Basics of enzyme reaction kinetics
Enzyme reaction kinetics is a branch of enzymology that studies how the rate of an enzymatic process depends on the chemical nature of substances and environmental conditions. The reaction rate is assessed not directly, but through the change in substrate concentration (its consumption) or through the rate of product accumulation.
The rate of an enzymatic reaction is influenced by:
- amount and catalytic activity of the enzyme;
- substrate concentration;
- ambient temperature;
- ambient pH;
- presence of activators and inhibitors.
The dependence of the initial reaction rate on substrate concentration is graphically represented as a hyperbola. At low substrate concentrations, active sites of enzymes are free, and the rate increases in proportion to [S]. As active sites become saturated with the substrate, a plateau is reached — the maximum reaction rate (Vmax), at which all enzyme molecules are part of the enzyme-substrate complex and do not have time to "switch" to new substrate molecules.
The Michaelis constant and its biological meaning
The Michaelis constant (Km) is the substrate concentration at which the reaction rate reaches half of the maximum ($\frac{1}{2}$ Vmax). Km is expressed in units of concentration (e.g., mmol/L) and characterizes the affinity of the enzyme for the substrate:
- the lower the Km, the higher the enzyme's affinity for the substrate — the enzyme "recognizes" the substrate even at low concentrations;
- the higher the Km, the lower the affinity — a higher substrate concentration is required for the enzyme to work actively.
A classic example is isoenzymes that phosphorylate glucose to glucose-6-phosphate using ATP:
- Hexokinase is present in most tissues; its Km is approximately 0.1 mmol/L. This is significantly lower than the physiological concentration of glucose in the blood (3.3–5.5 mmol/L), so the enzyme works efficiently even during hypoglycemia.
- Glucokinase is located predominantly in hepatocytes; its Km is approximately 10 mmol/L. It "switches on" only at high glucose concentrations, for example, after a meal, ensuring glucose deposition in the liver as glycogen.
The Michaelis–Menten equation
The dependence of the initial reaction rate (V₀) on substrate concentration is described by the Michaelis–Menten equation:
V₀ = Vmax · [S] / (Km + [S])
The equation allows calculating V₀ given Vmax, Km, and [S], or finding one of the parameters given the other two. Graphically, in V₀ versus [S] coordinates, it yields a hyperbola, which is inconvenient for accurately determining Vmax and Km in an experiment — the asymptote to Vmax is reached only theoretically.
The Lineweaver–Burk plot
For the convenience of experimental analysis, the Michaelis–Menten equation is transformed into double reciprocal coordinates:
1/V₀ = (Km/Vmax) · (1/[S]) + 1/Vmax
This is a straight-line equation — the Lineweaver–Burk plot. On this plot:
- the intersection of the line with the ordinate axis corresponds to 1/Vmax;
- the intersection with the abscissa axis corresponds to −1/Km;
- the slope is equal to Km/Vmax.
The linear form allows precise determination of kinetic parameters from experimental points and provides a clear comparison of the effects of different types of inhibitors.
Reversible inhibition: competitive and non-competitive
Inhibition is the decrease in the catalytic activity of an enzyme under the action of inhibitors. A distinction is made between irreversible (with the formation of strong covalent bonds) and reversible inhibition. Among reversible inhibitors, competitive and non-competitive ones are distinguished.
Competitive inhibition
A competitive inhibitor is a structural analog of the substrate that binds to the active site of the enzyme but is not converted into a product. Examples: malonate as an inhibitor of succinate dehydrogenase (substrate is succinate); neostigmine and edrophonium as inhibitors of acetylcholinesterase.
- Vmax does not change — the inhibitor can be displaced by an excess of substrate;
- Km increases — the apparent affinity of the enzyme for the substrate decreases.
On the Lineweaver–Burk plot, the lines with and without the inhibitor intersect on the ordinate axis (same 1/Vmax), but have different slopes and different −1/Km values.
Non-competitive inhibition
A non-competitive inhibitor binds to the enzyme outside the active site (e.g., at an allosteric site), altering the conformation of the active site. Increasing [S] does not restore enzyme activity.
- Km does not change;
- Vmax decreases.
On the Lineweaver–Burk plot, the lines with and without the inhibitor originate from the same point on the abscissa axis (common −1/Km), but the line with the inhibitor intersects the ordinate axis higher (larger 1/Vmax value).
Analysis of a typical problem
If three lines are presented on the Lineweaver–Burk plot, identification is carried out by two features — the intersection points with the axes.
- Two lines intersecting on the ordinate axis differ in their Km values. The line with the larger Km (the −1/Km point is located closer to the ordinate axis) corresponds to a competitive inhibitor; the second corresponds to the reaction without inhibitor.
- The third line, originating from the same point on the abscissa axis as the line without inhibitor but intersecting the ordinate axis higher, corresponds to a non-competitive inhibitor.
To calculate Vmax from the intersection point with the ordinate axis, the reciprocal relationship is used: if 1/Vmax = 0.3, then Vmax = 1/0.3 ≈ 3.33 (in corresponding velocity units).
Key points
- The rate of an enzymatic reaction is assessed by the change in substrate or product concentration.
- Vmax is reached at complete saturation of the enzyme's active sites with the substrate.
- Km is the substrate concentration at $\frac{1}{2}$ Vmax; a lower Km means a higher affinity of the enzyme for the substrate.
- Hexokinase has a low Km and works at any glucose concentrations; glucokinase with a high Km is active only during hyperglycemia.
- The Michaelis–Menten equation describes the hyperbolic dependence of V₀ on [S].
- The Lineweaver–Burk plot linearizes this dependence in double reciprocal coordinates.
- A competitive inhibitor increases Km without changing Vmax; the lines intersect on the 1/V₀ axis.
- A non-competitive inhibitor decreases Vmax without changing Km; the lines originate from a common point on the 1/[S] axis.