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**PROGRAM:**

**NAME**

melting - nearest-neighbor computation of nucleic acid hybridation

**SYNOPSIS**

**melting**[

__options__]

**DESCRIPTION**

**Melting**computes, for a nucleic acid duplex, the enthalpy and the entropy of the helix-

coil transition, and then its melting temperature. Three types of hybridisation are

possible: DNA/DNA, DNA/RNA, and 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 ISO C and

can be compiled on any operating system. Some perl scripts are provided to show how

melting can be used as a block to construct more ambitious programs.

**OPTIONS**

The options are treated sequentially. If there is a conflict between the value of two

options, the latter normally erases the former.

**-A**

__file.nn__

Informs the program to use

__file.nn__as an alternative set of nearest-neighbor

parameters, rather than the default for the specified hybridisation type. The

standard distribution of melting provides some files ready-to-use:

__all97a.nn__

(Allawi et al 1997),

__bre86a.nn__(Breslauer et al 1986),

__san96a.nn__(SantaLucia et al

1996),

__sug96a.nn__(Sugimoto et al 1996)

__san04a.nn__(Santalucia et al 2004) (DNA/DNA),

__fre86a.nn__(Freier et al 1986),

__xia98a.nn__(Xia et al 1998), (RNA/RNA), and

__sug95a.nn__

(Sugimoto et al 1995), (DNA/RNA).

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. Be careful, the option

**-A**changes the default parameter

set defined by the option

**-H.**

**-C**

__complementary_sequence__

Enters the complementary sequence, from 3' to 5'. This option is mandatory if there

are mismatches 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.**

**-D**

__dnadnade.nn__

Informs the program to use the file

__dnadnade.nn__to compute the contribution of

dangling ends to the thermodynamic of helix-coil transition. The dangling ends are

not taken into account by the approximative mode.

**-F**

__factor__

This is the a correction factor used to modulate the effect of the nucleic acid

concentration in the computation of the melting temperature. See section ALGORITHM

for details.

**-G**

__x.xxe-xx__

Magnesium concentration (No maximum concentration for the moment). The effect

of ions on thermodynamic stability of nucleic acid duplexes is complex,

and the correcting functions are at best rough approximations.The published

Tm correction formula for divalent Mg2+ ions of Owczarzy et al(2008) can

take in account the competitive binding of monovalent and divalent ions on DNA.

However this formula is only for DNA duplexes.

**-h**Displays a short help and quit with EXIT_SUCCESS.

**-H**

__hybridisation_type__

Specifies the hybridisation type. This will set the nearest-neighbor set to use if

no alternative set is provided by the option

**-A**(remember the options are read

sequentially). Moreover this parameter determines the equation to use if the

sequence length exceeds the limit of application of the nearest-neighbor approach

(arbitrarily set up by the author). Possible values are

__dnadna,__

__dnarna__and

__rnadna__

(synonymous), and

__rnarna.__For reasons of compatibility the values of the previous

versions of melting

__A,B,C,F,R,S,T,U,W__are still available although

**strongly**

deprecated. Use the option

**-A**to require an alternative set of thermodynamic

parameters. IMPORTANT: If the duplex is a DNA/RNA heteroduplex, the sequence of the

DNA strand has to be entered with the option

**-S.**

**-I**

__input_file__

Provides the name of an input file containing the parameters of the run. The input

has to contain one parameter per line, formatted as in the command line. The order

is not important, as well as blank lines. example:

###beginning###

-Hdnadna

-Asug96a.nn

-SAGCTCGACTC

-CTCGAGGTGAG

-N0.2

-P0.0001

-v

-Ksan96a

###end###

**-i**

__file.nn__

Informs the program to use file.nn as an alternative set of inosine pair

parameters, rather than the default for the specified hybridisation type.

The standard distribution of melting provides some files ready-to-use:

san05a.nn

(Santalucia et al 2005) for deoxyinosine in DNA duplexes, bre07a.nn (Brent M

Znosko

et al 2007)for inosine in RNA duplexes. Note that not all the inosine

mismatched

wobble's pairs have been investigated. Therefore it could be impossible to

compute

the Tm of a duplex with inosine pairs. Moreover, those inosine pairs are not

taken

into account by the approximative mode.

**-K**

__salt_correction__

Permits one to chose another correction for the concentration in sodium. Currently,

one can chose between

__wet91a,__

__san96a,__

__san98a.__See section ALGORITHM. TP. BI.

"-k" "x.xxe-xx"

Potassium concentration (No maximum concentration for the moment). The effect

of ions

on thermodynamic stability of nucleic acid duplexes is complex, and the

correcting

functions are at best rough approximations.The published Tm correction

formula for

sodium ions of Owczarzy et al (2008)is therefore also applicable to buffers

containing Tris or

KCl. Monovalent K+, Na+, Tris+ ions stabilize DNA duplexes

with similar potency, and their effects on duplex stability are additive.

However this formula

is only for DNA duplexes.

**-L**Prints the legal information and quit with EXIT_SUCCESS.

**-M**

__dnadnamm.nn__

Informs the program to use the file

__dnadnamm.nn__to compute the contribution of

mismatches to the thermodynamic of helix-coil transition. Note that not all the

mismatched Crick's pairs have been investigated. Therefore it could be impossible

to compute the Tm of a mismatched duplex. Moreover, those mismatches are not taken

into account by the approximative mode.

**-N**

__x.xxe-xx__

Sodium concentration (between 0 and 10 M). The effect of ions on thermodynamic

stability of nucleic acid duplexes is complex, and the correcting functions

are at best rough approximations. Moreover, they are generally reliable only

for [Na+] belonging to [0.1,10M]. If there are no other ions in

solution, we can use only the sodium correction. In the other case, we use the

Owczarzy's

algorithm.

**-O**

__output_file__

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

file can be omitted. An automatic name is then generated, of the form

meltingYYYYMMMDD_HHhMMm.out (of course, on POSIX compliant systems, you can emulate

this with the redirection of stdout to a file constructed with the program date).

**-P**

__x.xxe-xx__

Concentration of the nucleic acid strand in excess (between 0 and 0.1 M).

**-p**Return the directory supposed to contain the sets of calorimetric parameters and

quit with EXIT_SUCCESS. If the environment variable NN_PATH is set, it is returned.

Otherwise, the value defined by default during the compilation is returned.

**-q**Turn off the interactive correction of wrongly entered parameter. Useful for run

through a server, or a batch script. Default is OFF (i.e. interactive on). The

switch works in both sens. Therefore if

**-q**has been set in an input file, another

**-q**on the command line will switch the quiet mode OFF (same thing if two

**-q**are set

on the same command line).

**-S**

__sequence__

Sequence of one strand of the nucleic acid duplex, entered 5' to 3'. IMPORTANT: If

it is a DNA/RNA heteroduplex, the sequence of the DNA strand has to be entered.

Uridine and thymidine are considered as identical. The bases can be upper or

lowercase.

**-T**

__xxx__Size threshold before approximative computation. The nearest-neighbour approach

will be used only if the length of the sequence is inferior to this threshold.

**-t**

__x.xxe-xx__

Tris buffer concentration (No maximum concentration for the moment).

The effect of ions on thermodynamic stability of nucleic acid

duplexes is complex, and the correcting functions are at best

rough approximations.The published Tm correction formula for sodium ions of

Owczarzy et al(2008)is therefore also applicable to buffers containing Tris or

KCl. Monovalent K+, Na+, Tris+ ions stabilize DNA duplexes with similar

potency, and

their effects on duplex stability are additive. However this formula is only for

DNA

duplexes. Be careful, the Tris+ ion concentration is about half of the total

tris buffer

concentration.

**-v**Control the verbose mode, issuing a lot more information about the current run (try

it once to see if you can get something interesting). Default is OFF. The switch

works in both sens. Therefore if

**-v**has been set in an input file, another

**-v**on

the command line will switch the verbose mode OFF (same thing if two

**-v**are set on

the same command line).

**-V**Displays the version number and quit with EXIT_SUCCESS.

**-x**Force the program to compute an approximative tm, based on G+C content. 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.

**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.

Therefore, the 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). This program

first computes the hybridisation enthalpy and entropy from the elementary parameters of

each Crick's pair.

DeltaH = deltaH(initiation) + SUM(deltaH(Crick's pair))

DeltaS = deltaS(initiation) + SUM(deltaS(Crick's pair))

See Wetmur J.G. (1991) and SantaLucia (1998) for deep reviews on the nucleic acid

hybridisation and on the different set of nearest-neighbor parameters.

**Effect**

**of**

**mismatches**

**and**

**dangling**

**ends**

The mismatching pairs are also taken into account. However the thermodynamic parameters

are still not available for every possible cases (notably when both positions are

mismatched). In such a case, the program, unable to compute any relevant result, will quit

with a warning.

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

The dangling ends, that is the umatched terminal nucleotides, can be taken into account.

**Example**

DeltaH(

AGCGATGAA-

-CGCTGCTTT

) = DeltaH(AG/-C)+DeltaH(A-/TT)

+DeltaH(initG/C)+DeltaH(initA/T)

+DeltaH(GC/CG)+DeltaH(CG/GC)+2xDeltaH(GA/CT)+DeltaH(AA/TT)

+Delta(AT/TG mismatch) +DeltaG(TC/GG mismatch)

(The same computation is performed for DeltaS)

**The**

**melting**

**temperature**

Then the melting temperature is computed by the following formula:

Tm = DeltaH / (DeltaS + Rx ln ([nucleic acid]/F))

__Tm__

__in__

__K__(for [Na+] = 1 M )

+ f([Na+]) - 273.15

__correction__for the salt concentration (if there are only sodium cations in the

solution)and to get the temperature in degree Celsius. (In fact some corrections are

directly included in the DeltaS see that of SanLucia 1998)

**Correction**

**for**

**the**

**concentration**

**of**

**nucleic**

**acid**

If the concentration of the two strands are similar, F is 1 in case of self-complementary

oligonucleotides, 4 otherwise. If one strand is in excess (for instance in PCR

experiment), F is 2 (Actually the formula would have to use the difference of

concentrations rather than the total concentration, but if the excess is sufficient, the

total concentration can be assumed to be identical to the concentration of the strand in

excess).

Note however, MELTING makes the assumption of no self-assembly,

__i.e.__the computation does

not take any entropic term to correct for self-complementarity.

**Correction**

**for**

**the**

**concentration**

**of**

**salt**

If there are only sodium ions in the solution, we can use the following corrections:

The correction can be chosen between

__wet91a,__presented in Wetmur 1991

__i.e.__

16.6 x log([Na+] / (1 + 0.7 x [Na+])) + 3.85

__san96a__presented in SantaLucia et al. 1996

__i.e.__

12.5 x log[Na+]

and

__san98a__presented in SantaLucia 1998

__i.e.__a correction of the entropic term without

modification of enthalpy

DeltaS = DeltaS([Na+]=1M) + 0.368 x (N-1) x ln[Na+]

Where N is the length of the duplex (SantaLucia 1998 actually used 'N' the number of non-

terminal phosphates, that is effectively equal to our N-1). CAUTION, this correction is

meant to correct entropy values expressed in cal.mol-1.K-1!!!

**Correction**

**for**

**the**

**concentration**

**of**

**ions**

**when**

**other**

**monovalent**

**ions**

**such**

**as**

**Tris+**

**and**

**K+**

**or**

**divalent**

**Mg2+**

**ions**

**are**

**added**

If there are only Na+ ions, we can use the correction for the concentration of salt(see

above). In the opposite case , we will use the magnesium and monovalent ions correction

from Owczarzy et al (2008). (only for DNA duplexes)

[Mon+] = [Na+] + [K+] + [Tris+]

Where [Tris+] = [Tris buffer]/2. (in the option -t, it is the Tris buffer concentration

which is entered).

If [Mon+] = 0, the divalent ions are the only ions present

and the melting temperature is :

1/Tm(Mg2+) = 1/Tm(1M Na+) + a - b x ln([Mg2+]) + Fgc x (c + d x ln([Mg2+]) + 1/(2 x (Nbp -

1)) x (- e +f x ln([Mg2+]) + g x ln([Mg2+]) x ln([Mg2+]))

where : a = 3.92/100000. b = 9.11/1000000. c = 6.26/100000. d = 1.42/100000. e =

4.82/10000. f = 5.25/10000. g = 8.31/100000. Fgc is the fraction of GC base pairs in

the sequence and Nbp is the length of the sequence (Number of base pairs).

If [Mon+] > 0, there are several cases because we can have a competitive DNA binding

between monovalent and divalent cations :

If the ratio [Mg2+]^(0.5)/[Mon+] is inferior to 0.22, monovalent ion influence is

dominant, divalent cations can be disregarded and the melting temperature is :

1/Tm(Mg2+) = 1/Tm(1M Na+) + (4.29 x Fgc - 3.95) x 1/100000 x ln([mon+]) + 9.40 x 1/1000000

x ln([Mon+]) x ln([Mon+])

where : Fgc is the fraction of GC base pairs in the sequence.

If the ratio [Mg2+]^(0.5)/[Mon+] is included in [0.22, 6[, we must take in account both

Mg2+ and monovalent cations concentrations. The melting temperature is :

1/Tm(Mg2+) = 1/Tm(1M Na+) + a - b x ln([Mg2+]) + Fgc x (c + d x ln([Mg2+]) + 1/(2 x (Nbp -

1)) x (- e + f x ln([Mg2+]) + g x ln([Mg2+]) x ln([Mg2+]))

where : a = 3.92/100000 x (0.843 - 0.352 x [Mon+]0.5 x ln([Mon+])).

b = 9.11/1000000. c = 6.26/100000.

d = 1.42/100000 x (1.279 - 4.03/1000 x ln([mon+]) - 8.03/1000 x ln([mon+] x

ln([mon+]). e = 4.82/10000. f = 5.25/10000. g = 8.31/100000 x (0.486 -

0.258 x ln([mon+]) + 5.25/1000 x ln([mon+] x ln([mon+] x ln([mon+]).

Fgc is the fraction of GC base pairs in the sequence and Nbp is the length of the sequence

(Number of base pairs).

Finally, if the ratio [Mg2+]^(0.5)/[Mon+] is superior to 6, divalent ion influence is

dominant, monovalent cations can be disregarded and the melting temperature is :

1/Tm(Mg2+) = 1/Tm(1M Na+) + a - b x ln([Mg2+]) + Fgc x (c + d x ln([Mg2+]) + 1/(2 x (Nbp -

1)) x (- e + f x ln([Mg2+]) + g x ln([Mg2+]) x ln([Mg2+]))

where : a = 3.92/100000. b = 9.11/1000000. c = 6.26/100000. d = 1.42/100000. e =

4.82/10000. f = 5.25/10000. g = 8.31/100000.

Fgc is the fraction of GC base pairs in the sequence and Nbp is the length of the sequence

(Number of base pairs).

**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 is computed by the following formulas:

DNA/DNA:

Tm = 81.5+16.6*log10([Na+]/(1+0.7[Na+]))+0.41%GC-500/size

DNA/RNA:

Tm = 67+16.6*log10([Na+]/(1.0+0.7[Na+]))+0.8%GC-500/size

RNA/RNA:

Tm = 78+16.6*log10([Na+]/(1.0+0.7[Na+]))+0.7%GC-500/size

This mode is nevertheless

**strongly**

**disencouraged.**

**Miscellaneous**

**comments**

Melting is currently accurate only when the hybridisation is performed at pH 71.

The computation is valid only for the hybridisations performed in aqueous medium.

Therefore the use of denaturing agents such as formamide completely invalidates the

results.

**REFERENCES**

Allawi H.T., SantaLucia J. (1997). Thermodynamics and NMR of internal G.T mismatches in

DNA.

__Biochemistry__36: 10581-10594

Allawi H.T., SantaLucia J. (1998). Nearest Neighbor thermodynamics parameters for

internal G.A mismatches in DNA.

__Biochemistry__37: 2170-2179

Allawi H.T., SantaLucia J. (1998). Thermodynamics of internal C.T mismatches in DNA.

__Nucleic__

__Acids__

__Res__26: 2694-2701.

Allawi H.T., SantaLucia J. (1998). Nearest Neighbor thermodynamics of internal A.C

mismatches in DNA: sequence dependence and pH effects.

__Biochemistry__37: 9435-9444.

Bommarito S., Peyret N., SantaLucia J. (2000). Thermodynamic parameters for DNA sequences

with dangling ends.

__Nucleic__

__Acids__

__Res__28: 1929-1934

Breslauer K.J., Frank R., Blï¿½ker H., Marky L.A. (1986). Predicting DNA duplex stability

from the base sequence.

__Proc__

__Natl__

__Acad__

__Sci__

__USA__83: 3746-3750

Freier S.M., Kierzek R., Jaeger J.A., Sugimoto N., Caruthers M.H., Neilson T., Turner D.H.

(1986). Improved free-energy parameters for predictions of RNA duplex stability.

__Biochemistry__83:9373-9377

Owczarzy R., Moreira B.G., You Y., Behlke M.B., Walder J.A. (2008) Predicting stability

of DNA duplexes in solutions containing Magnesium and Monovalent Cations. Biochemistry 47:

5336-5353.

Peyret N., Seneviratne P.A., Allawi H.T., SantaLucia J. (1999). Nearest Neighbor

thermodynamics and NMR of DNA sequences with internal A.A, C.C, G.G and T.T mismatches.

dependence and pH effects.

__Biochemistry__38: 3468-3477

SantaLucia J. Jr, Allawi H.T., Seneviratne P.A. (1996). Improved nearest-neighbor

parameters for predicting DNA duplex stability.

__Biochemistry__35: 3555-3562

Sugimoto N., Katoh M., Nakano S., Ohmichi T., Sasaki M. (1994). RNA/DNA hybrid duplexes

with identical nearest-neighbor base-pairs hve identical stability.

__FEBS__

__Letters__354:

74-78

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: 11211-11216

Sugimoto N., Nakano S., Yoneyama M., Honda K. (1996). Improved thermodynamic parameters

and helix initiation factor to predict stability of DNA duplexes.

__Nuc__

__Acids__

__Res__24:

4501-4505

Watkins N.E., Santalucia J. Jr. (2005). Nearest-neighbor t- hermodynamics of deoxyinosine

pairs in DNA duplexes. Nucleic Acids Research 33: 6258-6267

Wright D.J., Rice J.L., Yanker D.M., Znosko B.M. (2007). Nearest neighbor parameters for

inosine-uridine pairs in RNA duplexes. Biochemistry 46: 4625-4634

Xia T., SantaLucia J., Burkard M.E., Kierzek R., Schroeder S.J., Jiao X., Cox C., Turner

D.H. (1998). Thermodynamics parameters for an expanded nearest-neighbor model for

formation of RNA duplexes with Watson-Crick base pairs.

__Biochemistry__37: 14719-14735

For review see:

SantaLucia J. (1998) A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-

neighbor thermodynamics.

__Proc__

__Natl__

__Acad__

__Sci__

__USA__95: 1460-1465

SantaLucia J., Hicks Donald (2004) The Thermodynamics of DNA structural motifs. Annu.

Rev. Biophys. Struct. 33: 415 -440

Wetmur J.G. (1991) DNA probes: applications of the principles of nucleic acid

hybridization.

__Crit__

__Rev__

__Biochem__

__Mol__

__Biol__26: 227-259

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