A brief explanation of how LabCalculator calculates Oligo T_{m}

Introduction

The calculation of the thermal properties of primers is certainly a complex one. Although simple methods exist for such calculations, they often don't take into account the composition and orientation of primer bases and also often neglect to take into account environmental conditions such as salt content, primer concentration, and the concentrations of addatives added to your reaction solution.

LabCalculator employs 3 methods of T_{m} calculation: **basic, salt-adjusted, and nearest-neighbour**.
These are explained below, with equations to show how the values are derived. Furthermore, we calculate much more than just
primer T_{m}! We also calculate **molecular weight, GC percentage, and thermodynamic constants (RlnK, deltaG, deltaS, and deltaH).**

Please note that these calculations are only estimates and many other factors can affect the melting temperature, including detergents, presence of other counter ions, solvents (ethanol for instance), formamide, etc.

Basic T_{m} Calculation

Basic T_{m} calculation is the most basic form of T_{m} calculation. Two calculations are used, with the calculator
deciding which is best based on primer length. Both equations assume that the annealing occurs under the standard conditions of 50 nM primer, 50 mM Na+, and pH 7.0.

**For sequences less than 14 nucleotides the formula is:**

T_{m} = (nA + nT) * 2 + (nG + nC) * 4

Where nA, nT, nG, and nC are the number of the bases A,T,G,C in the sequence. This forumla is derived from *Marmur,J., and Doty,P. (1962)
J Mol Biol 5:109-118 [PubMed]*.

**For sequences longer than 13 nucleotides, the equation used is:**

T_{m} = 64.9 + 41 * (nG + nC - 16.4) / (nA + nT + nG + nC)

For further reading and the experimental derivation of this equation please see *Wallace,R.B., Shaffer,J., Murphy,R.F., Bonner,J., Hirose,T., and Itakura,K. (1979) Nucleic Acids Res 6:3543-3557
[
Abstract]* and *Sambrook,J., and Russell,D.W. (2001) Molecular Cloning: A Laboratory Manual.
Cold Spring Harbor Laboratory Press; Cold Spring Harbor, NY. [CHSL Press]*

Salt-Adjusted T_{m} Calculation

Salt-adjusted T_{m} calculation takes into account differing salt concentrations in the reaction solution.
Variations on the two basic equations are used to account for salt concentration changes. At >50bp in length,
the effects of formamide are also taken into account when calculating salt-adjusted T_{m}.
All equations assume that the annealing occurs under the standard conditions of 50 nM primer and pH 7.0.

**For sequences less than 14 nucleotides the formula is:**

T_{m} = (nA + nT) * 2 + (nG + nC) * 4 - 16.6 * log_{10}(0.050) + 16.6 * log_{10}([Na^{+}])

Where nA, nT, nG, and nC are the number of the bases A,T,G,C in the sequence. The term 16.6 * log_{10}([Na^{+}]) adjusts the Tm for changes in the salt
concentration, and the term log_{10}(0.050) adjusts for the salt adjustment at 50 mM Na^{+}.
Whilst other monovalent and divalent salts will have an effect on the T_{m} of the oligonucleotide, sodium ions have a much greater effect on the formation of
salt bridges between DNA strands and therefore have the greatest effect in stabilizing double-stranded DNA. It should be noted, however, that trace amounts of divalent cations have
significant and often overlooked affects (See *Nakano et al, (1999) Proc. Nuclec Acids Res. 27:2957-65. [**Abstract]*). This forumla is derived from *Marmur,J., and Doty,P. (1962)
J Mol Biol 5:109-118 [PubMed]*.

**For sequences of 14 to 50bp, the equation used is:**

T_{m} = 100.5 + (41 * (nG + nC) / (nA + nT + nG + nC)) - (820 / (nA + nT + nG + nC)) + 16.6 * log_{10}([Na^{+}])

This equation is most accurate for sequences in teh 18-25bp range as described by *Howley,P.M., Israel,M.F., Law,M-F., and Martin,M.A. (1979) J Biol Chem 254:4876-4883
[Abstract]*, and is used by Lab Calculator for sequences of 13 to 50bp.

**For sequences of >50bp the following equation is used:**

T_{m}= 81.5 + (41 * (nG + nC) / (nA + nT + nG + nC)) - (500 / (nA + nT + nG + nC)) + log_{10}([Na^{+}]) - 0.62*F*

This equation is used for salt-adjusted T_{m} calculation when the sequence is greater than 50bp in length. Furthermore, it is only valid from pH 5 to 9.
**(41 * (nG + nC) / (nA + nT + nG + nC))** accounts for G/C content, with **(500 / (nA + nT + nG + nC))** adjusting for the length
of the sequence. Finally **0.62F** accounts for formamide concentration. A default value of 5% formamide is used if not specified in the calculator.
Further reading on this equation can be found in *Howley,P.M., Israel,M.F., Law,M-F., and Martin,M.A. (1979) J Biol Chem 254:4876-4883
[Abstract]*.

Nearest-Neighbour T_{m} Calculation

Nearest-neighbour T_{m} calculation is the most comprehensive form of T_{m} calculation, taking into account specific composition of
primers, and their thermodynamic properties. Lab Calculator uses nucleotide pairs for calculation using data from Sugimoto, 1996
(*Sugimoto, N., Nakano, S., Yoneyama, M., and Honda, K. (1996) Nucleic Acids Research, Vol. 24, No. 22 4501–4505
[Abstract]*) using the nearest neighbor and thermodynamic calculations essentially
as described by *Breslauer et al., (1986) Proc. Nat. Acad. Sci. 83:3746-50 [Abstract]*.

**Thermodynamic Values (From Sugimoto, 1996):**

Pair | ∆H° kcal/mol | ∆S° cal/mol/K | ∆G°37 kcal/mol |
---|---|---|---|

dTT dAA |
8.0 | 21.9 | 1.2 |

dAT dTA |
5.6 | 15.2 | 0.9 |

dTA dAT |
6.6 | 18.4 | 0.9 |

dCA dGT |
8.2 | 21.0 | 1.7 |

dGT dCA |
6.6 | 16.4 | 1.5 |

dCT dGA |
8.8 | 23.5 | 1.5 |

dGA dCT |
9.4 | 25.5 | 1.5 |

dCG dGC |
11.8 | 29.0 | 2.8 |

dGC dCG |
10.5 | 26.4 | 2.3 |

dGG dCC |
10.9 | 28.4 | 2.1 |

initiation | -0.6 | 9.0 | -3.4 |

self-complementary | 0 | 0 | 1.4 |

**Thermodynamic calculations**

The melting temperature calculations are based on the thermodynamic relationship between entropy, enthalpy, free energy and temperature.

**Calculation of deltaS (entropy):**

The change in entropy (order or a measure of the randomness of the oligonucleotide) is represented as ∆S. The total ∆S is calculated by finding the sum of all nucleotide pair ∆S values (∆S°) as listed above.

∆S = ∑∆S°

**Calculation of deltaH (enthalpy):**

Delta H represents the enthlapy of the nucleotide molecules. The total ∆H is calculated by finding the sum of all nucleotide pair ∆H values (∆H°) as lsited above.

∆H = ∑∆H°

Furthermore, ∆H can be described by the following formula, where T is temperature:

∆H = ∆G - T∆S

**Calculation of deltaG:**

The total ∆G is calculated by finding the sum of all nucleotide pair ∆G values (∆G°) as listed above.

∆G = ∑∆G°

**Calculation of RlnK:**

RlnK is used in the calculation of nearest neighbour calculation and is calculated as follows:

RlnK = 1.987 * ln(1/[Primer])

Where R = 1.987 cal/(mole*K) and [Primer]the concentration of the primer in nanomoles

**Nearest-neighbour calculation**

We can assume that the concentration of DNA and the concentration of the DNA-primer complex are equal (that is,
the concentration of primer is in excess of the target DNA and the melting point is where the concentration
of bound and unbound DNA are at equilibrium), so this simplifies the equation considerably. If the two strands are
in equal concentration, the effective concentration is 0.25 the total concentration of
oligonucleotide (*Wetmur,J.G., (1991) Crit Rev Biochem Mol Biol 26:227-259 [
Abstract]*).
It has been determined empirically that there is a 3.4 kcal free energy change during the transition from single stranded to B-form DNA.
This represents the helix initiation energy.

T = 1000 * ( ( deltaH - Sym ) / ( deltaS + RlnK ) )

Where Sym is 3.4 in the event that the strand is symmetrical (EG: ACTACTTCATCA). Following this, a salt adjustment is added for the salt concentration specified:

T_{SA} = T + 7.21 * ln([Na^{+}])

Where [Na^{+}] is the salt concentration in moles. Finally the value is converted from Kelvin to Celcius.

Molecular Weight Calculation

The molecular weight, typically for synthesized DNA oligonucleotides, uses the following formula:

Anhydrous Molecular Weight = (nA x 313.21) + (nT x 304.2) + (nC x 289.18) + (nG x 329.21) - 61.96

Lab Calculator calculations assume that there is not a 5' monophosphate, and nA, nT, nC, and nG are the number of each respective nucleotide within the polynucleotide.
The subtraction of 61.96 gm/mole from the oligonucleotide molecular weight takes into account the removal of HPO_{2} (63.98) and the addition of two hydrogens (2.02).
Alternatively, you could think of this of the removal of a phosphate and the addition of a hydroxyl, since this formula calculates the molecular weight of 5' and 3' hydroxylated oligonucleotides.