# 4.3: Tertiary and Quaternary Structures

note: this chapter takes a little while to load because of the numerous iCn3D molecular models. Be patient and wait!

### Tertiary Structure

The tertiary structure of a single chain protein is the overall 3D structure of the protein. A protein of a given primary structure folds to form a 3D structure with imbedded secondary structures, super secondary structures and domains. Folded proteins can have a variety of shapes from a roughly spherical or "globular" to a more extended "fibrillar" form. Let's consider the more globular one first. How a protein folds will be discussed in greater detail later, but a more descriptive and simpler view will help us understand structural features of the folded protein in its tertiary structure.

Start with an unfolded protein. It has a polar backbone with dangling polar charged, polar uncharged, and nonpolar sides attached to the alpha carbon of each amino acid in the primary sequence. On folding, where do these side chains of varying polarity end up? To a first approximation, you may think that a globular protein might fold such that all the hydrophobic amino acid side chains are buried in the interior of the protein, surrounded by other hydrophobic side chains. In a similar fashion, you might expect the polar and charged side chains could be on the surface, exposed to water.

Such a model would be analogous to a micelle, which has an almost "perfect" separation of polar (on the surface) and nonpolar atoms (buried). Look at the dynamic model of a micelle below, which consists of 54 self-associated molecules of dodecylphosphocholine fatty acids surrounded by water.

If protein folding was only that simple!. Topologically, it is impossible for a protein to fold in an intramolecular fashion in strict analogy to the the intermolecular aggregation of single chain amphiphiles into a micelle. Consider also that the entire backbone is polar! To a first approximation we would expect the bulk of nonpolar groups would be buried surrounded by other nonpolar groups. Likewise we would expect the bulk of polar and charged groups would be on the surface. The dynamic molecular models below show the structure of human low molecular weight protein tyrosyl phosphatase (1xww). It shows one buried nonpolar side chain (Phe 10) surrounded by essentially all nonpolar side chains of other amino acids.

https://structure.ncbi.nlm.nih.gov/i...8zHryts5uz7j28

The ompletely nonpolar Phe 10 side chain is shown in cyan.  The atoms with 5 Angstroms are color-coded using the Wimley–White whole residue hydrophobicity scales, which includes not only sidechain but peptide bond contributions and are determined experimentally by determining free energy of transfer to nonpolar environments.    Like a micelle, the protein is roughly spherical.

Noncovalent interactions between atoms within a protein chains help drive protein folding.  The noncovalent interactions (also termed intermolecular forces in traditional introductory chemistry classes, include ion-ion, ion-dipole, hydrogen bonds, dipole-dipole, induced dipole - induced dipole (often called London Dispersion Forces) and variants including ion - induced dipole, etc.  We generally use the same terms when describing these interactions within and between proteins.  Ion-Ion are usually called salt bridges, and induced dipole-induced dipole are often called hydrophobic interactions.

Let's look at some specific interactions with a given protein chain (the light chain of the mouse immunoglobulin G, PDB 1D = 4hdi).  Manipulate the iCn3D model below and answer the following questions.

Exercise $$\PageIndex{1}$$

Name the types of interactions between the following side chains in the iCn3D image above.  A large images can see by using this link: https://structure.ncbi.nlm.nih.gov/icn3d/share.html?DrdnVubujRaihTcr9

a.  Leu 52 and Ile 53, Val 63, Phe 67 and Leu 78

b.  Arg 24 and Asp 75

c.  Asp 170 and Lys 108

d.  Tyr 178 and Lys 147

e.  Glu 190 and Arg 160

f.  Tyr 191 and Phe 214

Add texts here. Do not delete this text first. a

a.  hydrophobic interactions, induced dipole-induced dipole

b.  salt bridge, ion-ion

c. salt bridge, ion-ion

d. pi-cation

e. salt bridge, ion-ion

f.  Aromatic-aromatic, induced dipole-induced dipole

You can analyze the noncovalent interactions within and between a protein using PIC- protein intteractions calculator

Identify the like hydrogen donors and acceptors in the pairs shown in the model below.

Exercise $$\PageIndex{1}$$

Are these hydrogen bonds

• side chain to side chain?
• main chain to main chain?
• side chain to main chain?

Obtain a large images at https://structure.ncbi.nlm.nih.gov/i...ewUC9hJs2Gyj77

a.  Ile 111: Gln 171

b.  Gln 6: Thr 107

c.   Ile 53: Trp 40

d.  Try 37:Thr 97

a.  Ile 111: Gln 171 - side chain to side chain

b.  Gln 6: Thr 107 - side chain to side chain

c   Ile 53: Trp 40  - main chain to main chain

d.  Try 37:Thr 97 - main chain to main chain

### A more realistic understanding of noncovalent interactions

But are all the nonpolar side chains buried? How about the polar uncharged and polar charged side chains? What are the preferred dispositions of side chains in proteins as evidenced from the crystal structure of thousands of proteins? Here are some conclusions from a paper by Pace (Biochemistry. 40, pg 310 (2001)

• On average, about 50% of the amino acids are in secondary structure. On average, there is about 27% alpha helix, and 23% beta structure. Of course, some proteins are almost all alpha-helical, and some are almost all beta structure, but most are a mixture.
• The side chain location varies with polarity. Nonpolar side chains, such as Val, Leu, Ile, Met, and Phe are predominately (83%) in the interior of the protein.
• Charged polar side chains are almost equally partitioned between being buried or exposed on the surface. (54% - Asp, Glu, His, Arg, Lys are buried away from water, a bit startling!)
• Uncharged polar groups such as Asn, Gln, Ser, Thr, Tyr are mostly (63%) buried, and not on the surface (a bit startling!) .
• Globular proteins are quite compact, with water excluded. The packing density (Volvdw/Voltot) is about 0.75, which is like the NaCl crystal and equals the closest packing density of 0.74. This compares to organic liquids, whose density is about 0.6-0.7.

#### Tertiary structure and pKa Values

If a charged side chain is buried in a protein, you would expect that it would be surrounded, in general, by either oppositely charged side chains, to which it could form an internal salt bridge (ion-ion interaction), or a polar uncharged group with which it could interact through dipole-dipole or, more specifically, H bond interactions. You would also expect that if it were not near an oppositely charged side chain, that it would exist, if buried, in an uncharged state.

Hence the pKa of side chains would be dramatically affected by the nature of its microenvironment (as we have already seen with the pKa of acetic acid in solvents of different polarity). NMR spectroscopy has been used to determine the pKa values of specific side chains in proteins whose crystal structure is known. Pace et al (2009) summarize data on the properties of ionizable side chains in a series of proteins whose structure has been determined. The intrinsic pKa, pKaint or prototypical pKa value for a side chain exposed to water can be determined using a pentapeptide containing the target amino acid X surrounded by 2 Ala ion either each side with both the N and C termini of the peptide blocked so they are uncharged. The table below shows the pKa values of ionizable side chains in a series of protein compared to that in the control pentapeptide.

Group Content % Buried % pKa int in AAXAA pKa avg low pKa high pKa # measurements
Asp 5.2 56 3.9 3.5 + 1.2 0.5 9.2 139
Glu 6.5 48 4.3 4.2 + 0.9 2.1 8.8 153
His 2.2 72 6.5 6.6 + 1.0 2.4 9.2 131
Cys 1.2 90 8.6 6.8 + 2.7 2.5 11.1 25
Tyr 3.2 67 9.8 10.3 + 1.2 6.1 12.1 20
Lys 5.9 34 10.4 10.5 + 1.1 5.7 12.1 35
Arg 5.1 56 12.3
C term     3.7 3.3 + 0.8 2.4 5.9 22
N term     8.0 7.7 + 0.5 6.8 9.1 16

A quick glance a the table shows a huge variation in the pKas of ionizable side chains in proteins with the pKa of Asp varying over a range of 8.7 pH units, showing that it can act at physiological pH as either a strong acid or a moderate base. Three majors effects can perturb the pKa of ionizable side chains:

1. Dehydration of the side chain as it is buried in a protein (Born Effect): The stability of a charged group depends on the polarity of the medium in which it exists. Ions are more stable in water than in nonpolar solvents as the water molecules can reorient and interact with the ion through ion-dipole or ion-H bond interactions, which effectively shields the ion from other counter ions. The shielding effect of water is related to the dielectric constant, ε, of the solvent. Coulombs law can be written as:

$\mathrm{F}=\frac{\mathrm{k} \mathrm{Q}_{1} \mathrm{Q}_{2}}{\mathrm{r}^{2}}=\frac{\mathrm{Q}_{1} \mathrm{Q}_{2}}{4 \pi \varepsilon \mathrm{r}^{2}}$

Epsilon is the dielectric constant of the solvent. Water has a higher dielectric constant (80) than nonpolar solvents (4-10) and shields opposing charges more, stabilizing them. Hence the pKa of side chains of those amino acids whose deprotonated state are charged will have their pKa values raised (so they are less acidic) in nonpolar environments. The reverse holds for side chains whose protonated form is charged. Pace cites as an example two mutant of staphylococcal nuclease in which a buried Val 66 is changed either to Asp or Lys. The buried Asp has a pKa of 8.9 compared to 5.5 for the buried Lys. These changes were not compensated for with new charge-charge interactions, so the change can be attributed to the dehydration (or Born) effect.

2. Ion-Ion interactions with another charged side chain through Coulombic forces: This effect can be most readily observed at the surface of the protein. Pace cites a study of RNase S that is devoid of Lys and has a pI of 3.5. Five Asp and Glu were replaced on the surface using site-specific mutagenesis with Lys, which changed the pI of the protein to 10.2. At pH 7, the protein without Lys had a charge of -7 while the protein with 5 Lys had a charge of +3. The crystal structures were similar so Coulombic interactions would determine the differences in the pKa of the 11 common side chains. On average the mutant pKas were higher by 0.75 pH units, which makes sense as the mutant had a high pI. Calculated pKa values were similar to those determined by NMR. These data are consistent with the idea that Coulombic interactions are the chief cause of pKa changes in surface side chains.

3. Charge-dipole interactions and H bonds: It should be obvious that charge states of ionizable side chains would be adjusted to optimize H bond (and more generally charge-dipole) interactions in proteins. If the interactions are optimal in the charged state, pKa values for His and Lys would be increased and for Asp, Glu, Cys, and Tyr they would be decreased. Pace cites the buried Asp 76 in RNase T1 in which the Asp is charged but does not form an internal salt bridge. It has a depressed pKa of 0.6 and has 3 H bonds to the side chains of Asn 9, Tyr 11 and Thr 91. Mutants were made to remove the H bonds to see the effect on the pKa of Asp 76. Removing 1, 2, or 3 H bonds changed the pKa to 3.3, 5.1, and 6.4 respectively. The 6.4 value is much higher than the pKint, which can be attributed to the Born effect.

## Quarternary Structure

Primary structure is the linear sequence of the protein. Secondary structure is the repetitive structure formed from H-bonds among backbone amide H and carbonyl O atoms. Tertiary structure is the overall 3D structure of the protein. Quaternary structure is the overall structure that arises when tertiary structures aggregate with self to form homodimers, homotrimers, or homopolymers OR aggregate with different proteins to form heteropolymers. Most protein subunits in a larger protein displaying quaternary structure are held together by noncovalent interactions (intermolecular forces), although in some, they are aloso held together by disulfide bonds (example: immunoglobulins).

Here is a dynamic model of a homodimer, the variable domain of the T cell receptor delta chain (1tvd). Carefully rotate the model to see the two identical chains held together by noncovalent interactions

Here is a dynamic model of a heterodimer, reverse transcriptase, (1rev). The two different subunits are show in different colors.

### Macromolecule Oligomer Formation and Symmetry

Many proteins are found in aggregated states and have quaternary structure.  Hemoglobin consists of two alpha and two beta monomers (or protomers) which assemble to produce the biologically relevant heterotetrameric protein.  A given monomer can self aggregate to form homooligomers such as dimers (M2), trimers (M3), tetramers(M4), or or higher oligomers (Mn).   The polymers display symmetry with respect to the geometric arrangement  of the subunits.  Symmetry is an important component of the many kinetic models for catalysis.

Most oligomeric proteins contain protomers that are symmetrically arranged.  What mechanism determines whether a monomeric protein forms a homooligomer?  Why do they stop at a certain n value?  Can proteins be engineered to do so?   If mutation can induce oligomer formation, then fewer mutations would be required to produce a symmetric oligomer from subunits since fewer mutations would be required as a single mutation in a single monomer would be represented n times in a single oligomer of n monomers.  This fact probably underlies the reason that oligomers display exquisite symmetry.  Hence a basic knowledge of symmetry of protein oligomers is necessary.

In the study of small molecules, chemists describe symmetry through the use of mathematical symmetry operations and elements, which find great use in analysis of structure and in molecular spectroscopy.  These concepts are usually first encountered in physical and inorganic chemistry classes so a brief introduction is warranted.  A symmetry operation is a movement of an object like a  molecule that leads to an identical, superimposable molecule.  Each operation has a symmetry element (point, line, or plane) about which the motion occurs.   Some examples are shown below:

Table:  Symmetry Elements and Operations

 Element (with Jmol link) Operation inversion center (i) projection through center  (point) of symmetry of point x,y,z to point -x,-y,-z proper rotation axis (Cn) rotation around a Cn axis by 360o/n where C denotes Cyclic horizontal (σh) and vertical (σv) symmetry plane reflection across a horizontal (h) or vertical (v)plane improper rotation axis (Sn) rotation around a Sn axis by 360o/n followed by reflection in plane perpendicular to the axis.

Luckily for students trying to apply these rules to protein oligomers, biomolecules made up of chiral monomers (such as the L-amino acids of proteins) can not be converted to identical structures using inversion or reflection since the chirality of monomer would change - for proteins this would entail and L to D amino acid change.  That excludes all but proper rotation axes (Cn) from the list above.

A point group is a collection of symmetry operations that define the symmetry about a point.  The 4 types of symmetries around a point are those described above:  rotational symmetry, inversion symmetry, mirror symmetry, and improper rotation.  The types of point groups around a point include:

• cyclic (Cn) - contain one single Cn rotation axis.  A biological example is the tobacco mosaic virus double disk (34 monomers, C17).  In this point group note that the n in Cn is equal to the number of monomers and the angle of rotation is 360o/n.

• dihedral (Dn) - These have mutually perpendicular rotation axes.  Specifically they contain at least 1 C2 axis perpendicular to a Cn axis (Canter and Schimmel.  Biophysical Chemistry - Part 1).  The minimal number of subunits is n.  Most protein oligomers fall into this category. The packing (or asymmetric) unit does not have to be a single monomer but could be a heterodimer.

1. A D2 point group has 1 C2 axis and 2 perpendicular C2 axes, and 4 monomers (like Hb). These proteins can dissociate into two dimers (such as two α/β dimers for Hb).  Note that a different arrangment of 4 monomers could produce a oligomer with C4 symmetry instead of D2.

2. A D4 point group has 1 C4 axis and 4 C2 axes, along with 2n=8 subunits.   An example of a D4 point group is ribulose bisphosphate carboxylase/oxygenase (RuBisCO) which has 8 subunits (where a subunit, or more technically the assymetric subunit, is a dimer of a small and large molecular weight protein).    This point group could arise from quaternary structure of two C4 tetramers or four C2 dimers.

Figure:  D2 Symmetry

• cubic  - contain four C3 axes connecting opposite corners of a cube (so the lines are effectively diagonals) arranged as the four body diagonals (lines connecting opposite corners) of a cube. The tetrahedron (4 sides), cube (6), octahedron (8), and icosohedron (20), perfect Platonic solids (in which all faces, edges and angles are congruent) all have related 3 C3 axes (diagonals connecting opposite corners for cubes, diagonals from a vertex to the opposite face for tetrahedrons, line connecting two opposite faces for octahedron, etc ) so they all can be considered to be part of the cubic  point group.

Cubes have a total of 13 symmetry axes comprising 3 types (three C4 axes passing through the centers of opposite faces,  four C3 axes passing through opposite vertices, and six C2 axes passing through the the centers of opposite edges).  On octahedron can be aligned with a cube and be shown to have the same symmetry axes.

Tetrahedrons have a total of 7 symmetry axes comprising two types (four C3 axes of the cube and  three C2 axes which are the same as the C4 axes of the cube.  First note the relationship between a cube and an inscribed tetrahedron.

A dodecahedron with 12 regular pentagon faces (green) and an icosohedron with 20 equilateral triangle sides (red) can be aligned with each other (as can cubes and octahedrons) and have 31 symmetry axes, as shown below.  Note also the relations between a cube inside a dodecahedron and a octahedron inside of a dodecahedron that makes sharing of symmetry axes between these pairs more obvious.

vrml files for movies from  http://www.georgehart.com/virtual-polyhedra/symmetry_axes.html

Examples of protein complexes with these point groups are:

• aspartate-ß-decarboxylase, tetrahedral, 12 asymmetric units

• dihydrolipoyl transsuccinylase, octahedral,  24 asymmetric subunits

• many spherical viruses, icosahedral, 60 asymmetric units

Jmol: Updated  Symmetry in Protein Oligomers (beta version with lots of work left to do)  Jmol14 (Java) |  JSMol  (HTML5)

Proteins, especially those involved in cytoskeletal filaments, can form fibers which contain helical symmetry which differs from those described above since the monomers at the ends of helical fibers, although they have the same tertiary structures as those in the middle of the helical fibers, do not contact the same number of monomers as monomers internal in the oligomer and hence have different microenvironments.

A recent article by Grueninger et al. addresses the question of whether the process of oligomerization can be programmed into the genome.   Can simple amino acid substitutions lead to oligomerization?  Oligomerization can be beneficial (formation of cytoskeleton filaments) or detrimental (formation of fibers in sickle cell anemia and mad cow disease).   Oligomers with long half-lives (for example cytoskeletal filament such as actin and tubulin) and short half-lives (for example proteins causes transient activities are regulated by oligomer formation) are both necessary.

It has long been noted that if a protein chain forms oligomers, then a single amino acid change in the chain would be found n times in an oligomer of n chains.  Mutations could either promote chain contact and oligomer formation or dissociation into monomeric or other asymmetric subunit composition if the mutation were in a region involved in subunit association (a contact region).   Experimental work in this field of study is hampered by the fact that mutants made by site-specific mutagenesis to prefer the monomeric state often fail to fold (due to hydrophobic exposure and aggregation.   Studies have shown that most contact areas between monomers or other asymmetric units are hydrophobic in nature and the contact regions must be complementary in shape.  Obviously mutations that replace hydrophobic side chains involved in subunit contact with polar, polar charged, or bulkier hydrophobic side chains would inhibit oligomer formation.

Grueninger et al were able to successfully engineer dimer formation and oligomer formation as well.   First consider the simplest case of a mutation in a monomer that can produce a dimer with C2 symmetry.  This is illustrated below, which also shows how a mutation that produces a weak interaction in a monomer could also produce a long helical aggregate (which can't be crystallized) without symmetry (as described above).  A mutation at 2 could  promote either oligomer  helix formation or dimerization.

(adapted from Grueninger et al. Science, 319, 206-209 (2008)

It should be noted that mutation could lead to dimer or oligomer formation by producing a more global conformational change in the monomer (not indicated in the example above) which leads to aggregate formation, as we have seen previously in the formation of dimers and aggregates of proteins associated with neurodegenerative diseases (like mad cow disease).

Grueninger produces mutants of two different proteins that showed dimer formation as analyzed by gel filtration chromatography (but did not crystallize so no 3D structures were determined).  In addition the group modified urocanase, a C2 dimer, at 3 side chains to form a tetramer with D2 symmetry.  Also, they modified L-rhamnulose-1-phosphae, a C4 tetramer, at a single position to form an octamer with D4 symmetry.  The latter two were analyzed through x-ray crystallography.   Their work suggests ways that complex symmetric protein structures arose in nature from simple mutation and evolutionary selection.

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