Question

An important step in the blood coagulation process is the enzymatic conversion of the protein prothrombin to the lower-molecular-weight clotting agent, thrombin, via cleavage of a portion of the prothrombin polypeptide.

Prothrombin → thrombin + cleaved peptide

The values of s20,w and D20,w for prothrombin have been found to be 4.85S and 4.93×10−11m2s−1 , respectively. The diffusion coefficient for thrombin is 8.76×10−11m2s−1. Assuming that both thrombin and prothrombin are unhydrated spheres with vB=0.70mLg−1, calculate the molecular weight of the cleaved peptide. [Express your answer in units of kg/mol]

Answer 1

Svedberg equation allows one to calculate molar mass of a protein with known sedimentation

coefficient and diffusion coefficient at a given temperature as given below:

M = RTs / D (1- vB)

Calculation of molecular weight of prothrombin:

R = Gas constant = 8.314 J/K/mol

T = Temperature in Kelvin = 298.15 K (assumed Standard temperature: 25^oC)

S = sedimentation coefficient = 4.85 S (Svedbergs) = 4.85 X 10^-13 (Seconds)

D = diffusion coefficient = 4.93×10−11m2s−1

vB = Partial specific volume = 0.70 mLg⁻¹ = 0.70 cm³g⁻¹

​ = Density = 1.00 gcm^-3

Substituting all the values in the above formula one may calculate molecular weight of

prothrombin as shown below:

= 8.314 x 298.15 x 4.85 X 10^-13 / 4.93×10⁻¹¹ (1 – (0.70x1)

= 8.314 x 298.15 x 4.85 X 10^-13 / 4.93×10⁻¹¹ x 0.30

= 8.314 x 298.15 x 4.85 X 10^-2 / 4.93 × 0.30

= 8.314 x 298.15 x 0.0485 / 1.479

= 120.22/1.479

= 81.28 Kg mol^-1

Molecular weight of prothrombin = = 81.28 Kg mol-1

Calculation of molecular weight of thrombin:

R = Gas constant = 8.314 J/K/mol

T = Temperature in Kelvin = 298.15 K (assumed Standard temperature: 25^oC)

S = sedimentation coefficient = 4.85 S (Svedbergs) = 4.85 X 10^-13 (Seconds) (assumed same as

that of prothrombin as it’s not given in the data)

D = diffusion coefficient = 8.76×10⁻¹¹m2s−1

vB = Partial specific volume = 0.70 mLg⁻¹ = 0.70 cm³g⁻¹

= Density = 1.00 gcm^-3

Substituting all the values in the above formula one may calculate molecular weight of thrombin as shown below:

= 8.314 x 298.15 x 4.85 X 10^-13 / 8.76×10⁻¹¹ (1 – (0.70x1)

= 8.314 x 298.15 x 4.85 X 10^-13 / 8.76×10⁻¹¹ x 0.30

= 8.314 x 298.15 x 4.85 X 10^-2 / 8.76 x 0.30

= 8.314 x 298.15 x 0.0485 / 2.628

= 120.22/2.268

= 45.75 Kg mol^-1

Molecular weight of thrombin = 45.75 Kg mol^-1

Molecular weight of the cleaved peptide = Molecular weight of prothrombin - Molecular weight

of thrombin

                                                                          = 81.28 - 45.75 = 35.53 Kg mol-1

Molecular weight of the cleaved peptide = 35.53 Kg mol-1