melting - Online in the Cloud

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.

-Afile.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.

-Ccomplementary_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.

-Ddnadnade.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.

-Ffactor
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.

-Gx.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.

-Hhybridisation_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.

-Iinput_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###

-ifile.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.

-Ksalt_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.

-Mdnadnamm.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.

-Nx.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.

-Ooutput_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).

-Px.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).

-Ssequence
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.

-Txxx Size threshold before approximative computation. The nearest-neighbour approach
will be used only if the length of the sequence is inferior to this threshold.

-tx.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., Bl�ker 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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