Enzymes are biological catalysts. They are specific to one type of reaction and to one or a small group of reactants called substrates. A catalyst speeds up the rate of a reaction without being changed itself. They are necessary as most biological reactions are very slow.

Kinetics is the study of reaction rates. This will be considered in the context of enzymes where the rate of the reaction means the rate of product formation. In this article we will look at the structure, function and clinical significance of enzyme kinetics.

Enzyme Structure

Most enzymes are globular proteins with the exception of a few RNA enzymes (ribozymes). They have an active site made up of a few amino acids. This is where the reaction occurs. The rest of the enzyme acts as a scaffold, bringing these key amino acids together.

The active site forms a cleft or crevice that the substrate can sit in during the reaction. The cleft creates a better environment for the reaction to take place. They may do this, for example, by excluding water.

The active site is almost complementary to the substrate’s shape. Therefore, when the substrate binds, the enzyme must change shape slightly to fit it. This forms the enzyme-substrate complex, also called “ES”. This is the induced fit model, which is an addition to the lock and key hypothesis. Only weak bonds between the enzyme and substrate hold them in place. This is necessary to allow dissociation later on.

Enzymes have an optimum temperature and pH where they work best. Changes in pH can alter critical ionization states, while changes in temperature can disrupt important bonds. Deviations from these optimum conditions will disrupt the enzyme’s structure and impact on its kinetics, eventually completely denaturing and disabling it.

By Thomas Shafee (Own work) [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons

Fig 1 – Image of Hexokinase. The Blue region corresponds to the active site and the black molecules are the substrates.

Enzyme Function

Enzymes lower the activation energy, E_a, of a particular reaction. They can do this because they have a high affinity for a transition state. The activation energy is the minimum energy needed for a reaction to occur. Enzymes assist in the reaction so that less energy is needed. This means the reaction can occur more easily. This speeds up the rate of the reaction as it allows the product to be formed faster.

An enzyme has a high affinity for the transition state (even higher than for its substrate). Therefore when the substrate binds, it is quickly forced into the transition state. This is a state that exists between the substrate and the product. The enzyme is said to facilitate the formation of the transition state.

The transition state has a high energy, making it very unstable. It can only exist transiently. The transition state spontaneously turns into the more stable product with lower energy. The enzyme will have a low affinity for the product and so the product is released.

Rate Limiting Steps

The rate limiting step in any reaction is its slowest step. It sets the pace for the entire reaction. After all, a production line can only be as productive as its slowest worker. In enzymatic reactions, the conversion of the enzyme-substrate complex to the product is normally rate limiting. The rate of this step (and therefore the entire enzymatic reaction) is directly proportional to the concentration of ES.

The concentration of ES changes as the reaction progresses. Therefore, the rate of product formation also changes over time. When the reaction reaches equilibrium (steady state) the concentration of ES (and therefore the rate) remains relatively constant.

Reaction Kinetics

When an enzyme is added to a lot of substrate, the reaction that follows occurs in three stages with distinct kinetics:

The pre-steady state phase is very short as equilibrium is reached within microseconds. If you measure the rate in the first few seconds of a reaction (V₀) you are actually measuring the steady state. This is the rate used in Michaelis-Menten Kinetics.

Michaelis-Menten Kinetics

Two terms that are important within Michaelis-Menten Kinetics are:

• Vmax – the maximum rate of reaction when all enzyme active sites are saturated with substrate
• Km – the substrate concentration that gives half maximal velocity. Km is a measure of the affinity an enzyme has for its substrate, as a lower Km means that less of the substrate is required to reach half of Vmax.

This equation concerns the steady state of an enzymatic reaction with one substrate, and is given by:

It describes how the initial rate of reaction, V₀, is affected by the initial substrate concentration, [S]₀. It only looks at the start of the reaction. This allows it to ignore the reverse reaction where substrate is formed from product. This is because at the start of the reaction there is no product present to become substrate.

The plot of rate against concentration has the shape of a rectangular hyperbola. However, a more useful representation of Michaelis–Menten kinetics is a graph  called a Lineweaver–Burk plot. The equation used to generate this plot is given by:

This allows an easier interpretation of various quantities from the graph, such as the presence of an inhibitor. This is shown in figure 3, where an inhibitor decreases Km and therefore shifts the original line upwards.

By U+003F (Own work) [CC0], via Wikimedia Commons

Fig 2 – image of an enzyme displaying Michaelis–Menten kinetics.

By TimVickers (Own work) [Public domain], via Wikimedia Commons

Fig 3 – Image of a Lineweaver–Burk plot.