatch nucleotides.

$\delta{}h_\mathrm{mismatch-NN interaction}$ accounts for the interaction between the mismatch nucleotides and the nearest neighbors. (R purine, Y pyrimidine)

$\delta{}h_\mathrm{AU/GU}$ accounts for AU or GU nearest neighbors.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{AUC}} \choose \mbox{\texttt{UUG}}} = ... ... \Delta H {\mbox{\texttt{RYY}} \choose \mbox{\texttt{YYR}} } \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

Model from Zhi Johm Lu, Douglas H. Turner and David H. Mathews, 2006

$$\begin{multline*} \Delta h {(\mbox{single-mismatch})} = \delta{}h_\mathrm{initia... ...per-AU/GU} + \delta{}h_\mathrm{GG} + \delta{}h_\mathrm{RU/YU}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{initiation-loop-of-2}$ accounts for the initiation of a single non canonical pair.

$\delta{}h_\mathrm{GG}$ accounts for a GG single mismatch.

$\delta{}h_\mathrm{RU/YU}$ accounts for a 5'RU/3'YU stack with R a purine and Y a pyrimidine.

$\delta{}h_\mathrm{per-AU/GU}$ accounts for AU or GU nearest neighbors.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{AUC}} \choose \mbox{\texttt{UUG}}} = \... ... + \Delta H {\mbox{\texttt{RU}} \choose \mbox{\texttt{YU}} } \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
allsanpey	DNA	Allawi and SantaLucia (1997)
		Biochemistry 36: 10581-10594
		Allawi and SantaLucia (1998)
		Biochemistry 37: 2170-2179
		Allawi and SantaLucia (1998)
		Nuc Acids Res 26: 2694-2701
		Allawi and SantaLucia (1998)
		Biochemistry 37: 9435-9444
		Peyret et al. (1999)
		Biochemistry 38: 3468-3477
wat11	DNA/RNA	Watkins et al. (2011)
tur06	RNA	Lu et al (2006)
		Nucleic Acids Research 34: 4912-4924
zno07	RNA	Davis and Znosko (2007)
		Biochemistry 46: 13425-13436
zno08	RNA	Davis and Znosko (2008)
	at least	Biochemistry 47: 10178-10187
	one adjacent
	GU base pair

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing one single mismatch. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Tandem mismatches effect

The tandem mismatches (two adjacent mismatches) are taken into account but the two first and positions cannot be mismatched. Moreover the thermodynamic parameters are still not available for every possible cases. In such a case, the program, unable to compute any relevant result, will quit with a warning.

For DNA duplexes, this program computes the hybridisation enthalpy and entropy from the elementary parameters of each Crick's pair containing the mismatch(es).

$$\begin{multline*} \Delta{}h_\mathrm{tandem-mismatch} = \delta{}h_\mathrm{Crick's... ... \sum \delta{}h_\mathrm{Crick's-pair-containing-single-mismatch} \end{multline*}$$

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{ATGC}} \choose \mbox{\texttt{TCAG}}} =... ...+ \Delta H {\mbox{\texttt{GC}} \choose \mbox{\texttt{AG}} } \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing one tandem mismatch. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 4\cdot{}10^{-4}$ M

For RNA duplexes, the different models to computes the thermodynamic contribution of tandem mismatch to the helix coil stability are more complex.

Symmetric tandem mismatches : Model from Zhi Johm Lu, Douglas H. Turner and David H. Mathews, 2006

$$\begin{multline*} \Delta h {(\mbox{tandem-mismatch})} = \delta{}h_\mathrm{tandem-mismatch+closing-base-pairs} \\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{mismatch-nucleotides}$ accounts for the identity of the double mismatch nucleotides and the identity of the base pairs adjacent to the tandem mismatches.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{G AC C}} \choose \mbox{\texttt{C CA G}... ...mbox{\texttt{AC}} \choose \mbox{\texttt{CA}}} -adjacent-to-GC\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

Asymmetric tandem mismatches : Model from Zhi Johm Lu, Douglas H. Turner and David H. Mathews, 2006

$$\begin{multline*} \Delta h {(\mbox{tandem-mismatch})} = ( \delta{}h_\mathrm{symm... ...ex-2} )}{2} + \delta{}h_\mathrm{GG} + \delta{}h_\mathrm{p}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{symmetric-duplex-1}$ accounts for the enthalpy of a symmetric tandem mismatch composed of the first closing base pair and the first mismatch nucleotides.

$\delta{}h_\mathrm{symmetric-duplex-2}$ accounts for the enthalpy of a symmetric tandem mismatch composed of the second closing base pair and the second mismatch nucleotides.

$\delta{}h_\mathrm{GG}$ accounts for a GG pair adjacent to a AA pair or any non canonical pair containing a pyrimidine.

$\delta{}h_\mathrm{p}$ accounts for an AG or GA pairs adjacent to a UC, CC or CU pair and a UU pair adjacent to an AA pair .

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{A GC C}} \choose \mbox{\texttt{U AU G}... ...lta H {\mbox{\texttt{GA}} -adjacent-to- \mbox{\texttt{CU}} } \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
allsanpey	DNA	Allawi and SantaLucia (1997)
	only GT	Biochemistry 36: 10581-10594
	mismatches	Allawi and SantaLucia (1998)
	and TA/TG	Biochemistry 37: 2170-2179
	mismatches	Allawi and SantaLucia (1998)
		Nuc Acids Res 26: 2694-2701
		Allawi and SantaLucia (1998)
		Biochemistry 37: 9435-9444
		Peyret et al. (1999)
		Biochemistry 38: 3468-3477
tur99	RNA	Mathiews et al (1999)
	no adjacent	J.Mol.Biol. 288: 911-940
	GU or UG base
	pairs

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing one tandem mismatch. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Internal loop effect

The internal loops (more than two adjacent mismatches) are taken into account but the two first and positions cannot be mismatched. Moreover the thermodynamic parameters are still not available for every possible cases. In such a case, the program, unable to compute any relevant result, will quit with a warning. Moreover, the thermodynamics of the nucleic acids within the internal loop are salt independent and no salt correction will be applied to it. However, the thermodynamics of the terminal mismatches are salt dependent and a salt correction will be applied to them. The thermodynamic model for DNA and RNA duplexes are similar.

DNA duplexes :Model from John Santalucia, Jr. and Donald Hicks, 2004

$$\begin{multline*} \Delta h {(\mbox{internal-loop(n)})} = \delta{}h_\mathrm{asymm... ...nal-mismatch} + \delta{}s_\mathrm{right-terminal-mismatch}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{internal-loop(n)}$ accounts for the internal loop of n nucleotides.

$\delta{}h_\mathrm{asymmetry}$ accounts for the internal loop asymmetry (when the number of nucleic acid within the internal loop is higher in one of the strand).

$\delta{}h_\mathrm{left-terminal-mismatch}$ accounts for the identity of the first mismatch nucleotides of the loop.

$\delta{}h_\mathrm{right-terminal-mismatch}$ accounts for the identity of the last mismatch nucleotides of the loop.

Example : Symmetric internal loop

$$\begin{multline*} \Delta H {\mbox{\texttt{G ACCG C}} \choose \mbox{\texttt{C CAT... ...}} + \Delta S {\mbox{\texttt{GC}} \choose \mbox{\texttt{AG}}}\\ \end{multline*}$$

RNA duplexes :Model from Zhi Johm Lu, Douglas H. Turner and David H. Mathews, 2006

$$\begin{multline*} \Delta h {(\mbox{internal-loop(n)})} = \delta{}h_\mathrm{initi... ...{asymmetry} + \delta{}h_\mathrm{first-non-canonical-pairs}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{initiation-loop(n)}$ accounts for the internal loop of n nucleotides.

$\delta{}h_\mathrm{asymmetry}$ accounts for the internal loop asymmetry (when the number of there is an unequal numbers of nucleotides on each side) with n1 and n2 the number of nucleotides on each strand..

$\delta{}h_\mathrm{per_AU/GU}$ accounts for each AU or GU base pair adjacent to the internal loop.

$\delta{}h_\mathrm{first-non-canonical-pairs}$ accounts for each sequence specific first mismatch (bonus). It is not applied to loops of the form 1 x (n-1) with n > 2.

Example : asymmetric internal loop

$$\begin{multline*} \Delta H {\mbox{\texttt{A ACCG C}} \choose \mbox{\texttt{U C-U... ...{\mbox{\texttt{per-AU}}} + (4 - 3)\Delta H {\mbox{asymmetry}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
san04	DNA	Santalucia and Hicks (2004)
	missing asymmetry	Annu. Rev. Biophys. Biomol. Struct 33 : 415-440
	penalty,
	not tested
	with experimental
	results
tur06	RNA	Lu et al (2006)
	not tested	Nucleic Acids Research 34: 4912-4924
	with experimental
	results

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing one 1x2 internal loop. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

GU wobble base pairs effect

The wobble GU base pairs are taken into account. This pairing is a non-Watson-Crick base pairing between two nucleotides in RNA molecules, but the thermodynamic stability of a wobble base pair is comparable to that of a Watson-Crick base pair. Melting can also compute the thermodynamic of patterns with several adjacent GU base pairs. This program computes the hybridisation enthalpy and entropy from the elementary parameters of each Crick's pair containing the GU base pairs.

$$\begin{array}[t]{ccc} \Delta{}h_\mathrm{pattern-composed-of-GU-b... ...=&\sum \delta{}h_\mathrm{Crick's pair-containing-GU-base-pairs}\\ \end{array}$$

Examples : One GU base pair

$$\begin{multline*} \Delta H {\mbox{\texttt{GUC}} \choose \mbox{\texttt{CGG}}} = ... ...}} + \Delta H {\mbox{\texttt{UC}} \choose \mbox{\texttt{GG}}}\\ \end{multline*}$$

Examples : Two adjacent GU base pairs

$$\begin{multline*} \Delta H {\mbox{\texttt{GUGC}} \choose \mbox{\texttt{CGUG}}} =... ...}} + \Delta H {\mbox{\texttt{UC}} \choose \mbox{\texttt{GG}}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
tur99	RNA	Mathiews et al (1999)
		J.Mol.Biol. 288: 911-940
model	limits	Article
ser12	RNA	Serra et al (2012)
		Biochemistry 51: 3508-3522

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing GU base pairs. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Single dangling end effect

The single dangling ends, that is the unmatched terminal nucleotides, can be taken into account, but all the thermodynamic parameters are not available. In such a case, the result is unpredictable, and all cases are possible.

For DNA and RNA duplexes, this program computes the hybridisation enthalpy and entropy from the elementary parameters of the Crick's pair containing the single dangling end.

$$\begin{array}[t]{ccc} \Delta{}h_\mathrm{single-dangling-end}&=&\delta{}h_\mathrm{Crick's-pair-containing-the-dangling-end}\\ \end{array}$$

Example : If the duplex is :

GCTAG-
CGATCA

$$\begin{multline*} \Delta H {\mbox{\texttt{GCTAG-}} \choose \mbox{\texttt{CGATCCA... ...} + \Delta H {\mbox{\texttt{G-}} \choose \mbox{\texttt{CA}}} \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
bom00	DNA	Bommarito et al. (2000)
		Nuc Acids Res 28: 1929-1934
sugdna02	DNA	Ohmichi et al. (2002)
	only terminal	J. Am. Chem. Soc. 124: 10367-10372
	poly A
	self complementary
	sequences
sugrna02	RNA	Ohmichi et al. (2002)
	only terminal poly A	J. Am. Chem. Soc. 124: 10367-10372
	self complementary
	sequences
ser08	RNA	O'tool et al. (2006)
	only 3' UA,	Nucleic Acids research 34: 3338-3344
	GU and UG terminal	Miller et al. (2008)
	base pairs	Nucleic Acids research 36: 5652-5659
	only 5' UG and GU
	terminal base pairs

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing single dangling ends. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing single dangling ends. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Double dangling end effect

The double dangling ends, that is the two adjacent unmatched terminal nucleotides, can be taken into account (mostly for RNA sequences). This program computes the hybridisation enthalpy and entropy in two times : First, it computes the energy from the single dangling end as if the duplex contained only a single danging end and then, it adds a bonus for the second dangling end if it is necessary.

$$\begin{multline*} \Delta{}h_\mathrm{double-dangling-end} = \delta{}h_\mathrm{sin... ...gling-end} + \delta{}h_\mathrm{bonus-second-dangling-end}\\ \end{multline*}$$

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{UAC}} \choose \mbox{\texttt{A-}}} = \... ...{UA}} + \Delta H {\mbox{bonus-pyrimidine-purine-pyrimidine}} \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
sugdna02	DNA	Ohmichi et al. (2002)
	only terminal	J. Am. Chem. Soc. 124: 10367-10372
	poly A
	self complementary
	sequences
sugrna02	RNA	Ohmichi et al. (2002)
	only terminal	J. Am. Chem. Soc. 124: 10367-10372
	poly A
	self complementary
	sequences
ser05	RNA	O'toole et al. (2005)
	depends on	RNA 11: 512-516
	the available
	thermodynamic
	parameters for
	single dangling
	ends
ser06	RNA	O'toole et al. (2006)
		Nucleic Acids research 34: 3338-3344

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing double dangling ends. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Long dangling end effect (poly A)

The long dangling ends, that is all the adjacent unmatched terminal nucleotides, can be taken into account (only for polyA dangling ends for the moment). It is possible to compute the thermodynamic form one to four poly A dangling end. This program computes the hybridisation enthalpy and entropy from the parameters of the long dangling end with the adjacent terminal base pair.

$$\begin{multline*} \Delta{}h_\mathrm{long-dangling-end} = \delta{}h_\mathrm{adjacent-terminal-base-pair+polyA} \\ \end{multline*}$$

Example :

If the duplex is :

GCTAG--
CGATCAAA

$$\begin{multline*} \Delta H {\mbox{\texttt{GCTAG-}} \choose \mbox{\texttt{CGATC... ...\Delta H {\mbox{\texttt{G-}} \choose \mbox{\texttt{CAAA}}} \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
sugdna02	DNA	Ohmichi et al. (2002)
	only terminal	J. Am. Chem. Soc. 124: 10367-10372
	poly A
	self complementary
	sequences
sugrna02	RNA	Ohmichi et al. (2002)
	only terminal	J. Am. Chem. Soc. 124: 10367-10372
	poly A
	self complementary
	sequences

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing long polyA dangling ends. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing long polyA dangling ends. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Single bulge loop effect

The single bulge loops, that is the single unmatched internal nucleotides, can be taken into account. , but all the thermodynamic parameters are not available. In such a case, the result is unpredictable, and all cases are possible. There are several different models to compute the thermodynamic of single bulge loop:

DNA and RNA duplexes :nearest neighbor model "NNN"

$$\begin{multline*} \Delta h {(\mbox{single-bulge-loop})} = \delta{}h_\mathrm{unpaired-nucleotid+adjacent-base-pairs} \\ \end{multline*}$$

Example : If the duplex is :

GCTTAGGC
CGA-TCCG

$$\begin{multline*} \Delta H {\mbox{\texttt{GCTTAGGC}} \choose \mbox{\texttt{CGA-T... ... \Delta H {\mbox{\texttt{AGGC}} \choose \mbox{\texttt{TCCG}}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

However, some types of single bulge loop can't be only modelled with a NNN nearest neighbor model and the following models can give more reliable and accurate results (mostly for RNA single bulge loops.)

DNA duplexes :Model from John Santalucia, Jr. and Donald Hicks, 2004

$$\begin{multline*} \Delta h {(\mbox{single-bulge-loop})} = \delta{}h_\mathrm{inte... ...athrm{intervening-NN} + \delta{}s_\mathrm{closing-AT-penalty}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{bulge-loop-of-1}$ accounts for the bulge loop of 1 nucleotide.

$\delta{}h_\mathrm{intervening-NN}$ accounts for the intervening base pair stack.

$\delta{}h_\mathrm{closing-AT-penalty}$ accounts for each AT base pair adjacent to the single bulge loop.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{GAC}} \choose \mbox{\texttt{C-G}}} = \... ...} + \Delta S {\mbox{\texttt{GC}} \choose \mbox{\texttt{CG}}} \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

RNA duplexes :Model from Zhi Johm Lu, Douglas H. Turner and David H. Mathews, 2006

$$\begin{multline*} \Delta h {(\mbox{single-bulge-loop})} = \delta{}h_\mathrm{initiation-bulge-loop-of-1} + \delta{}h_\mathrm{intervening-NN} \\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{initiation-bulge-loop-of-1}$ accounts for the initiation of bulge loop of 1 nucleotide.

$\delta{}h_\mathrm{intervening-NN}$ accounts for the intervening base pair stack.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{GAC}} \choose \mbox{\texttt{C-G}}} = \... ...} + \Delta H {\mbox{\texttt{GC}} \choose \mbox{\texttt{CG}}} \\ \end{multline*}$$

(The same computation is performed for $\Delta S$) For further information, see the referenced articles.

model	limits	Article
tan04	DNA	Tanaka et al (2004)
		Biochemistry 43 : 7143-7150
san04	DNA	Santalucia and Hicks (2004)
	missing	Annu. Rev. Biophys. Biomol. Struct 33 : 415-440
	closing AT
	penalty
ser07	RNA	Blose et al (2007)
	les reliable	Biochemistry 46 : 15123-15135
	results
	some missing
	parameters
tur06	RNA	Lu et al (2006)
		Nucleic Acids Research 34: 4912-4924

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing one single bulge loop. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing one single bulge loop. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

long bulge loop effect

The long bulge loops, that is all the adjacent unmatched internal nucleotides, can be taken into account. , but all the thermodynamic parameters are not available. In such a case, the result is unpredictable, and all cases are possible. The RNA and DNA thermodynamic models are similar :

DNA duplexes :Model from John Santalucia, Jr. and Donald Hicks, 2004

$$\begin{multline*} \Delta h {(\mbox{long-bulge-loop})} = \delta{}h_\mathrm{closin... ...thrm{bulge-loop-of-n} + \delta{}s_\mathrm{closing-AT-penalty}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{bulge-loop-of-n}$ accounts for the bulge loop of n nucleotides.

$\delta{}h_\mathrm{closing-AT-penalty}$ accounts for each AT base pair adjacent to the long bulge loop.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{GACGC}} \choose \mbox{\texttt{C-G}}}... ...e \mbox{\texttt{C-G}}} = \Delta S {\mbox{bulge-loop-of-3}} \\ \end{multline*}$$

RNA duplexes : Model from Zhi Johm Lu, Douglas H. Turner and David H. Mathews, 2006

$$\begin{multline*} \Delta h {(\mbox{long-bulge-loop})} = \delta{}h_\mathrm{initiation-bulge-loop-of-n} + \delta{}h_\mathrm{per-AU/GU-penalty}\\ \end{multline*}$$

Where :

$\delta{}h_\mathrm{initiation-bulge-loop-of-n}$ accounts for the initiation of the bulge loop of n nucleotides.

$\delta{}h_\mathrm{per-AU/GU-penalty}$ accounts for each AU or GU base pair adjacent to the long bulge loop.

Example :

$$\begin{multline*} \Delta H {\mbox{\texttt{AACGC}} \choose \mbox{\texttt{U-G}}}... ...ulge-loop-of-3}} + 1 \times \Delta H {\mbox{per-AU-penalty}} \\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
san04	DNA	Santalucia and Hicks (2004)
	missing closing	Annu. Rev. Biophys. Biomol. Struct 33 : 415-440
	AT penalty
	not tested
	with experimental
	results
tur06	RNA	Lu et al (2006)
	not tested	Nucleic Acids Research 34: 4912-4924
	with experimental
	results

Inosine bases effect

The inosine bases (I) are taken into account, but all the thermodynamic parameters are not available. In such a case, the result is unpredictable, and all cases are possible, so the program quit with a warning. For the RNA duplexes, only the thermodynamic parameters for IU base pairs are available for the moment. This program computes the hybridisation enthalpy and entropy from the elementary parameters of each Crick's pair containing the inosine base.

$$\begin{array}[t]{ccc} \Delta{}h_\mathrm{pattern-containing-inosi... ...&\sum \delta{}h_\mathrm{Crick's pair-containing-inosine-bases}\\ \end{array}$$

Examples : One inosine base

$$\begin{multline*} \Delta H {\mbox{\texttt{AIC}} \choose \mbox{\texttt{TAG}}} = ... ...}} + \Delta H {\mbox{\texttt{IC}} \choose \mbox{\texttt{AG}}}\\ \end{multline*}$$

Examples : Two adjacent base pairs containing inosine

$$\begin{multline*} \Delta H {\mbox{\texttt{GIAC}} \choose \mbox{\texttt{CAIG}}} =... ...}} + \Delta H {\mbox{\texttt{AC}} \choose \mbox{\texttt{IG}}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
san05	DNA	Watkins and Santalucia (2005)
	missing parameters	Nucleic acids research 33 : 6258-6267
	for tandem
	base pairs
	containing
	inosine bases
zno07	RNA	Wright et al. (2007)
	only IU base	Biochemistry 46 : 4625-4634
	pairs

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing inosine. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA sequences containing inosine. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Azobenzenes effect

The trans azobenzenes (X_T) and cis azobenzenes (X_C) in DNA duplexes are taken into account. Be aware : when the number of cis azobenzenes increases in the sequence, the predictions are less accurate and less reliable.

$$\begin{multline*} \Delta{}h_\mathrm{pattern-containing-azobenzene} = \delta{}h_\mathrm{Crick's pair-containing-azobenzene+adjacent-base-pairs}\\ \end{multline*}$$

Example : If the duplex is :

GCTX_CAGGC
CGATCCG

$$\begin{multline*} \Delta H {\mbox{\texttt{GCTX\_CAGGC}} \choose \mbox{\texttt{CG... ... \Delta H {\mbox{\texttt{AGGC}} \choose \mbox{\texttt{TCCG}}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
asa05	DNA	Asanuma et al. (2005)
	less reliable	Nucleic acids Symposium Series 49 : 35-36
	results when
	the number
	of cis azobenzene
	increases

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing azobenzene. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 2\cdot{}10^{-6}$ M

2-Hydroxyadenine bases effect

The 2-hydroxyadenine bases (A*) in DNA duplexes are taken into account, but only in this two different sequence contexts : 5' GA*C 3' and 5' TA*A 3'. The program computes the enthalpy and the entropy in two times : first it computes the enthalpy and entropy of the two Crick's pairs containing the hydroxyadenine as if the base pair containing the hydroxyadenine was a simple AT base pair, and then it computes the hydroxyadenine increments.

$$\begin{multline*} \Delta{}h_\mathrm{pattern-containing-hydroxyadenine} = \sum \d... ...h-AT-base-pair} + \delta{}h_\mathrm{hydroxyadenine-increment} \end{multline*}$$

Examples

$$\begin{multline*} \Delta H {\mbox{\texttt{GA*C}} \choose \mbox{\texttt{CCG}}} = ... ...x{\texttt{CG}}} + \Delta H {\mbox{increment-for-GA*C/CCG}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

For further information, see the referenced articles.

model	limits	Article
sug01	DNA	Kawakami et al.(2001)
	only in 5'	Nucleic acids research 29 : 3289-3296
	GA*C 3'
	and 5' TA*A
	contexts

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing hydroxyadenine. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Single Locked nucleic acid effect

The locked nucleic acids (AL, GL, CL, TL) in DNA duplexes are taken into account.

DNA duplexes : Model from McTigue et al., 2004

The program computes the enthalpy and the entropy in two times : first it computes the enthalpy and entropy of the two Crick's pairs containing the locked nucleic acid as if the locked nucleic acid was a simple nucleic acid, and then it computes the locked nucleic acid increments for each Crick's base pair containing the locked nucleic acid.

$$\begin{multline*} \Delta{}h_\mathrm{pattern-containing-Locked-Nucleic-Acid} = \s... ...elta{}h_\mathrm{increment-Crick's pair-with-Locked-Nucleic-Acid} \end{multline*}$$

Examples

$$\begin{multline*} \Delta H {\mbox{\texttt{GALC}} \choose \mbox{\texttt{CTG}}} = ... ...crement-for-GAL/CT}} + \Delta H {\mbox{increment-for-ALC/TG}}\\ \end{multline*}$$

(The same computation is performed for $\Delta S$)

DNA duplexes : Model from Owczarzy et al., 2011

The program computes the enthalpy and the entropy following the same nearest-neighbor formula as for perfectly matching Crick's pairs.

Examples

$$\begin{multline*} \Delta H {\mbox{\texttt{GALC}} \choose \mbox{\texttt{CTG}}} = ... ... + \Delta H {\mbox{\texttt{ALC}} \choose \mbox{\texttt{CG}}} \\ \end{multline*}$$

For further information, see the referenced articles.

model	limits	Article
mct04	DNA	McTigue et al.(2004)
		Biochemistry 43 : 5388-5405
owc11	DNA	Owczarzy et al.(2011)
		Biochemistry 50 : 9352-9367

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing single Locked Nucleic Acid. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 5\cdot{}10^{-6}$ M

Consecutive Locked nucleic acids effect

The consecutive locked nucleic acids (AL, GL, CL, TL) in DNA duplexes are taken into account. The program computes the enthalpy and the entropy following the same nearest-neighbor formula as for perfectly matching Crick's pairs.

Examples

$$\begin{multline*} \Delta H {\mbox{\texttt{GALCLC}} \choose \mbox{\texttt{CTGG}}}... ... + \Delta H {\mbox{\texttt{CLC}} \choose \mbox{\texttt{GG}}} \\ \end{multline*}$$

For further information, see the referenced articles.

model	limits	Article
owc11	DNA	Owczarzy et al.(2011)
		Biochemistry 50 : 9352-9367

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing consecutive Locked Nucleic Acids. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 2\cdot{}10^{-6}$ M

Consecutive Locked nucleic acids with a single mismatch effect

The consecutive locked nucleic acids with a single mismatch (AL, GL, CL, TL) in DNA duplexes are taken into account. The program computes the enthalpy and the entropy following the same nearest-neighbor formula as for perfectly matching Crick's pairs.

Examples

$$\begin{multline*} \Delta H {\mbox{\texttt{GALCLGLC}} \choose \mbox{\texttt{CTTCG... ...} \Delta H {\mbox{\texttt{GLC}} \choose \mbox{\texttt{CG}}} \\ \end{multline*}$$

For further information, see the referenced articles.

model	limits	Article
owc11	DNA	Owczarzy et al.(2011)
		Biochemistry 50 : 9352-9367

Figure: Comparison of experimental and computed Tm for various sets of DNA sequences containing consecutive Locked Nucleic Acids and a single mismatch. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 2\cdot{}10^{-6}$ M

The melting temperature

Then the melting temperature is computed by the following formula:

Tm	=	$\frac{\Delta{}H}{\Delta{}S + R \ln (C_T/F)} - 273.15$
		Tm in K (for [Na$^+$] = 1 M)

In case of self complementary sequences, if the sequence (5' 3') is a sequence of type G(CNG)xC and x > 4, the sequence mainly turns into hairpin loops and this program will compute the melting temperature with this formula :

Tm	=	$\frac{\Delta{}H}{\Delta{}S} - 273.15$
		Tm in K

Moreover, no ion correction will be applied to this formula.

Correction for the concentration of nucleic acid

F is 1 in the case of self-complementarity oligonucleotides. If the ODNs are not self-complementary, F is 4 if both strands are present in equivalent amount and F is 1 if one strand is in excess (for instance in PCR experiments). As a matter of facts, when the oligonucleotides are not self-complementary, the formula in the denominator is $C_{\mbox{max}} - C_{\mbox{min}}/2$ where $C_{\mbox{max}}$ is the concentration of the strand in excess and $C_{\mbox{min}}$ the concentration of the other strand. If the excess is sufficient, the total concentration is equivalent to the concentration of the strand in excess. Therefore, if one strand is in excess, the actual formula is effectively $C_{\mbox{max}} - C_{\mbox{min}}/2$ but if $C_{\mbox{max}} \gg C_{\mbox{min}}$, $C_{\mbox{max}} - C_{\mbox{min}}/2$ is equivalent to the total concentration $C_T$. If $C_{\mbox{max}}$ is close to $C_{\mbox{min}}$, $C_{\mbox{max}} - C_{\mbox{min}}/2$ is equivalent to $C_T/4$, which is the default correction.

F is 4 by default but note that MELTING can detect self complementary sequences for perfectly matching sequences even though there is(are) dangling end(s). In this case, the program will automatically change F to 1. In addition to that, the computation takes an entropic term to correct for self-complementarity. In case of other self complementary sequences which doesn't match perfetcly, the option -self must be used to inform the program of the self complementarity.

Figure: Comparison of experimental and computed Tm for various sets of DNA self complementary sequences. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA self complementary sequences. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 1\cdot{}10^{-4}$ M

Correction for the concentration of cations

After the program computed the melting temperature for $[$Na$^+]$=1, an ion correction wille be applied either directly on the computed melting temperature or on the computed entropy. In the last case, the melting temperature is computed using the first formula of the Melting temperature section. We must enter at least one of the following ion concentrations : $[$Na$^+]$, $[$K$^+]$, $[$Tris$^+]$ or $[$Mg$^{2+}]$ and several ion corrections are proposed (see the reference table to have more information):

Sodium corrections

• ahs01
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}+0.847 \times (N - 1) \times \log [\mbox{Na}^+]$$
  Where N is the length of the duplex.
• kam71
  $$Tm=Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}+(7.95 - 3.06 \times \chi_{GC}) \times \ln [\mbox{Na}^+]$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex.
• marschdot
  $$Tm=Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}+ (8.75 - 2.83 \times \chi_{GC}) \times \ln [\mbox{Na}^+]$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex.
• owc1904
  $$Tm=Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}+ (-3.22 \times \chi_{GC} - 6.39) \times \ln [\mbox{Na}^+]$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex.
• owc2004
  $$\frac{1}{Tm}=\frac{1}{Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}}+ (3.85 \times \chi_{GC} - 6.18) \times \frac{1}{100000} \times \ln [\mbox{Na}^+]$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex.
• owc2104
  $$Tm=Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}+ (-4.62 \times \chi_{GC} + 4.52) \times \ln [\mbox{Na}^+]$$
  $$- 0.985 \times \ln [($$Na$$^+)^2]$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex.
• owc2204
  $$\begin{multline*} \frac{1}{Tm}=\frac{1}{Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}}+ (4.29 \times \chi_{GC} - 3.95) \times \end{multline*}$$
  
  
  $$\begin{multline*} \frac{1}{100000} \times \ln [\mbox{Na}^+] + 9.40 \times \frac{1}{1000000} \times \ln [\mbox{Na}^+] \end{multline*}$$
  
  
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex.
• san96
  $$12.5 \log [$$Na$$^+]$$

• san04
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}+ 0.368 * (N - 1) \times \ln [\mbox{Na}^+]$$
  Where N is the length of the duplex.
• schlif
  $$Tm=Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}+ 16.6 \times \log [\mbox{Na}^+]$$

• tanna06
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}- 3.22 \times (N - 1) \times g1$$
  Where N is the length of the duplex.
  $$g1=a1 + \frac{b1}{N}$$
  $$a1= -0.07 \times \ln [$$Na$$^+] + 0.012 \times (\ln [$$Mg$$^{2+}])^2$$
  $$b1= 0.013 \times (\ln [$$Mg$$^{2+}])^2$$
  item tanna07
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}- 3.22 \times (N - 1) \times g1$$
  Where N is the length of the duplex.
  $$g1=a1 + \frac{b1}{N}$$
  $$a1= -0.075 \times \ln [$$Na$$^+] + 0.012 \times (\ln [$$Mg$$^{2+}])^2$$
  $$b1= 0.018 \times (\ln [$$Mg$$^{2+}])^2$$

• wet91
  $$Tm=Tm_{[\mbox{Na}^+]=1\;\mathrm{M}}+ 16.6 \log \frac{[\mbox{Na}^+]}{1 + 0.7 [\mbox{Na}^+]} + 3.85$$

correction	contexts	Article
ahs01	DNA	von Ahsen et al ,2001
	Na>0	Clinical Chemistry, 47, 1956-1961.
kam71	DNA	Frank-Kamenetskii et al. 1971
	Na>=0.069	Biopolymers 10, 2623-2624.
	Na<=1.02
marschdot	DNA	Marmur, J., and Doty, P. (1962)
	Na>=0.069	J. Mol. Biol. 5, 109-118.
	Na<=1.02	Blake and Delcourt. (1998) Nucleic Acids Res. 26, 3323-3332
		and corrigendum.
owc1904	DNA	Owczarzy et al.,2004
	Na>0	Biochemistry,43, 3537-3554.
owc2004	DNA	Owczarzy et al., 2004
	Na>0	Biochemistry, 43, 3537-3554.
owc2104	DNA	Owczarzy et al., 2004
	Na>0	Biochemistry, 43, 3537-3554.
owc2204	DNA	Owczarzy et al., 2004
	Na>0	Biochemistry, 43, 3537-3554.
owc2204	DNA	Owczarzy et al., 2004
	Na>0	Biochemistry,43, 3537-3554.
san96	DNA	SantaLucia et al.(1996)
	Na>=0.1	Biochemistry 35 : 3555-3562
san04	DNA	Santalucia and Hicks (2004)
	Na>=0.05	Annu. Rev. Biophys. Biomol. Struct 33 : 415-440
	Na<=1.1	John Santalucia, Jr., 1998
		Proc. Natl. Acad. Sci. USA, 95, 1460-1465
	oligonucleotides
	inferior to 16 bases
schlif	DNA	Schildkraut, C., and Lifson, S. (1965)
	Na>=0.07	Biopolymers 3, 195-208.
	Na<=0.12
tanna06	DNA	Tan et al. 2006,
	Na>=0.001	Biophysical Journal, 90, 1175-1190.
	Na<=1
tanna07	RNA	Tan et al, 2007
	Na>=0.003	Biophysical Journal, 92, 3615-3632.
	Na<=1
wet91	RNA, DNA	Wetmur 1991
	and RNA/DNA	Critical reviews in biochemistry and molecular
	Na>0	biology, 26, 227-259

Magnesium corrections

• owcmg08
  $$\frac{1}{Tm_{[\mbox{Mg}^{2+}]}} = \frac{1}{Tm_{[\mbox{Na}^+]=1\;\... ...ox{Mg}^{2+}]) + \chi_{GC} (c + d \ln [\mbox{Mg}^{2+}]) + \frac{1}{2 (Nbp-1)}$$
  $$(-e + f \ln [$$Mg$$^{2+}] + g (\ln [$$Mg$$^{2+}])^{2}])$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex. Nbp is the number of base pairs and a, b, c, d, e, f, g fixed to :

  a = 3.92 x $10^{-5}$
  b = 9.11 x $10^{-6}$
  c = 6.26 x $10^{-5}$
  d = 1.42 c $10^{-5}$
  e = 4.82 x $10^{-4}$
  f = 5.25 x $10^{-4}$
  g = 8.31 x $10^{-5}$.
  

• tanmg06
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}- 3.22 \times (N - 1) \times g2$$
  Where N is the length of the duplex.
  $$g2=a2 + \frac{b2}{(N)^2}$$
  $$a2= 0.02 \times \ln [$$Mg$$^{2+}] + 0.0068 \times (\ln [$$Mg$$^{2+}])^2$$
  $$b2= 1.18 \times \ln [$$Mg$$^{2+}] + 0.344 \times (\ln [$$Mg$$^{2+}])^2$$
  item tanmg07
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}- 3.22 \times (N - 1) \times g2$$
  Where N is the length of the duplex.
  $$g2=a2 + \frac{b2}{(N)^2}$$
  $$a2= \frac{-0.6}{N} + 0.025 \times \ln [$$Mg$$^{2+}] + 0.0068 \times (\ln [$$Mg$$^{2+}])^2$$
  $$b2= \ln [$$Mg$$^{2+} + 0.38 \times (\ln [$$Mg$$^{2+}])^2$$

correction	limits	Article
oxcmg08	DNA	Owczarzy et al.,2008
	Mg>=0.0005	Biochemistry, 47, 5336-5353.
	Mg<=0.6
tanmg06	DNA	Tan et al. 2006
	Mg>=0.0001	Biophysical Journal, 90, 1175-1190.
	Mg<=1
	oligomer
	length
	superior to
	6 base pairs
tanmg07	RNA	Tan et al, 2007
	Mg>=0.1	Biophysical Journal, 92, 3615-3632.
	Mg<=0.3

Mixed Na Mg corrections

• owcmix08
  $$\frac{1}{Tm_{[\mbox{Mg}^{2+}]}} = \frac{1}{Tm_{[\mbox{Na}^+]=1\;\... ...ox{Mg}^{2+}]) + \chi_{GC} (c + d \ln [\mbox{Mg}^{2+}]) + \frac{1}{2 (Nbp-1)}$$
  $$(-e + f \ln [$$Mg$$^{2+}] + g (\ln [$$Mg$$^{2+}])^{2}])$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the duplex. Nbp is the number of base pairs. b, c, e, f are fixed as in the magnesium correction owcmg08.
  $$a = 3.92\cdot{}10^{-5} (0.843 - 0.352 [$$Mon$$^+]^{0.5} \ln [$$Mon$$^+])$$
  $$d = 1.42\cdot{}10^{-5} (1.279 - 4.03\cdot{}10^{-3} \ln [$$Mon$$^+] - 8.03\cdot{}10^{-3} \ln [$$Mon$$^+]^{2})$$
  $$g = 8.31\cdot{}10^{-5} (0.486 - 0.258 \ln [$$Mon$$^+] + 5.25\cdot{}10^{-3} \ln [$$Mon$$^+]^{3}$$

• tanmix07
  $$\Delta{}S=\Delta{}S_{[\mbox{Na}^+]=1\;\mathrm{M}}- 3.22 \times ((N - 1) \times (x1 \times g1 + x2 \times g2) + g12))$$
  Where N is the length of the duplex.
  $$g12 = -0.6 \times x1 \times x2 \times \ln [$$Na$$^+] \times \frac{\ln [(\frac{1}{x1} - 1) \times \mbox{Na}^+]}{N}$$
  See what is g1 and g2 in the sodium corrections tanna06 and tanna07 (g1) and magnesium corrections tanmg06 and tanmg07 (g2). Formula representing the fractional contribution of Na+ ions.
  $$x1 = \frac{[\mbox{Na}^+]}{(\mbox{Na}^+ + (\frac{8.1 - 32.4}{N}) \times (5.2 - \ln [\mbox{Na}^+]) \times \mbox{Mg}^{2+})}$$
  Formula representing the fractional contribution of Mg2+ ions.
  $$x2= 1-x1$$

correction	limits	Article
oxcmix08	DNA	Owczarzy et al.,2008
	Mg>=0.0005	Biochemistry, 47, 5336-5353.
	Mg<=0.6
	Na+K+Tris/2>0
tanmix07	DNA	Tan et al, 2007
	and RNA	Biophysical Journal, 92, 3615-3632.
	Mg>=0.1
	Mg<=0.3
	Na+K+Tris/2>=0.1
	Na+K+Tris/2<=0.3

If the user doesn't enter any ion correction, the algorithm from Owczarzy et al. (2008) will be used by default :

$$[$$Mon$$^+] = [$$Na$$^+] + [$$k$$^+] + [$$Tris$$^+]$$

Where $[$Tris$^+]$ is equal to half of total tris buffer concentration. (in the option -t, it is the Tris buffer concentration which is entered).

• if $[$Mon$^+]$ = 0, a default sodium correction will be used.
• if $[$Mg$^{2+}]^0.5$ / $[$Mon$^+]$ < 0.22, a default sodium correction is used. Monovalent ion influence is dominant, divalent cations can be disregarded.
• if $[$Mg$^{2+}]^0.5$ / $[$Mon$^+]$ >= 0.22 and $[$Mg$^{2+}]^0.5$ / $[$Mon$^+]$ < 6, a default mixed Na Mg correction is used. We can have a competitive DNA or RNA binding between monovalent and divalent cations.
• if $[$Mg$^{2+}]^0.5$ / $[$Mon$^+]$ >= 6, a default magnesium correction is used. Divalent cation influence is dominant, monovalent cations can be disregarded.

Moreover, if the user wants to use a sodium correction but also enters a potassium, Tris buffer and/or a magnesium concentration, a sodium equivalent concentration which takes into account the other ion concentrations is computed before applying the sodium correction. Several sodium equivalence ready to use are proposed by this program :

• ahs01
  $$[$$NaEq$$^+] = [$$Na$$^+] + [$$K$$^+]+\frac{[\mbox{Tris}^+]}{2}+3.79 \sqrt{[\mbox{Mg}^{2+}] - [\mbox{dNTP}]}$$

• mit96
  $$[$$NaEq$$^+] = [$$Na$$^+] + [$$K$$^+]+\frac{[\mbox{Tris}^+]}{2}+4 \sqrt{[\mbox{Mg}^{2+}] - [\mbox{dNTP}]}$$

• pey00
  $$[$$NaEq$$^+] = [$$Na$$^+] + [$$K$$^+]+\frac{[\mbox{Tris}^+]}{2}+3.3 \sqrt{[\mbox{Mg}^{2+}] - [\mbox{dNTP}]}$$

For further information, see the referenced articles :

correction	limits	Article
ahs01	DNA	von Ahsen et al. 2001
		Clinical Chemistry, 47, 1956-1961.
mit96	DNA	Mitsuhashi. et al, 1996
		J. Clin. Lab. Anal, 10, 277-284.
pey00	DNA	Peyret, 2000
		Ph.D Thesis, Section .5.4.2, 128, Wayne State
		University, Detroit, MI

Correction for the concentration of denaturing agents

MELTING is currently accurate when the hybridisation is performed at pH $7\pm 1$, but some temperature corrections for the formamide and DMSO concentrations exists and can be applied. However, these corrections are rough approximations and results accuracy may be lost.

DMSO corrections, DMSO in %

• ahs01
  $$Tm=Tm(DMSO=0)-0.75 \times DMSO$$

• cul76
  $$Tm=Tm(DMSO=0)-0.5 \times DMSO$$

• esc80
  $$Tm=Tm(DMSO=0)-0.675 \times DMSO$$

• mus81
  $$Tm=Tm(DMSO=0)-0.6 \times DMSO$$

For further information, see the referenced articles :

correction	limits	Article
ahs01	DNA	von Ahsen et al. 2001
	not tested	Clinical Chemistry, 47, 1956-1961.
	with experimental
	values
cul76	DNA	Cullen et al., 1976
	not tested	3, 49-62.
	with experimental
	values
esc80	DNA	Escara et al., 1980
	not tested	19, 1315-1327.
	with experimental
	values
mus80	DNA	Musielski et al., 1981
	not tested	Z allg Microbiol 1981; 21, 447-456.
	with experimental
	values

formamide corrections

• bla96
  $$Tm=Tm(formamide=0)+ (0.453 \times \chi_{GC} - 2.88) \times formamide$$
  Where $\chi_{GC}$ is the frequence of GC base pairs in the sequence. formamide is in mol/L
• lincorr
  $$Tm=Tm(formamide=0)-0.65 \times formamide$$
  Where formamide is in %.

For further information, see the referenced articles :

correction	limits	Article
bla96	DNA	Blake and Delcourt, 1996
	not tested	Vol. 24, No. 11 2095-2103
	with experimental
	values
	formamide in mol/L
lincorr	DNA	McConaughy et al., 1969
	not tested	Biochemistry 8, 3289-3295.
	with experimental	Record, M.T., Jr, 1967
	in %	Biopolymers, 5, 975-992.
	values	Casey et al, 1977
	Formamide in	Nucleic acids research, 4, 1539-1532.
	%	Hutton, 1977
		Nucleic acids research, 4, 3537-3555.

Long sequences

It is important to realise that the nearest-neighbor approach has been established on small oligonucleotides. Therefore the use of MELTING in the non-approximative mode is really accurate only for relatively short sequences (Although if the sequences are two short, let's say $<$ 6 bp, the influence of extremities becomes too important and the reliability decreases a lot). For long sequences an approximative mode has been designed. This mode is launched if the sequence length is higher than the value given by the option -T (the default threshold is 60 bp).

The melting temperature can be computed by one of the following formulas:

• ahs01
  $$Tm = 80.4 + 0.345 \times \%GC + \log[$$Na$$^+] \times (17.0 - 0.135 \times \%GC) - \frac{550}{size}$$

• che93
  $$Tm = 69.3 + 0.41 \times \%GC - \frac{650}{size}$$

• che93corr
  $$Tm = 69.3 + 0.41 \times \%GC - \frac{535}{size}$$

• marschdot
  $$Tm = 81.5 + 16.6 \times \log[$$Na$$^+] + 0.41 \times \%GC - \frac{675}{size}$$

• owe69
  $$Tm = 87.16 + 0.345 \times \%GC + \log[$$Na$$^+] \times (20.17 - 0.066 \times \%GC)$$

• san98
  $$Tm = 77.1 + 11.7 \times \log[$$Na$$^+] + 0.41 \times \%GC - \frac{528}{size}$$

• wetdna91
  $$Tm = 81.5 + 16.6\log\frac{[\mbox{Na}^+]}{1+0.7[\mbox{Na}^+]} + 0.41\% GC - \frac{500}{size} - \%Mismatching$$

• wetrna91
  $$Tm = 78 + 16.6\log\frac{[\mbox{Na}^+]}{1+0.7[\mbox{Na}^+]} + 0.7\% GC - \frac{500}{size} - \%Mismatching$$

• wetdnarna91
  $$Tm = 67 + 16.6\log\frac{[\mbox{Na}^+]}{1+0.7[\mbox{Na}^+]} + 0.8\% GC - \frac{500}{size} - \%Mismatching$$

For further information, see the referenced articles :

formula	limits	Article
ahs01	DNA	von Ahsen et al. 2001
	no mismatch	Clinical Chemistry, 47, 1956-1961.
che93	DNA	Marmur et al., 1962
	no mismatch	Journal of molecular biology, 5, 109-118.
	Na=0	Chester N et al. 1993
	Mg=0.0015	Analytical Biochemistry, 209, 284-290.
	Tris=0.01
	K=0.05
che93corr	DNA	Marmur et al., 1962
	no mismatch	Journal of molecular biology, 5, 109-118.
	Na=0	Chester N et al. 1993
	Mg=0.0015	Analytical Biochemistry, 209, 284-290.
	Tris=0.01	Nicolas Von Ahsen et al. 2001
	K=0.05	Clinical Chemistry, 47, 1956-1961.
marschdot	DNA	Wetmur,1991
	no mismatch	Critical reviews in biochemistry
		and molecular biology, 26, 227-259
		Marmur et al., 1962
		Journal of molecular biology, 5, 109-118.
		Chester et al., 1993
		Analytical Biochemistry, 209, 284-290.
		Schildkraut et al., 1965
		Biopolymers, 3, 95-110.
		Wahl et al., 1987
		Methods Enzymol;152:399 - 407.
		Britten et al.,1974
		Methods Enzymol ;29:363-418.
		Hall et al., 1980
		J Mol Evol ;16:95-110.
owe69	DNA	Owen et al., 1969
	no mismatch	Biopolymers, 7:503-16.
		Frank-Kamenetskii,1971
		Biopolymers;10:2623- 4.
		Blake, 1996
		Encyclopedia of molecular biology and
		molecular medicine, Vol. 2., :1-19.
		Blake et al.,1998
		Nucleic Acids Res;26:3323-32.
san98	DNA	Santalucia, 1998
	no mismatch	Proc Nacl Acad Sci USA
		95, 1460-1465.
		von Ahsen et al. 2001,
		Clinical Chemistry, 47, 1956-1961.
wetdna91	DNA	Wetmur,1991,
		Critical reviews in biochemistry
		and molecular biology, 26, 227-259
wetrna91	RNA	Wetmur,1991,
		Critical reviews in biochemistry
		and molecular biology, 26, 227-259
wetdnarna91	DNA/RNA	Wetmur,1991,
		Critical reviews in biochemistry
		and molecular biology, 26, 227-259

Figure: Comparison of experimental and computed Tm for various sets of DNA approximative formulas. $[$Na$^+] = 1$ M

Figure: Comparison of experimental and computed Tm for various sets of RNA approximative formulas. $[$Na$^+] = 1$ M

Figure: Comparison of experimental and computed Tm for various sets of DNARNA approximative formulas. $[$Na$^+] = 1$ M, $[$nucleic acid$] = 4\cdot{}10^{-4}$ M

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See Also

New versions and related material can be found at

http://www.pasteur.fr/recherche/unites/neubiomol/meltinghome.html

https://sourceforge.net/projects/melting/

http://www.ebi.ac.uk/compneur-srv/melting/

You can use MELTING through a web server at http://bioweb.pasteur.fr/seqanal/interfaces/melting.htmlhttp://www.ebi.ac.uk/compneur-srv/melting/melt.php

Copyright

Melting is copyright ©1997, 2014 by Nicolas Le Novère, Marine Dumousseau and William John Gowers.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

Acknowledgements

Thanks to Richard Owczarzy for reporting typos in several thermodynamic parameters and reporting new public parameters. Nicolas Joly is an efficient and kind debugger and advisor. Catherine Letondal wrote the HTML interface to melting. Thanks to Nirav Merchant, Taejoon Kwon, Leo Schalkwyk, Mauro Petrillo, Andrew Thompson, Wong Chee Hong, Ivano Zara for their bug fixes and comments. Thanks to Richard Owczarzy for his magnesium correction. Thanks to Charles Plessy for the graphical interface files. Thanks to Daniel McGreal for the SOAP interface of MELTING at the EMBL-EBI. Thanks to Nicolas Rodriguez for the current web interface and finally thanks to the usenet helpers, particularly Olivier Dehon and Nicolas Chuche.

Authors

Nicolas Le Novère, Marine Dumousseau and William John Gowers,
EMBL-EBI, Wellcome-Trust Genome Campus Hinxton Cambridge, CB10 1SD, UK n.lenovere@gmail.com

History

The Java version has been rewriten from the beginning. See the file ChangeLog for the changes of the versions 4 and more recent.

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MELTING - nearest-neighbor computation of nucleic acid hybridation

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