Question

Process Synthesis A process for isolating an antibody against insulin has, as a unit operation, the reaction of the antibody with the antigen in a continuous-stirred tank reactor. The reaction product is a precipitate that is continuously removed from the reactor with \(10 \%\) of the solution, which is mouse serum. Since insulin is an expensive reagent, only stoichiometric amounts can be added to the mouse serum, which contains \(8 \mathrm{mg} / \mathrm{liter}\) of anti-insulin. If this particular monoclonal antibody precipitates with its antigen in a \(1: 1\) ratio, how many milligrams of insulin must be added to the reactor per hour to process \(100 \mathrm{ml}\) of mouse serum per hour? (Assume that equilibrium is achieved in this reactor.) Sketch a flowchart of this process.

Short answer

The amount of insulin that must be added to the reactor per hour to process 100 ml of mouse serum per hour is equal to the amount of antibody processed per hour, which is calculated as 0.8 mg/hr. The sketch of the process would involve a continuously stirred tank reactor where insulin is added to the mouse serum, the antibody reacts with the antigen in a 1:1 ratio, and the reaction product is continuously removed along with 10% of the solution.

Step-by-step solution

Determine the amount of Antibody

Calculate the amount of antibody in the processed mouse serum. The concentration of the antibody in the mouse serum is given as 8 mg/l. To process 100 ml of mouse serum per hour, the amount of antibody will be: \( \frac{8 mg}{1 liter}\) x \( \frac{100 ml}{1 hour}\) x \( \frac{1 liter}{1000 ml}\)

Apply Stoichiometry

Use stoichiometry for the reaction. Since the antibody and antigen react in a 1:1 ratio, the amount of insulin needed per hour is the same as the amount of antibody processed per hour, calculated in step 1.

Sketch the Flowchart

For the flowchart, visualize the process as a series of operations. Start with the addition of mouse serum and insulin into the continuously stirred tank reactor. Show the antigen-antibody reaction in the reactor. Represent the outlet from the reactor, where the product is continuously removed along with 10% of the solution.

Key concepts

Continuous-Stirred Tank Reactor (CSTR)

A Continuous-Stirred Tank Reactor (CSTR) is a common type of mixing reactor used in industrial processes, particularly in chemical engineering and bioengineering. The main characteristic of a CSTR is its ability to maintain a uniform composition of reactants and products throughout the tank. This is achieved through continuous stirring or agitation. In the context of bioseparations, a CSTR is employed for reactions such as antigen-antibody binding, where a consistent and controlled environment is crucial for achieving equilibrium between reactants.

In the exercise, the CSTR is used to facilitate an antigen-antibody reaction, with the antibody being mixed with the antigen, insulin, to form a precipitate. As part of the process design, one must ensure that the reaction occurs efficiently and that the precipitate can be removed continuously. Factors such as the mixing intensity, residence time, temperature, and reactant concentrations have to be taken into account to optimize the operation of a CSTR.

Antigen-Antibody Reaction

The antigen-antibody reaction is a highly specific interaction between an antigen, which in our case is insulin, and an antibody that is designed to recognize and bind to it. This specificity is akin to a lock and key, where the antibody binds to a unique part of the antigen's structure. The purpose of such reactions in bioseparations is often to isolate one component, either the antigen or the antibody.

Upon binding, antigens and antibodies can form a complex that precipitates out of solution, which is used in some bioseparation processes to separate the target protein from other components in the mixture. It's important for students to understand that this reaction takes place in the CSTR, and the precise stoichiometry, meaning the ideal 1:1 ratio of antigen to antibody, is crucial for the process efficiency and to minimize waste of expensive reagents like insulin.

Stoichiometry in Bioseparations

Stoichiometry is the calculation of reactants and products in chemical reactions. In the bioseparation context, it is vital for determining the precise amounts of biological reagents needed for a reaction to proceed to completion. Since reagents can be expensive, as insulin is in this exercise, using only stoichiometric amounts minimizes cost and waste.

In our example, since the antibody and insulin react on a 1:1 molar basis, the stoichiometry allows us to straightforwardly calculate that the same amount of insulin by mass is needed to process the given amount of antibody in the mouse serum. This is fundamental to designing efficient and cost-effective bioseparation processes, ensuring that the amount of insulin added matches the amount of anti-insulin antibody present in the serum to form precipitate for removal.

Process Flowchart

A process flowchart is a diagrammatic representation of the sequence of operations within a system. It is used to visualize and understand the steps involved in a process, making it an essential tool in engineering for process design and analysis.

In the exercise, a process flowchart would depict the addition of mouse serum and insulin into the CSTR, the antigen-antibody reaction resulting in precipitate formation, and the continuous removal of the precipitate along with a portion of the solution. Clear flowcharts help in recognizing the equipment needed, understanding the sequence of unit operations, and identifying where materials are added or removed in a process, all of which are imperative for effectively designing and controlling bioseparation processes.