Table of Contents
Enzyme activity depends strongly on the concentrations of all partners involved in the reaction. In this chapter, we focus on how concentration affects the rate of an enzyme‐catalyzed reaction and what typical patterns and concepts are used to describe this.
Basic idea: collisions and binding
Enzymes must bind their substrate to form an enzyme–substrate complex ($ES$). The more substrate molecules there are per unit volume (higher substrate concentration), the more often they collide with enzyme molecules and the greater the chance that binding occurs. This initially increases the reaction rate.
Similarly, the concentration of the enzyme itself determines how many “workplaces” are available for processing substrate.
Two main variables are therefore crucial:
- Substrate concentration: $[S]$
- Enzyme concentration: $[E]$
Other molecules, such as inhibitors or activators, can also influence the effective concentration of “usable” enzyme or substrate, but their detailed role is treated elsewhere.
Effect of substrate concentration on reaction rate
If enzyme concentration, temperature, and pH are kept constant, the reaction rate $v$ typically changes with substrate concentration $[S]$ in a characteristic way.
At very low substrate concentrations
When $[S]$ is very low:
- Only a small proportion of enzyme molecules have bound substrate at any moment.
- Adding more substrate increases the chance of enzyme–substrate encounters almost proportionally.
In this range, the reaction rate $v$ increases approximately linearly with $[S]$:
- Double $[S]$ → about double $v$ (as long as everything else is constant).
This is sometimes called the “first-order” region with respect to substrate.
At intermediate substrate concentrations
As $[S]$ increases further:
- More enzyme active sites are occupied at any given time.
- The rate still increases with $[S]$, but not as steeply as in the low-concentration region.
The curve of $v$ versus $[S]$ begins to bend and approach a maximum instead of rising linearly.
Saturation and maximum velocity
At sufficiently high $[S]$:
- Nearly all enzyme active sites are occupied by substrate most of the time.
- The enzyme is said to be saturated with substrate.
- Adding more substrate does not significantly increase the reaction rate, because there are no more free active sites to occupy.
The reaction rate approaches a maximum value called the maximum velocity $V_\text{max}$.
Qualitatively, the relationship between reaction rate $v$ and substrate concentration $[S]$ for many enzymes can be graphed as:
- $v$ increases quickly at low $[S]$.
- $v$ increases more slowly at intermediate $[S]$.
- $v$ approaches a plateau $V_\text{max}$ at high $[S]$.
Mathematically, for enzymes that follow simple (Michaelis–Menten) behavior, the dependence is expressed as:
$$
v = \frac{V_\text{max} \,[S]}{K_m + [S]}
$$
where $K_m$ is the Michaelis constant (its meaning is covered elsewhere). You only need to note here that $K_m$ depends on how tightly the enzyme binds its substrate and affects how quickly the rate rises with increasing $[S]$.
In the saturation region at high $[S]$:
- The reaction becomes “zero order” in substrate: changing $[S]$ has almost no effect on $v$, which is near $V_\text{max}$.
Effect of enzyme concentration on reaction rate
Now consider what happens if you change the concentration of the enzyme itself, while keeping substrate concentration high enough (near saturation) and other conditions constant.
Proportional relationship at non-limiting substrate
If enough substrate is available to saturate all enzymes:
- Doubling the amount of enzyme approximately doubles the number of active sites.
- As a result, $V_\text{max}$ roughly doubles, and so does the observed reaction rate at saturating $[S]$.
In this situation, the reaction rate is approximately directly proportional to $[E]$:
- $[E]$ ↑ → $V_\text{max}$ ↑ proportionally.
In living cells, changing enzyme concentration is one of the main ways to regulate how fast a metabolic pathway can run (for example, by adjusting how much of an enzyme is synthesized or degraded).
Limiting enzyme concentration at low substrate
At very low substrate concentrations, both $[S]$ and $[E]$ can limit the reaction rate. If the enzyme is very scarce, even a moderate $[S]$ might not lead to a high rate, because there are few active sites.
In summary:
- At a given $[S]$, more enzyme gives a higher reaction rate (up to the point where other steps in the pathway become limiting).
- At a given $[E]$, more substrate increases the reaction rate until saturation is reached.
Internal vs. external concentration
In experiments, one often controls concentrations in a test tube (external environment). In cells and organisms, the situation is more complex:
- Cells regulate the internal concentration of substrates and products by transport across membranes, storage, and conversion in other pathways.
- Local concentrations can be very high in specific cellular compartments (e.g., near membranes, or within organelles), which can strongly favor or limit certain enzyme reactions.
Thus, “concentration effects” in vivo are not just a matter of the overall amount of a substance, but also where it is located and how it is distributed within the cell.
Competitive effects of other molecules
Some molecules resemble the substrate and compete for the same active site. Even without going into detail on inhibition:
- If a competitor binds to the active site, the effective concentration of free enzyme available to bind the real substrate is reduced.
- Increasing the substrate concentration can often outcompete such molecules, because higher $[S]$ favors formation of the normal enzyme–substrate complex.
The apparent relationship between $v$ and $[S]$ is therefore influenced not only by $[S]$ and $[E]$, but also by the presence of competing or modifying molecules.
Biological relevance of concentration control
Organisms use concentration changes as a flexible control mechanism for enzyme activity:
- Nutrient supply: After a meal, blood glucose rises, increasing substrate concentration for enzymes that process glucose; certain pathways then run faster.
- Metabolic switching: When a substrate is depleted, its low concentration slows down the respective enzyme reactions, helping the cell to switch to other substrates or pathways.
- Compartmentation: By concentrating certain substrates and enzymes in specific organelles, cells can drive particular reactions efficiently without having to change overall cellular concentrations.
In many cases, concentration control interacts with other regulatory mechanisms (such as allosteric regulation or covalent modification), which are covered separately.