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HW5. Diffusion as a Design Constraint in Biological Systems
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Due Friday 3/4/2011
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should meet before completing the assignment. However, you must write your answers
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Class means from the Simulations in the Diffusion GAE
Fick - Relationship between concentration
gradient and diffusion rate
Einstein – Relationship between time and
distance traveled
Initial particle
number = conc.
gradient (∆C/∆x)
Particles crossing the 4
circle line = diffusion
rate (J)
Time (t)
Distance traveled (∆x)
0
0
0
0
50
6.1
20
2.1
100
11.7
40
3.5
150
14.2
60
3.9
80
5.2
For all questions, show your work, which means that you must write the correct equations, plug in the correct numbers, do the calculations, and write the answer, including the correct units. 1. On graph paper (which can be downloaded from http://incompetech.com/graphpaper)
plot the data from the simulations attempting to relate the concentration gradient and
diffusion rate. Describe the curve seen in your graph, and relate that curve to Fick’s
First Law.
2. Circle the correct answers to describe the mathematical properties of Fick’s First Law
ΔC
J=D
Δx
A. If the concentration gradient (ΔC/Δx)) decreases, then the diffusion rate (J) must:
1) increase, 2) decrease, or 3) remain the same.
B. If the concentration gradient (ΔC/Δx)) increases, then the diffusion rate (J) must:
1) increase, 2) decrease, or 3) remain the same.
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The diffusion coefficient (D) in Fick’s First Law depends on the properties of the
molecule (molecular wt, etc.) and the medium (water, air, cell, membrane, etc.). For
example, a low molecular weight molecule is expected to have a higher diffusion
coefficient (D) as a high molecular weight molecule. Therefore,
C. A certain concentration gradient for a high molecular weight molecule should result in
a 1) higher, 2) equal, or 3) lower diffusion rate than the same concentration gradient of
low molecular weight molecule.
2. On graph paper, plot the data from the simulations attempting to relate the time that a
molecule takes to travel a given distance. Describe the curve seen in your graph, and
relate that curve to the Einstein-Smoluchowski relation (also called the time-to-diffuse
equation.
-5
Calculate the time it takes a molecule of oxygen (diffusion coefficient = 1.6 x 10
2
cm /s) to diffuse across various structures. (Don’t forget to pay attention to units).
Use the equation:
(Δx)2
t=
2D
A. Cell membrane 8 nm in thickness:
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B. Eukaryotic cell 10 µm in length:
C. Human heart wall 2 cm in thickness (calculate in seconds and then convert to hours):
D. Using your answer in C, explain the role of the coronary blood vessels.
3. We can cite multiple examples to illustrate the role of diffusion in the evolution of
multicellular organisms. One common example is to compare the body plans of
flatworms (Freeman Fig. 33.13) and roundworms (Freeman Fig. 32.9) having the same
width.
A. Flatworms
Flatworms lack circulatory systems so that O2 can only diffuse in their bodies.
Assuming a body width of 2.5 cm and a thickness of 1 mm (corresponding to a diffusive
distance of 0.5 mm), how much time does it take O2 to diffuse to the center of their
bodies? (Assume the D of O2 = 1.6 x 10-5 cm2/s)
B. Roundworms – several phyla exhibit the shape of round worms
Can roundworms of comparable width survive without a circulatory system to carry O2?
Assuming a body diameter of 2.5 cm (corresponding to a diffusive distance of 1.25 cm),
how much time does it take O2 to diffuse to the center of their bodies? (Assume the
same D of O2 as above) Calculate in seconds and then convert to hours.
C. Using your answers above, describe the constraints that the diffusion of O2 places on
the size and shape of these worms, and how they overcome those constraints.