Difference between revisions of "DNA Melting Thermodynamics"
From Course Wiki
Line 1: | Line 1: | ||
==DNA solution== | ==DNA solution== | ||
− | {{LecturePoint|Consider a solution of complementary DNA oligonucleotides <math>\left . A \right .</math> and <math>\left . A' \right .</math>.}} | + | {{LecturePoint|Consider a solution containing equal quantities of complementary single stranded DNA oligonucleotides <math>\left . A \right .</math> and <math>\left . A' \right .</math>.}} |
− | {{LecturePoint|The | + | |
− | + | {{LecturePoint|Some of the strands combine to form double stranded DNA. The reaction is governed by the equation <math>1 A + 1 A' \Leftrightarrow 1 A \cdot A'</math>}} | |
− | {{LecturePoint|At equilibrium, the concentrations of the reaction products are | + | |
− | K = \frac{\left [ | + | {{LecturePoint|At equilibrium, the concentrations of the reaction products are governed by the relation: <math> |
+ | K = \frac{\left [ A \cdot A' \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 ] | + | {{LecturePoint|<math>\left . C_T \right .</math> is the total concentration of single stranded DNA. |
+ | :<math> | ||
+ | \begin{align} | ||
+ | C_T & = \left [ A \right ] + \left [ A' \right ] + 2 \left [ AA' \right ] \\ | ||
+ | & = 2 \left [ A \right ] + 2 \left [ AA' \right ] | ||
+ | \end{align} | ||
</math>}} | </math>}} | ||
− | {{LecturePoint|<math>\left . f \right .</math> | + | |
− | f = \frac{2 \left [ | + | {{LecturePoint|Let <math>\left . f \right .</math> be the fraction of DNA that is double stranded |
+ | <math> | ||
+ | f = \frac{2 \left [ A\cdot A' \right ]}{C_T} | ||
</math>}} | </math>}} | ||
+ | |||
{{LecturePoint|Solving for <math>\left . K \right .</math> in terms of <math>\left . f \right .</math>: | {{LecturePoint|Solving for <math>\left . K \right .</math> in terms of <math>\left . f \right .</math>: | ||
:<math> | :<math> |
Revision as of 03:56, 3 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 $ | $ \left . C_T \right . $ is the total concentration of single stranded DNA.
|
$ \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 . $:
|
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} $