Created by Susan Stagg-Williams, Dieter Andrew Schweiss, Gavin Sy, and H. Scott Fogler, 1994

Updated by Apeksha Bandi, Gustav Sandborgh, and Arthur Shih, 2013

### 6. Concentration of Free Sites

The number of free sites would change by irreversible attachment of venom molecules (reaction 1) and the reversible attachment of antivenom molecules (reaction 2) and the reaction of venom with antivenom molecules already bound onto the site and vice versa (reaction 3 and 4).

The rate of generation of free sites would be the sum of rates of generation from the reactions above. The material balance equation is:

(E-33)

The terms on the right hand side are rates of generation of free sites in reactions 1,2, 3 and 4 respectively.

The rate equations for the elementary reactions are as follows:

(E-34)

(E-35)

(E-36)

(E-37)

Combining the batch reactor design equation (equation E-4) with the material balance (equation E-33)and rate laws (equations E-34 to E-37) gives us the governing equation for the concentration of free sites in the blood.

(E-38)

Dividing by C

_{s0} allows us to arrive at the governing equation for fraction of sites occupied by antivenom:

(E-39)

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