Question

Irreversible Inhibition of an Enzyme Many enzymes are inhibited irreversibly by heavy metal ions such as \(\mathrm{Hg}^{2+}, \mathrm{Cu}^{2+}\), or \(\mathrm{Ag}^{+}\), which can react with essential sulfhydryl groups to form mercaptides: $$ \text { Enz-SH }+\mathrm{Ag}^{+} \rightarrow \text { Enz-S-Ag }+\mathrm{H}^{+} $$ The affinity of \(\mathrm{Ag}^{+}\)for sulfhydryl groups is so great that \(\mathrm{Ag}^{+}\) can be used to titrate - SH groups quantitatively. An investigator added just enough \(\mathrm{AgNO}_{3}\) to completely inactivate a \(10.0 \mathrm{~mL}\) solution containing \(1.0 \mathrm{mg} / \mathrm{mL}\) enzyme. A total of \(0.342 \mu \mathrm{mol}\) of \(\mathrm{AgNO}_{3}\) was required. Calculate the minimum molecular weight of the enzyme. Why does the value obtained in this way give only the minimum molecular weight?

Short answer

The enzyme's minimum molecular weight is approximately 29,240 g/mol. This is the minimum value because the calculation assumes all sulfhydryl groups belong to one enzyme molecule.

Step-by-step solution

Understanding the Reaction

In the given reaction, each mole of enzyme's sulfhydryl group (Enz-SH) reacts with one mole of silver ion (\(\mathrm{Ag}^{+}\)) to form a product and release a hydrogen ion (\(\mathrm{H}^{+}\)). The chemical equation is \[\text { Enz-SH }+\mathrm{Ag}^{+} \rightarrow \text { Enz-S-Ag }+\mathrm{H}^{+}\] This one-to-one reaction ratio is critical for calculating the enzyme's minimum molecular weight.

Calculate Total Enzyme Mass

The enzyme solution has a concentration of 1.0 mg/mL. For a total volume of 10.0 mL, the total mass of the enzyme becomes:\[\text{Total enzyme mass} = \text{concentration} \times \text{volume} = 1.0 \text{ mg/mL} \times 10.0 \text{ mL} = 10 \text{ mg}\].

Convert Enzyme Mass to Moles of Sulfhydryl Group

We are given that 0.342 \(\mu\text{mol}\) of \(\mathrm{AgNO}_{3}\) was used to inactivate the enzyme completely, which means 0.342 \(\mu\text{mol}\) of enzyme's sulfhydryl groups were titrated. This represents the moles of the enzyme because each active sulfhydryl group reacts with one silver ion according to the balanced equation.

Find Minimum Molecular Weight

Using the mass of the enzyme (10 \(\text{mg}\) or 0.010 \(\text{g}\)) and the moles of enzyme (0.342 \(\mu\text{mol}\) or 0.342\(\times10^{-6}\) \text{mol}), calculate the minimum molecular weight as:\[\text{Molecular weight} = \frac{\text{mass in grams}}{\text{moles}} = \frac{0.010 \text{ g}}{0.342 \times 10^{-6} \text{ mol}} \approx 29,240 \text{ g/mol}\].

Explanation of Minimum Molecular Weight

The value gives the minimum molecular weight because each \(\mathrm{Ag}^{+}\) ion can react with only one sulfhydryl group on the enzyme. If an enzyme contains multiple sulfhydryl groups, it will react with multiple \(\mathrm{Ag}^{+}\) ions, implying each count of \(\mathrm{Ag}^{+}\) titrates only the number of active sulfhydryl sites but not the entire enzyme, thus providing the minimum molecular weight estimation.

Key concepts

Irreversible Inhibition

Irreversible inhibition is a process where an enzyme's activity is permanently reduced or stopped. This occurs when a molecule binds covalently with the active site on the enzyme. One common example of irreversible inhibition involves heavy metal ions. These ions, such as mercury

• Act by binding strongly to the active site.
• Alter the enzyme structure, preventing it from functioning.

In the case of our exercise, heavy metal ions irreversibly bind to sulfhydryl groups, a vital component of many enzymes, through the formation of stable complexes. This binding is strong and cannot be undone by removing the heavy metal ion. As a result, the enzyme is permanently inactivated, which is why the inhibition is termed 'irreversible.' Understanding this principle is crucial for determining how heavy metal ions affect enzyme functions in biological systems.

Heavy Metal Ions

Heavy metal ions are atoms of metals with a relatively high atomic mass and density. Known for their reactive nature, some common examples include mercury

• Mercury ( Hg^{2+} )
• Copper ( Cu^{2+} )
• Silver ( Ag^{+} )

These ions are renowned inhibitors of enzymes due to their propensity to react with sulfhydryl groups. Heavy metals possess a high affinity for these groups, resulting in the formation of stable complexes called mercaptides, effectively blocking the enzyme's active sites. Such interactions render the enzymes inactive, contributing to the irreversible inhibition seen in many biochemical reactions. Additionally, the unique reactivity of heavy metals with sulfhydryl groups allows for their use in titration experiments, helping scientists determine structural features of certain proteins.

Sulfhydryl Groups

Sulfhydryl groups are functional components in many proteins and enzymes and are represented by the -SH chemical group. These groups are highly reactive due to the presence of sulfur and are crucial for maintaining the structural integrity and function of proteins. When a heavy metal ion, such as Ag^{+} , interacts with an enzyme, it targets these sulfhydryl groups. The reaction forms a stable compound, often leading to the enzyme's inactivation. Sulfhydryl groups can be found in the side chain of amino acids like cysteine. A key function of these groups is forming disulfide links that help stabilize protein structure. Their reactivity also makes them instrumental in titration experiments that estimate enzymes' active sites and, consequently, their minimum molecular weight.

Molecular Weight Calculation

Molecular weight calculation is an essential part of understanding enzyme and protein behavior. By determining the molecular weight of an enzyme, researchers can infer properties such as the number of active sites. In the provided exercise,

• The enzyme mass is 10 mg (or 0.010 g).
• The amount of AgNO_{3} used gives moles of enzyme's sulfhydryl groups (0.342 \mumol).

To find the minimum molecular weight, divide the enzyme mass by the moles of sulfhydryl groups: \[\text{Molecular weight} = \frac{0.010 \text{ g}}{0.342 \times 10^{-6} \text{ mol}} \approx 29,240 \text{ g/mol}\]This estimate gives the minimum molecular weight because it assumes each enzyme molecule has at most one sulfhydryl group. If the enzyme has multiple sulfhydryl groups, the actual molecular weight would be higher, as each sulfhydryl group can independently bind to a heavy metal ion.