Problem 11 - Biochemistry: Concepts and Connections

Question

The following data describe the catalysis of cleavage of peptide bonds in small peptides by the enzyme elastase. \begin{tabular}{ccc} Substrate & \(\boldsymbol{K}_{\mathbf{M}}(\mathbf{m} \mathbf{M})\) & \(\boldsymbol{k}_{\text {cat }}\left(\mathbf{s}^{-1}\right)\) \\ \hline PAPA \(\downarrow \mathrm{G}\) & \(4.0\) & 26 \\ PAPA \(\downarrow \mathrm{A}\) & \(1.5\) & 37 \\ PAPA \(\downarrow \mathrm{F}\) & \(0.64\) & 18 \\ \hline \end{tabular} The arrow indicates the peptide bond cleaved in each case. (a) If a mixture of these three substrates was presented to elastase with the concentration of each peptide equal to \(0.5 \mathrm{mM}\), which would be digested most rapidly? Which most slowly? (Assume enzyme is present in excess.) (b) On the basis of these data, suggest what features of amino acid sequence dictate the specificity of proteolytic cleavage by elastase. (c) Elastase is closely related to chymotrypsin. Suggest two kinds of amino acid residues you might expect to find in or near the active site.

Step-by-Step Solution

Answer

(a) PAPA \( \downarrow \text{F} \) is digested fastest and PAPA \( \downarrow \text{G} \) slowest. (b) Elastase favors smaller, hydrophobic amino acids like A and F. (c) Expect Glycine and Valine near the active site.

Step 1: Calculate Catalytic Efficiency

To determine which substrate will be digested most or least rapidly, calculate the catalytic efficiency (\(\frac{k_{\text{cat}}}{K_M}\) for each substrate. This measure indicates how efficiently an enzyme converts a substrate to product.- **For PAPA \( \downarrow \text{G} \):** \[\frac{k_{\text{cat}}}{K_M} = \frac{26}{4.0} = 6.5\] - **For PAPA \( \downarrow \text{A} \):** \[\frac{k_{\text{cat}}}{K_M} = \frac{37}{1.5} \approx 24.67\] - **For PAPA \( \downarrow \text{F} \):** \[\frac{k_{\text{cat}}}{K_M} = \frac{18}{0.64} \approx 28.125\]The higher the catalytic efficiency, the faster the substrate is digested.

Step 2: Rank Substrate Digestion Rate

Using the catalytic efficiency calculated:- **Fastest Digestion:** PAPA \( \downarrow \text{F} \) with \( \frac{k_{\text{cat}}}{K_M} = 28.125 \)- **Slowest Digestion:** PAPA \( \downarrow \text{G} \) with \( \frac{k_{\text{cat}}}{K_M} = 6.5 \)Thus, PAPA \( \downarrow \text{F} \) will be digested most rapidly and PAPA \( \downarrow \text{G} \) most slowly.

Step 3: Analyze Substrate Cleavage Specificity

Examine the sequence and efficiencies to determine specificity. Elastase may prefer smaller, hydrophobic amino acids like Alanine (A) and Phenylalanine (F) for cleavage, as indicated by the higher efficiencies for substrates cleaving after these residues.

Step 4: Predict Amino Acid Residues in Active Site

Given that elastase is closely related to chymotrypsin, which prefers large aromatic residues, elastase might contain residues near the active site that bind and stabilize small hydrophobic side chains. Possible residues in the active site could include Glycine (G) and Valine (V), which are both small and non-polar, complementing hydrophobic and small side chains of substrates.

Key Concepts

Catalytic Efficiency

Enzymes serve as biological catalysts that speed up reactions in biological systems. One of the key factors in determining how effective an enzyme is at catalyzing a reaction is its catalytic efficiency. Catalytic efficiency is defined as the ratio of the catalytic rate constant \(k_\text{cat}\) to the Michaelis-Menten constant \(K_M\), which is mathematically expressed as \(\frac{k_\text{cat}}{K_M}\). This ratio provides insights into how efficiently an enzyme converts a substrate into a product.For the enzyme elastase, analyzing the substrates PAPA ↓ G, PAPA ↓ A, and PAPA ↓ F gives different catalytic efficiencies:

• PAPA ↓ F has the highest catalytic efficiency at approximately 28.125, indicating it will be digested most rapidly.
• PAPA ↓ A follows with an efficiency of approximately 24.67.
• PAPA ↓ G has the lowest efficiency at 6.5.

When enzymes have high catalytic efficiency, it suggests that they effectively accelerate the conversion of substrate to product even at lower concentrations. This makes the determination of catalytic efficiency crucial for understanding enzyme kinetics and functionality.

Protease Specificity

Protease specificity refers to the ability of proteases like elastase to selectively cleave peptide bonds in substrates based on certain sequence features. In studying the activity of elastase, it becomes apparent that the enzyme has preferences based on the size and nature of the amino acid residues near the cleaved bond. The data suggest that elastase displays a preference for small, hydrophobic amino acids such as alanine (A) and phenylalanine (F). This is inferred from the higher catalytic efficiencies observed for substrates PAPA ↓ F and PAPA ↓ A. Such preferences in cleavage specificity are due to the enzyme's active site being optimized to interact more favorably with these residues. A protease specificity essentially dictates which amino acid sequences are optimal targets for cleavage, allowing biochemists to predict enzyme behavior and tailor substrates for experimental needs. Understanding these preferences is critical for applications in molecular biology and pharmacology, where controlled enzyme-substrate interactions can lead to desired outcomes.

Amino Acid Sequence

Amino acid sequences in peptides dictate how enzymes recognize and interact with substrates. For enzymes like elastase, the sequence around the cleavage site can determine how efficiently the enzyme can recognize and process the peptide. Elastase is closely related to the enzyme chymotrypsin, sharing structural features that influence substrate recognition. The active sites of these enzymes may contain residues adept at stabilizing small and hydrophobic side chains. For instance:

• Glycine (G), which is small, might be prevalent in or near the active site due to its ability to fit into tight spaces without steric hindrance.
• Valine (V), known for being non-polar and hydrophobic, might also stabilize interactions with similar substrate side chains.

Amino acid sequencing is thus a pivotal facet in understanding enzyme specificity and catalytic action. It can provide biochemical insights into the evolution of enzyme function and open pathways for industrial and medical enzyme applications.