Goldfarb D. Biophysics DeMYSTiFied

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262 Biophysics D e mystifieD

Quiz

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

book.

1. What do A-, B-, C-, and Z-DNA describe?

The four nucleotide bases found in dNA.

Four DNA secondary structures: hairpins, loops, cruciforms, and tails.

C. Double-helical structures that differ in pitch and width of the helix.

D. The four types of single-stranded DNA.

2. Which statements are true?

S1. The DNA double helix must unwind for transcription and replication.

S2. Whether the DNA will unwind depends on the Gibbs energy change.

S3. Unwinding circular DNA will change the writhe of the helix.

S1 and S2

B. S2 and S3

S1 and S3

D. S1, S2, and S3

3. What is a nucleic acid palindrome?

A nucleotide sequence that can form a stem-and-loop or cruciform structure.

A nucleotide sequence that reads the same forward or backward.

c. A protein that binds to certain dNA sequences.

D. A curved, dome-shaped secondary structure in nucleic acids.

4. What is homogenous DNA?

dNA that has been blended together.

dNA from only one species.

c. dNA with a sequence made from only a single nucleotide.

d. dNA with a simple sequence that repeats throughout the molecule.

5. The root mean square end-to-end distance of a freely jointed chain is propor-

tional to what?

A. The length of a segment and the square root of the number of segments.

B. The square root of the length of a chain segment.

c. The number of segments and the square root of the length of each segment.

d. The difference between the length of one end of the chain and the other.

6. What is the primary driving force that causes DNA to take a helical shape?

A. hydrogen bonds between base pairs

B. Aromatic base stacking

c. steric interactions

Ionic charges on the phosphate backbone

chapter 10 Nucleic Acid Biophysics 263

7. What is the nearest-neighbor approximation?

A. Approximating the DNA sequence of one organism with the organisms that live

nearby.

B. Assuming that the dNA sequence of one gene can only affect the genes that are imme-

diately next to it.

Ignoring interactions between nucleotides that are not immediately next to one another

in the dNA sequence.

D. Approximating the DNA sequence by looking at which nucleotides are next to one

another.

8. Which of the following statements is false?

S1. Superhelical DNA requires a force to hold the superhelix in place.

S2. Circular DNA is always superhelical.

S3. A superhelix is a quaternary structure.

S4. Energy stored in the superhelix can be used to unwind the DNA.

S1 and S2

S1 and S3

c. s1 and s4

D. S2 and S3

S2 and S4

9. What is a topological invariant?

A. A property that does not change under smooth deformations of shape

B. The writhe

C. The linking number

d. A and B

e. B and c

F. C and A

10. A 5000-base-pair circular DNA has a linking number of 500, and its most stable

amount of twist is 10 base pairs per turn. What is the writhe?

A. 10

B. –10

c. 0

d. –0.1

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Quar

De Broglie’s photon

sin

Electr yclosity

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ty closit

Relativist

Ong

265

In Chaps. 7 and 8 we learned some basics of lipids and cell membranes. In this

chapter we explore membrane biophysics. Biological membranes do more than

just providing a barrier between the cell and the outside world, and they are

made up of more than just lipids.

CHAPTer OBJeCTiVeS

In this chapter, you will

review the basic structure of biological membranes.

•

Learn the principles that govern self-assembly in lipid bilayers.

•

Learn about the fluid mosaic model.

•

study phase transitions in lipids and the forces that affect them.

•

Gain an understanding of the energetics of membrane permeability.

•

Learn about active and passive transport across membranes.

•

chapter

Membrane Biophysics

266 Biophysics DemystifieD

Membrane Functions

Membranes play important biological functions. They provide a barrier between

the cell and the outside world, and regulate what can enter the cell and what

leaves it. Many organelles within the cell are themselves membrane bound,

providing an isolated biophysical environment even within the cell. In eukary-

otes a membrane surrounds the nucleus, keeping the activities of DNA (tran-

scription and replication) separate from the rest of the cell. Membranes also

provide surfaces on which biochemical reactions take place. One such example

is the endoplasmic reticulum, a network of membranes and tubules on which

synthesis of proteins and lipids occurs. Membranes also provide anchorage

points for the cytoskeleton which gives shape and rigidity to cells and plays a

role in intracellular transport of biomolecules.

Membrane Structure

The main structural components of biological membranes are amphipathic lip-

ids (see Chap. 7). Although biological membranes also contain carbohydrates

and proteins (some membranes contain as much as 50% protein), the primary

character of biological membranes is derived from its amphipathic lipids. The

most common lipids found in biological membranes are two-chain phospholip-

ids. These are molecules with a phosphate head group, attached to a two-chain

fatty acid. The amphipathic character comes from the combination of the

hydrophobic, hydrocarbon tails, along with the hydrophilic phosphate head

group. In biological membranes, the phospholipids arrange themselves into a

bilayer, in which the hydrocarbon tails face each other and are isolated from the

surrounding environment by the phosphate head groups. See Fig. 11-1.

Figure 11-1 • The basic structure of a biological membrane is a phospholipid bilayer with

hydrophobic tails in the center of the bilayer and hydrophilic heads at the surfaces. Biological

membranes also typically contain proteins, nonpolymeric lipids such as cholesterol, and

carbohydrates typically in the form of glycolipids (a carbohydrate attached to a lipid).

chapter 11 MeMBrane Biophysics 267

Phospholipid Behavior and Self-Assembly

Phospholipids exhibit a physical behavior that makes them ideal for the forma-

tion of membranes. Biophysicists call this behavior self-assembly. Self-assembly

means that the molecules will aggregate together to form various structures

without need for energy input, catalysts, or other helper molecules. Let’s first

look at self-assembly for single-chain phospholipids and then for double-chain

phospholipids.

Single-Chain Phospholipids and Micelle Formation

If we slowly add a single-chain phospholipid to an aqueous solution, at first the

lipid molecules are dispersed among the water molecules. Later, as the concentra-

tion of lipids is increased, a point is reached where the lipid molecules merge

together forming aggregates called micelles. A micelle is simply a lipid ball with the

hydrocarbon chains pointed in toward the center, as illustrated in Fig. 11-2. The

concentration, at which the lipids self-assemble into micelles, is called the critical

micelle concentration (CMC). The aggregation process is highly cooperative. Once

the critical micelle concentration is reached, any further lipid added to the solution

either associates with existing micelles or forms new micelles. This causes the con-

centration of micelles to increase, while the concentration of free lipid molecules

remains relatively constant, as shown in Fig. 11-3.

There are a number of forces that contribute to self-assembly in micelle

formation. As the hydrocarbon tails approach one another, dispersion forces

(see Chap. 6) provide a strong attractive force pulling them together. Close

association of the tails is also favored by the hydrophobic effect. As the tails are

Figure 11-2 • Single-chain phospholipids self-assemble into micelle

structures.

268 Biophysics DemystifieD

drawn together, water molecules along the length of the hydrophobic tails are

disrupted (disorganized) and excluded (pushed away). Recall from Chap. 6 that

water along the edge of a hydrophobic molecule has its motion restricted; this

in turn limits its ability to hydrogen-bond with other water molecules. As the

hydrocarbon tails come together, the water along their surface is pushed aside.

This increases the entropy of the water by allowing it to rotate freely. The free

rotation of the water molecules also increases the possibilities for hydrogen

bond formation with other water molecules in solution. The increased entropy

and the formation of water-water hydrogen bonds both contribute favorably to

the Gibbs energy of micelle formation.

In addition to these forces there is a mixed effect from the negatively charged

phosphate head groups. On the one hand, the charge on the head groups creates

a repulsive force between them. This is, in part, what gives the micelle its spheri-

cal shape. As the hydrocarbon tails come together by virtue of the dispersion

forces and the hydrophobic effect, we need to somehow reduce the repulsive

force of the head groups. To do this, nature puts the head groups on the outside

of the micelle and shapes the micelle like a sphere. This configuration maximizes

the distance between the head groups; this reduces their repulsive interaction. It

CMC

Concentration of

micelles

Concentration of

free phospholipid

(not micelles)

Concentration

Amount of single-chain phospholipid added to solution

Figure 11-3 • As single-chain phospholipid is added to an aqueous

solution, the concentration of free phospholipid increases, until the critical

micelle concentration is reached.

above the cMc, micelle formation is highly

cooperative, and additional lipid added to the solution increases the micelle

concentration.

chapter 11 MeMBrane Biophysics 269

also allows space between the head groups for water molecules and counterions,

both of which act to reduce the repulsive force. The water molecules do so by

aligning their dipole moment opposite the electric field (as was explained in

Chap. 6). If cations such as calcium, magnesium, or sodium are present, they

associate as counterions with the negative charge on the phosphate. This effec-

tively neutralizes the negative charge. Neutralizing the negative charges elimi-

nates the need for energy (enthalpy) to overcome the repulsive force, so the

Gibbs energy of micelle formation becomes even more negative, making it easier

to form micelles. The critical micelle concentration is the concentration of lipid

necessary for all of these forces combined to produce a negative Gibbs energy of

micelle formation. At that point formation of micelles is highly cooperative, pro-

ceeding in an almost all-or-none fashion. The fact that counterions act to elimi-

nate the repulsive force between head groups means that fewer lipid molecules

are required to provide the energy (from dispersion forces and the hydrophobic

effect) needed to achieve micelle formation. Fewer lipid molecules required

means the critical micelle concentration is lower. This explains why, as the con-

centration of positive ions increases, the CMC decreases.

Two-Chain Phospholipids and Liposome Formation

Although micelles can be formed from two-chain phospholipids, this is usually

not the preferred configuration. Compare Fig. 11-4 with Fig. 11-2. In the case

of two-chain phospholipids, the hydrocarbon chains from adjacent lipid mol-

ecules are not able to pack as closely together as they can when all of the lipids

have only a single hydrocarbon chain. The single-chain phospholipids get closer

together both in terms of aligning side by side, as well as in terms of reaching

deep into the center of the micelle. The extra width of the two-chain phospho-

lipids causes steric interactions that increase the distance between hydrocarbon

chains of adjacent molecules. This reduces the strength of dispersion forces. The

extra width also blocks the hydrocarbon chains from reaching as deep into the

micelle. This creates a void in the center of the micelle and increases the size of

micelle, compared to a micelle made from the same number of single-chain

lipid molecules. Both the void and the increased size (per number of lipid mol-

ecules) increase the energy cost of micelle formation. The void does so either

because it will contain water molecules, thus putting them right next to the

ends of the hydrophobic tails, or because somehow the water must be excluded

from the center of the micelle without filling that space with something else

(e.g., hydrocarbon, as with the single-chain lipids). Both of these are energeti-

cally unfavorable. The increased size of the micelle decreases its curvature.

270 Biophysics DemystifieD

Given the same number of lipid molecules, a decreased curvature puts the

repulsive phosphate head groups closer together. This is also unfavorable. So

altogether it’s a lot more expensive to make two-chain lipid micelles than it is

to make single-chain lipid micelles.

Nature solves this problem by bringing a second layer of lipids opposite the

ends of the hydrocarbon chains. It’s as if the sides of the micelle split open,

allowing the ends of the phospholipid chains across from each other to collapse

into the void of the micelle and line up to form a lipid bilayer. This process is

also highly cooperative, and it continues aggregating phospholipids in this way

until a liposome has formed. A liposome is a lipid bilayer sphere with a void in

the middle, as illustrated in Fig. 11-5. In this case, however, the void in the

middle is favorable. It can be filled with water molecules and counterions which

stabilize the liposome (contribute to a favorable Gibbs energy change) by inter-

acting with the phosphate head groups. The interaction between water,

Figure 11-4 • A micelle made of two-chain

phospholipids. in the micelle configuration, the

lipid molecules are not able to pack as closely

together as is the case with single-chain

phospholipids. The lipid chains are also not able to

reach as deep into the center of the micelle. This

reduces the amount of contact between the

hydrocarbon chains; this reduces the favorable

energy from dispersion forces. These factors make

micelle formation more difficult to achieve with

two-chain phospholipids.

instead two-chain

phospholipids prefer a bilayer configuration.

(Courtesy of Wikimedia Commons.)

chapter 11 MeMBrane Biophysics 271

counterions, and the negatively charged phosphates is the same as was described

for micelles earlier. But in the case of a liposome, there are two surfaces of

phosphate head groups on which this favorable interaction can take place.

Lipid Bilayer energetics and Permeability

The lipid bilayer is semipermeable meaning that some molecules can pass

through the bilayer while others can’t. The ease with which any molecule can

pass through the lipid bilayer depends on the Gibbs energy change of getting

the molecule past the charged phosphate head groups and into the hydropho-

bic interior of the bilayer. After that we have the Gibbs energy change for

removing the molecule from the hydrophobic interior and getting past the

charged phosphate head groups on the other side of the bilayer. Both of these

Gibbs energy changes depend largely on the strength of the forces that hold

the bilayer together. They also depend on the interaction of these forces with

the particular molecule attempting to pass through the bilayer. We’ll look at the

factors that affect the strength of these forces in a minute, but first let’s take

some general examples of molecules and how they interact with the bilayer.

Charged and polar molecules experience a significant increase in Gibbs

energy just to penetrate the hydrophobic interior of the bilayer. As a result, they

are typically not able to pass through the bilayer. (If a charged or polar molecule

Lipid bilayerLiposome

Figure 11-5 • Liposome formation. Two-chain phospholipids prefer liposomes to

micelles because the energy cost is less.