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Other related functions

There are now two additional PPFs available in this software that are based on the Flory polymer swelling model, and the McKenzie-Domb model that takes on the more general form of the equation above. The weight on the distribution function ( $ A_{2 \gamma} (r_{ij})^{2 \gamma}
\Delta r$) is a partial measure of the self-avoidance of the polymer chain. The effect is to cause the chain to expand. We can estimate the root-mean-square separation distance of the polymer chain from Eq. (8) from the following thermodynamic relationship


\begin{displaymath}
f(r) = \frac{ \partial S(r) }{\partial r}
= 2 k_B T \left\{ \frac{\gamma}{r}
- \frac{ \vartheta_{ij} }{b^2} r
\right\}.
\end{displaymath} (10)

where solving Eq. (10) for $f(r) = 0$ yields


\begin{displaymath}
R = \left( \frac{ \gamma}{ \vartheta_{ij}} \right)^{1/2} b.
\end{displaymath} (11)

where $R$ represents the stationary point in the entropy.

Increasing the size of your self-avoiding or ``excluded volume'' weight ($\gamma$) will tend to encourage your stems to form shorter domains. Likewise, compacting the size of the polymer to a globular structure will encourage longer stems. Understanding the solvent environment is very important in such cases.

Selection of one polymer distribution function excludes all others from consideration. If you do not know which one to use, you should probably start with the JS equation because this is the one that has been historically used in RNA secondary structure prediction for the last 30 years. It appears to give reliable results for domains of enclosed lengths of 100 to 200 nt.


next up previous
Next: About this document ... Up: Jacobson Stockmayer model Previous: Advice on changing the
Wayne Dawson 2005-02-03