Structural Biochemistry/Enzyme/Activation energy

The activation energy required to achieve the transition state is a barrier to the formation of product. It is the minimum amount of energy required for a reaction to proceed. This barrier is the reason why the rate of many chemical reactions is very slow without the presence of enzymes, heat, or other catalytic forces. There are two common ways to overcome this barrier and thereby accelerate a chemical reaction. First, the reactants could be exposed to a large amount of heat. For example, if gasoline is sitting at room temperature, nothing much happens. However, if the gasoline is exposed to a flame or spark, it breaks down rapidly, probably at an explosive rate. A second strategy is to lower the activation energy barrier. Enzymes lower the activation energy to a point where a small amount of available heat can push the reactants to a transition state. The question that arises is: How do enzymes work to lower the activation energy barrier of chemical reactions?

Enzymes are large proteins that bind small molecules. When bound to an enzyme, the bonds in the reactants can be strained (that is stretched) thereby making it easier for them to achieve the transition state. This is one way for which enzymes lower the activation energy of a reaction. When a chemical reaction involves two or more reactants, the enzyme provides a site where the reactants are positioned very close to each other and in an orientation that facilitates the formation of new covalent bonds. This technique also lowers the needed activation energy for a chemical reaction. Straining the reactants and bringing them close together are two common ways the enzymes use to lower the activation energy. There are other methods that the enzymes use to facilitate a chemical reaction. Changing the local environment of the reactants is one of these methods. In some cases, enzymes lower the activation energy by directly participating in the chemical reaction. For example, certain enzymes that hydrolyze ATP form a covalent bond between phosphate and amino acid in the enzyme that may have a charge that affects the chemistry of the reactants. This is very temporary condition. The covalent bond between phosphate and the amino acid is quickly broken, releasing phosphate and returning the amino acid back to its original condition.

Arrhenius equation

Arrhenius equation is a description of the relationship between the activation energy and the reaction rate.

k = Ae^(-E_a/RT)

where: k = chemical reaction, T = temperature in Kelvin, E_a = activation energy, A = the pre-exponential factor, R = the gas constant

According to this equation, it is observed that at a higher temperature, the probability that the two molecules will collide is higher, resulting in a higher kinetic energy, which leads to the lower requirement on the activation energy.

The Arrhenius equation is particularly helpful when calculating the rate of production of products over time, which is characterized by the following:

d[products]/dt = rate = Ae^(-E_a/RT)[A^mBⁿ]

where the [A] and [B] are the concentrations of the reactants and m and n are their respective reaction

Lowering the Activation Energy

A catalyst is something that lowers the activation energy; in biology it is an enzyme. The catalyst speeds up the rate of reaction without being consumed; it does not change the initial reactants or the end products.

The graph above shows how the activation energy is lowered in the presence of an enzyme (blue line) that is doing the catalysis, exempflified with the carbon anhydrase reaction. The transition state is usually the most unstable part of the reaction since it is the one with the highest free energy. The difference between the transition state and the reactants is the Gibbs free energy of activation, commonly known as activation energy $(\Delta G^{\ddagger })$.

Enzymes (blue line) change the formation of the transition state by lowering the energy and stabilizing the highly energetic unstable transition state. This allows the reaction rate to increase, but also the back reaction occurs more easily.

Common Misconceptions

Some common misconceptions about activation energy barriers and catalysts to speed up the reaction. The catalyst does NOT lower activation energy of the same barrier, but rather chooses another chemical pathway with a lower activation energy.The catalysts lead to new pathways which don't require as high of an energy of activation in turn speeding up the reaction.

Another big misconception about activation energy is that reactions will not always give the most thermodynamically stable products. Sometimes, the product that forms is the one that is more kinetically stable, or forms faster. However, if a catalyst is available, the thermodynamically more stable product will be able to form, even if the energy barrier is high.