Difference between revisions of "DNA Melting Thermodynamics"
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==DNA solution== | ==DNA solution== | ||
| − | + | {{LecturePoint|Consider a solution of complementary DNA oligonucleotides <math>\left . A \right .</math> and <math>\left . A' \right .</math>.}} | |
| − | + | {{LecturePoint|The oligos combine by the reaction <math>1 A + 1 A' \Leftrightarrow 1 AA'</math>}} | |
| − | + | {{LecturePoint|The concentration of the unpaired oligos are denoted by <math>\left [ A \right ]</math> and <math>\left [ A' \right ]</math>. <math>\left [ AA' \right ]</math> is the concentration of paired oligos.}} | |
| − | + | {{LecturePoint|At equilibrium, the concentrations of the reaction products are related by: <math> | |
K = \frac{\left [ AA' \right ]}{\left [ A \right ] \left [ A' \right ]} | K = \frac{\left [ AA' \right ]}{\left [ A \right ] \left [ A' \right ]} | ||
| − | </math> | + | </math>}} |
| − | + | {{LecturePoint|<math>\left . C_T \right .</math> is the total concentration of single stranded DNA. <math> | |
C_T = \left [ A \right ] + \left [ A' \right ] + 2 \left [ AA' \right ] | C_T = \left [ A \right ] + \left [ A' \right ] + 2 \left [ AA' \right ] | ||
| − | </math> | + | </math>}} |
| − | + | {{LecturePoint|<math>\left . f \right .</math> is the fraction of DNA that is double stranded <math> | |
f = \frac{2 \left [ AA' \right ]}{C_T} | f = \frac{2 \left [ AA' \right ]}{C_T} | ||
| − | </math> | + | </math>}} |
| − | + | {{LecturePoint|Solving for <math>\left . K \right .</math> in terms of <math>\left . f \right .</math>: | |
:<math> | :<math> | ||
\begin{align} | \begin{align} | ||
| Line 20: | Line 20: | ||
= \frac{\frac{2 \left [ AA' \right ]}{C_T}}{2 C_T \left ( \frac{1}{2} - \frac{1}{2}\frac{2 \left [ AA' \right ]}{C_T} \right ) ^ 2} \\ | = \frac{\frac{2 \left [ AA' \right ]}{C_T}}{2 C_T \left ( \frac{1}{2} - \frac{1}{2}\frac{2 \left [ AA' \right ]}{C_T} \right ) ^ 2} \\ | ||
& = \frac{f}{2 C_T \left ( \frac{1}{2} - \frac{1}{2} f \right ) ^2} | & = \frac{f}{2 C_T \left ( \frac{1}{2} - \frac{1}{2} f \right ) ^2} | ||
| − | \end{align} | + | \end{align} |
| − | </math> | + | </math>}} |
==Free energy== | ==Free energy== | ||
Revision as of 22:34, 31 March 2008
DNA solution
| $ \bullet $ | Consider a solution of complementary DNA oligonucleotides $ \left . A \right . $ and $ \left . A' \right . $. |
| $ \bullet $ | The oligos combine by the reaction $ 1 A + 1 A' \Leftrightarrow 1 AA' $ |
| $ \bullet $ | The concentration of the unpaired oligos are denoted by $ \left [ A \right ] $ and $ \left [ A' \right ] $. $ \left [ AA' \right ] $ is the concentration of paired oligos. |
| $ \bullet $ | At equilibrium, the concentrations of the reaction products are related by: $ K = \frac{\left [ AA' \right ]}{\left [ A \right ] \left [ A' \right ]} $ |
| $ \bullet $ | $ \left . C_T \right . $ is the total concentration of single stranded DNA. $ C_T = \left [ A \right ] + \left [ A' \right ] + 2 \left [ AA' \right ] $ |
| $ \bullet $ | $ \left . f \right . $ is the fraction of DNA that is double stranded $ f = \frac{2 \left [ AA' \right ]}{C_T} $ |
| $ \bullet $ | Solving for $ \left . K \right . $ in terms of $ \left . f \right . $:
|
Free energy
- $ \begin{align} \Delta G & = \Delta H - T \Delta S \quad (1)\\ & = -R T \ln K \quad (2)\\ \end{align} $
where
- $ \Delta G $ is the change in free energy
- $ \Delta H $ is the enthalpy change
- T is the absolute temperature
- $ \Delta S $ is the entropy change
- R is the gas constant
- K is the dissociation constant
Let $ C_T \quad $ be the total concentration of ssDNA.
- $ \begin{align} C_{ss} & = \left [ A \right ] = \left [ A' \right ] \quad (3) \\ C_{ds} & = \left [ AA' \right ] \quad (4) \\ \end{align} $
