Question

Problems 1-4: For a globular protein of diameter 6 nm, corresponding to a molecular mass of 100 kDa, 1. Calculate the mass in kg. 2. Calculate drag coefficient assuming η_1mPa's 3. Calculate viscous force at 25°C given: The average instantaneous thermal speed of a protein v-(3k*T/m)0.5 k is Boltzmann constant, 1.381 x 10-23 J/HK Tis the absolute temperature, 0 K-273.15°C 1J 1 N'm. 4. Calculate the speed of the protein caused by the centrifugal force. Assume that the centrifugal force is 100,000 times larger than the gravitational force subjected to the protein. Use Stokes' law for a sphere. Problems 5-7: For a typical bacterial cell the shape of which is 2 um in length and 1 um in diameter as shown in the figure below, pili flagella 2 pm 5. Calculate the surface area and volume. Also, estimate the mass of the bacterium assuming that the density of the bacterium is the same as that of water

Answer 1

molecular mass = 100 kDa = 10^5 Da = 10^5 g/mole = 10^5 times 10^-3/6.02 times 10^23 kg mars = m = 1.66 times 10^-22 kg. v = (3 kT/m)^1/2 k drag = 6 pi eta R R = 6 times 10^-9/2 = 3 times 10^-9 = 6 pi times 1 times 10^-3 times 3 times 10^-9 k drag = 5.65 times 10^-11 1g/s viscous force implies ? v = (3kT/m)^1/2 = (3 times 1.38 times 10^-23 times (273.15)/(1.66 times 10^-22))^1/2 = (1.130 times 10^+ 3 times 10^-23 times 10^-20/1.66 times 10^-22 10^-2)^1/2 = ((0.68) times 10^-2)^1/2 \r\n v = 0.82 times 10^1 v = 8.2 m/s F = 6 pi eta rv = k drag v = 5.65 times 10^-11 times 0.2 = 46.33 times 10^-11 N \r\n mg times 1000 = 6 pi eta rv = k drag v 1.66 times 10^-22 times 9.81 times 1000 = 5.65 times 10^-11 times v v = 2.88 times 10^-7 m/s