Fick's law and oxygen diffusion in salmon
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Fick's law and oxygen diffusion in salmon
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[ID] => 558262
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[post_date] => 2025-01-09 07:56:43
[post_date_gmt] => 2025-01-09 12:56:43
[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
Fick's first law of diffusion states that the flux J of a substance (units: mol x m⁻² x s⁻¹) is proportional to the gradient for the substance:
where C is the difference in initial and final concentration of the substance (units: mol x m-3 ), 𝒙 is the distance of diffusion (in meters), and D is the diffusion constant, which depends on environmental conditions and increases with temperature. Fick's second law of diffusion states that the time it takes a particle to diffuse a given distance is proportional to the square of that distance:
Fick's laws can be used to model the rate of oxygen diffusion across biological membranes (MO₂) using the following equation
where K is Krogh's diffusion coefficient, A is the surface area of the membrane, L is the thickness of the membrane, and ΔPO₂ is the oxygen partial pressure difference across the membrane.
The physical restrictions modeled by these equations have lead to interesting evolutionary adaptations in the structures that animals use to absorb oxygen. For instance, Atlantic salmon hatchlings absorb the oxygen needed for cellular respiration cutaneously (through the skin). However, over the course of juvenile development, these animals experience a rapid increase in body size, and absorption of oxygen shifts almost totally to the branchial tissue of the gills. Researchers studied the measurable consequences of this developmental process by measuring oxygen absorption (MO₂) in branchial and cutaneous tissue and compared the results to measurements of surface area and anatomical diffusion factor (ADF), two different measures of the oxygen-absorbing capacity of tissues (figure 2). ADF is defined as the ratio of mass-specific surface area to harmonic mean diffusion distance. The harmonic mean of a data set is a measure of the average value of the data set. Data for measurements of harmonic mean diffusion distance are given in figure 2.
Figure 1. Relation between body mass and change in cutaneous and branchial oxygen absorption (MO₂), surface area (area), and anatomical diffusion factor (ADF) as a proportion of total body MO₂ , area, and ADF over the course of juvenile development of atlantic salmon hatchlings.
Figure 2. Measurement of harmonic mean diffusion distance for filaments, skin, and lamellae for atlantic salmon (filaments and lamellae are types of branchial tissue).
Passage and figures adapted from:
Wells, P., & Pinder, A. (1996). The respiratory development of Atlantic salmon. I. Morphometry of gills, yolk sac and body surface. J Exp Biol, 199 (Pt 12), 2725-2736.
Wells, P., & Pinder, A. (1996). The respiratory development of Atlantic salmon. II. Partitioning of oxygen uptake among gills, yolk sac and body surfaces. J Exp Biol, 199 (Pt 12), 2737-2744.
[post_title] => Fick's law and oxygen diffusion in salmon
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[question] => Based on data and equations presented in the passage, by what factor does the time required for oxygen-absorption across the skin increase when atlantic salmon increase in mass from ~0.1g to ~10g?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
Fick’s second law is the only equation in the passage that explicitly involves time.
Figure two indicates that when mass increaes from ~0.1 g to ~10 g, harmonic mean diffusion distance for skin increases from ~20 m to ~100 m.
One way to solve proportional increase problems is to set up a ratio of two equations, cancel common terms, and solve for the final variable (in this case, diffusion time after the increase in weight) in terms of the initial variable (in this case, diffusion time before the increase in weight).
Time increases by a factor of ~25.
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[answers] => Array
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[0] => Array
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[each_answer] => A. A factor of ~1
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[1] => Array
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[each_answer] => B. A factor of ~5
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[2] => Array
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[each_answer] => C. A factor of ~25
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[3] => Array
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[each_answer] => D. A factor of ~100
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => What are the SI units for D, the diffusion coefficient?
[value] => Array
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[answer] => 1
[description] => Reason for the Correct Answer:
The units for the diffusion coefficient D can be obtained by rearranging either of Fick’s laws.
For instance, using Fick’s law, the units for D can be obtained by dividing the units of flux by the units of gradient.
The SI units for D are S⁻¹ x m²
)
[answers] => Array
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[0] => Array
(
[each_answer] => A. s⁻¹ x m²
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[1] => Array
(
[each_answer] => B. s² x m⁻² x mol
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[2] => Array
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[each_answer] => C. s x m⁻²
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[3] => Array
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[each_answer] => D. s⁻¹ x m² x mol
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => According to figure one, cutaneous surface area as a percentage of total surface area decreased ~20% over the course of Atlantic salmon juvenile development, while cutaneous ADF as a percentage of total ADF decreased ~80% over the same time frame. What is the best explanation for this divergence?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
Filaments are a type of branchial tissue and thus are not related to cutaneous oxygen absorption.
Harmonic mean diffusion distance for skin did not decrease over the relevant time period.
Harmonic mean diffusion distance for skin increased.
)
[answers] => Array
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[0] => Array
(
[each_answer] => A. Harmonic mean diffusion distance for filaments increased.
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[1] => Array
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[each_answer] => B. Harmonic mean diffusion distance for filaments decreased.
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[2] => Array
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[each_answer] => C. Harmonic mean diffusion distance for skin increased.
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[each_answer] => D. Harmonic mean diffusion distance for skin decreased.
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[quiz_unique_key] => 2261298308
[question] => Why did researchers choose to measure ADF in addition to surface area?
[value] => Array
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[answer] => 2
[description] => Reason for the Correct Answer:
Based on the equations discussed in the passage, oxygen absorption depends on surface area, diffusion distance, and differences in partial pressures.
ADF is defined as the ratio of mass-specific surface area to harmonic mean diffusion distance.
ADF takes the dependence of oxygen absorption on distance traveled into account.
)
[answers] => Array
(
[0] => Array
(
[each_answer] => A. ADF takes the dependence of oxygen absorption on partial pressure into account.
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[1] => Array
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[each_answer] => B. ADF takes the dependence of oxygen absorption on distance traveled into account.
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[2] => Array
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[each_answer] => C. ADF takes the dependence of oxygen absorption on temperature into account.
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[3] => Array
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[each_answer] => D. DF takes the dependence of oxygen absorption on membrane type into account.
)
)
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[4] => Array
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[quiz_unique_key] => 574431310
[question] => If researchers measured O2 flux as a function of gradient under different temperatures, which of the following graphs would most likely represent the results?
[value] => Array
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[answer] => 2
[description] => Reason for the Correct Answer:
Fick’s first law of diffusion states that the relationship between flux and gradient takes the form of a first-order polynomial y = -m x 𝒙, with 𝑚 equal to D, the diffusion coefficient.
The passage states that the diffusion coefficient increases with temperature.
The graph of flux as a function of gradient is a line through the origin with negative slope, and the negative slope of this line increases with temperature.
Graph B represents the most likely result of measuring O₂ flux as a function of gradient under different temperatures.
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[answers] => Array
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[0] => Array
(
[each_answer] => A. Graph A.
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[1] => Array
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[each_answer] => B. Graph B.
)
[2] => Array
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[each_answer] => C. Graph C.
)
[3] => Array
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[each_answer] => D. Graph D.
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[558262|1] => C
[558262|2] => A
[558262|3] => C
[558262|4] => B
[558262|5] => B
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