Processes of diffusion of oxygen can be described in a formalized and simplified manner in formulas such as Fick's laws of diffusion. For a sound understanding of the interconnections of anatomical structure, biological function, and environmental factors in a living system, however, real-life case studies need to be employed to explore what is captured in the equation and what is not, and which other structures and behaviors may play a role in respiratory physiology. I use four anuran examples to illustrate, starting with Fick's first law, respiratory processes as influenced by surface-area-to-volume ratio and turbulence in the surrounding medium.

Respiratory Diffusion as a Process Affected by Multiple Environmental Factors

Sufficient availability of oxygen is a conditio sine qua non for oxidative reactions and all dependent metabolic processes in higher animals. Fick's laws of gas diffusion can be used to describe the path that oxygen can take into a tissue and factors that influence the oxygen flux. Understanding of diffusion processes can be developed by inductive reasoning, progressing from an observed phenomenon to its abstract description in a formula or equation, or in a deductive manner, recognizing the rules described in the formula in examples found in nature.

In the simple equation of Fick's laws, m/t = DS(ΔC/x), m/t describes the oxygen flux, D is the diffusion constant, S is the area of the surface through which the diffusion happens, ΔC/x is the concentration gradient that diffusing molecules follow, and x is the distance that a given molecule moves. For correct understanding of Fick's first law of gas diffusion, it needs to be established that, for oxygen flux (m/t) to become large, S and ΔC need to be large, with the denominator x being small. D is a constant that remains unchanged.

Nature provides a wealth of examples in which structures in living organisms correspond in a very obvious way to the factors included in this equation. For instance, ΔC/x, the concentration gradient being either large or small in cold, oxygen-rich seawater or in warm, flat, slow-flowing or stagnant (and hence low-oxygen) bodies of water, is reflected in the physiological and anatomical adaptations of species such as the ice fish or lungfish (Robischon, 2014). In the latter case of an air-breathing fish, however, the “optimization” of O2 uptake by turning to a different medium is beyond what is captured in Fick's equation. The air-breathing organism does, in a manner of speaking, “avoid” the actual problem of diffusion of oxygen in aqueous solution in the given circumstances by reaching out for oxygen in a different medium.

To progress to higher levels of complexity in the discussion of diffusion processes as formalized in Fick's first law, the formula needs to be understood as a simplified description of an interaction of two or more factors that excludes other factors for clarity's sake. Biological systems thinking can be expected to profit from studying cases in which the formula does not cover what happens in nature, and from discussion of which additional factors play a role in the individual case study. Additional factors that could be included are the body shape of the animal, rather than just its size, as well as the potential lack of stability of the surrounding medium. Here, I develop real-life examples that build on the existing examples and that enable a deeper understanding of the laws of diffusion in biology. These case studies are taken from the wealth of unusual and striking physiological and anatomical adaptations, thus also fostering an understanding of the value of biological diversity as a source of insights and learning in the life sciences. A group of animals in which cutaneous respiration is of particular importance, and that have thus evolved a large number of anatomical structures and behaviors that optimize diffusion, is the amphibian order Anura, the frogs and toads (Figure 1). Each of the species discussed here belongs to a different family. The genera Telmatobius and Trichobatrachus are both of the suborder Neobatrachia, while the genera Barbourula and Ascaphus belong to the suborder Archaeobatrachia. Therefore, the feature of having reduced or absent lungs in the species addressed here appears to be evolutionarily unrelated and independently developed. It can thus be considered an example of convergent evolution.

Figure 1.

The diversity of frogs and toads worldwide delivers a plethora of examples for teaching diffusion processes in living nature. (A) The hairy frog (Trichobatrachus robustus; original size: 80–130 mm) develops villose papillae that increase the surface for diffusion and O2 uptake in the breeding season. (B) The tailed frog (Ascaphus sp.; original size: 37–55 mm) and (C) the Bornean flat-headed frog (Barbourula kalimantanensis; 68–78 mm) have significantly diminished lungs or none at all, a high surface-area-to-volume ratio and live in turbulent waters. (D, E) The giant frog from Lake Titicaca (Telmatobius culeus; original size: ~250 mm) enhances diffusion by creating its own water turbulence by body motion. Images are not to scale. Sources: (A) https://upload.wikimedia.org/wikipedia/commons/a/a0/TrichobatrachusGreen.jpg. (B) Images modified from http://biologi.lipi.go.id/bio_bidang/zoo_english/images/herpet/bombinatoridae/bombinatoridae1.jpg. (C) Used with kind permission of Dr. Helen Kurniati, Research Center for Biology, Indonesian Institute of Sciences. (D, E) https://upload.wikimedia.org/wikipedia/commons/f/f6/Telmatobius_culeus.jpg?uselang=de.

Figure 1.

The diversity of frogs and toads worldwide delivers a plethora of examples for teaching diffusion processes in living nature. (A) The hairy frog (Trichobatrachus robustus; original size: 80–130 mm) develops villose papillae that increase the surface for diffusion and O2 uptake in the breeding season. (B) The tailed frog (Ascaphus sp.; original size: 37–55 mm) and (C) the Bornean flat-headed frog (Barbourula kalimantanensis; 68–78 mm) have significantly diminished lungs or none at all, a high surface-area-to-volume ratio and live in turbulent waters. (D, E) The giant frog from Lake Titicaca (Telmatobius culeus; original size: ~250 mm) enhances diffusion by creating its own water turbulence by body motion. Images are not to scale. Sources: (A) https://upload.wikimedia.org/wikipedia/commons/a/a0/TrichobatrachusGreen.jpg. (B) Images modified from http://biologi.lipi.go.id/bio_bidang/zoo_english/images/herpet/bombinatoridae/bombinatoridae1.jpg. (C) Used with kind permission of Dr. Helen Kurniati, Research Center for Biology, Indonesian Institute of Sciences. (D, E) https://upload.wikimedia.org/wikipedia/commons/f/f6/Telmatobius_culeus.jpg?uselang=de.

A Hairy Frog from Africa: The Embodiment of Surface Area/Volume Ratio Optimization

In the equation m/t = DS(ΔC/x), one way to increase m/t is to increase S – that is, to enlarge the surface area (or, in a cutaneously respirating amphibian example, the skin area). The relation of surface area to volume – and, thus, that of O2 uptake to the animal's body mass – is dependent on the size and shape of the body. First, in compact shapes, the ratio of surface area to volume is inversely proportional to size. In smaller animals, the diffusion of oxygen into the body is thus more efficient than in larger ones of the same shape. Second, a deviation from compact and, in particular, globular shapes can drastically increase the ratio of surface area to volume.

A striking example is provided by the West African frog Trichobatrachus robustus (Arthroleptidae). At a size between 80 and 130 mm (length of snout to vent; Vitt & Caldwell, 2013), it has remarkably small lungs, which suggests that cutaneous respiration is of vital importance to this species. While many students are likely to be most fascinated by this animal's highly unusual defense mechanism of breaking the bones in its own feet to protrude as sharp claws from its skin (thus sometimes dubbed the “Wolverine frog”), it is a different feature that is of importance in the discussion of diffusion. During the breeding season, the male grows a “pelage” of villose papillae that cover the animal's lower flanks, hips, and upper thighs. This unusual “sideburn” feature led to the hirsute animal being commonly referred to as the “hairy frog.” These “hairs” consist of highly vascularized filaments, present only in the breeding season, that allow for a more efficient gas exchange at a time of high metabolic activity. Metaphorically speaking, this frog grows an “aqualung.” Remarkably, T. robustus is typically found only in streams during breeding (Jameson, 2012) but lives most of the year, and most of its life, in terrestrial habitats. There, the larger body surface would result not in enhanced oxygen uptake, but in greater evaporation of water. The papillae thus disappear in the “terrestrial phase.” By expanding and shrinking the surface area with only a minimal change in volume, the diffusion is thus optimized for the given body mass according to the seasonal physiological needs and the qualities of the surrounding medium.

Dressed in Tails & Leading a Turbulent Life: Increasing the Gradient of Diffusion

The concentration gradient is described by ΔC/x. It is easily neglected, when teaching diffusion, that during – and as a consequence of – the diffusion process, the very gradient that drives diffusion will typically decrease, resulting in reduced diffusion. Diffusion through adjacent layers with similar concentrations of, for example, O2 is a slow process, unless the laminar layers are disturbed by turbulent flow, and the steepness of the concentration gradient thus restored. The importance of turbulence in the medium is well illustrated in several batrachians that have small lungs, are skin-breathing, have evolved body shapes that enhance the ratio of surface area to volume, and live in fast-moving, turbulent water.

Small lungs are a feature found in other frogs, too – for example, in the primarily aquatic American bell toads Ascaphus truei and A. montanus (Ascaphidae). Their other name, “tailed frogs,” indicates that they too have body appendages that may play a role in increasing the surface-area-to-volume ratio. These two species are, at a snout-to-vent length of ≤5.5 cm (Dodd, 2013), only about half the length of T. robustus, which suggests that less elaborate structures are required to enhance their surface area and, thus, their surface-area-to-volume ratio. They are described in general as being rather sluggish (Stebbins, 1951), which suggests a comparatively low metabolic rate. The main factor that enables these species to survive is their habitat: fast-running, turbulent, cold (and hence oxygen-rich) water. Their appendages, though surely contributing to an enlarged surface area, are more likely to have their main function in mating behavior. The Ascaphus species are “tailored” for life in a turbulent environment. The turbulence is thought to significantly enhance the diffusion gradient, thus supporting oxygen uptake. It has been reported that “The nearly lungless Ascaphus very soon dies if exposed to the air at ordinary temperature” (Noble, 1925), which may not be due to dehydration or hyperthermia, but rather to insufficient oxygen uptake. This frog is likely to experience respiratory distress in warmer water, too.

A Lungless Wonder from Kalimantan

An extreme example of reduced lungs – which is nothing less than “a reversal of one of the most important physiological adaptations for terrestrial life” (Bickford et al., 2008) – is found in Barbourula kalimantanensis (Bombinatoridae), with a snout-to-vent length of 6.8–7.8 cm (Iskandar, 1995). This long anuran is known as the “Bornean flat-headed frog,” a name indicating that its shape deviates from the globular, thus producing an increased surface-area-to-volume ratio. In fact, as described by Iskandar (1995), “the sides of the body, femur and tibia are armed with a ridge or skin fold,” so that not only the animal's head but its entire body is “extremely flat and streamlined,” protecting it from high water pressure in the fast-flowing streams in which it lives “among stones or crevices.” However, Iskandar (1978, 1995) did not realize what makes this frog unique among all anurans described to date: it does not merely have reduced lungs, but in fact it possesses no lungs at all – a feature otherwise known among amphibians only in a few salamanders and caecilians. Bickford et al. (2008) suggest that “loss of lungs may be an adaptation to the combination of higher oxygen content in fast-flowing cold water, the species’ presumed low metabolic rate, severe flattening to increase the surface area of the skin…and selection for negative buoyancy.”

All three batrachians – Trichobatrachus, Ascaphus, and Barbourula – have reduced or absent lungs and a nonglobular body shape that optimizes the surface-area-to-volume ratio, and all live at least seasonally in streams rather than stagnant ponds. The problem of the enhanced surface-area-to-volume ratio and the significance of turbulence in the surrounding medium is further illustrated by another frog, one that lives in water not noted for its turbulence.

Into Thin Air, or the Giant from Lake Titicaca

An extreme example of the aquatic lifestyle is encountered in the Lake Titicaca water frog (or rana gigante del Lago Titicaca). According to an early description (Allen, 1922), Telmatobius culeus (Telmatobiidae) “was never observed to emerge from the water; was never found out of the water; was never seen rising to the surface to breathe; and never seen swimming more than a few inches from the bottom.” This species is thus, in fact, more aquatic than quite a few fishes (Graham, 1997). From the description (Allen, 1922), it appears to be generally rather slow-moving, which suggests comparatively low metabolic activity. Continuous submerged swimming or floating may be eased by a reduced buoyancy, given that its “lungs are one-third those of equally sized ranids” (McNab, 2002), though a claim that it is lungless, as put forward by Bartlett and Bartlett (1996), has no basis. Perhaps its lungs function mainly as a swimming bladder. In spite of having a low metabolic rate at low ambient temperatures in the icy Lake Titicaca water (which, due to the temperature, has high oxygen solubility), T. culeus faces the problem of low oxygen partial pressure at an altitude of 3812 m above sea level, making the reduced lungs a most contradictory adaptation to high elevations. It apparently relies entirely on cutaneous respiration and exemplifies Fick's laws of diffusion (Fick, 1855): it evidently enhances diffusion by expanding its body surface by means of its extensive, baggy skin flaps and folds. Being a rather large species, with snout-to-vent length of ~25 cm (Vitt & Caldwell, 2013) and reaching up to 1 kg in weight, such an optimization of body shape is particularly important. Parker (1940) points out that in T. culeus “there appears to be a definite correlation between absolute size and bagginess.”

In contrast to the three species addressed before, the lacustrine Telmatobius does not live in fast-running, turbulent water. Therefore, the diffusion gradient is not enhanced by “fresh” oxygen-rich water replacing the “old” low-oxygen water. The surface-enlarging “flabby” skin may, in fact, create a risk for the animal, with the “used-up,” low-oxygen water being caught in the baggy skin as in pockets. The advantage of the extra surface is lost in a nonturbulent environment. With the surrounding medium being much less mixed than, for example, in the streams inhabited by Ascaphus species, the Lake Titicaca frog has developed a most peculiar behavior to compensate for the reduced or absent pulmonary gas exchange: It has a habit of regularly bobbing up and down to rinse and to ventilate all the nooks and crannies (Hutchison et al., 1976), thus purging low-oxygen “used” water. Each of these “rinsing motions” locally and temporarily enhances the gradient in oxygen concentration between the fresh water and the animal's blood. A standstill would be death.

Teaching with Toads

The batrachian examples given here offer unusual and fascinating case studies that lend themselves to colorful and exciting approaches for teaching respiratory physiology. They can be used to deliver an impulse and trigger for learning activities, for example by establishing a research question on, say, the link between surface area, gas exchange, and metabolic activity. Showing pictures of the animals that highlight morphological features can serve as a “silent impulse” for forming hypotheses on the interrelationship of structure and function based on Fick's laws. Pictures of the animals can also be used to illustrate the biological significance of principles that were previously derived theoretically on the basis of physical laws; this can form an exercise in the scientific process of testing a hypothesis against a real-life case study. But first and foremost, the presentation and study of these intriguing cases can be expected to induce epistemic curiosity, which is the most fundamental prerequisite for learning in biology and, in fact, any other science.

References

References
Allen, W.R. (
1922
).
Notes on the Andean Frog
Telmatobius coleus
(
Garman
).
Copeia,
108
,
52
54
.
Bartlett, R.D. & Bartlett, P.P. (
1996
).
Frogs, Toads, and Treefrogs: Everything about Selection, Care, Nutrition, Breeding, and Behavior
.
Hauppauge, NY
:
Barron's Educational Series
.
Bickford, D., Iskandar, D. & Barlian, A. (
2008
).
A lungless frog discovered on Borneo
.
Current Biology
,
18
,
R374
R375
.
Dodd, C.K. (
2013
).
Frogs of the United States and Canada
.
Baltimore, MD
:
Johns Hopkins University Press
.
Fick, A. (
1855
).
Über Diffusion
.
Poggendorff's Annalen der Physik und Chemie
,
94
,
59
86
.
Graham, J.B. (
1997
).
Air-Breathing Fishes: Evolution, Diversity, and Adaptation
.
San Diego, CA
:
Academic Press
.
Hutchison, V.H., Haines, H.B. & Engbretson, G. (
1976
).
Aquatic life at high altitude: respiratory adaptations in the Lake Titicaca frog, Telmatobius culeus
.
Respiration Physiology
,
27
,
115
129
.
Iskandar, D.T. (
1978
).
A new species of Barbourula: first record of a discoglossid anuran in Borneo
.
Copeia
,
4
,
564
566
.
Iskandar, D.T. (
1995
).
Note on the second specimen of Barbourula kalimantanensis (Amphibia: Anura: Discoglossidae)
.
Raffles Bulletin of Zoology
,
43
,
309
311
.
Jameson, E.W., Jr. (
2012
).
Patterns of Vertebrate Biology
.
Berlin, Germany
:
Springer Science & Business Media
.
McNab, B.K. (
2002
).
The Physiological Ecology of Vertebrates: A View from Energetics
.
Ithaca, NY
:
Cornell University Press
.
Noble, G.K. (
1925
).
The integumentary, pulmonary, and cardiac modifications correlated with increased cutaneous respiration in the amphibia: a solution of the ‘hairy frog’ problem
.
Journal of Morphology and Physiology
,
40
,
341
416
.
Parker, H.W. (
1940
).
The Percy Sladen Trust Expedition to Lake Titicaca in 1937. XII. Amphibia
.
Transactions of the Linnean Society of London (3rd series)
,
1
,
203
216
.
Robischon, M. (
2014
).
A tale of two fishes or a quick fix for Fick's law
.
American Biology Teacher
,
76
,
270
271
.
Stebbins, R.C. (
1951
).
Amphibians of Western North America
.
Berkeley, CA
:
University of California Press
.
Vitt, L.J. & Caldwell, J.P. (
2013
).
Herpetology: An Introductory Biology of Amphibians and Reptiles
, 4th Ed.
London, UK
:
Academic Press
.