Part of the TeachMe Series

# Enzyme Kinetics

star star star star star
based on 18 ratings

Original Author(s): Farhaana Surti
Last updated: 9th March 2021
Revisions: 31

Enzymes are biological catalysts which act to increase the rate of a reaction without being used up or changed themselves. They are specific to one type of reaction and one, or a small number of, closely related reactants known as substrates. Enzymes are a vital component of the cell as without them, many biological reactions would be too slow to sustain life.

Enzyme kinetics is the study of enzyme reactions rates and the conditions which affect them. In this article, we will discuss the structure and function of enzymes, their clinical significance and theories of enzyme kinetics.

## Enzyme Structure

Enzymes are proteins and usually have a globular tertiary structure. Their structure is highly specific to the reaction they catalyse, and hence the reactants involved, due to the presence of an active site where the reaction itself occurs. This is a small cleft within the enzyme with a specific amino acid structure allowing the substrate to bind and form the enzyme-substrate complex (ES), which is held together by weak bonds to allow dissociation of the complex when the reaction is finished. The rest of the enzyme acts as a scaffold, bringing these key amino acids together.

The active site is complementary to its specific substrate’s shape. There are two main models for how this interaction occurs:

• Lock and key model – the active site is a perfect fit for the substrate and does not require any changes for it to bind.
• Induced fit model – the active site is almost complementary to the substrate but when it binds, the enzyme undergoes conformational changes to make its active site’s shape better fit. This theory is more generally accepted than the lock and key model.

Enzymes have an optimum temperature and pH at which they work best, which varies depending on the enzyme’s function and both cellular and organ location. Changes in pH can alter critical ionisation states, while changes in temperature can disrupt important bonds, affecting the enzyme’s structure and therefore function. If exposed to severe changes in temperature and/or pH, the shape of the active site may change. This is referred to as enzyme denaturation and means the enzyme will no longer be able to bind its substrate or carry out its biological function.

Fig 1 – Enzyme active site changing shape upon binding with its substrate (induced fit model). The blue region represents the active site and the black molecules are its substrates.

## Enzyme Function

Enzymes provide an alternative pathway for a reaction, which has a lower activation energy (Ea) – the minimum energy input needed for a reaction to occur and convert the substrates into products.

The transition state is a molecular intermediate between the substrate and its product, through which the reaction passes. For example, in the equation below, X is the transition state. This transition state has a higher free energy than both the substrate and its product, however, the transition state is stabilised upon the addition of an enzyme.

Substrate → X → Product

Upon weak substrate binding, the enzyme’s active site changes conformation such that it fits the transition state better than the initial substrate, hence has a higher affinity for this transition state. This reduces the activation energy required to reach it. Therefore, when the substrate binds to the active site, it is encouraged to continue the reaction and is converted into the transition state, and ultimately the final product of the reaction. This energetically favourable process allows more substrate molecules to be converted into products in a given period of time.

Since the transition state has a high energy, it is unstable and can only exist transiently. It spontaneously converts into the more stable product, which has a lower energy. The enzyme’s active site has a low affinity for this product, so it dissociates and is released.

### Rate-limiting Steps

The rate-limiting step of any reaction is its slowest step, and this is what sets the pace of the entire reaction. 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 the enzyme-substrate complex.

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

### Reaction Kinetics

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

 Phase Concentration of ES Rate of product formation Pre-steady state Rapid burst of ES complexes form Initially slow, waiting for ES to form, then speeds up Steady state(equilibrium) ES concentration remains constant as it is being formed as quickly as it breaks down Constant rate of formation, faster than pre-steady state Post-steady state Substrate depletes so fewer ES complexes form Slow as there are fewer ES complexes; slows down as substrate runs out

The pre-steady state phase is very short, as equilibrium is reached within microseconds. Therefore, if you measure the rate in the first few seconds of a reaction, you will be measuring the reaction rate in the steady state. This is the rate used in Michaelis-Menten Kinetics.

## Michaelis-Menten Kinetics

Michaelis-Menten kinetics is a model of enzyme kinetics which explains how the rate of an enzyme-catalysed reaction depends on the concentration of the enzyme and its substrate. Let’s consider a reaction in which a substrate (S) binds reversibly to an enzyme (E) to form an enzyme-substrate complex (ES), which then reacts irreversibly to form a product (P) and release the enzyme again.

S + E ⇌ ES → P + E

Two important terms within Michaelis-Menten kinetics are:

• Vmax – the maximum rate of the reaction, when all the enzyme’s active sites are saturated with substrate.
• Km (also known as the Michaelis constant) – the substrate concentration at which the reaction rate is 50% of the Vmax. Km is a measure of the affinity an enzyme has for its substrate, as the lower the value of Km, the more efficient the enzyme is at carrying out its function at a lower substrate concentration.

The Michaelis-Menten equation for the reaction above is:

$v = \frac{V_{max}\left[S\right]}{K_{M}+\left[S\right]}$

This equation describes how the initial rate of reaction (V) is affected by the initial substrate concentration ([S]). It assumes that the reaction is in the steady state, where the ES concentration remains constant.

When a graph of substrate concentration against the rate of the reaction is plotted, we can see how the rate of reaction initially increases rapidly in a linear fashion as substrate concentration increases (1st order kinetics). The rate then plateaus, and increasing the substrate concentration has no effect on the reaction velocity, as all enzyme active sites are already saturated with the substrate (0 order kinetics).

Fig 2 – Graph of rate of reaction against substrate concentration, demonstrating Michaelis–Menten kinetics, with Vmax and Km highlighted.

This plot of rate of reaction against substrate 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, which plots the inverse of the reaction rate (1/r) against the inverse of the substrate concentration (1/[S]). The equation used to generate this plot is given by:

$\frac{1}{V} = \frac{K_{m}}{V_{max}} \frac{1}{S} + \frac{1}{V_{max}}$

This produces a straight line, allowing for the easier interpretation of various quantities and values from the graph. For example, the y-intercept of the graph is equivalent to the Vmax. The Lineweaver-Burk plot is also useful when determining the type of enzyme inhibition present by, comparing its effect on Km and Vmax.

Fig 3 – Different types of enzyme inhibition as shown on a Lineweaver-Burk plot

## Clinical Relevance – Plasma Enzyme Assays

Plasma enzyme assays can detect abnormal levels of enzymes in the blood. The assay measures units of activity in a sample and so will only measure functional enzyme.

• If levels of an enzyme are abnormally raised, it may indicate leakage from damaged tissue that the enzyme is normally found in.
• If levels are abnormally low, it may indicate that the enzyme is either non-functional, being produced more slowly than usual or is being broken down quickly, possibly due to a genetic abnormality.
 Enzyme Location Causes of raised levels Causes of low levels Lactate dehydrogenase Expressed everywhere Specific isoenzymes: LDH1 – heart, erythrocytes LDH2 – white blood cells LDH3 – lung LDH4 – white blood cells, kidney, pancreas LDH5 – liver, skeletal muscle Acute/chronic tissue damage, e.g. myocardial infarction Degree of elevation can indicate extent of damage Isoenzymes may help localise the site of injury Aspartate transaminase (AST) Widely distributed but predominantly found in liver, heart, skeletal muscle, kidneys, brain and erythrocytes Hepatocellular injury (acute/chronic liver disease), gall bladder disease, kidney failure, rhabdomyolysis, MI Degree of elevation can indicate the extent of damage Pregnancy, diabetes, beriberi (vitamin B1 deficiency) Alanine transaminase (ALT) Widely distributed but predominantly in liver Hepatocellular injury (acute/chronic liver disease), bile duct problems More specific marker of hepatic injury than AST Alkaline phosphatase (ALP) Greatest concentration in prostate Specific isoenzymes also found in the liver, bone, kidney, intestine and placenta Prostate carcinoma, biliary obstruction, high bone turnover (physiological or pathological) Creatine kinase Expressed in various tissues Specific isoenzymes: MM – skeletal muscle, heart MB – heart BB – brain, neurons, thyroid, kidney, intestine MM – skeletal muscle dystrophy MB – myocardial infarction in last 2-3 days BB – brain tumour Amylase Exocrine pancreas, saliva Pancreatitis, infections, DKA, perforated ulcer, renal failure Lipase Exocrine pancreas Pancreatitis (more specific than amylase) Acid phosphatase Widely expressed Specific isoenzymes in liver, erythrocytes, platelets and bone Diagnosis and treatment of prostate cancer