Goldfarb D. Biophysics DeMYSTiFied
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52 Biophysics De mystifieD
Quiz
Refer to the text in this chapter if necessary. Answers are in the back of the
book.
1. An ultracentrifuge operates on the principle of
a. electrophoresis.
B.
spinning very fast.
c. sedimentation.
D. gravity.
2. The various forms of EM spectroscopy typically measure some property of the
EM radiation as a function of
A.
wavelength.
B.
intensity.
C. speed of light.
d. density.
3. Oxygen-free hemoglobin absorbs 10 times more light at 690 nm than fully oxy-
genated hemoglobin. If a sample of hemoglobin is found to absorb only 5 times
as much light as fully oxygenated hemoglobin, what percentage of the hemo-
globin molecules have oxygen bound to them? (Assume that each hemoglobin
molecule is either fully bound or fully unbound.)
A.
5%
B.
10%
C. 50%
D. 690%
4. Fluorescence is the opposite of
A. darkness.
B. incandescence.
c. absorption.
D.
X-ray crystallography.
5. A mass spectrograph characterizes molecules according to their molecular
weight by
A. placing them on a scale.
B. weighing them in a vacuum.
C. ionizing them and passing them through a magnetic field in a vacuum.
D.
ionizing them and passing them through an electric field in a gel.
6. In order for X-ray crystallography to work,
A. the X-rays must be focused using a glass crystal.
B. the X-rays must be bound to the molecules being studied.
C.
the molecules must be in a regular, repeating arrangement.
D. the molecules must not cause electromagnetic interference.
chapter 3 Biophysical Techniques and applicaTions 53
7. Which of the following statements is most true?
A. NMR is preferred over X-ray crystallography because the resolution is higher with NMR.
B. X-ray crystallography provides very precise, high-resolution, structural information.
C. Optical tweezers can be used to place a voltage clamp on the optic nerve.
D.
AFM works in theory, but has yet to be proved.
8. Gel electrophoresis
a. operates on the principle of sedimentation.
B. can be used to separate molecules on the basis of size.
c. is both an analytical and a preparative technique.
d. all of the above
9. The sedimentation force in gel electrophoresis comes from
a. the sedimentation coefficient.
B. gravity.
c. an electric field.
d. all of the above
10. Which of the following statements is most true?
a. a calorimeter is a convenient way to count calories.
B. a microcalorimeter can measure very small amounts of heat.
c. a limitation of calorimetry is that it cannot be used to measure the heat of conforma-
tional transitions.
d. a microcalorimeter can fit on the head of a pin.
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55
Energy is fundamental to life. Therefore, every branch of biophysics requires a
thorough understanding of the principles of energy. To that end, in this chapter
we study thermodynamics, which is the branch of physics that deals with
energy.
CHAPTEr OBJECTiVES
In this chapter, you will
Learn the laws of thermodynamics as they apply to biophysical systems.
•
Be able to explain how gibbs energy determines whether a biophysical pro-
•
cess will take place.
Quar
k
w
B
E
De Broglie’s photon
sin
sin
S
D
ec
ec
2
B
B
Electr yclosity
E
lec
ty closit
y
Relativist
Ong
in
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a
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chapter
4
Energy and Life
56 Biophysics DemystifieD
The First Law of Thermodynamics
Thermodynamics is the study of energy and how it operates in the physical
universe. Statistical mechanics (which we review in the next chapter) is closely
related to thermodynamics. Statistical mechanics is the study of how probabili-
ties and statistical averages of particles can be related to the overall thermody-
namic measurements of a system. For example, the average speed (or average
kinetic energy) of water molecules in a glass of water is directly related to
the temperature of the water. In biophysics, the particles whose statistics we are
interested in are biomolecules or, sometimes, residues and subunits within
biomolecules.
The first law of thermodynamics is simple and intuitive. It states that any
change to the amount of energy contained in a system is equal to the amount
of energy put into the system minus the amount of energy taken out of the
system.
DE
sys
5 E
in
2 E
out
(4-1)
This makes sense and is just another way of saying that energy cannot be
created or destroyed. As an analogy, imagine a bucket of marbles. The first law
says that any change to the number of marbles in the bucket is equal to the
number of marbles we put into the bucket minus the number of marbles we
take out.
What is less intuitively obvious is the more conventional way to write
Eq. (4-1). In practice we don’t usually break up the right side of the equation
in terms of whether the energy is coming in or going out. Instead we break it
up in terms of the type of energy entering or leaving our system and let the sign
on each energy term (positive or negative) indicate the direction of energy flow.
By convention we write the first law of thermodynamics like this.
DU 5 q 2 w (4-2)
where U is the symbol for the internal energy of a system (what we previously
called E
sys
), q represents heat put into the system, and w is work done by the
system.
Equation (4-2) presents the first law in terms of heat energy on the one hand,
and all other forms of energy on the other, which we lump together into a single
term called work. This is like saying that any change in the number of marbles
in our bucket is equal to specifically the number of yellow marbles we put into
chapter 4 EnErgy and LifE 57
the bucket minus the number of all other marbles we take out of our bucket.
This is not the most obvious way to break things up. At least, not until you
consider that maybe there’s something special about yellow marbles.
Indeed this is the case: there is something special about heat as a form of
energy. In fact there are three reasons why heat is special. It is primarily the first
of these three reasons that explains why, by convention, we account for heat
separately from other forms of energy. But the other reasons also provide moti-
vation for thinking of heat separately.
Heat Is Special
The first reason we account for heat separately is historical. The laws and equa-
tions of thermodynamics were originally developed through the study of heat
engines. A heat engine is a motor that converts heat energy into motion, for
example, a steam engine or an internal combustion engine. This is why the
conventional way to write the first law of thermodynamics is in terms of heat
put into a system and work (motion) done by the system. Historically, almost
all of our early experiences with thermodynamics involved lighting fires, boiling
water, and trying to get some useful work out if it.
The second reason heat is special is that heat is the only type of energy that
is always readily available to measure and possibly use. This might not seem the
case on a very cold winter’s day, but it’s true. Heat is the kinetic energy and
random motion of molecules. Even on a cold winter’s day molecules are con-
stantly vibrating or moving about. Even in solid ice, the crystallized water mol-
ecules are continually vibrating. Molecular kinetic energy (heat), as we will see,
can contribute to biochemical processes. Molecular motion is always present.
Only at a temperature of absolute zero (2273.15°C)—far colder than the cold-
est of winter days (and certainly far colder than we ever expect to find any
living things that we study in biophysics)—does molecular motion stop.
The third reason heat is special is that heat is, in a sense, the lowest form of
energy. Heat is the least organized form of energy. It is this disorganized quality
of heat that also makes it often the most inefficient form of energy from which
to extract useful work.
What Is a System?
All of the above assumes we know what we mean by system. In thermody-
namics, a system is simply that part of the universe that we are interested in.
The rest of the universe is called the surroundings. Thermodynamic systems
58 Biophysics DemystifieD
are further qualified in terms of their contact with the surroundings. An open
system can exchange both matter and energy with its surroundings. A closed
system can exchange energy, but not matter. An adiabatic system is thermally
isolated from its surroundings; there is no exchange of heat or matter, but it
is possible for the system to do work on its surroundings (or to have work
done on it).
In thermodynamics energy is typically measured in units of calories or joules.
One calorie is the amount of energy it takes to increase the temperature of 1 g
of water from 14.5°C to 15.5°C at 1 atmosphere of pressure. One joule is the
amount of energy it takes to lift an object weighing 1 N a distance of 1 m. That
is, 1 joule (J) 5 1 newton meter (Nm). One calorie is equal to 4.184 J.
PROBLEM 4-1
A 225-lb athlete drinks a glass of orange juice (120 calories) and walks up
to the top of the Empire State Building. What is the change in his internal
energy, assuming the only heat transfer is the 120 calories from the orange
juice, and the only work done by the athlete is lifting his own weight to the
102nd floor? Assume 3 m per floor.
SOLUTION
We are going to use Eq. (4-2) to solve the problem. To begin with, however,
we need to know that food calories are actually kilocalories. So when the
problem says a glass of orange juice has 120 calories, then in terms of the
scientific unit of energy called calorie, this is 120,000 calories (cal), or 120
kilocalories (kcal).
The amount of heat entering our athlete is 120 kcal, or 502 kJ (120 kcal
4.184 kJ/kcal). Work is force times distance. Therefore the amount of work
done is the weight of the athlete (the force) times the distance he is lifted.
Converting to SI units, 225 lb is about 1000 N of force. So the amount of
work to lift the athlete to the 102nd floor is
1000 N (102 floors 3 m/floor) 5 306,000 Nm 5 306 kJ of work.
The change in the athlete’s internal energy is
DU 5 q 2 w 5 502 kJ 2 306 kJ 5 196 kJ
The athlete’s internal energy has increased (by 196 kJ) because the glass of
orange juice contained more energy than is necessary to lift 225 lb to the
PROBLEM
A 225-lb athlete drinks a glass of orange juice (120 calories) and walks up
to the top of the Empire State Building. What is the change in his internal
PROBLEM
A 225-lb athlete drinks a glass of orange juice (120 calories) and walks up
SOLUTION
We are going to use Eq. (4-2) to solve the problem. To begin with, however,
✔
chapter 4 EnErgy and LifE 59
top of the Empire State Building. Our athlete used up less than 2/3 the
calories in the glass of orange juice.
If you have some concept as to what it feels like to walk up almost 2000
steps, and how you might feel after such a workout, then it may seem
odd that walking up 102 flights of stairs burns off fewer calories than are
in 2/3 of a glass of orange juice. The apparent discrepancy (from our
everyday experience) here is that we have made some simplifying
assumptions that perhaps include a little too much simplification.
Simplifying Assumptions
In science, we often make simplifying assumptions. We purposely assume some-
thing to be the case, even though we know it’s not true, in order to keep things
simple. Keeping things simple can allow us to make a calculation or discover
something that we would otherwise not be able to do or discover.
Then, after we understand our system better, after we have calculated what
we need to calculate, we can (if we choose) refine our calculations and refine
our understanding by gradually removing or changing our simplifying assump-
tions. Of course, the most important aspect of this is to know what our assump-
tions are and to make a judgment as to whether the assumptions are reasonable
or at least practically workable. By practically workable we mean that (1) even
if our assumptions are wrong, we understand that they are wrong and we have
some idea where they are off (or where they differ from the more correct solu-
tion) and (2) most importantly the simplifying assumptions allow us to accom-
plish something that we would otherwise not be able to accomplish without
their help.
As an example of accomplishing something practical even with assumptions
that are incorrect, imagine if we were to measure the energy content in food by
drinking a glass of orange juice, doing some work, and seeing how much work
we can get done before we get hungry again. If the athlete in Prob. 4-1 got
hungry when he reached the top of the Empire State Building, we would say
that the orange juice had 306 kJ of energy. To say such a thing, we have to make
some simplifying assumptions, not the least of which is the idea that the athlete
could tell by his hunger when he has burned off the glass of orange juice. Even
so, this method still gives us some clue as to how much energy is in the orange
juice. Assuming the athlete can achieve some accuracy in reporting his hunger,
even if the resulting energy content is way off, we can still compare various
60 Biophysics D emystifieD
foods, and get an idea of their energy content relative to one another. Or, at the
very least we have a measure of how well various foods (relative to one another)
stave off hunger during exercise, which is somewhat related to energy content
of the food.
This example is perhaps a bit far fetched, but you get the idea. Making simpli-
fying assumptions is a useful tool. Later we will see more practical examples of
how making simplifying assumptions enables us to accomplish many things.
So what are the simplifying assumptions that we made in Prob. 4-1? Here
are a few of them. You should try to think of others. The first and probably
largest assumption is that 100% of the energy of the orange juice is converted
into work done by our athlete. As a general rule, animals are not the most effi-
cient heat engines. Humans, at best, convert only about 10% of their caloric
intake into useful work. The majority of the energy content of the food we eat
is either dissipated as heat or excreted as waste.
Another assumption we made, explicitly mentioned in the problem, is that
the only work done by the athlete is lifting his own weight to the 102nd floor.
This is not entirely correct. There is also work done to pump blood around the
body and work to expand and contract the lungs. And there is even some work
overcoming friction of the athlete’s shoes against the floor and of air resistance
while walking up stairs.
What other assumptions did we make? See if you can come up with two or
three additional assumptions, perhaps not as big and significant (in terms of the
calculated result) as those just mentioned, but assumptions none-the-less. (See
the Quiz at the end of this chapter for a few more assumptions.)
Enthalpy
Enthalpy is a classic thermodynamic property of a system, defined as the sum
of the internal energy of a system plus its pressure times its volume.
H 5 U 1 PV (4-3)
Although it may not be intuitively obvious how such a quantity can be useful,
we will see later that enthalpy can be easy to measure and it plays a role in
calculating whether a given biological process will occur spontaneously.
You can think of a system’s enthalpy in much the same way you think of
heat. A change in enthalpy DH is very similar to q, heat flowing into the system
(or flowing out if q is negative). The main difference between heat and enthalpy
is in the way we account for changes in pressure. If you want, you can skip over
chapter 4 EnErgy and LifE 61
the remainder of this section and start reading the section on Entropy, without
losing any understanding toward our chapter objectives. The rest of this section
provides experience with manipulating thermodynamic quantities and can give
you a deeper understanding into the nature of enthalpy.
By the definition of enthalpy, Eq. (4-3), the change in enthalpy is equal to
the change in internal energy plus the change in the product of pressure and
volume.
DH 5 DU 1 D(PV) (4-4)
We can see the relationship between enthalpy and heat by rearranging Eq. (4-4).
First, we rewrite it in a form similar to Eq. (4-2), in which we expressed the
first law of thermodynamics with the internal energy on the left and all other
terms on the right.
DU 5 DH 2 D(PV) (4-5)
Next, we account for pressure and volume changes in separate terms. That is,
we can rewrite D(PV) as
D(PV) 5 P DV 1 V DP (4-6)
This step may seem a bit like hand waving to you or may be familiar (if you
are familiar with calculus or differential equations). The general principle is
that the change of a product or two or more variables, D(PV) in our example,
is equal to a sum of two or more products, where each product contains the
change in only one variable multiplied by the value of each of the other vari-
ables held constant. Thus D(ABC) for example, would be equal to (DA)BC 1
A(DB)C 1 AB(DC). We will not take the time to prove this mathematic
concept here, but we do demonstrate its truthfulness by way of example in
Probl. 4-2.
If we take the right side of Eq. (4-6) and substitute it for D(PV) in Eq. (4-5),
we get
DU 5 DH 2 V DP 2 P DV (4-7)
The last term on the right P DV is the work done by the system. We save the
proof for Prob. 4-3. In short, since work is defined as force times distance, pres-
sure times a change in volume is just the three-dimensional version of force
times distance. Therefore we can rewrite Eq. (4-7) as
DU 5 DH 2 V DP 2 w (4-8)