Enzyme Kinetics

Activation Energy

Activation energy is the amount of energy required to bring the reactant molecules to a higher energy level (activated state) where a chemical bond may be formed or broken to form product or products. Like chemical catalysts, enzymes accelerate the rate of biochemical reactions by lowering the activation energy. When the reactant molecules reach this activated condition, they are energy-rich and are in a transition state. In enzyme reactions, the enzyme-substrate complex represents the transition state.

The enzyme functions to lower the amount of energy required to bring the substrate to the transition state. An example may be cited to explain the significance of activation energy. A mixture of hydrogen and oxygen will remain unchanged indefinitely, although they have the ability to combine producing water.

An electric spark will bring them to the transition state and they combine with release of energy. Here, the electric spark provides the activation energy. The same reaction is catalysed by an enzyme, called hydrogenase, at ordinary temperature, because the enzyme lowers activation energy.

 

Figure adapted from biologydiscussion.com

Units of Enzyme activity

The enzyme unit, or international unit for enzyme (symbol U, sometimes also IU) is a unit of enzyme's catalytic activity

1 U (μmol/min) is defined as the amount of the enzyme that catalyzes the conversion of one micromole of substrate per minute under the specified conditions of the assay method

The specified conditions will usually be the optimum conditions, which including but not limited to temperature, pH and substrate concentration, that yield the maximal substrate conversion rate for that particular enzyme. In some assay method, one usually takes a temperature of 25°C.

Enzyme velocity and Substrate Concentration

It has been shown experimentally that if the amount of the enzyme is kept constant and the substrate concentration is then gradually increased, the reaction velocity will increase until it reaches a maximum. After this point, increases in substrate concentration will not increase the velocity (delta A/delta T)

Ka is affinity constant or association constant Ka = K1 /K2

 

It is theorized that when this maximum velocity had been reached, the entire available enzyme has been converted to ES, the enzyme substrate complex. This point on the graph is designated Vmax. Using this maximum velocity and equation, Michaelis developed a set of mathematical expressions to calculate enzyme activity in terms of reaction speed from measurable laboratory data.

Three basic assumptions required for the development of rate equations:

·       ES complex is in steady state

·       Under saturating conditions the entire enzyme is converted to ES complex and none is free. This occurs when substrate concentration is high.

·       If the entire enzyme is in ES complex, then rate of formation of product is maximum.

Vmax= K3 [ES].

Steady state expression for the formation and breakdown of ES complex is

Km = K2 + K3/ K1

Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate {\displaystyle v}V (rate of formation of product {\displaystyle [{\ce {P}}]}[P] to {\displaystyle [{\ce {S}}]}[S], the concentration of a substrate S. Its formula is given by

This equation is called the Michaelis–Menten equation.  Here, {\displaystyle V_{\max }}V_max represents the maximum rate achieved by the system, happening at saturating substrate concentration. The value of the Michaelis constant {\displaystyle K_{\mathrm {M} }}K_M is numerically equal to the substrate concentration at which the reaction rate is half of {\displaystyle V_{\max }} V_max .

Often, in vitro or in vivo enzyme-mediated catalytic events occur far from equilibrium and, therefore, substrate affinity measured as the inverse of ES ⇄ E+S dissociation equilibrium constant (K_d) has a doubtful physiological meaning; in practice it is almost impossible to determine K_d.. The Michaelis-Menten constant (K_m), the concentration of substrate ([S]) providing half of enzyme maximal activity, is not the (K_d)

Significance

Michaelis constants have been determined for many of the commonly used enzymes. The size of Km tells us several things about a particular enzyme.

• A small Km indicates that the enzyme requires only a small amount of substrate to become saturated. Hence, the maximum velocity is reached at relatively low substrate concentrations.
• A large Km indicates the need for high substrate concentrations to achieve maximum reaction velocity.
• The substrate with the lowest Km upon which the enzyme acts as a catalyst is frequently assumed to be enzyme's natural substrate, though this is not true for all enzymes.
• Km indicates the affinity of an enzyme for its substrate.
• Change in Km of a particular enzyme means either a mutation in Enzyme –binding site occurred or an isoenzyme with altered Km is expressed.
• If Km value is known, the fraction of sites occupied by the substrate can be calculated.

 

 Lineweaver-Burk Plot

In an Enzyme catalysed reaction V max is attained asymptomatically. Therefore calculating Km from rectangular hyperbola graph may not yield accurate values. Lineweaver-Burk, the manipulation is using the reciprocal of the values of both the velocity and the substrate concentration. The inverted values are then plotted on a graph as 1/V  instead of V and vs. 1/[S] instead of [S]. Because of these inversions, Lineweaver-Burk plots are commonly referred to as 'double-reciprocal' plots.

Here the value of Km on a LB plot is easily determined as negative reciprocal of x intercept and Vmax as reciprocal of y intercept. There are other related manipulations similar to LB plot. Eg: Eadie-Hotstee plot. It demonstrate V versus V/[S]. Vmax is Y intercept and slope is -Km. LB plot is also used extensively in identifying Enzyme- Inhibitor interactions.