Saturday, January 29, 2011
Oligos Melting Temperature
Melting Temperature:
Technical Bulletin (Adobe Acrobat)
Download File (91 K PDF)
The melting temperature, Tm, of an oligonucleotide is its most critically important value. The most reliable and accurate determination of melting temperature is determined empirically [1], however, this is cumbersome and not usually necessary.
Several useful, handy formulas have been developed to provide the Tm for PCR, Southern and Northern blots, and in situ hybridization.
The main factors affecting Tm are salt concentration, strand concentration, and the presence of denaturants (such as formamide or DMSO). Other effects such as sequence, length, and hybridization conditions can be important as well.
Definitions
Tm - The temperature at which 50% of the oligonucleotide and its perfect complement are in duplex.
Td - The temperature at a particular salt concentration, and total strand concentration at which 50% of an oligo and its perfect filter-bound complement are in duplex.
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Equations
The simplest equation for Td is the Wallace rule [2]:
(1) Td = 2°C(A+T) + 4°C(G+C)
Td is a filter-based calculation where A, G, C, and T are the number of occurrences of each nucleotide. This equation was developed for short DNA oligos of 14-20 base pairs hybridizing to membrane bound DNA targets in 0.9M NaCl.
The melting temperature for the sequence TGCTCA is, 2(1+2) + 4(1+2) = 18°C. The nature of the immobilized target strand provides a net decrease in the Tm observed when both target and probe are free in solution. The magnitude of the decrease is approximately 7-8°C.
Another familiar equation [3] for DNA which is valid for oligos longer than 50 nucleotides from pH 5 to 9 is:
(2) Tm = 81.5 + 16.6 log M + 41(XG+XC) - 500/L - 0.62F
Where M is the molar concentration of monovalent cations, XG and XC are the mole fractions of G and C in the oligo, L is the length of the shortest strand in the duplex, and F is the molar concentration of formamide.
This is a far more useful equation to most researchers, as it includes adjustments for salt (although the equation is < when M=0) and formamide , the two most common agents for changing hybridization temperatures.
Thus, at M = 0.9, and F = 0, Tm = 81.5+16.6(log(0.9))+41(.17+.33)-500/6-0.62(0)=17.9° C. Similar equations apply for RNA. [4]
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Theoretical
Several studies have derived accurate equations for Tm using thermodynamic basis sets for nearest neighbor interactions. [5] The equation for DNA and RNA is:
Theoretical_image
Where ΔH (Kcal/mol) is the sum of the nearest neighbor enthalpy changes for hybrids, A is a small, but important constant containing corrections for helix initiation, ΔS (eu) is the sum of the nearest neighbor entropy changes, R is the Gas Constant (1.987 cal deg-1 mol-1) and Ct is the total molar concentration of strands. If the strand is self complementary, Ct /4 is replaced by Ct.
ΔH and ΔS values for nearest neighbor interactions of DNA and RNA are shown in Table 1. Please note that this equation includes a factor to adjust for salt concentration.
For example, our sample sequence would result in the following expression assuming 200 nM strand concentration at 900 mM NaCl:
1000*(-5.8-11.1-7.8-5.6-5.8)
---------------------------------------------------------- - 273.15 + 16.6log(0.9)
[(-10.8)+(-12.9-26.7-20.8-13.5-12.9)+(1.987)ln[(2.0E-7)/4]]
Therefore: Tm = 1.725°C
Notice the considerable difference between the results of equations (1) and (3) in this case. This shows how much of an effect sequence can have on the Tm.
back to top
Comparisons
So which value do we use? Remember that Equation 1 was derived for 14-20mers used in membrane hybridizations and may be expected to have a limited range of applicability - an important point, as this equation is used by almost all researchers for oligos used for PCR as well as blots. Equation 3 is certainly more appropriate in this case. On the other hand, Equation 3 becomes inappropriate for oligos longer than a 50-mer. For long oligos, equation 2 is probably the best choice. The best equation for a particular researcher will depend on the oligo and the type of experiment involved.
Solution based amplification strategies can use the Wallace rule for convenience, but one should add 8° C to the result to convert Td to Tm. Accuracy will also be compromised if the salt concentration varies much from 0.9 M. Researchers doing Southern, Northern or other filter hybridizations can use equation (1) as is. As with any theoretical approach, the results of these equations should be used with caution. Many experiments involve reagents or conditions that invalidate the results of these equations. Sometimes only an empirical approach provides a satisfactory answer. For instance, in situ hybridizations provide sufficiently different environments from case to case that anomalous results may occur.
Counter ion identity, solvation effects, conjugated groups (biotin, digoxigenin, alkaline phosphatase, fluorescent dyes, etc.), and impurities may also affect the Tm. In these cases, theoretical equations are inaccurate, but still provide a useful estimate to begin development.
back to top
Conclusions
At Genosys, all oligo Tm are calculated using the nearest neighbor method with values of 50 mM for cation concentration and 0.5 micromolar for the strand concentration. [6] For individuals, it may make more sense to use the less complicated equations. Whichever equations one uses, one will obtain accurate results as long as one remembers to correct for salt or formamide concentration and to observe the limits of applicability of each equation.
back to top
References
1. The common way to determine the actual melting point is to use a thermostatted cell in a UV spectrophotometer. If temperature is plotted vs. absorbance, an S-shaped curve with two plateaus will be observed. The absorbance reading halfway between the plateaus corresponds to Tm.
2. Wallace, R.B.; Shaffer, J.; Murphy, R.F.; Bonner, J.; Hirose, T.; Itakura, K. Nucleic Acids Res. 6, 3543 (1979).
3. Howley, P.M; Israel, M.F.; law, M-F.; Martin,M.A. J. Biol. Chem. 254, 4876.
The equations for RNA are:
Tm = 79.8 + 18.5 log M + 58.4 (XG+XC) + 11.8(XG+XC)2 - 820/L - 0.35F
And for DNA-RNA hybrids:
Tm = 79.8 + 18.5 log M + 58.4 (XG+XC) + 11.8(XG+XC)2 - 820/L - 0.50F
These equations are derived for oligo-immobilized target hybrids. In general, one can say that RNA-RNA hybrids are highest in stability, then RNA-DNA, and then DNA-DNA.
5. For DNA see: Breslauer, K.J.; Frank, R.; Blšcker, H.; Marky, L.A. Proc. Natl. Acad. Sci. USA 83, 3746-3750(1986). For RNA see: Freier, S.M.; Kierzek, R.; Jaeger, J.A.; Sugimoto, N.; Caruthers, M.H.; Neilson, T.; Turner, D.H. Proc. Natl. Acad. Sci. 83, 9373-9377 (1986).
6. These values have been found to be the most appropriate for PCR. Rychlik, W.; Spencer, W.J.; Rhoads, R.E. (1990) Nucl. Acids Res. 18(21), 6409-6412.
Technical Bulletin (Adobe Acrobat)
Download File (91 K PDF)
The melting temperature, Tm, of an oligonucleotide is its most critically important value. The most reliable and accurate determination of melting temperature is determined empirically [1], however, this is cumbersome and not usually necessary.
Several useful, handy formulas have been developed to provide the Tm for PCR, Southern and Northern blots, and in situ hybridization.
The main factors affecting Tm are salt concentration, strand concentration, and the presence of denaturants (such as formamide or DMSO). Other effects such as sequence, length, and hybridization conditions can be important as well.
Definitions
Tm - The temperature at which 50% of the oligonucleotide and its perfect complement are in duplex.
Td - The temperature at a particular salt concentration, and total strand concentration at which 50% of an oligo and its perfect filter-bound complement are in duplex.
back to top
Equations
The simplest equation for Td is the Wallace rule [2]:
(1) Td = 2°C(A+T) + 4°C(G+C)
Td is a filter-based calculation where A, G, C, and T are the number of occurrences of each nucleotide. This equation was developed for short DNA oligos of 14-20 base pairs hybridizing to membrane bound DNA targets in 0.9M NaCl.
The melting temperature for the sequence TGCTCA is, 2(1+2) + 4(1+2) = 18°C. The nature of the immobilized target strand provides a net decrease in the Tm observed when both target and probe are free in solution. The magnitude of the decrease is approximately 7-8°C.
Another familiar equation [3] for DNA which is valid for oligos longer than 50 nucleotides from pH 5 to 9 is:
(2) Tm = 81.5 + 16.6 log M + 41(XG+XC) - 500/L - 0.62F
Where M is the molar concentration of monovalent cations, XG and XC are the mole fractions of G and C in the oligo, L is the length of the shortest strand in the duplex, and F is the molar concentration of formamide.
This is a far more useful equation to most researchers, as it includes adjustments for salt (although the equation is < when M=0) and formamide , the two most common agents for changing hybridization temperatures.
Thus, at M = 0.9, and F = 0, Tm = 81.5+16.6(log(0.9))+41(.17+.33)-500/6-0.62(0)=17.9° C. Similar equations apply for RNA. [4]
back to top
Theoretical
Several studies have derived accurate equations for Tm using thermodynamic basis sets for nearest neighbor interactions. [5] The equation for DNA and RNA is:
Theoretical_image
Where ΔH (Kcal/mol) is the sum of the nearest neighbor enthalpy changes for hybrids, A is a small, but important constant containing corrections for helix initiation, ΔS (eu) is the sum of the nearest neighbor entropy changes, R is the Gas Constant (1.987 cal deg-1 mol-1) and Ct is the total molar concentration of strands. If the strand is self complementary, Ct /4 is replaced by Ct.
ΔH and ΔS values for nearest neighbor interactions of DNA and RNA are shown in Table 1. Please note that this equation includes a factor to adjust for salt concentration.
For example, our sample sequence would result in the following expression assuming 200 nM strand concentration at 900 mM NaCl:
1000*(-5.8-11.1-7.8-5.6-5.8)
---------------------------------------------------------- - 273.15 + 16.6log(0.9)
[(-10.8)+(-12.9-26.7-20.8-13.5-12.9)+(1.987)ln[(2.0E-7)/4]]
Therefore: Tm = 1.725°C
Notice the considerable difference between the results of equations (1) and (3) in this case. This shows how much of an effect sequence can have on the Tm.
back to top
Comparisons
So which value do we use? Remember that Equation 1 was derived for 14-20mers used in membrane hybridizations and may be expected to have a limited range of applicability - an important point, as this equation is used by almost all researchers for oligos used for PCR as well as blots. Equation 3 is certainly more appropriate in this case. On the other hand, Equation 3 becomes inappropriate for oligos longer than a 50-mer. For long oligos, equation 2 is probably the best choice. The best equation for a particular researcher will depend on the oligo and the type of experiment involved.
Solution based amplification strategies can use the Wallace rule for convenience, but one should add 8° C to the result to convert Td to Tm. Accuracy will also be compromised if the salt concentration varies much from 0.9 M. Researchers doing Southern, Northern or other filter hybridizations can use equation (1) as is. As with any theoretical approach, the results of these equations should be used with caution. Many experiments involve reagents or conditions that invalidate the results of these equations. Sometimes only an empirical approach provides a satisfactory answer. For instance, in situ hybridizations provide sufficiently different environments from case to case that anomalous results may occur.
Counter ion identity, solvation effects, conjugated groups (biotin, digoxigenin, alkaline phosphatase, fluorescent dyes, etc.), and impurities may also affect the Tm. In these cases, theoretical equations are inaccurate, but still provide a useful estimate to begin development.
back to top
Conclusions
At Genosys, all oligo Tm are calculated using the nearest neighbor method with values of 50 mM for cation concentration and 0.5 micromolar for the strand concentration. [6] For individuals, it may make more sense to use the less complicated equations. Whichever equations one uses, one will obtain accurate results as long as one remembers to correct for salt or formamide concentration and to observe the limits of applicability of each equation.
back to top
References
1. The common way to determine the actual melting point is to use a thermostatted cell in a UV spectrophotometer. If temperature is plotted vs. absorbance, an S-shaped curve with two plateaus will be observed. The absorbance reading halfway between the plateaus corresponds to Tm.
2. Wallace, R.B.; Shaffer, J.; Murphy, R.F.; Bonner, J.; Hirose, T.; Itakura, K. Nucleic Acids Res. 6, 3543 (1979).
3. Howley, P.M; Israel, M.F.; law, M-F.; Martin,M.A. J. Biol. Chem. 254, 4876.
The equations for RNA are:
Tm = 79.8 + 18.5 log M + 58.4 (XG+XC) + 11.8(XG+XC)2 - 820/L - 0.35F
And for DNA-RNA hybrids:
Tm = 79.8 + 18.5 log M + 58.4 (XG+XC) + 11.8(XG+XC)2 - 820/L - 0.50F
These equations are derived for oligo-immobilized target hybrids. In general, one can say that RNA-RNA hybrids are highest in stability, then RNA-DNA, and then DNA-DNA.
5. For DNA see: Breslauer, K.J.; Frank, R.; Blšcker, H.; Marky, L.A. Proc. Natl. Acad. Sci. USA 83, 3746-3750(1986). For RNA see: Freier, S.M.; Kierzek, R.; Jaeger, J.A.; Sugimoto, N.; Caruthers, M.H.; Neilson, T.; Turner, D.H. Proc. Natl. Acad. Sci. 83, 9373-9377 (1986).
6. These values have been found to be the most appropriate for PCR. Rychlik, W.; Spencer, W.J.; Rhoads, R.E. (1990) Nucl. Acids Res. 18(21), 6409-6412.
Deductive and Inductive Thinking
Deduction & Induction
Deductive and Inductive Thinking
http://www.socialresearchmethods.net/kb/dedind.php
In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach (please note that it's "bottom up" and not "bottoms up" which is the kind of thing the bartender says to customers when he's trying to close for the night!). In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different "feel" to them when you're conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning. Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project. In fact, it doesn't take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and back up again to theories. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories.
Deductive and Inductive Thinking
http://www.socialresearchmethods.net/kb/dedind.php
In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach (please note that it's "bottom up" and not "bottoms up" which is the kind of thing the bartender says to customers when he's trying to close for the night!). In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different "feel" to them when you're conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning. Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project. In fact, it doesn't take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and back up again to theories. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories.
