Enzyme Kinetics

Enzymes often require cofactors to function, which can be inorganic molecules (often metals) or complex organic molecules known as coenzymes.
Coenzymes that are tightly bound to the enzyme are referred to as prosthetic groups.
In the absence of a coenzyme, the active form of the enzyme (holoenzyme) is described as an apoenzyme.
Enzymes are highly efficient and promote reactions that would typically occur at slow rates.
Properties of enzymes:
- Extremely efficient—often more so than inorganic catalysts.
- Highly specific and stereospecific.
- Function optimally at physiological temperature and pH.

Catalysts, including enzymes, enhance the rate of chemical reactions by lowering the activation energy needed to reach the transition state.
Example: Breakdown of hydrogen peroxide (H2O2) into water (H2O) and oxygen (O2) can be catalyzed by the enzyme catalase or certain metal ions (e.g., Fe+3).

Enzyme kinetics began with Adrian Brown in 1902, describing the hydrolysis of sucrose into glucose and fructose using the enzyme b-fructo-furanosidase.
The initial reaction rate increased with substrate concentration until enzyme saturation occurred.

At high substrate concentrations, the initial reaction rate (v0) becomes constant and is termed Vmax.
Vmax reflects the maximum rate achievable by an enzyme at saturating substrate concentrations.

Proposed by Michaelis and Menten in 1913 to explain enzyme kinetics:
- Formation of an enzyme-substrate complex (ES) has rates governed by constants k1 and k-1.
- k1 is a second-order rate constant (depends on substrate concentration) and has units of M-1 s-1.
- k-1 is a first-order rate constant (depends on the dissociation of ES) and has units of s-1.

The slowest step in the enzymatic reaction (usually the breakdown of ES) is the rate-limiting factor.
At pre-saturation levels, the reaction rate is proportional to substrate concentration ([S]). At saturation, the velocity is maximal (Vmax) and independent of [S].

Basic equation: Vo = Vmax [S] / (Km + [S]), where:
- Vo = initial velocity,
- Vmax = maximum velocity,
- Km = Michaelis constant (indicates enzyme affinity for substrate).
Km values can be expressed in molarity (M) and reflect the concentration of substrate needed to reach half of Vmax.

Km is often mistakenly interpreted as a measure of enzyme affinity. While it correlates with affinity, it is not directly equivalent to the dissociation constant (Kd).
Kd is defined as: Kd = [E][S] / [ES] and relates directly to the rates of formation and dissociation of the enzyme-substrate complex.

The term kcat describes maximum reaction velocity per unit enzyme concentration.
To evaluate overall enzyme efficiency, scientists examine the ratio kcat / Km, termed the specificity constant.
This ratio has an upper limit due to diffusion constraints, typically around 10^8 to 10^9 M-1 s-1.

A double-reciprocal plot helpful in determining Vmax and Km, characterized by:
- Slope = Vmax / Km
- x-intercept = -1/Km
- y-intercept = 1/Vmax

Aside from substrate concentration, other factors affecting enzyme reaction rates include:
- pH
- Temperature
Example: Chymotrypsin's activity relies on specific deprotonation and protonation states at optimal pH levels.

The active site of an enzyme is crucial for its catalytic action:
- Displays specificity and high affinity for the correct substrate.
- Shape complements that of the substrate, facilitating binding.
- Substrates interact via weak, non-covalent interactions within the active site.

Enzyme inhibition is vital for regulating biological processes and drug actions.
Inhibitors can be classified into:
- Reversible (can dissociate from the enzyme)
- Irreversible (form a permanent bond with the enzyme)

Competitive Inhibition: Competes with substrate for the active site, altering Km (apparent Km increases).
Uncompetitive Inhibition: Binds to the enzyme-substrate complex, decreasing both Vmax and apparent Km.
Mixed Inhibition: Can bind both free and bound enzymes, affecting both Vmax and Km in different ways.

Involves a covalent bond between the inhibitor and enzyme, permanently inactivating it.
Example: Some drugs that treat diseases (like sleeping sickness) target enzymes vital for pathogen survival, rendering them inactive without harming human enzymes significantly.