Fumarase has a native molecular weight of 200000 or slightly

Fumarase has a native molecular weight of 200,000 or slightly less. It was dissolved in 6M guanidine hydrochloride in the presence of reducing agent. Under these conditions the proteins polypeptide chains (if more than 1) dissociate from each other. The resulting mixture was sedimented at 27, 690 rpm and 4 degree C for 132 hours and examined by interference optics, which monitors protein concentration. The following fringe displacements (microns) were obtained. The density of the solvent was 1.160 g/cc. A value of 0.715 cc/g was used for the apparent partial specific volume. The solution was assumed to be ideal because of the very low protein concentration. Use R = 8.314 times 10^7 erg/deg/mol. An erg = g cm^2/sec^2. Use only nonzero fringe measurements. Calculate the molecular weight. How many polypeptide chains does fumarase appear to have? The value of the apparent partial specific volume is not known with certainty because of the high guanidine concentration used. You can obtain the probable error resulting from this uncertainty (which is of the order of 0.01 cc/g) by repeating the calculation with upsilon\' = to 0.70 or 0.73.

Solution

Molecular weight(M)=s^o x Rx T/D^o(1-partial specific volume x density), D=R xT/Nx f, f=1.2 for globular proteins.

D=8.314 x 10⁷ x 277/6.022 x 10²³x 1.2=2302.978/6.022 x 10^-16=382.42 x 10^-16.

s^o=sedimentation velocity/(angular rotations per minute) x distance from the axis of rotation.(radius of lower meniscus)

sedimentation velocity=u=distance at the centre of the axis of rotation(midpoint)/time=7.005/132=0.0530.

s^o=0.0530/27690 x 7.092=0.0530/196377.48=0.0530/196378=0.0000026988=2.69 x 10^-6.

Molecular weight=2.69x 10^-6x 8.314 x 10⁷x 277/382.42 x 10^-16(1-0.71x 1.160)=6195.01 x 10/382.42 x10^-16x 0.1764=

61950.1/382.42 x 10^-16=162 x 10¹⁶.

Answer--162 x 10¹⁶ for avogadro number of fumarase molecules and has four polypeptide chains for four subunits in one enzyme molecule and molecular weight of one fumarase molecule =6.023 x 10²³/162 x 10¹⁶=0.0371790123  x 10⁷=3,71,790 for four polypeptides of fumarase enzyme, and molecular weight of one fumarase polypeptide=3,71,790/4=92,948 with aggregate of enzyme formed during cetrifugation and analysis by schlerein optics during analytical ultracentrifugation but under normal conditions the molecular weight of fumarase molecule is 1,94,000 with four polypeptides.

Further 1 min of rotation can be converted to seconds as 1min =60 seconds.