Question

For enzyme-catalyzed reactions that follow the mechanism $$ \begin{aligned} \mathrm{E}+\mathrm{S} & \rightleftharpoons \mathrm{E} \cdot \mathrm{S} \\ \mathrm{E} \cdot \mathrm{S} & \rightleftharpoons \mathrm{E}+\mathrm{P} \end{aligned} $$ a graph of the rate as a function of [S], the concentration of the substrate, has the following appearance: Note that at higher substrate concentrations the rate no longer changes with [S]. Suggest a reason for this.

Short answer

In summary, the plateau in the reaction rate at higher substrate concentrations occurs because the enzymes become fully saturated with substrate molecules and are working at their maximum capacity. Increasing substrate concentration at this point does not affect the reaction rate, as the enzyme concentration becomes the limiting factor.

Step-by-step solution

Understanding the enzyme-catalyzed reaction mechanism

We are given a two-step enzyme-catalyzed reaction mechanism: \[ \begin{aligned} \mathrm{E}+\mathrm{S} \rightleftharpoons \mathrm{E} \cdot\mathrm{S} \\ \mathrm{E} \cdot\mathrm{S} \rightleftharpoons\mathrm{E}+\mathrm{P} \end{aligned} \] Here, E represents the enzyme, S represents the substrate, and P represents the product. The reaction consists of two reversible steps, where the enzyme (E) binds with the substrate (S) to form the enzyme-substrate (E · S) complex. This complex then transforms into the product (P) and releases the enzyme back into the system.

Analyzing the graph of the reaction rate

The graph of the reaction rate as a function of [S], the concentration of the substrate, depicts an initial increase in the reaction rate as the substrate concentration increases. However, at high substrate concentrations, the reaction rate plateaus and does not change further with an increase in [S].

Reason for the plateau in the reaction rate at higher substrate concentrations

As the substrate concentration increases, the reaction rate initially increases due to more frequent collisions between substrate molecules and enzyme molecules, resulting in the formation of enzyme-substrate complexes. This increases the rate of product formation. However, as the substrate concentration continues to increase, enzymes become saturated or fully occupied by the substrate molecules because there are already sufficient substrate molecules available for interaction. When all available enzyme molecules are bound to the substrate, no further increase in reaction rate is observed, as the enzyme is working at its maximum capacity. In this case, adding more substrate molecules does not affect the reaction rate because the enzyme concentration becomes the limiting factor. In conclusion, the reason for the plateau in the reaction rate at higher substrate concentrations is that the enzyme becomes fully saturated with substrate molecules and is working at its maximum capacity. Further increases in substrate concentration do not affect the reaction rate, as the enzyme concentration becomes the limiting factor.

Key concepts

Michaelis-Menten kinetics

Michaelis-Menten kinetics describes how the rate of enzyme-catalyzed reactions depends on substrate concentration. In this model, an enzyme binds to a substrate to form an enzyme-substrate complex. This complex can either dissociate back into the enzyme and substrate, or it can proceed to form a product and release the enzyme. The rate of reaction is initially proportional to the concentration of the substrate. However, as substrate concentration increases, the reaction rate approaches a maximum velocity (\(V_{max}\)).
This characteristic sigmoidal curve on a graph is essential for understanding the kinetics of these reactions.

• At low substrate concentrations, the reaction rate rises sharply because plenty of the enzyme's active sites are available.
• As more substrate molecules fill these active sites, the rate of reaction starts to slow.
• Eventually, the reaction reaches a plateau at maximum velocity (\(V_{max}\)), revealing that the rate is not solely dependent on substrate concentration.

The Michaelis constant (\(K_m\)) is also a key concept here. It represents the substrate concentration at which the reaction rate is half of \(V_{max}\). A lower \(K_m\) indicates higher affinity between enzyme and substrate.

enzyme saturation

Enzyme saturation occurs when all active sites of an enzyme are occupied by substrate molecules. This leads to the observation that increasing substrate concentration further will not increase the rate of reaction. Enzyme saturation signifies that the enzyme is working at its maximum capacity.
At this stage, every enzyme molecule is busy converting substrate to product as quickly as possible. No matter how much more substrate you add, there's simply no increase in conversion rate.

• Each enzyme molecule can only handle a limited number of substrate molecules at a time.
• When all enzyme molecules are actively engaged, the reaction rate plateaus.
• This saturation point is a key reason for the maximum velocity (\(V_{max}\)) in Michaelis-Menten kinetics.

This concept highlights why, in biological systems, enzyme availability is often the limiting factor in reactions. Increasing enzyme concentration would be necessary to achieve a higher reaction rate beyond this saturation point.

substrate concentration

Substrate concentration (\([S]\)) is a pivotal factor in enzyme kinetics. It refers to the amount of substrate available for the enzyme to act upon in a biochemical reaction. The effect of substrate concentration on reaction rate is illustrated through the shape of a hyperbolic curve on a graph.
Initially, increasing \([S]\) leads to a higher reaction rate, as more substrate molecules are available to form enzyme-substrate complexes. This is due to the increased frequency of collisions between substrate and enzyme molecules, leading to more product formation.

• At low substrate concentrations, the reaction rate is highly sensitive to changes in \([S]\).
• As \([S]\) increases, more enzyme active sites are filled, causing a rise in reaction rate.
• Eventually, if \([S]\) continues to rise, the system reaches a saturation point where the enzymes are fully occupied.

Beyond this saturation point, the reaction rate reaches a plateau because it is limited by the availability of free enzyme molecules, not substrate concentration. Understanding how substrate concentration affects reaction kinetics is essential for controlling biochemical processes like metabolic pathways and drug reactions.