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Enzymes and Equilibrium

If you ever studied chemistry at high school, you're probably familiar with the concept of a chemical equation. Basically in its most simple form it looks like (Figure 1).


Figure 1: A simple description of an chemical reaction whereby one chemical on the left hand side becomes another chemical on the right hand side. This is a simple way to understand the changes to compounds that we see every day.

Basically, reactants have a reaction and produce a product. However most reactions don't actually work strictly like this. Instead they're in an equilibrium (Figure 2), which means there are two reactions taking place at the same time, going each direction, and the rate at which those reactions take place will vary depending on the concentration of either chemical, when the concentration of a chemical is higher, the rate of reaction from that chemical will be higher. Over time, the rate of reaction in both directions will be equal, and the reaction is said to be in equilibrium.


Figure 2: An equilibrium reaction. In an equilibrium reaction, there is a rate of reaction in both directions. As the rate of reaction in either direction will be dependent on the concentration of the starting chemicals in the reaction, with higher concentrations leading to fast reaction rates away from those chemicals. Over time, there will be an equilibrium, whereby the rates of reaction in either direction are equal. This equilibrium may favour the chemicals on one side of the reaction over the other, but it will nevertheless be an equilibrium.

The ratio of the concentrations of products and reactants required for a system to be in equilibrium is fixed. Enzymes do not change them and so do not change the equilibrium constant, rather enzymes make reactions reach this equilibrium faster than they would otherwise. It is for this reason that the enzyme alcohol dehydrogenase both detoxifies alcohol in humans, and produces alcohol in yeast, in both cases the reaction approaches equilibrium.

So this means that the food you eat (glucose) is in equilibrium with the carbon dioxide and water you produce, thus meaning you never really change anything when eating, and you turn air and water back into food, right? Not quite, this is where metabolic pathways come in. While an enzyme will keep its reaction in equilibrium, enzymes exist in pathways with other enzymes (Figure 3). Simple cellular respiration is dozens of steps (not just 4), all kept in equilibrium by their own enzymes. The enzymes in these pathways only keep their own reactions in equilibrium, which will change the concentrations of reactants and products in adjacent reactions in the metabolic pathway, thus there is continual activity of the enzymes to keep the reactions in equilibrium.


Figure 3: A template for an enzyme catalyzed metabolic pathway. The start and end steps of the pathway will be linked by many enzyme catalyzed reactions between intermediate compounds. All of these reactions will, if no compounds are added or removed from the system, over time reach an equilibrium where the reaction rates in both directions in all reactions will be equal.

As well as the metabolic processes being a number of different reactions all being kept in different equilibria, the chemicals involved at the beginning or the ends of reaction pathways may be added to or removed from the reaction environments respectively. In the reaction pathway for cellular respiration for example, food and oxygen enters the system, increasing the concentration of these starting products, which will have to be equilibrated by the enzymes in the metabolic pathway. At the other end, the excretion of carbon dioxide and water take these products away from the metabolic pathway, and so the system never reaches equilibrium. This creates a flux through the system (Figure 4), as reactants are being added at one end, and products are removed from the other, allowing the metabolic pathways in organisms to consume nutrients and generate energy. Also in the earlier case of alcohol dehydrogenase, the alcohol and aldehydes which are the products of these reactions are transported away from where the enzymes and their reactions are taking place, thus the equilibrium maintains formation of these products as favourable.


Figure 4: A simple schematic of the metabolic pathway that an organism uses to generate energy from food. Food enters the system at the right hand side via eating, and the waste products of metabolism (CO2 and water) are ex. As this destabilizes the equilibrium, the enzymes in the intermediate steps constantly have to maintain the equilibria of those reactions, which leads to flux through the pathway, and over time the food will become waste.

Just a final note about enzymes and equilibrium constants, enzymes do not change the equilibrium constant of a reaction. Enzymes changing an equilibrium constant would violate the first law of thermodynamics. This is because when a reaction is progressing towards equilibrium it produces energy. This means that if an enzyme changed an equilibrium constant, a device could be set up that adds and removes enzyme repeatedly from the reaction system to keep it approaching equilibrium, and therefore generating energy, which would be perpetual motion, and violate the first law of thermodynamics that energy cannot be created or destroyed.

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