Goldfarb D. Biophysics DeMYSTiFied

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212 Biophysics DemystifieD

still struggling

A f, c contour diagram is just a convenient way to visualize which bond angles

are favorable and which are not. the shaded area represents the favorable val-

ues of f and c. the larger the shaded area, the more favorable possibilities exist

for the bond angles f and c. this means the larger the shaded area, the more

flexible is the polypeptide chain. Knowing the structure and shape of each

amino acid, we can calculate a f, c contour diagram for any pair of adjacent

amino acids. some will have a lot of shaded area. others will have less. in this

way we can get some idea as to how the amino acid sequence affects the flexi-

bility of a protein.

180∅

(degrees)

∅

–180

180

FIgure 9-7 • An example of what a f, c contour diagram might

look like, depending on which amino acid side chains are consid-

ered. the shaded region shows the values for which f and c

result in a negative free energy. in other words these values of f

and c result in an energetically stable conformation. the

unshaded regions represent f and c values that are prohibited

due to either steric hindrances or an unfavorable (repulsive)

dipole interaction.

chapter 9 protein Biophysics 213

Alpha Helix

The alpha helix is a secondary structure in which the polypeptide chain forms

a right-handed helical shape. The backbone of the chain is on the inside of the

helix with the various amino acid side chains on the outside. (This is in contrast

to DNA secondary structure in which the backbone is on the outside of the

helix and the nucleotide bases are on the inside.)

One of the characteristic features of the alpha helix is that it maximizes the

number of hydrogen bonds that can form among the amide and carbonyl groups

of the polypeptide backbone. The hydrogen atom from each of the backbone

amides (N-H) forms a hydrogen bond with the peptide carbonyl oxygen (C = O)

that is four residues further along on the chain. The result is 3.6 amino acid

residues, or peptide bonds, per turn of the helix. The pitch of the alpha helix is

54 nm; that is, each turn of the helix is about 54 nm long (or 15 nm per amino

acid residue). The backbone bond angles are f = 257° and c = 247°. Figure 9-8

shows a schematic diagram of an alpha helix. Some of the hydrogen bonds are

shown as dotted lines.

The alpha helix is also a conformation that maximizes the energy benefit

from the peptide bond dipoles (Fig. 9-4). Adjacent peptide bond dipoles are

somewhat side by side, so their dipole interaction (which varies as 1/r

) is

repulsive. But peptide bond dipoles further along the helix are lined up nearly

end to end (see Fig. 9-9). As explained above, end-to-end dipole-dipole interac-

tions are approximately equivalent to charge-charge interactions. This makes

them significantly stronger over longer distances (compared with the adjacent

FIgure 9-8 • Diagram of a polypeptide alpha helix.

214 Biophysics DemystifieD

peptide dipoles) since their interaction energy varies as 1/r. The result is that

overall in the alpha helix dipole-dipole attractions outweigh the dipole-dipole

repulsions. This means that overall the peptide bond dipoles contribute to sta-

bilizing the helix. They also cause the entire helix to behave as one large dipole,

as shown schematically in Fig. 9-9. In this way alpha-helical portions of globular

proteins can interact with each other as dipoles, thus affecting tertiary confor-

mation. The alpha-helical parts also interact as dipoles with other molecules

and proteins while carrying out protein functions (binding, catalysis, etc.). Heli-

cal segments within proteins range anywhere from 3 to 40 or more residues in

length, but about 10 residues is average. Proteins, however, can have many

alpha-helical segments separated by bends or other secondary structures.

FIgure 9-9 • Peptide bond dipoles contribute to the

stability of the alpha helix.

chapter 9 protein Biophysics 215

Beta Sheet

The beta sheet (denoted as b sheet and also called beta pleated sheet) is the

second most common secondary structure found in proteins. A beta sheet

consists of two polypeptide strands with their backbones hydrogen bonded

to one another. The two strands are called beta strands and are actually one

strand of a single polymer that has folded back on itself. A beta strand then

Antiparallel beta sheetParallel beta sheet

NHNH

HN HN

FIgure 9-10 • Beta sheet polypeptide secondary structure.

216 Biophysics DemystifieD

is a stretch of amino acids within a polypeptide. Each beta strand is typically

five to ten residues long. The key here is that the hydrogen bonds between

the amide hydrogen atoms and the carbonyl oxygen atoms are from one

strand to another (as opposed to within the same strand, four residues away,

as was the case with the alpha helix). The two strands next to one another

create a sheetlike effect. In the alpha helix the carbon bond angles are

tighter and twisted. But in the b sheet configuration, these bond angles are

more stretched out, creating a back-and-forth pattern that gives the b sheet

a pleated appearance.

1800

–180

180

FIgure 9-11 • f, c contour diagram showing where the

alpha helix (a) and beta sheet (b) fall on the f,c plot. each

black dot represents a residue in a protein.

each contour

line represents a level of potential energy, with lower ener-

gies represented by the inner lines and higher energies by

the outside lines.

notice that the alpha helix and beta sheet

fall in areas of very low potential energy, indicating that

they are both very stable secondary structures. notice also

that the majority of residues (black dots) fall close to the

helix and beta sheet, indicating that most of the residues of

the protein are in one of these two configurations.

the

small, darkly shaded area on the right side represents favor-

able bond angles for residues in configurations other than

alpha helix and beta sheet. (Courtesy of Wikimedia

Commons.)

chapter 9 protein Biophysics 217

Beta sheets can be parallel or antiparallel. As mentioned, the polypeptide

backbone consists of a repeating chain of three covalent bonds, or three atoms:

(1) the amide nitrogen, (2) the a-carbon, and (3) the carbonyl-carbon. If we

denote the a-carbon as C

, and the carbonyl-carbon as C´, then a parallel beta

sheet means that as we move along the sheet, both strands have the backbone

atoms in the same order. For example: N, C

, C´, N, C

, C´. Antiparallel means

that the atoms on one strand go in the order N, C

, C´; the atoms on the other

strand go in the order N, C´, C

. Figure 9-10 shows hydrogen bonding in parallel

and antiparallel beta sheets.

218 Biophysics De mystifieD

Quiz

Refer to the text in this chapter if necessary. Answers are in the back of the book.

1. The 20 major amino acids are typically classified into what three groups?

nonpolar, uncharged polar, and charged

hydrophobic, hydrophilic, and hydroponic

c. Acidic, basic, and aromatic

D. Side chains, linear, and circular

2. Which two polar bonds contribute to making a peptide bond polar?

the a-carbon-h and the carbonyl c = o

B. the amide n-h and the a-carbon-h

c. the amide n-h and the carbonyl c = o

D. The a-carbon-h and the disulfide s-s

3. Which has the largest influence on stabilizing protein structure?

Zwitterions

hydrophilic dipoles

c. hydrophobic forces

D. Hydrogen bonds

4. Which of the following is not true?

A. Membrane protein structure is inside-out relative to cytoplasmic proteins.

B. in an aqueous environment, nonpolar residues fold into the center of a protein.

c. Aromatic side chains are most likely to hydrogen-bond with water.

A lower potential energy means the conformation is more stable.

5. What are disulfide bonds?

A. hydrogen bonds between sulfur atoms

B. covalent sulfur-sulfur bonds between two methionine residues

c. covalent sulfur-sulfur bonds between two cysteine residues

Ionic sulfur-sulfur bonds between two cysteine residues

6. A f,  contour diagram is based on

A. plotting energy levels for various values of bond angles f and c.

B. energy due to steric hindrances and dipole interactions.

c. both of the above

D. none of the above

7. A beta sheet is pleated because

A. the bond angles in the polypeptide backbone alternate back and forth.

B. each beta strand folds back on the polypeptide chain.

c. the alpha helix is more stable.

D. hydrophobic residues alternate with hydrophilic residues.

chapter 9 protein Biophysics 219

8. In an alpha helix

A. the backbone is on the outside.

B. the side chains have dipoles.

c. the dipoles are every fourth residue.

the hydrogen bonds are every fourth residue.

9. What are antiparallel strands?

A. one strand is oriented at 90° to the other.

B. one strand goes up and the other strand goes down.

c. one strand is an alpha helix, and the other is a beta helix.

One strand is a double helix and the other is a beta sheet.

10. Cooperative protein folding means that

A. several proteins cooperate to fold each other.

B. the protein is either all alpha helix or all beta sheet.

c. the alpha helix and the beta sheet stabilize one another.

the protein folds into its native state all at once.

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221

In Chap. 7 you learned some basics of nucleic acids structure and function. In

this chapter we dig deeper into nucleic acid biophysics. Of the two main types

of nucleic acids in nature, DNA (deoxyribonucleic acid) and RNA (ribonucleic

acid), more attention is paid to DNA because of its central importance to

genetics. Still the role of RNA is critical, and we have a lot to learn about the

biophysics of nucleic acids from both.

CHAPTer OBJeCTIVeS

In this chapter, you will

learn about dNA and RNA structures.

•

come to understand the relationship between nucleic acid structure and

•

function.

study the forces and factors that stabilize nucleic acid structures.

•

learn how energy can affect genetic functioning.

•

chapter

Nucleic Acid Biophysics