Molecular Biology: Protein Structure and Function - Stepanov, V.M. 2005

Tertiary Protein Structure
Stability of the Three-Dimensional Protein Structure

The tertiary Structure refers to the three-dimensional arrangement of all atoms within a protein molecule, disregarding any interactions between this globule and neighboring globules or subunits. Often, METABOLISM/2.html">THE CONCEPT OF tertiary structure is narrowed to focus on its most stable element: the characteristic spatial folding pattern of the polypeptide chain for a given protein. Notably, for large groups of evolutionarily related Proteins—which may differ significantly in their Primary Structure and, consequently, in the spatial distribution of all atoms—the folding pattern of the polypeptide chain remains largely unchanged. This demonstrates that such simplification is well-justified, as it captures the essential Features of the tertiary structure.

The apparent similarity between the aforementioned definition of tertiary structure and the concept of Secondary structure is merely superficial. Secondary structure characterizes a relatively small segment of a protein and is determined by local non-covalent interactions, whereas tertiary structure depends on the sum total of all interactions—both covalent and non-covalent—within the protein globule.

The tertiary structure is the foundation of protein functionality, which requires precise Spatial Organization of large assemblies composed of numerous amino acid residues and their side chains. These assemblies form active sites of Enzymes, binding domains for other biological molecules, effector centers of proteins, and so forth. Consequently, the disruption of a protein's tertiary structure (Denaturation) inevitably leads to the loss of its biological activity.

The stability of the tertiary structure relies on a network of non-covalent interactions within the protein globule. Some proteins are additionally stabilized by covalent Disulfide Bonds; however, many proteins, including quite stable ones, lack them entirely.

Among the non-covalent interactions involved in The formation of the spatial Cell/13.html">Protein Structure, Hydrogen Bonds provide the highest precision in fixing interatomic distances and angles. As is well known, they play a decisive role in the Formation of secondary structure, particularly its periodic elements: $\alpha$-helices and $\beta$-sheets. In addition, hydrogen bonds link numerous Functional groups of amino acid side chains to one another and to the main chain, for example

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Crucially, at least 90% of all possible Hydrogen bonds are realized within the interior of the protein globule.

The system of hydrogen bonds, along with other non-covalent interactions—such as Van der Waals forces and electrostatic contacts—is extremely important for stabilizing the compact native protein globule. Indeed, The change in Free energy, and thus the Equilibrium Constant $K$ for the peptide chain $\leftrightarrow$ protein globule transition, is determined in the first approximation by the equation

(It should be emphasized that we are currently neglecting The Role of the surrounding Water, treating the protein molecule as if it were in a vacuum, which is indicated by the subscript "chain".)

In this expression, the term $\Delta H_{\text{chain}}$ is negative, reflecting THE CONTRIBUTION OF non-covalent interactions established within the protein globule. To stabilize the globule, this value must compensate for the entropic term $-T\Delta S_{\text{chain}}$, which is positive. This is because the folding of a random coil—an unstructured polypeptide chain—into a globule orders the structure and results in a decrease in the Entropy of the peptide chain, meaning $\Delta S$ is negative. Once this compensation is achieved, $K$ will equal unity, and consequently, the proportions of native and denatured protein molecules will become equal. For the equilibrium to shift markedly toward the formation of a compact structure, the value of $\Delta H_{\text{chain}}$ must significantly exceed $T\Delta S_{\text{chain}}$.

The ratio between these two quantities depends primarily on the number of non-covalent bonds formed during the folding of the polypeptide chain into a globule, and thus on the length of the peptide chain. This explains the previously discussed boundary between Peptides and Proteins. At the same time, it is evident that as the Temperature $T$ rises, the $T\Delta S$ term will sooner or later exceed $\Delta H$ in absolute value, causing the Spatial Structure to lose its stability—resulting in thermal denaturation of the protein.

However, the actual picture depends significantly on accounting for the interaction between the protein and the solvent, usually water. Indeed, water is capable of forming hydrogen bonds with both peptide groups and functional groups of the protein, thereby competing with the formation of intramolecular bonds.

If we compare the extended, denatured state of a protein with its folded, Native State, we find that when a polar group is packed into the interior of the globule:

1) it forms a Hydrogen bond with another polar group of the protein;

2) the hydrogen bonds that both groups—donor and acceptor—previously formed with water in the extended chain are broken;

3) new hydrogen bonds are established between the "liberated" water molecules and other water molecules.

Let us consider, for example, The behavior of two polar groups—the Serine hydroxyl and the asparagine amide group—which form an intramolecular hydrogen bond during the folding of the chain into a compact structure

Overall, no net gain in the number of hydrogen bonds can occur upon folding of the globule, since chain-water hydrogen bonds are simultaneously lost. It is essential that the inevitable penalty—a reduction in the number of hydrogen bonds resulting from certain polar groups being buried within the globule without finding a partner to form a hydrogen bond—does not prove too significant (this dictates the necessity of forming the maximum possible number of bonds within the globule: as already noted, at least 90%). Clearly, such a high degree of saturation of the globule with hydrogen bonds cannot be achieved randomly. Regular elements of secondary structure are far more efficient in this regard.

During globule folding, the entropy of the peptide chain decreases, but simultaneously, the entropy of the solvent (water) increases. The latter plays a decisive role in stabilizing the Tertiary Structure of the protein, which can be explained by the following considerations.

As is well known, water is a highly unusual and remarkably structured solvent. Each of its molecules is capable of participating in the formation of four hydrogen bonds with other water molecules. As a result, relatively extensive quasi-crystalline, ice-like structures coexist in dynamic equilibrium with free water molecules. Polar compounds, including the polar groups of proteins, are integrated into these structures relatively easily by establishing hydrogen bonds with the water surrounding the protein.

The situation is more complex when interacting with the non-polar side chains of a protein. Model studies using the simplest Hydrocarbons have shown that they are sparingly soluble in water. Their molecules, being incapable of forming hydrogen bonds, are accommodated within peculiar "voids" or cavities in the dynamic structure of water. These cavities are formed by water molecules linked together by hydrogen bonds (Fig. 6.1).

Essentially, this resembles so-called inclusion compounds. The appearance of such cavities implies an ordering and restriction of the random motion of a significant number of water molecules, i.e., a decrease in the entropy of the solvent (water). This entropy decrease, which is greater the larger the non-polar group-water interface, limits the dissolution of hydrocarbons in water: phase Separation into an aqueous phase and a hydrocarbon phase proves thermodynamically favorable.

Something similar accompanies the dissolution in water of a peptide chain bearing non-polar side groups. Each of these groups ends up in a cage surrounded by structured water molecules, leading to a decrease in the system's entropy. "Stripping off" the hydrocarbon radicals in this case is clearly impossible, as they are tethered to the polypeptide backbone. Therefore, another process takes place: the folding of the globule, during which a significant portion (at least half) of the hydrophobic side chains are shielded from contact with the water surrounding the protein. This is often accompanied by the formation of unique intramolecular "droplets" of hydrophobic amino acid side chains, forming "hydrophobic cores" of varying complexity. Sometimes these cores are elongated, resembling a crescent moon, and sometimes they break down into two or three independent smaller cores. Crucially, the reduction in the contact surface between hydrophobic groups and water leads to the establishment of so-called hydrophobic contacts between them. Note that the bringing together of non-polar groups entails the establishment of van der Waals contacts between them, which also contributes to stabilizing the protein globule to a certain extent. However, the contribution of these very weak interactions to the energetics of protein folding is small, whereas the role of hydrophobic contacts—in other words, the role of solvent entropy changes during protein folding—is extremely significant.

Fig. 6.1. Dodecahedron formed by water molecules connected via hydrogen bonds.

Inside the dodecahedron, a cavity with a diameter of about 5 Å is formed, which can accommodate a hydrophobic compound—i.e., one that does not form hydrogen bonds with water. The formation of a dodecahedron or similar regular structures with larger cavities requires ordering of the water molecule arrangement; this ordering becomes more extensive as the surface area of the compound accommodated in the cavity increases. This leads to a decrease in the system's entropy and makes the association of hydrophobic protein elements into a core thermodynamically favorable.

The Thermodynamics of protein globule folding are characterized by the fact that the factors promoting the formation of a compact native structure and those acting in the opposite direction are nearly balanced. The change in free energy during the folding of a protein containing approximately 100 amino acid residues is about 10 kcal/mol, or merely 0.1 kcal per single amino acid residue. For comparison, the energy of a single hydrogen bond is about 3 kcal.

What is even more important is that this remarkably small value is the difference between two fairly large, yet balanced, quantities. Consequently, the protein globule can lose stability and unfold upon relatively small changes in these parameters. For instance, the loss of just a single hydrogen bond due to the substitution of Threonine for isoleucine in T4 phage Lysozyme decreased the Protein Denaturation temperature by 11°. Crucially, the destabilization of the protein tertiary structure can be triggered not only by direct impacts on the protein itself, but also by alterations in The structure of the solvent, namely water.

Several Methods are known for estimating the Hydrophobicity of amino acid side chains composing a protein. According to one such method, proposed by R. Wolfenden, researchers determine the distribution of compounds modeling the side chain of a given residue between Water and Its vapor at equilibrium. For example, the threonine side chain was approximated by ethanol, the Alanine radical by methane, and so on. Under these conditions, hydrophobic compounds tend to leave the water and pass into the vapor phase.

It turned out that, based on the vapor phase/water equilibrium constant (i.e., the propensity to transition into the vapor phase), The amino acid side chains can be classified into the following groups:

1. A constant on the order of 10² — Glycine, leucine, isoleucine, valine, alanine.

2. A constant on the order of 10¹ — phenylalanine, Cysteine, Methionine.

3. A constant on the order of 10^-4 — threonine, serine, Tryptophan, Tyrosine.

4. A constant on the order of 10^-8 — asparagine, Lysine, glutamine, glutamate, Histidine, aspartate.

5. A constant of 10^-14 — Arginine.

The first two groups comprise hydrophobic Amino Acids whose side chains tend to avoid contact with water. The placement of glycine in the first group is explained by the fact that a hydrogen molecule poorly models the hydrogen atom in glycine. In reality, when packing glycine residues within a protein, the contribution of the peptide backbone group —NH—СН—СО— is particularly significant, which is why it is difficult to classify glycine as a hydrophobic residue. Nevertheless, instances are known where, within a fixed tertiary structure of a protein, the methylene group of a glycine residue —СН₂— acts as a hydrophobic unit.

The third through fifth groups include hydrophilic amino acid residues. Proline cannot be modeled within the framework of this approach. An Analysis of the spatial structures of numerous proteins demonstrates that classifying these Amino acids as either hydrophobic or hydrophilic generally correlates with their predominant distribution either inside or On the surface of the protein globule (Tables 6.1, 6.2).