0.9993). The diffusion coefficient, D, can also be calculated from the data by monitoring the spread of the boundary region, as this becomes less sharp with time. A value of the boundary spreading, denoted as Z, is calculated for each data set according to Muramatsu and Minton (1988). Plotting the boundary spreading parameter versus time gives a linear relationship, with the slope being equal to the diffusion coefficient (figure 4.6). The D value derived from figure 4.6 is 9.22 x 10'^ cm^ s'^ (with the fit having a correlation coefficient ofO.9968).
Sedimentation coefficients can be used to obtain an idea of the shape of the solute molecules using the Svedberg equation (Waxman et a l, 1994);
s = A/( 1-wpyNf equation 5
to obtain an estimate of the fiictional coefficient /.
Taking s to be 2.06 x 1 0"^^ seconds. A/to be 21000 g mol**, v to be 0.725 ml g'*, p to be
1.00389 g mT* and Nxo be 6.023 x lo^ mol'*, the value o f/is calculated to be 4.60 x 1 0‘*
8 s '.
/ can also be derived using the diffusion coefficient from the relationship (Ralston, 1993):
D = RTINf equation 6
Taking D to be 9.22 x 1 0*^ cm^ s'*, R to be 8.314 x 10^ erg mol'* K'*, T to be 293 K and N
to be 6.023 x lo ^ mol'*,/is calculated to be 4.39 x 10“* g s'*.
There is thus a relatively good agreement in the values of f obtained using the sedimentation and diffusion coefficients.
The shape of the molecule can be determined by taking the ratio of the / value to the fiictional coefficient for a theoretical sphere fg.
Figure 4.5; Determination of the Sedimentation Coefficient S
Each absorbance scan shown in figure 4.4 was fitted to the second-moment method to obtain values of the boundary position. Plotting ln(boundary) versus the product of the square of the angular velocity and time produced a linear relationship. The solid line is a linear fit to the data with a slope of 2.06 x 1 0’^^ seconds, which corresponds to the
sedimentation coefficient.
1.905 1.900- 1.895- 1 .890- 1.885 - im C 1.880- 1.875 - 1.870- 1.865- 1.860 0.21 0.24 0.27 0.30 0.33 0.36 0.39 0.42
w^t* 10'" (s'*)
Figure 4,6: Determination of the Diffusion Coefficient, D
Each scan of absorbance against radius shown in figure 4.3 was analysed by the second- moment method of boundary position determination, and produced a value of boundary spreading (Z). Plotting Z against time shows a linear relationship with a slope corresponding to a difiusion coefficient of 9.22 x 10'^ cm^ s'\
1.00 0.90 — 0 .8 0 - o 0 .7 0 - N 0 .6 0 - 0 .5 0 - 0.40 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time * 10 ^ (s)
where t| is the viscosity of the solvent, Ô is the hydration (gH20/g protein), M is 21000 g moI'\ V is 0.725 ml g"^ and N is 6.023 x 10^ mol'\ Taking r\ to be the viscosity of water (10 X 10'^ poise) and ô to be 0.4, which was calculated from the amino acid composition by Hazlett et al. (1993) and is also an average value for the hydration of proteins (usually between 0.33 and 0.42 (Cantor and Schimmel, 1980)),/^ is 3.84 x 10'* g s'\ Since the value of Ô is not well defined, the limiting values of 0.33 and 0.42 for ô (for proteins using the technique of NMR-fieezing) were also used to calculate/o, which becomes 3.77 x lO'* g s'^ and 3.86 X 10'* g s'^ respectively.
C alculating^ for each of the calculatedvalues are as follows :
f f o
fis, s'*)
/(, = 3.84x ID *
(gs-*)/„=3.77x 10-*
(g
s'*)/„ = 3.86x 10-*
(g S'*)4.60 X 10-*
1.20
1.22
1.19
4.39 X 10-«
1.14
1.16
1.14
Varying the hydration of the protein between 0.33 and 0.42 cm^ per gram of protein, therefore, has little effect on the value offo and subsequently has little effect on the ratio of the fiictional coefficient to the fiictional coefficient for a spherical molecule (/%). The ratio values show that ras has some asymmetry but is fairly globular in agreement with the crystal structure of ras (Pai et a l, 1989, 1990; Milbum et a l, 1990). The ffo ratio represents an axial ratio a/b of the ellipsoid model of 3.5-4.5 (prolate) or 3.75-5.00 (oblate), suggesting that the length of the protein is 3.5-5 times the width of the protein. This is probably due to the C-terminus of ras which one would expect to be elongated as it serves to anchor the protein in the plasma membrane in cells.
4.4: Analytical Ultracentrifugation of Neurofibromin
There is no structure information on neurofibromin at present, and the molecular weight and the shape of the neurofibromin fi-agment were calculated using a combination of equilibrium and velocity sedimentation.
4.4,1; Equilibrium Sedimentation of Neurofibromin
To determine the molecular weight of the neurofibromin fragment a solution of neurofibromin exchanged into fresh buffer A plus lOOmM NaCl with an Ajgo of 0.5 was centrifuged at 16,000 rpm taking five A2go scans along the length of the cell at two-hour
intervals, after a delay of 15 hours. All five runs were superimposible indicating that the solute distribution was at equilibrium. The selected exponential data at equilibrium was fitted to the single solute model (figure 4.7). Using values of 0.741 ml g'^ for v, calculated fi-om the amino acid composition (Laue et a l, 1992), and 1.00389 g ml*^ for p, calculated fi'om the buflfer constituents, the molecular weight was found to be 38137 +/-180 g mol'*, with the residuals demonstrating that the model is likely to be correct. As the monomer molecular weight of the neurofibromin fi-agment is 38494 g mol'^ this shows that, under these conditions, neurofibromin exists as a monomer.
4i4,2i .YfitodtiLSedLqifcntatiQii of NgprQfibrQmin
A solution of neurofibromin exchanged into fi-esh buffer A plus lOOmM NaCl with an absorbance of 1.0 at 280nm was centrifuged at 48000 rpm at 20°C. After a delay of 100 minutes, 10 A2 8 0 scans were made along the length of the cell at 10 minute intervals. The
data obtained was analysed by the second-moment method to produce an estimates of the sedimentation coefficient, and the diffiision coefficient was determined from the spreading of the boundary region (as described in section 4.3.2 for ras). The sedimentation coefficient was calculated to be 2.86 x 10'^^ s and the diffiision coefficient was calculated to be 8.54 X 10'^ cm^ s'\ with the correlation coefficients of the fits were 0.999 for the calculation of the sedimentation coefficient and 0.993 for the calculation of the diffiision coefficient. Using these s and D values to calculate the fiictional coefficient/ (as described in section 4.3.2) where M is 36000 g mol"\ v is 0.741 ml g"% p is 1.00389 g m l'\ N is 6.023 x 10^ mol'\ R is 8.314 x 10^ erg mol'^ K'^ and T is 293 K, gives the following values:
Method / ( g s‘‘)
Using j 5.35 X 10-*
Using D 4.74 X 10 *
Calculating^ for the neurofibromin fragment (as described in section 4.) taking M to be 36000 g m ol'\ V to be 0.741 ml g '\ N to be 6.023 x i ( p mol*^, r\ to be the viscosity of water (10 x 10'^ poise) and ô to be 0.4, gives a value of 4.63 x 10** g s’^ Using this to
Figure 4.7; Equilibrium Sedimentation of Neurofibromin
A solution of neurofibromin in buffer A plus lOOmM NaCl with an absorbance of 0.5 at 280nm was centrifuged at 16000 rpm for 23 hours at 20°C. The absorbance of the selected exponential increase in solute concentration (after 23 hours) is plotted against the distance, r, fi'om the centre of rotation. The solid line is the best fit to a single exponential equation for a single solute species. The molecular weight obtained fi'om the fit is 38137 +/- 180 Da. The residuals show that the fit is appropriate for the data.