# Structural Biochemistry/Enzyme/Effects of Temperature on Enzyme Activity
## Equilibrium Model

It is important to understand how enzymes work because they lead to the understanding of the functions of cells and manipulations of enzymes. One of such factors that affect the enzyme activity is temperature. The widely accepted Classical Model on how temperature affects enzymatic activity states that the exponential increase in rate of reaction corresponds to a decrease in the amount of enzyme, resulting from irreversible thermal destruction of enzymatic activity. However, research showed that the experimental data do not match the Classical Model. For example, one study found that once passing the optimum temperature of the enzyme, there is a greater decrease in catalytic rate in enzyme than from that expected from irreversible thermal inactivation. A second similar study also revealed that some enzyme becomes less active at high temperature compare to at its thermal stability and that some of the loss of activity is reversible if at enzyme's optimum temperature; hence, thermal stability is needed but not enough for thermal activity.
An Equilibrium Model is introduced in replace of the Classical Model to account for aspects that were neglected in the Classical Model. After incorporating all possible factors, the Equilibrium Model turns out to closely fit the experimental data and gives insights to temperature control, adaptation and evolution of enzymes. The Equilibrium Model explains the thermal behavior of enzymes by the introduction of inactive but not denatured intermediate enzyme in equilibrium with its active intermediate. This additional term describes how temperature affects the equilibrium between the active and inactive forms of the enzyme. This relationship can be shown in the following reaction:
E$_{act}$ ↔ E$_{inact}$ → X
Where E$_{act}$ is the active form of the enzyme, E$_{inact}$ is the inactive but not denatured form of the enzyme, X is the fully inactivated form of the enzyme, K$_{eq}$ is the equilibrium constant between E$_{act}$ and E$_{inact}$ , and K$_{inact}$ is the rate constant from E$_{inact}$ to X.
Initially, the rate is determined by the increasing concentration of products formed over a short time and then the concentration falls back down. This shows that there is an optimal temperature for the enzyme, which further states the loss of enzymatic activity, meaning there is a change in ratio of the active and inactive enzymes. The active and inactive enzymes reversible equilibrium protects the enzyme from thermal inactivation, meaning that the equilibrium term acts like a buffer. The difference between the Equilibrium Model and the Classical Model is that the experimental data for enzymes showed activity optimum at to, which is consistent with Equilibrium Model; however, Classical Model does not show such an optimum. Moreover, many enzymes from the least reactive to the most reactive groups are examined and shown to match with the Equilibrium Model. Therefore, the Equilibrium Model is universal, with no dependency of the reaction undergoing and structure of enzyme itself.

## Previous models

There are several models prior to the establishment of the Equilibrium Model, which contained some similarities to the Equilibrium Model. One previous model showed time-independent changes in activity, meaning that the only changes of catalytic rate are affected by temperature, with total active enzymes as constant. This excluded the possible time-dependent irreversible inactivation. This model is similar to the Equilibrium Model for they are both time-independent. However, the level of enzyme activity varies in the Equilibrium Model.
A second model described the equilibrium between more than one active form of reactants. In this model, proteins were used instead of enzymes, but the basic concept of establishing equilibrium remained. This model says that the total active proteins decrease with time; however, it assumed that level of activity does not vary with temperature and assumed both protected and native antibodies are active.
Another model in which the equilibrium is reached between the native and unfolded forms of the enzymes concluded that overall process is constrained by a reversible step, especially in unfolding then grouping proteins, such that an irreversible denaturation process follows. This model differs with the Equilibrium Model since the inactive enzyme is significantly folded in the Equilibrium Model. In addition, it is usually rare for thermal unfolding of an enzyme to be reversible in the Equilibrium Model.

## E$_{act}$-E$_{inact}$ interconversion

A plot of the initial enzyme rate versus temperature shows each enzyme has its own optimal temperature. As the temperature passes the threshold of the optimum, it results in a faster enzyme activity loss than what the initial rate can measure; therefore, the equilibrium of the active and inactive form the enzyme is a valid assumption. From looking that the top reaction, the denaturation rate is much slower than the rate of converting active to inactive enzyme because the conversion of the active to inactive form is temperature dependent. The interconversion is restricted at the active sites of the enzyme. The active sites needs flexibility to carry out catalysis, leading to a greater possibility of temperature induced changes in conformation and/or dynamics. Active sites also control the effect of temperature on activity and the kinds of activity that enzyme has over a wide range of temperature. Although the big picture of interconversion between the two forms is well known, the detailed local changes from active to inactive form is hard to detect because there might be only small structural changes, and there is time constraints due to rapid denaturation to producing dominantly inactive form.

## Implications of the Equilibrium Model

Mutagenesis, the mutation in which the genetic information changes in a slow and stable way, can be used to improve enzyme stability in two ways. First, mutagenesis helps to uncover the structural basis of protein stability. Second, it increases the temperature at which the enzyme can function. More specifically, mutagenesis changes a single amino acid at the active site, thus leading to changes in optimal temperature and enthalpy without changing the free Gibbs energy of the inactive enzyme. This means with the same amount of energy, the level of enzyme activity increases due to a rise in the optimal temperature. However if the temperature is, in general, increased, there would be a corresponding decrease in the enzyme stability and reaction rate.

## Conclusion

The Equilibrium model tests the relationship between the thermal properties of enzyme and effect of temperature has on the host organism. In other words, the Equilibrium Model provides an explanation on how temperature affects the enzyme activity. In detail, the active sites are governed by how temperature affects the enzyme activity, which means that the evolution of actives sites is limited by temperature. A note to keep in mind is that the Equilibrium Model works for ideal situations. Indeed, the establishment of the Equilibrium Model does not eliminate the possibility that a more complex model might also fit the data equally as well.

## Reference

Roy M. Daniel and Michael J. Danson. A New Understanding of How Temperature Affects the Catalytic Activity of Enzymes. Trends in Biochemical Sciences, Volume 35, Issue 10, October 2010, Pages 584-591, ISSN 0968-0004, 10.1016/j.tibs.2010.05.001.
(http://www.sciencedirect.com/science/article/pii/S0968000410000897)