Difference between revisions of "DNA Melting Thermodynamics"
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</math>}} | </math>}} | ||
| − | {{LecturePoint|Let <math>C_{SS} = {\left [ A \right ] = \left [ A' \right ]}</math>.}} | + | {{LecturePoint|Let <math>\left . C_{SS} \right .</math> represent the concentration of either single stranded oligonucleotide: <math>C_{SS} = {\left [ A \right ] = \left [ A' \right ]}</math>.}} |
| − | {{LecturePoint| | + | {{LecturePoint|Similarly, let <math>\left . C_{DS} \right .</math> be the concentration of double stranded DNA: <math>C_{DS} = {\left [ A \cdot A' \right ]}</math>}} |
{{LecturePoint|<math>\left . C_T \right .</math> is the total concentration of DNA strands. <math>\left . C_T = 2 C_{SS} + 2 C_{DS}\right .</math>}} | {{LecturePoint|<math>\left . C_T \right .</math> is the total concentration of DNA strands. <math>\left . C_T = 2 C_{SS} + 2 C_{DS}\right .</math>}} | ||
Revision as of 20:28, 8 April 2008
DNA solution
| $ \bullet $ | Consider a solution containing equal quantities of complementary single stranded DNA oligonucleotides $ \left . A \right . $ and $ \left . A' \right . $. |
| $ \bullet $ | Some of the strands combine to form double stranded DNA. The reaction is governed by the equation $ 1 A + 1 A' \Leftrightarrow 1 A \cdot A' $ |
| $ \bullet $ | At equilibrium, the concentrations of the reaction products are governed by the relation: $ K = \frac{\left [ A \cdot A' \right ]}{\left [ A \right ] \left [ A' \right ]} $ |
| $ \bullet $ | Let $ \left . C_{SS} \right . $ represent the concentration of either single stranded oligonucleotide: $ C_{SS} = {\left [ A \right ] = \left [ A' \right ]} $. |
| $ \bullet $ | Similarly, let $ \left . C_{DS} \right . $ be the concentration of double stranded DNA: $ C_{DS} = {\left [ A \cdot A' \right ]} $ |
| $ \bullet $ | $ \left . C_T \right . $ is the total concentration of DNA strands. $ \left . C_T = 2 C_{SS} + 2 C_{DS}\right . $ |
| $ \bullet $ | Let $ \left . f \right . $ be the fraction of DNA that is double stranded
$ f = \frac{2 \left [ A\cdot A' \right ]}{C_T} $ |
| $ \bullet $ | Solving for $ \left . K \right . $ in terms of $ \left . f \right . $: |
- $ \begin{align} K & = \frac{\left [ AA' \right ]}{\left ( \frac{1}{2} C_T - \left [ AA' \right ] \right ) ^ 2} = \frac{\left [ AA' \right ]}{C_T^2 \left ( \frac{1}{2} - \frac{\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} \end{align} $
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} $
