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# Calculating Melting Temperatures using Mfold Two-state Melting (hybridization)

Hello, I am working on a project using the Two-state melting (hybridization) to design molecular beacons the implement a stem-loop structure. In order to optimize binding I need to drive my reaction equilibrium, K, to the right, while retaining an elevated melting temperature. I've been having trouble with the optimization, however, so I have begun looking into how mfold performs these calculations, specifically the melting temperature.

The melting temperature of a strand of DNA should be when half is bound and the other half unbound; in other words, when deltaG = 0. By this, Tm = deltaH/deltaS (and the according unit adjustments). I have found two sources that confirm this is how mfold performs this calculation (http://nar.oxfordjournals.org/content/33/suppl_2/W577.full and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC169194/ ), but the reported values do not seem to match.

Here is an example that I have been working with:

Sequence 1: cGAGTCGCCAGACTCg;

Sequence 2: cGAGTCGCCAGACTCg; (identical)

DNA binding at 60C, [Na+] = 50 mM, [Mg++] = 1.5 mM, [strand] = 0.00001 M

Output:

ΔG = -1.7 ΔH = -29.3 ΔS = -82.9 Tm = 3.7°C

The listed Tm is 3.7C, but when I do the calculation myself, Tm = (-29.3/-0.829) - 273.15 = 80.3C.

Can you help me understand this apparent discrepancy? This is the last obstacle we need to overcome before ordering supplies to perform tests.

As far as I can tell, the Two-State Melting uses the equation

TM = H × 1000/(S + R × ln(CT/x)) − 273.15,

http://www.math.utah.edu/~palais/pcr/papers/SL2004.pdf

Where H is the Enthalpy, S is the Entropy, R is the Gas Constant 1.9872 cal/K/mol, ln is the natural logarithm, CT is the concentration, and x is 4 if the sequence is self-complementary and 1 if not.

For your example x=1:

Tm= -29.3*1000/(-82.9+1.9872*ln(.00001/1))-273.15 = 3.844

The small discrepancy is in rounding in the calculations I believe. Here is an example of a sequence that is not self-complementary (x=4):

Sequence 1: CCCCGGGGAAAATTTT

Sequence 2: AAAATTTTCCCCGGGG

1. ΔG = -9.4 ΔH = -108.0 ΔS = -295.9 Tm = 62.7°C

Tm = -108*1000/(-295.9+1.9872*ln(.00001/4))-273.15 = 62.7405

Which is a match.

As far as I can tell, the x-value has to do with whether the bound duplex would have any symmetry. Symmetry would reduce the number of distinguishable microstates which changes thermodynamics. If the duplex is indistinguishable when it is right side up from when it is upside down, x=1. Otherwise, x=4.

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