Download Web Problem 24

Web Problem 24.2:
In this problem, the dependence of the velocity sedimentation coefficient S20,w for DNA
is investigated as a function of the molecular mass of the DNA. Specifically, in the low
molecular weight range (M<105 g mol-1), DNA can be considered a rigid rod. For DNA
greater than this molecular weight range, the DNA structure becomes more flexible. The
impact of DNA shape and flexibility on S20,w will be investigated..
The equation for the sedimentation constant is
m
M
S20,w  1  V2   
1  V2  
f
NA f
where m is the mass of a single DNA molecule, M is the weight of a mole (i.e. molecular
weight) of the DNA. All other symbols can be found in the text.
The dependence of the sedimentation coefficient of DNA on the molecular
weight M of the DNA reflects changes in the structure of the DNA. At low molecular
weights DNA has the hydrodynamic properties of a rigid rod. At higher molecular
weights, DNA behaves as a flexible chain. This dependence can be discerned from Figure
24.13, which is a log-log plot of the sedimentation coefficient of DNA as a function of
molecular weight M.
Task 1: The sedimentation data in Figure 14.13 is reproduced in the Web
simulation. It has been long known (Crothers, D.M. & Zimm, B.H. (1965) Viscosity and
Sedimentation of DNA from Bacteriophages T2 and T7 and the Relation to Molecular
Weight J. Mol. Biol. 12, 525-536) that the sedimentation coefficient plotted as a function
of DNA weight M fits the empirical equation
S  2.7  0.01517 M x
where x is a constant to be determined. Adjust the slide wire on the diagram and from the
best fit to the data determine x.
Task 2: The physical meaning of the coefficient x becomes clear if one remembers
M
M
1  V2   and so S20,w 
that S20,w 
. However, the coefficient of translational

NA f
f
friction f is also a function of M. The coefficient of friction f varies with the shape of the
DNA and so does the dependence of f on M. Therefore the physical meaning of x is that
it reflect the dependence of f on M and therefore gives information on the shape of DNA
Consider three models for the shape of high molecular weight DNA:
1) A hydrated sphere: f  6 Rh . All symbols are given in the text
2) A rigid chain of N spherical beads f 
3 N 
, where  is the diameter of each
ln N
spherical bead.
3) A random coil polymer: f  6 R 2
1/ 2
where R 2 is the mean squared end-to-
end distance for a random coil polymer.
For each case, determine the dependence of f on M and calculate the ratio M/f. Compare
each result to x, determined in Task 1. Based on this comparison, which structural model
best fits the sedimentation data? Hint: M is proportional to volume.