Protein Folding and Tertiary Structure

The tertiary structure of a protein refers to the unique three-dimensional structure that a given polypeptide will adopt.

• All molecules of a polypeptide that share the same primary sequence will fold into the same tertiary structure
• The unique tertiary structure represents a global free-energy minimum. Of all possible conformations available to a polypeptide, the characteristic unique tertiary structure has the lowest free energy (and involves considerations of both enthalpy and entropy)
• The information contained within the primary sequence, and the interactions of the polypeptide with water, determine the unique tertiary structure (i.e. enthalpy and entropy changes contributing to the free energy can involve both the polypeptide and the solvent)
• Proteins adopt tertiary structures that tend to maximize and optimize hydrogen-bonding interactions between H-bond donor and acceptor groups within the polypeptide (side chain and main chain). Van der Waals interactions also tend to be optimized (i.e. the protein folds up to leave very little unfilled areas within the interior)
• Proteins in aqueous solutions adopt tertiary structures that tend to remove hydrophobic side chains from solvent exposure
• There are a relatively small number of fundamental structural motifs observed (e.g. soluble proteins generally fall into one of nine fundamental "super-fold" categories).

Tertiary and quaternary structure is described by the structural organization and association of polypeptides along a linear axis, resulting in a "fiber" or "stand" type of tertiary structure. These generally have high tensile strength (resistance to tension, or pulling, forces), and function as an essential structural element in holding the body together. Here are some examples:

a-keratin

• The polypeptide of
a-keratin adopts a long, a-helix conformation. It contains a repeating heptad (seven residue) amino acid sequence (a repeating amino acid sequence is typical of structural proteins).
• In addition to promoting formation of an
a-helix secondary structure, the amino acid sequence of the a-keratin protein is such that two a-helices readily associate to form a coiled-coil (an intertwined pair of a-helices).
• Subsequently, two coiled-coils can readily associate to form a "protofilament" of
a-keratin.
• Four protofilaments can associate to form a "filament" of
a-keratin (i.e. eight a-helices arranged in four bundles of coiled-coils)
• Hair, horns and claws of animals are made up of
a-keratin.

b-keratin

• A repeating -(Gly-X-Gly)- amino acid sequence
• Forms
b-sheet structures that associate to form anti-parallel b-sheet structures
• Structural element of silk fibers in insects and feathers in birds

Collagen

• Triple helix of collagen polypeptides. Each polypeptide adopts a left-handed twist (not an
a-helix ), and associate to produce a three-stranded fiber with an overall right-hand twist.
• Very high
tensile strength, component of tendon, cartilage, skin and blood vessel connective tissue
• Contains a repeating triplet motif rich in glycine and proline, -(Gly-X-Y)-, with X typically Pro, and Y typically hydroxyproline. The polypeptide also contains lysine residues.
• The stability of the triple strand is dependent upon hydroxylation of the proline and lysine residues, resulting in 3-hydroxproline (hydroxylation of the side-chain
b-carbon) and 5-hydroxylysine (hydroxylation of the side-chain d-carbon). The hydroxylation of these residues occurs after the collagen polypeptide is made (i.e. a post-translational modification), and requires vitamin C
• Without vitamin C, the collagen polypeptides will not form a stable triple-strand. The connective tissue in your body will begin to dissociate. Teeth fall out, skin easily tears open, internal organs lose support. Not pretty. Eat your fruits and vegetables.
• Collagen can also be "mineralized" by incorporating crystals of calcium phosphate known as hydroxyapatite: Ca₅(PO₄)₃OH. This confers upon the fiber tremendous
compressive strength, and forms bone. Thus, collagen is involved in forming the two fundamental structural elements within the body (i.e. tensile and compressive elements).

The most numerous category of protein, and exhibiting the most diverse functionality of any type of molecule in the body.

• Essential structural elements are
a-helices, b-sheets. These elements of secondary structure are connected by b-turns, or with connecting "loop" regions of various length and structure.
• Some proteins are composed primarily of
a-helices, others primarily of b-sheets, and many others contain combinations of these structural elements. Here is an example of a protein whose tertiary structure contains both a-helices and b-sheets, and various turns that connect them (this is an enzyme known as 2,5-diketo-D-gluconate reductase). The a-helices are represented in red, the b-sheets in cyan.

Click here for a vrml file of this structure

Why do globular proteins contain these types of secondary structures?

• They optimize intra-chain hydrogen bonding interactions
. Thus, they represent a lower-enthalpy state compared to the unfolded state (i.e. it takes the input of heat energy to disrupt a hydrogen bonded pair. Therefore, energy is released when a hydrogen bonding pair is formed. This release of energy means that the hydrogen-bonded structure is lower in enthalpy. Spontaneous processes go downhill in energetic terms)
• Both
a-helices and b-sheets have a structural organization that allows the organization of chemically different side chain groups
• Alternating amino acid side chains in a
b-sheet point in the same direction. For example, if a polypeptide contained alternating hydrophilic and hydrophobic side chains, and if this polypeptide adopted a b-sheet secondary structure, then all the hydrophilic side chains would be located on one side of the sheet, and all the hydrophobic side chains would be on the other. This partitioning could drive the spontaneous assembly of more complicated structures due to the hydrophobic effect.

Click here for such an example in a b-sheet

• The
a-helix has a pitch of 3.6 residues per turn. Therefore, the same hydrophilic and hydrophobic patterning of the polypeptide chain (i.e. a hydrophobic residue every 3-4 amino acids along the polypeptide) would partition hydrophilic residues on one side of the helix and hydrophobic on the other.

Click here for such an example in an a-helix

• These types of secondary structures are known as amphipathic (one side hydrophobic, the other hydrophilic)

Another optimization of interactions in globular proteins involves van der Waals interactions

• Hydrophobic core residues tend to pack together like jigsaw pieces - optimizing the dispersion forces that these types of residues participate in.
• Dispersion forces are weak, and require close distances between groups (strength proportional to 1/r⁶)
• Dispersion forces provide meaningful attractive forces only when many such interactions are combined. Thus, the core region must be well-packed with few cavities
• Here is an example of core packing in a protein called fibroblast growth factor (a primarily
b-sheet protein):

Molecular Dynamics

Images of protein structures often give the impression that proteins are "static" molecules with a rigid conformation. This impression can be reinforced when one is told that proteins fold up into a unique three-dimensional structure. But proteins are not rigid structures like a typical solid, they exhibit a range of molecular motions, or molecular dynamics. (Remember, only at 0K do you have a single conformation in a molecular structure).

• Atoms in a protein have kinetic energy related to the temperature. This kinetic energy is manifest as vibrational motions in atoms with distances <0.5Å

In addition to thermal motion, proteins may exhibit motions related to their function

• Catalysis in enzymes may require regions or specific side chains in the structure to move
• Binding and release of ligands also may require molecular motions
• Such motions can be large (1 nm) and can involve entire regions (i.e. "rigid body" motion of subsections within the protein structure)

Here is an example of molecular motion observed upon cofactor binding to an enzyme known as 2,5-diketo-d-gluconate reductase:

We can list some thermodynamic changes when globular proteins fold up:

• Entropic cost of folding the protein. The unfolded protein has many conformational states available, the native or folded form has essentially 1 (molecular motions notwithstanding).

Unfolded à Folded DS_protein < 0 (opposes folding)

• Change in enthalpy of the protein upon folding. If the protein folds up so as to optimize intrachain hydrogen bonds (by forming
a-helix and b-sheet secondary structure) then the folded state will result in a release of heat energy. Also, if core residues pack well, then the van der Waals forces will be optimized also:

Unfolded à Folded DH_protein < 0 (favors folding)

Which contribution wins out?

It turns out that if these were the only considerations, proteins would probably not fold (unfavorable entropy change would be larger than favorable enthalpy gain). However, there is another factor we have not considered, and that is the effects upon water when a protein folds:

• Reduction in entropy of solvent upon protein folding. The unfolded form of a globular protein exposes a number of hydrophobic side chains to solvent. This causes water to form an ordered clathrate around these nonpolar groups, and this is entropically costly. If a protein folds up so that the hydrophobic groups are removed from solvent (by locating in the core region) this releases the ordered clathrate waters, thus increasing the entropy of the solvent:

Unfolded à Folded DS_solvent > 0 (favors folding)

Molecular Chaperons

Although thermodynamics may indicate that protein folding is spontaneous, it says nothing about the rate of folding.

• Without help, some proteins fold very slowly, and may be considered "kinetically trapped" in some intermediate folded conformation.
• The environment within the cell is "crowded" and intermolecular interactions can prevent proper folding of some proteins

Molecular chaperones are proteins that help other proteins fold up. They may do so in several ways

• Prevent aggregation of misfolded forms. Misfolded proteins may have hydrophobic groups exposed on the surface. These can cause aggregation with other hydrophobic molecules (other misfolded proteins). Aggregated proteins are kinetically trapped and won't fold any further. Some chaperons interact with the hydrophobic regions of misfolded proteins, prevent aggregations and promote correct folding.
• Speed up the kinetics of proline isomerization. Proline residue isomerize slowly about their peptide bond, however, the folded conformation of a protein requires a specific proline isomer. Some proteins speed up this process in other proteins
• Promote disulfide bond exchange. Disulfide bonds are covalent bonds between cysteine residues in different regions of a polypeptide. What if they form a bond with the "wrong" cysteine partner? A mechanism is needed to allow disulfide bonds to break and reform correctly. An enzyme in the body provides this functionality.

This is an area of tremendous research effort and brings together experimentalists and theoreticians from a variety of disciplines including chemistry, physics, biology and computer science. It is one of the driving forces behind the development of bigger and faster supercomputers. Currently, we can simulate only a few picoseconds of protein folding and only for simple proteins.

The sequencing of the human genome allows us to infer the amino acid sequence of every polypeptide in the body. If we could accurately predict how proteins fold, we could determine the structures of every protein in the body.

Since intermolecular interactions between proteins is a variation of the protein folding problem, we could also predict how all proteins interact. This is important, since the basis of many diseased states lies in mutations within protein molecules and their effects upon protein structure, dynamics and molecular interactions.

Many proteins exist as oligomers - meaning that two or more identical molecules associate into a more complex assembly (defined as their quaternary structure).

• One molecule - monomer
• Two molecules - dimer
• Three molecules -trimer
• Four molecules - tetramer

The arrangement of such molecules in a complex almost always results in some type of identifiable axis (or axes) of rotational symmetry, including:

• Cyclic. Either a two-, three-, four-, five-fold, etc., axis of symmetry

To see a vrml file of a cyclic 2-fold symmetry click here

• Dihedral. Multimeric structure with a cyclic axis of symmetry and at least one other orthogonal 2-fold axis of symmetry

To see a vrml file of an example of dihedral symmetry click here

• Higher symmetries. These would be related to the symmetries of platonic solids (tetrahedron, cubic, octahedral, icosahedral). Some multimeric assemblies of viral coat proteins produce such symmetries. This points to one of the advantages of such structures: genetic efficiency and economy. A complex structure is produced by a few (or a single) structural element (i.e. protein) that can self-assemble into a complex structure.

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