Chapter 24, Problem 24.23P

Interpretation Introduction

Interpretation:

The effective diffusion coefficient for the given enzyme (urease) in the given pore is to be estimated.

Concept Introduction:

The formula to calculate the effective diffusion coefficient of an enzyme through a single cylindrical pore is:

  $D_{A,e}=D_{AB}^0\left(F_1\left(\phi \right)F_2\left(\phi \right)\right)$ ............. (1)

Here, $D_{AB}^0$ is the molecular diffusion coefficient of the solute in the solvent at infinite dilution, and $F_1\left(\phi \right)\text{ and }{F}_2\left(\phi \right)$ are the correction factors further defined as:

  $\begin{array}{c}{F}_1\left(\phi \right)={\left(1-\phi \right)}^2\mathrm{......}\text{(2)}\end{array}$

  $\begin{array}{c}{F}_2\left(\phi \right)=1-2.104\phi +2.09{\phi }^3-0.95{\phi }^5\mathrm{......}\text{ (3)}\end{array}$

Now, $\phi$ is defined as:

  $\phi =\frac{d_S}{d_{pore}}$ ............. (4)

Here, $d_S$ is the diameter of the solute (enzyme) and $d_{pore}$ is the pore diameter.