Assume a macromolecule A dimerizes according to 2AA2. Assume the kinetics follow

Question

Assume a macromolecule A dimerizes according to 2AA2. Assume the kinetics follows the second order integrated rate equation 1/[A]t=1/[A]0=2kt, where [A]t is the concentration of A at time t and [A]0 is the initial concentration of A. Assume the kinetics are diffusion controlled. Assume the initial concentration of A is [A]0=0.01mol/m3. Assume T=293K. a) Assume macromolecule A is a rigid cylinder in solution with length L=10nm and radius R=1nm. Calculate the diffusion coefficient at T=293K. Note for a rigid cylinder f=3L/ln(L/R). Assume =0.001kg m-1s-1.

b) Using your result from Part A, calculate the kinetic constant at T=293K.

c) Using your resdult from part B, calculate the amount of time required for the concentration of the monomer form of A to decrease to half of its initial concentration.

d) The dimer may have one of two geometries. Two molecules A may join end-to-end, to form a cylindrical dimer with L=20nm and R=1nm. Alternatively two molecuiles A may join side-by-side and form a cylindrical dimer for which L=10nm and R=2nm. At T=293K, the diffusion coefficient of the dimer was determined to be 6.35*10-11m2s-1. Which model of dimerization most closely reproduces the experimental diffuion coefficient.

Side-by-Side dimer

End-to-End Dimer

Cannot determine because both models differ from data by more thasn 5%.

Explanation / Answer

(a)

L=10 nm =10*10-9 m=10-8 m

R=1 nm =10-9 m

f=3L/ln(L/R)=3*3.14*0.001*10-8/ln(10-8/10-9)=4.09*10-11 kg/s

Diffusion coefficient

D=kBT/f

Where kB =Boltzmann constant =1.3806*10-23 J/K

T=temperature=293 K

D=1.3806*10-23*293/4.09*10-11 =9.89*10-11 m2/s

(B)

k=4LD*R=4*3.14*9.89*10-11*10-8*10-9=1.24*10-26 (mol/m-3)-1s-1

(C) for second order

t1/2 =1/k[A0]=1/(1.24*10-26*0.01)=8.064*1027 s

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