Question

A chemist at a pharmaceutical company is measuring equilibrium constants for reactions in which drug candidate molecules bind to a protein involved in cancer. The drug molecules bind the protein in a \(1: 1\) ratio to form a drugprotein complex. The protein concentration in aqueous solution at \(25^{\circ} \mathrm{C}\) is \(1.50 \times 10^{-6} \mathrm{M}\). Drug \(\mathrm{A}\) is introduced into the protein solution at an initial concentration of \(2.00 \times 10^{-6} \mathrm{M}\). Drug \(B\) is introduced into a separate, identical protein solution at an initial concentration of \(2.00 \times 10^{-6} \mathrm{M}\). At equilibrium, the drug A-protein solution has an A-protein complex concentration of \(1.00 \times 10^{-6} \mathrm{M}\), and the drug \(\mathrm{B}\) solution has a B-protein complex concentration of \(1.40 \times 10^{-6} \mathrm{M}\). Calculate the \(K_{c}\) value for the \(A\)-protein binding reaction and for the \(\mathrm{B}\) protein binding reaction. Assuming that the drug that binds more strongly will be more effective, which drug is the better choice for further research?

Short answer

The equilibrium constants for the drug-protein binding reactions are \(K_c^{A} = 2.00\) and \(K_c^{B} = 23.33\). Drug B binds more strongly to the protein due to its larger \(K_c\) value, making it a better choice for further research.

Step-by-step solution

Write down the binding reaction for each drug

For both drugs, the reaction can be represented as follows: \[Drug + Protein \rightleftharpoons Drug-Protein\] Now, let's calculate the equilibrium constant, \(K_c\), for each drug using the equilibrium concentrations of reactants and products.

Drug A equilibrium concentrations

We are given the following equilibrium concentrations for drug A: - Protein concentration: \(1.50 \times 10^{-6} M\) - Drug A concentration: \(2.00 \times 10^{-6} M\) - A-protein complex concentration: \(1.00 \times 10^{-6} M\)

Calculate the amount of bound drug A and protein

Since we know the complex concentration at equilibrium, we can calculate the amount of bound drug A and bound protein: Bound Drug A: \(2.00 \times 10^{-6} M - 1.00 \times 10^{-6} M = 1.00 \times 10^{-6} M\) Bound Protein: \(1.50 \times 10^{-6} M - 1.00 \times 10^{-6} M = 0.50 \times 10^{-6} M\)

Calculate Kc for Drug A

Now, we can calculate \(K_c\) for drug A using the equilibrium concentrations: \[K_c^{A} = \frac{[A-Protein]}{[Drug\: A][Protein]} = \frac{1.00 \times 10^{-6}\:(\:M\:)}{(1.00 \times 10^{-6}\:(\:M\:))(0.50 \times 10^{-6}\:(\:M\:))} = 2.00\]

Drug B equilibrium concentrations

We are given the following equilibrium concentrations for drug B: - Protein concentration: \(1.50 \times 10^{-6} M\) - Drug B concentration: \(2.00 \times 10^{-6} M\) - B-protein complex concentration: \(1.40 \times 10^{-6} M\)

Calculate the amount of bound drug B and protein

Again, we can calculate the amount of bound drug B and bound protein: Bound Drug B: \(2.00 \times 10^{-6} M - 1.40 \times 10^{-6} M = 0.60 \times 10^{-6} M\) Bound Protein: \(1.50 \times 10^{-6} M - 1.40 \times 10^{-6} M = 0.10 \times 10^{-6} M\)

Calculate Kc for Drug B

Now, we can calculate \(K_c\) for drug B using the equilibrium concentrations: \[K_c^{B} = \frac{[B-Protein]}{[Drug\: B][Protein]} = \frac{1.40 \times 10^{-6}\:(\:M\:)}{(0.60 \times 10^{-6}\:(\:M\:))(0.10 \times 10^{-6}\:(\:M\:))} = 23.33\]

Determine the more effective drug

The larger the \(K_c\) value, the stronger the drug binds to the protein. Therefore, drug B, with a larger \(K_c\) value of 23.33, is a better choice for further research due to its stronger binding efficiency.

Key concepts

Protein Binding

Protein binding is a crucial process in biological systems and plays an integral role in regulating various bodily functions. In the context of pharmaceuticals, it is the interaction between a drug and a protein, forming a drug-protein complex. This complex formation can influence the drug's effectiveness. The stronger the binding, the more likely the drug will perform its intended task.

• **Equilibrium Constant:** This is a measure of the affinity of the drug for the protein. A higher value indicates a stronger affinity, meaning the drug binds more effectively to the protein.


• **1:1 Ratio:** In our exercise, the binding is in a 1:1 mole ratio, indicating that one molecule of drug binds to one molecule of protein.


• **Calculating Bound Concentrations:** To find out how many drug molecules have formed a complex with proteins, we subtract the equilibrium concentration of the complex from the initial concentrations of the drug and protein.

Understanding these principles is key in evaluating a drug's potential effectiveness in treatment scenarios.

Pharmaceutical Chemistry

Pharmaceutical chemistry is the discipline concerned with the design, development, and synthesis of pharmaceuticals. It focuses on optimizing compounds for desirable pharmacological effects, ensuring effectiveness and safety. In the exercise, we assess drug candidates that might become treatments for cancer by examining their protein binding capacities.

• **Drug Design:** Initially involves the creation of molecules that can interact strongly with their target proteins.


• **Equilibrium Studies:** Such studies entail evaluating how well a drug molecule binds to a protein, often with a focus on achieving the required balance between binding strength and therapeutic safety.


• **Evaluation of Kinetic Parameters:** This involves understanding how fast reactions occur and how drugs interact within a biological environment.

By meticulously studying these parameters, chemists can predict which drugs will have the most potent therapeutic effects with minimal side effects.

Reaction Kinetics

Reaction kinetics delves into the rates at which chemical reactions occur. In the realm of pharmaceuticals, understanding how fast a drug binds to a target protein and forms a complex is essential. This knowledge helps in evaluating the drug's efficacy and duration of action.

• **Rate of Reaction:** This refers to the speed at which the reactants form the products. Faster reactions can imply a quicker onset of the drug's effects.


• **Equilibrium State:** Eventually, the system reaches a state where the formation of the drug-protein complex and its dissociation occur at the same rate. It is in this state that the equilibrium constant is derived.


• **Impact on Drug Efficiency:** A drug that quickly reaches and maintains equilibrium can be more reliable in therapeutic settings.

Understanding reaction kinetics provides valuable insights into not just efficacy, but also the optimal dosage and frequency of drug administration.