# Structural Biochemistry/Protein Folding Rates
## Overview

Determining how a protein will fold has been fairly difficult to predict even though the amino acid sequence is known. Instead of analyzing the structure of the protein and analyzing the mechanism of how a protein folds, understanding the kinetics of folding rates has proven to be a much more efficient way of understanding protein folding. The two-state folding kinetics of proteins is mostly studied, which analyzes the folding progress of a protein from its linear chain form, its primary structure, to its folded state, its tertiary structure. This process is dependent on the cooperative nature of the transition state. The kinetics of protein folding can be illustrated through the funnel energy landscape diagram, which is mathematically explained through the Gibbs free energy equation. This energy landscape diagram can follow the tract of the many pathways a protein can take until it reaches its native, or most stable, folded state. As a protein conforms to its most native state, a free energy barrier ends up controlling the kinetics of the protein folding. To illustrate the folding mechanisms, different Go-model simulations are used, which are coarse-grained topology-based models. However, although Go-model simulations provide the folding mechanism of proteins, they lack the ability to predict the folding rates of proteins based on the kinetic or thermodynamic cooperativity demonstrated by two-state proteins. Because of this reason, studies have been done to understand the cooperative nature of the two-state folding of proteins and the factors that affect the folding rates of proteins.

## Folding Rate Trends of Proteins

The folding rates of two-state proteins can be understood through two general properties of the folded conformations. One of the trends is that more structurally complex proteins tend to fold at slower rates in comparison to more simple structural proteins. For example, a tertiary structure containing beta sheet proteins and proteins combined with alpha helices and beta sheets tend to fold slower than proteins that are made up of only alpha helices. The second trend is that larger proteins tend to fold a lot more slowly than smaller proteins. The kinetics of alpha helical proteins and structurally complicated proteins such as globular proteins also differ due to long-range tertiary contacts. The transition states of globular proteins are expected to have a higher transitional energy barrier than alpha helical proteins because more entropic energy is required to make a more structurally complicated protein to fold in a more ordered fashion in comparison to a simpler structural protein. As the chain length of a protein also increases, the free energy barrier exponentially increases as well to reach the transition state of the protein.
In determining the transition state of an in-process folded protein, the native state topology of the protein has to be known in order to predict the structure of the transition state of the protein. Topology refers to the effect of the orientation of objects in space due to deformations of the objects. In the case for proteins, a folded structure might change its orientation in space if the protein is heated up as it would lead to denaturing. To examine this transition state of folded proteins, the formation of the transition state is determined by the free energy barrier that controls the kinetics of the folding reaction. This free energy barrier is the result of the compensation of energy and the loss in entropy due to the new interactions formed in the process of protein folding. The relationship between the kinetics of a folding protein and topology help to explain why the transition state of a protein is dependent upon its native state. This is known as the principle of minimum frustration of energy landscape theory, which can related to the funnel model of folded proteins. The more stable the protein is, the lower the energy it is at, and the energy of the native protein can help give information on how much energy is required for a protein to reach its transition state in the folding process.

## Cooperativity of Proteins

The use of Go models helps to give an identification of a protein in its most native state, which is held together by stabilizing interactions between native contacts. These stabilizing interactions are also known as non-additive forces, and these forces play a factor in the kinetics and thermodynamics of protein folding. These non-additive forces can also be thought of as intramolecular interactions that happen spontaneously within the protein such as side-chain ordering and hydrophobic forces. The effect of these non-additive forces have been shown to increase the free energy barrier of the two-state folded protein, and therefore, this makes these Go models more thermodynamically cooperative.
Upon using these Go models, the three-body interactions of the folding rates and what are known as phi values are examined in two-state proteins. The meaning of these phi values gives a relationship between the transition state of a two-state folded protein and its native state. The phi value explains the content of the native structure in its transition state. Therefore, the more native-like the structure of the transition state, the more likely this transition state will conform into its native state in a shorter period of time. In general, phi values improve when the transition state is more like its native state, but the ratio between its transition state and native state is different for each protein that varies in size and its secondary structure.
Many different types of Go models have been developed to better understand the cooperativity of the folding rates of proteins. For example, a Go model has been created in analyzing a small alpha-helical protein also known as a Calpha Go-like model. This model has also been altered by introducing solvent-mediated interactions to the model. The interactions between proteins are instead replaced by a desolvation barrier. Studies have shown that the thermodynamic and kinetic cooperativity of two-state folded proteins increase as the desolvation barrier increases in height. Desolvation is known as the removal of solvent from a material in solution. In general, desolvation has a property whee short-range contact proteins such as those that form alpha-helices have little cooperativity due to desolvation while long-range contacts such as those with a mix of beta sheets and alpha helices are expected to have high cooperativity because long-range contacts require persistence in bringing the proper chains together, and therefore, require a high amount of cooperativity. In conclusion, it is these topological models with nonadditive forces such as hydrophobic forces of proteins that help to better understand the folding rates of certain proteins.

## References

Portman, J. Cooperativity and protein folding rates. 2010, Current Opinion in Structural Biology. p. 2011-2015.