Biology 131
Spring 2009
Problem Set 1 – Answers
1. The pH of lily nectar is 5.5. What is the concentration of hydrogen ions in nectar?
How many hydrogen ions are in 1 mL of nectar? [H+]= 10-5.5= 10-5 x 10-0.5= 10-5 x 1/√10≈
10-5 x 0.3 = 3 x 10-6 moles/L
1000 mL = 1L so this is 3 x 10-9 moles/mL
In 1mL, the total number of H+ ions = (3 x 10-6 moles/L) x (1 L/10-3 mL) x (6 x 1023
ions/mole) = 18 x 1014 ions = 1.8 x 1015 ions Try this without a calculator and notice that
you can approximate by adding and subtracting exponents for multiplications and
divisions. Remember that 109 = 1/10-9 !
The pH of mammalian serum is about 7.4. What is the concentration of hydrogen ions in serum?
How many hydrogen ions are in 10 mL?
[H+]= 10-7.4 moles/L ≈ (10-7 x 10-0.4 ) moles/L meaning the concentration is less than
10-7 moles/L, about 0.4 x 10-7 moles/L or about 4 x 10-8 moles/L
In 10mL, the total number of H+ ions = 10 mL x (4 x 10-8 moles/L) x (1 L/103 mL) x (6 x
1023 ions/mole) or about 2 x 1014 ions
Alternatively, if a liter has about 4 x 10-8 moles/L, then 10 mL is 1/100th of a liter so
1/100th of 4 x 10-8 moles = 4 x 10-10 moles and (4 x 10-10 moles) x (6 x 1023 ions/mole) =
24 x 1013 ions or 2.4 x1014 ions. Try doing these in your head with approximations!
2. Suppose you were asked to make 1 L of a 3 M solution of NaCl in water. How many
grams of NaCl would you use? How many units of NaCl would that be? After
the NaCI is dissolved in the water, how many Na+ ions are there in the solution? How many Clions are there?
Molecular Weight of NaCl = 58.4 Daltons, so one mole weighs 58.4 grams. Add
175.2 grams to 1L for a 3M solution. Total number of NaCl = 3mol x (6 x 1023
ions/mol) = 1.8 x 1024 ions. After dissolving: 1.8 x 1024 Na+, 1.8 x 1024 Cl- = 3.6 x 1024
total ions.
3. The concentration of Na+ in your blood and in many physiological solutions is about
100 mM. How would you make 1 L of a 100 mM solution of NaCl, using your 3 M
solution from problem 2 as a starting point; that is, how much 3 M NaCl solution
would you add to how much water to make a 100 mM solution? (In the laboratory, it
is often useful to make concentrated stocks of common solutions such as NaCl and to
dilute them appropriately to make working solutions.)
The 3M solution must be diluted 30 fold to get a 100 mM solution, but this problem
asks you to make only 1 L of 100 mM solution. Thus, take 1/30 of 1 L of 3M stock
(meaning 1L/30 x 1000mL/L= 33 mL), and add enough distilled water (967 mL) to
make 1L. This answer requires you to explain what you would do!
Biology 131
Spring 2009
Problem Set 1 – Answers
4. Draw the structure of N-lys-ala-lys-ser-tyr-ala-asp-C. What is the net electrical
charge of this peptide at physiological pH (7.4)? (At pH 7.4, amino and carboxyl
groups are both ionized.) net charge = +1 because in addition to the charges on the
amino and carboxy ends, give lys R groups a +1 charge and asp R groups a -1 charge.
5. Draw the structure of phosphatidylserine. Assume that the two fatty acids are palmitic
(16 carbons). Note that serine is the amino acid and is esterified to the phosphate via
its hydroxyl group (-OH) on the side chain. To test yourself, circle glycerol below!
6. At pH 7, the amino acid, valine, IS neutral because the amino group has a charge of
+1 and the carboxyl group has a charge of-1 and the side chain is uncharged. What
would you expect the effect on the charge of the molecule to be if the pH were raised
to 9? If the pH were lowered to 5?
At pH 9, because the solution has a low number of hydrogen ions, valine will lose
its proton off the amino group and that loss of +1 charge will leave a net negative
charge on the molecule. In contrast, at pH 5 (the pH of tomato juice), a portion of
the valine molecules will acquire a proton on the carboxyl end, bringing a net
positive charge to those molecules that pick up a proton.
Biology 131
Spring 2009
Problem Set 1 – Answers
7. Calculate how many amino acids are required for an a-helix to span the hydrophobic
region of a membrane if the hydrophobic region is about 3 nm thick. All of the
information you need to solve this problem is found in this handout.
Membrane thickness = 3 nm. Each turn of helix is 0.5 nm, which requires 6 turns
of alpha-helix to span core. Each turn has 3.6 amino acids. Thus, 20-22 amino
acids are needed. Another good way to do this is to know the length of H-bonds
(0.3 nm) and covalent bonds (0.15 nm) and then use that with a picture like the
alpha helix in the lecture slide to figure out how many turns fit in 3 nm.
8. The diffusion constant, D, of a typical globular protein in an aqueous medium is
about 5 x 10-7 cm2/s. How long, on average, would it take such a protein to diffuse
from the center of a spherical cell (diameter 20 µm) to the plasma membrane? Be
sure to pay attention to units, or you will get wildly incorrect answers. A useful
relationship to know is that 1 µm = 10-4 cm. From the center, the distance is 10 µm.
9. The axons of motor neurons are long extensions of single cells and, in vertebrates,
reach from the cell body in the spinal cord to the muscles that they innervate.
Biology 131
Spring 2009
Problem Set 1 – Answers
Proteins are mainly made in the cell body and must move down the axon to reach the
terminal. How long, on average, would it take the same protein mentioned in
Problem 8 were to get to the synaptic terminal of a meter long axon (a reasonable
length for a human) by diffusion? Consider this to be a problem in one-dimensional
diffusion. How reasonable is it for these neurons to use diffusion as the mechanism
of transport for proteins?
10. If the permeability of a cell membrane to an uncharged substance is l0-8 cm/s, and
cytoplasmic concentration is 10 mM and the extracellular concentration is 1 mM,
what will the flux of the substance be? Be sure to state both the magnitude and
direction of the flux.
11. Suppose that the cytoplasm of a cell consists of 100 mM K+, 100 mM of organic
anions and 50 mM glucose. The medium bathing the cell has 125 mM NaCl and 25
mM glucose. Assuming that there is initially no hydrostatic pressure, which way will
water flow, into or out of the cell? Remember that the NaCl will be fully dissociated.
Note that to figure out only the direction of water flow, you do not have to do a full
calculation of the osmotic pressures, nor do you need to know or assume a
temperature.
Biology 131
Spring 2009
Problem Set 1 – Answers
12 A sea urchin egg has a cytoplasmic K+ concentration of about 200 mM. What is the
Nernst potential for potassium in this cell? To solve the problem, you will have to
look up the concentration of K+ in sea water. This is available from many books or from the
Internet. You should make the effort to find this concentration and you may have to do some
conversions to have the right units. It is very important that you be able to use resources such
as the library and the Internet for information. Even if you do not find the number, you can
still work the problem by assuming a number-any number-or by leaving the concentration as
an algebraic symbol (x). Of course, if you choose the latter course, your answer will include
the symbol.
For both 12 and 13 you need to look up the [K+] and [Na+] in seawater.
13. The cytoplasmic Na+ concentration of a sea urchin egg is 45 mM, What is the Nernst
(equilibrium) potential for sodium? Again, you need to find the concentration of Na+ in sea
water.
14. If the measured membrane potential of the unfertilized sea urchin egg is -75 mV,
what can you say about the relative permeability of the membrane to sodium and
potassium, assuming that those two ions are the only ones involved in setting the
membrane potential? If the membrane potential suddenly shifts to + 30 mV, what
change in permeability might explain the shift? Try to solve the following problems without
using a calculator. This will be good practicefor the exam.
The membrane potential is much nearer Vk than VNa, thus the membrane is much
more permeable to K+ than to Na+. If the membrane potential changes toward
VNa, the relative permeability to Na+ must have increased. This could occur if the
Na+ permeability increased, if K+ permeability decreased, or both.
15. Suppose that the K+ concentration of a cell is 100 mM and the external concentration
is 1 mM. What is the equilibrium potential for K+?
16. Suppose that certain molecules are suddenly created in the center of a spherical cell
(diameter 10 µm) and that it takes 10 s for them diffuse throughout the cell. How
Biology 131
Spring 2009
Problem Set 1 – Answers
long would it take to diffuse throughout a cell with diameter of 100 µm? What if the
diameter were 1000 µm? Note: You do not need to calculate the diffusion
coefficient. Use a simple proportionality: the time required for molecules of the same
kind to diffuse a certain distance varies directly with the square of the distance.
Another way to do this would be to use the equation to solve for D and then use
that value for D to work the 100 µm and 1000 µm examples.
17. Identify two immediate consequences of opening Ca2+ channels in the plasma
membrane of a cell.
Because Ca2+ concentration in the cytoplasm is far lower than equilibrium, Ca2+ will
enter though open channels and raise Ca2+ levels in the cell. For example, the Ca2+
concentration may rapidly increase from 100 nM to 1 µM. In addition, the opening of
Ca2+ channels increases the permeability of the membrane to Ca2+ and causes the
membrane potential, Vm, to move toward the Ca2+ equilibrium potential, which is
above + 100 mV.
18. Regarding the awarding of the 2003 Nobel Prize in Chemistry to Peter Agre for
discovery of water channel proteins (aquaporins) Preston GM, Carroll TP, Guggino
WB, and Agre P. Appearance of water channels in Xenopus oocytes expressing red cell
CHIP28 protein. Science 256: 385-387, 1992.
18 a. How did these scientists use treatments and response variables?
Treatment: control eggs and frog eggs from Xenopus laevis with the protein expressed
are immersed in isotonic solution and distilled water.
Response variable: all six control oocytes were unaffected whereas all six oocytes with
the 28 kDa membrane protein immediately exploded
18 b. Does this study include categorical or quantitative variables?
categorical variable (a) with and without the protein expressed
categorical variable (b) exploded or not (in isotonic or distilled water)
18 c. Sketch a graph to represent the findings of this investigation.
(The following example is not the best of all the possible graphs)
Biology 131
Spring 2009
Problem Set 1 – Answers
18 d. What would the x and y axes represent?
For this graph the x axis represents the number of eggs exploded and the y axis shows
the treatments for control eggs and those with aquaporins expressed in the membrane.
Perhaps a better graph would have the treatments on the X axis (independent variable)
and the response (number exploded) on the y axis. At least the numbers here should
have a label!
18 e. What units of measure would be appropriate? number of eggs
18 f. What would the bars or data points represent? The bars show that eggs explode in
distilled water if they have aquaporins but those without aquaporins do not explode and
no eggs explode in isotonic saline.
18 g. Explain why this kind of graph is appropriate to support the conclusion.
A bar chart is appropriate when the treatment variable is categorical. For this
experiment, because the response variable is also categorical (eggs exploded or not)
the results would often be presented in a table and not as a graph.
18 h. Does this investigation uses anecdotal evidence, an observational study, or an
experiment? Justify your answer.
Because the scientists deliberately imposed a treatment in order to observe the
response, this is an experimental investigation.
18 i. Does this investigation establish a cause-and-effect relationship between the
treatment and response variables?
Results show a dramatic difference that was clearly caused by expressing aquaporins
in the eggs. These scientists performed a carefully controlled experiment with a
comparison group to show causation. The alleged cause was plausible, given what we
know about osmosis; the water potential would be expected to move water into the egg
immersed in distilled water if the membrane were permeable to water.