Question

The enzyme invertase catalyzes the conversion of sucrose, a disaccharide, to invert sugar, a mixture of glucose and fructose. When the concentration of invertase is \(4.2 \times 10^{-7} \mathrm{M}\) and the concentration of sucrose is \(0.0077 \mathrm{M}\) invert sugar is formed at the rate of \(1.5 \times 10^{-4} \mathrm{M} / \mathrm{s}\). When the sucrose concentration is doubled, the rate of formation of invert sugar is doubled also. (a) Assuming that the enzyme-substrate model is operative, is the fraction of enzyme tied up as a complex large or small? Explain. (b) Addition of inositol, another sugar, decreases the rate of formation of invert sugar. Suggest a mechanism by which this occurs.

Short answer

(a) The fraction of enzyme tied up as a complex is small. This is because the reaction rate doubles when the concentration of sucrose doubles, indicating that the enzyme is not saturated with the substrate, and therefore, only a small fraction of the enzyme is present in the enzyme-substrate complex. (b) The addition of inositol likely causes competitive inhibition. Inositol may compete with sucrose to bind with the enzyme invertase due to structural similarities. This competition decreases the effective concentration of sucrose binding to the enzyme, resulting in a slower rate of invert sugar formation.

Step-by-step solution

(a) Determine the fraction of enzyme tied up as a complex

Since the rate of formation of invert sugar doubles when the concentration of sucrose doubles, this implies that the reaction is still under the influence of substrate concentration, which means the enzyme is not saturated with the substrate. This further means that there is a relatively small fraction of enzyme tied up as the enzyme-substrate complex. Because if it was large, the doubling of substrate concentration wouldn't have doubled the rate as the enzyme would have been saturated.

(b) Suggest a mechanism for the effect of inositol on the reaction rate

As the addition of inositol, another sugar, decreases the rate of formation of invert sugar, one possible mechanism by which this occurs may be competitive inhibition. In this case, inositol may compete with sucrose to bind with the enzyme invertase due to structural similarities, thus decreasing the effective concentration of sucrose that can bind to the enzyme, resulting in a slower rate of invert sugar formation. This competition for the enzyme's active site would result in a decrease in the rate of the reaction involving sucrose and invertase.

Key concepts

Invertase

Invertase is a specific enzyme that plays a vital role in the chemical digestion of sucrose. It catalyzes the breakdown of sucrose into its constituent monosaccharides, glucose and fructose. This enzymatic reaction is essential because it helps organisms, such as plants and microorganisms, convert complex sugars into simpler ones that are more readily absorbed or utilized. The process is often compared to unlocking a door, where invertase acts as the key that opens up sucrose and releases its simpler components.

• Invertase is commonly used in the food industry to produce invert sugar from sucrose.
• Invert sugar has a different sweetness profile, making it valuable in culinary applications.
• It improves stability and adds a sheen to products like confectionery.

The activity of invertase, like many enzymes, is influenced by various factors such as temperature, pH levels, and substrate concentration. Understanding these factors is essential for optimizing its use in scientific and industrial processes.

Enzyme-Substrate Complex

The enzyme-substrate complex is a temporary molecular structure formed when an enzyme binds to its substrate. This binding occurs at a specific region on the enzyme known as the active site. The active site is uniquely shaped to fit the substrate, facilitating a reaction that converts it into the product. In the context of invertase and sucrose, the enzyme-substrate complex is necessary for the conversion of sucrose into glucose and fructose.

• The rate of a reaction is influenced by the concentration of enzyme-substrate complexes.
• If too few complexes form, the reaction rate is slow; if many form, the rate is faster.
• The relationship between substrate concentration and reaction rate helps determine enzyme efficiency.

In the original exercise, it's highlighted that the fraction of enzyme tied up in the complex is relatively small. This conclusion is drawn because doubling the substrate results in a proportional increase in the rate of reaction, indicating that the enzymes are not saturated and can form additional complexes efficiently.

Competitive Inhibition

Competitive inhibition occurs when molecules similar in structure to the substrate compete for the enzyme's active site. This process can decrease the overall rate of the reaction by blocking the actual substrate from binding. In the original problem, inositol acts as a competitive inhibitor by mimicking the structure of sucrose, thereby occupying the binding sites on invertase that would otherwise facilitate the production of invert sugar. Competitive inhibition is an important concept because it shows how different molecules can influence enzyme activity:

• It highlights the specificity of enzymes and the importance of structural similarity.
• It demonstrates how enzymes can be regulated by other molecules in biological systems.
• Understanding this process is crucial for drug design and the control of metabolic pathways.

By introducing a competitive inhibitor, the reaction speed is reduced without permanently disabling the enzyme. This form of inhibition can often be overcome by increasing the concentration of the substrate, eventually outcompeting the inhibitor for binding sites.