Problem 94 - Chemistry The Molecular Science

Question

Carbonic anhydrase, an important enzyme in mammalian respiration, is a large zinc-containing protein with a molar mass of \(3.00 \times 10^{4} \mathrm{~g} / \mathrm{mol}\). The zinc is \(0.218 \%\) by mass of the protein. Determine how many zinc atoms each carbonic anhydrase molecule contains.

Step-by-Step Solution

Answer

Each carbonic anhydrase molecule contains 1 zinc atom.

Step 1: Find the Mass of Zinc per Mole

To find the total mass of zinc in one mole of carbonic anhydrase, we calculate:\[ \text{Mass of Zinc in Carbonic Anhydrase} = 0.218\% \times 3.00 \times 10^{4} \text{ g/mol} \]\[ = \frac{0.218}{100} \times 3.00 \times 10^{4} \text{ g/mol} \]\[ = 65.4 \text{ g/mol} \]

Step 2: Find Moles of Zinc

Next, convert the mass of zinc found in one mole of carbonic anhydrase to moles of zinc:\[ \text{Moles of Zinc} = \frac{\text{Mass of Zinc}}{\text{Molar Mass of Zinc}} \]\[ \text{Moles of Zinc} = \frac{65.4 \text{ g/mol}}{65.38 \text{ g/mol}} \]\[ \approx 1 \text{ mol} \]

Step 3: Determine Zinc Atoms per Molecule

Since 1 mole of zinc corresponds to Avogadro's number of zinc atoms (\(6.022 \times 10^{23}\) atoms), we conclude that each molecule of carbonic anhydrase contains approximately 1 zinc atom.

Key Concepts

Zinc in proteins

Zinc is an essential trace element and plays a critical role in many proteins. It acts as a stabilizer and is often a catalytic component in enzymes. Proteins that contain zinc, such as carbonic anhydrase, use this metal ion to enhance their functionality. In enzymes, zinc often assists in catalyzing biochemical reactions, helping to speed them up or make them more efficient.

Zinc ions interact with the enzyme's active site. This interaction can create a conducive environment for the enzyme to carry out its reaction. The presence of zinc is crucial, particularly in proteins where it must maintain the proper shape for function, known as a conformational role.

• Zinc helps in maintaining structural integrity by binding to protein subunits.
• It plays an enzymatic role, often directly participating in chemical reactions.
• The presence of zinc can also impact the protein's ability to bind substrates or other molecules.

Understanding the role of zinc creates a foundation for grasping enzyme mechanics and the necessity of trace elements in biological systems.

Molecular mass calculation

Calculating molecular mass, or molar mass, is essential in understanding the quantity of a substance in molecular form. In the context of carbonic anhydrase, its molecular mass is given as \(3.00 \times 10^{4} \text{ g/mol}\). This represents the mass of one mole of the enzyme molecules.

This value helps determine the amount of other elements in the compound, such as zinc. We use the percentage of zinc by mass to find its actual weight in the protein and subsequently calculate how many moles of zinc are present. We do this by:

• Multiplying the given mass percentage (0.218%) by the total molar mass.
• Converting the mass of zinc to moles using zinc’s molar mass, \(65.38 \text{ g/mol}\).

These steps help understand the composition of complex proteins and their quantitative makeup, which is crucial for biochemical studies and applications.

Enzyme structure

The structure of an enzyme is pivotal in its function and efficacy. Enzymes like carbonic anhydrase have specific three-dimensional shapes that allow them to interact with substrates and catalyze reactions effectively. This structure includes:

• The active site, where substrates bind and reactions occur.
• Catalytic domains, like the region responding to zinc binding in carbonic anhydrase.

The unique shape of an enzyme is stabilised by various factors, including metal ions like zinc, which can act as cofactors. This stabilization ensures the active site is optimally aligned for substrate interaction.

In carbonic anhydrase, the presence of zinc is crucial as it enables the enzyme to accelerate the conversion of carbon dioxide and water into bicarbonate and protons. This process is vital in many physiological functions, highlighting the importance of enzyme structure in biochemical pathways. Understanding these structures helps in designing drugs and treatments that can influence or mimic enzymatic activities.