Symmorphosis in the proximal pathway for oxygen in the leaf-eared mouse Phyllotis darwini

In this report, we explore the matching of structures to functional needs by comparing previously reported data of maximal oxygen consumption and the development of the lung in the leaf-eared mouse Phyllotis darwini in warm and cold environments. We discuss whether the state of structural design is commensurate with functional needs from regulated morphogenesis as predicted by the hypothesis of symmorphosis. We found a close match between respiratory structures and functional needs during postnatal development, expressed as safety factors close to unity. However, in the adult stage the safety factors were greater than two, which suggests that adult animals acquired a structure greater than that required considering their maximum capacities. A high safety factor in the respiratory system of adult mice may be a consequence of the symmorphosis that operates during ontogeny and does not necessarily support a rejection of this hypothesis. Key terms: Metabolism, Ontogeny, Phyllotis darwini, Symmorphosis Corresponding author: Mauricio Canals (*), Departamento de Ciencias Ecológicas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago-Chile. e-mail: mcanals@uchile.cl Received: 12-05-2009. In revised form: 07-10-2009. Accepted: 09-10-2009 INTRODUCTION Persistence and reproduction of animals depends upon energy acquisition, absorption, transformation, allocation and expenditure, all factors that are intrinsically limited by the design of the organism, probably in the context of extrinsic limitations, such as food availability (Karasov, 1986; Weiner, 1992; Speakman, 2000; Bacigalupe and Bozinovic, 2002). Regarding only physiological constraints, there are three principal hypotheses that attempt to explain physiological limitation of energy budgets: i) shared central machinery limits the sustained metabolic rate (“central limitation hypothesis”); ii) energy consuming machinery limits the sustained metabolic rate (“peripheral limitation hypothesis”); and iii) the capacity of the central machinery closely matches that of the peripheral tissues and energy requirements (Bacigalupe and Bozinovic, 2002). The first hypothesis implies that metabolic limits are independent of the manner of energy expenditure and peripheral organs always possess an excess capacity. The second hypothesis proposes that central organs have excess capacity. The third hypothesis proposes that organisms do not have excess capacities, but rather the capacity of central organs to supply energy matches the expenditure capacity of peripheral organs, just as proposed by the symmorphosis hypothesis (Taylor and Weibel, 1981). Symmorphosis is defined as “a state of structural design commensurate with functional needs resulting from regulated morphogenesis, whereby the formation of structural elements is regulated to satisfy but not exceed the requirements of the functional system” (Taylor and Weibel, 1981). Thus the symmorphosis hypothesis proposes that if matching structures to functional needs were combined with the CANALS ET AL. Biol Res 43, 2010, 75-81 76 strict economy of energy and materials, the result would be an optimal organ design for the specific function it serves (Weibel et al. 1991, 1992). This hypothesis contains three predictions: i) organism design will be optimized; ii) if the design is optimized in the sense of material economy, then structure is the key factor in determining maximal organ capacities, and adjustments to it require morphogenetic processes; and iii) if prediction ii) operates in each intermediate step of the whole function of an organ, each step contributes to the limitation of the whole function (Jones, 1998; Weibel, 1998; Canals, 2002). Although symmorphosis was first proposed for the oxygen pathway in mammals, it has been established as a general hypothesis of economic design (Weibel at al., 1998). The oxygen pathway was considered a good model for two reasons. First, it involves a series of linked structures in which the effect of the structural parameters on functional capacity can be defined. For example, VO2 = (ΔPO2) · DLO2 (Bohr’s equation), where VO2 is oxygen consumption, ΔPO2 is the alveoluscapillary pressure gradient, and DLO2 is the oxygen diffusion capacity or oxygen conductance. The latter depends directly on the alveolar and capillary surface, hematocrit and capillary volume, and inversely on the thickness of the alveoluscapillary barrier (Weibel et al., 1991). The second reason is that the overall function has a measurable upper limit, maximal oxygen consumption VO2max (Weibel, 1998). The symmorphosis hypothesis has generated great debate that remains unresolved. Evidence in favor of symmorphosis is as abundant as evidence against it (Bacigalupe and Bozinovic, 2002; Canals 2002). Regarding the oxygen pathway, Weibel et al (1992) found that mithocondrial volume, cardiac output and capillary volume varied with body mass with the same allometric exponent as maximal oxygen consumption, suggesting that mithochondria achieve the same rate of oxidative phosphorylation in all mammals, supporting the symmorphosis hypothesis (Weibel et al., 1991; 1992). However, the same authors reported that in the lung, the oxygen diffusion capacity did not adjust to functional needs, with the result that species of large body size have an excess capacity relative to that of small species (Weibel, 1998). Jones (1998) also reported an excess oxygen diffusion capacity in well-trained equines. The original approach of Weibel et al. (1981) was comparison between species, using animals of the same body mass adapted to environments with different energetic requirements (adaptive variation) and animals of different body masses in which the scaling of maximal capacities should be paralleled by structure (allometric variation). However, the concept of symmorphosis may be evaluated within particular species, using a similar protocol (Bacigalupe and Bozinovic, 2002). In this report we explore matching structures to functional needs by comparing previously reported data of maximal oxygen consumption and the development of the lung in the leaf-eared mouse Phyllotis darwini in warm and cold environments. We discuss whether the state of structural design is commensurate with functional needs from regulated morphogenesis as predicted by the symmorphosis hypothesis (i.e. at the upper limit of the overall function of the respiratory system, the maximum metabolic rate should be paralleled by structural changes) (Weibel et al. , 1991; 1992; Seymour et al., 2004; 2005; Runciman et al., 2005; Canals et al., 2005; Figueroa et al., 2007; Canals et al., 2007).


INTRODUCTION
Persistence and reproduction of animals depends upon energy acquisition, absorption, transformation, allocation and expenditure, all factors that are intrinsically limited by the design of the organism, probably in the context of extrinsic limitations, such as food availability (Karasov, 1986;Weiner, 1992;Speakman, 2000;Bacigalupe and Bozinovic, 2002).Regarding only physiological constraints, there are three principal hypotheses that attempt to explain physiological limitation of energy budgets: i) shared central machinery limits the sustained metabolic rate ("central limitation hypothesis"); ii) energy consuming machinery limits the sustained metabolic rate ("peripheral limitation hypothesis"); and iii) the capacity of the central machinery closely matches that of the peripheral tissues and energy requirements (Bacigalupe and Bozinovic, 2002).The first hypothesis implies that metabolic limits are independent of the manner of energy expenditure and peripheral organs always possess an excess capacity.The second hypothesis proposes that central organs have excess capacity.The third hypothesis proposes that organisms do not have excess capacities, but rather the capacity of central organs to supply energy matches the expenditure capacity of peripheral organs, just as proposed by the symmorphosis hypothesis (Taylor and Weibel, 1981).
Symmorphosis is defined as "a state of structural design commensurate with functional needs resulting from regulated morphogenesis, whereby the formation of structural elements is regulated to satisfy but not exceed the requirements of the functional system" (Taylor and Weibel, 1981).Thus the symmorphosis hypothesis proposes that if matching structures to functional needs were combined with the strict economy of energy and materials, the result would be an optimal organ design for the specific function it serves (Weibel et al. 1991(Weibel et al. , 1992)).This hypothesis contains three predictions: i) organism design will be optimized; ii) if the design is optimized in the sense of material economy, then structure is the key factor in determining maximal organ capacities, and adjustments to it require morphogenetic processes; and iii) if prediction ii) operates in each intermediate step of the whole function of an organ, each step contributes to the limitation of the whole function (Jones, 1998;Weibel, 1998;Canals, 2002).
Although symmorphosis was first proposed for the oxygen pathway in mammals, it has been established as a general hypothesis of economic design (Weibel at al., 1998).The oxygen pathway was considered a good model for two reasons.First, it involves a series of linked structures in which the effect of the structural parameters on functional capacity can be defined.For example, V O2 = (ΔPO 2 ) • D LO2 (Bohr's equation), where V O2 is oxygen consumption, ΔPO 2 is the alveoluscapillary pressure gradient, and D LO2 is the oxygen diffusion capacity or oxygen conductance.The latter depends directly on the alveolar and capillary surface, hematocrit and capillary volume, and inversely on the thickness of the alveoluscapillary barrier (Weibel et al., 1991).The second reason is that the overall function has a measurable upper limit, maximal oxygen consumption V O2max (Weibel, 1998).
The symmorphosis hypothesis has generated great debate that remains unresolved.Evidence in favor of symmorphosis is as abundant as evidence against it (Bacigalupe and Bozinovic, 2002;Canals 2002).Regarding the oxygen pathway, Weibel et al (1992) found that mithocondrial volume, cardiac output and capillary volume varied with body mass with the same allometric exponent as maximal oxygen consumption, suggesting that mithochondria achieve the same rate of oxidative phosphorylation in all mammals, supporting the symmorphosis hypothesis (Weibel et al., 1991;1992).However, the same authors reported that in the lung, the oxygen diffusion capacity did not adjust to functional needs, with the result that species of large body size have an excess capacity relative to that of small species (Weibel, 1998).Jones (1998) also reported an excess oxygen diffusion capacity in well-trained equines.
The original approach of Weibel et al. (1981) was comparison between species, using animals of the same body mass adapted to environments with different energetic requirements (adaptive variation) and animals of different body masses in which the scaling of maximal capacities should be paralleled by structure (allometric variation).However, the concept of symmorphosis may be evaluated within particular species, using a similar protocol (Bacigalupe and Bozinovic, 2002).
In this report we explore matching structures to functional needs by comparing previously reported data of maximal oxygen consumption and the development of the lung in the leaf-eared mouse Phyllotis darwini in warm and cold environments.We discuss whether the state of structural design is commensurate with functional needs from regulated morphogenesis as predicted by the symmorphosis hypothesis (i.e. at the upper limit of the overall function of the respiratory system, the maximum metabolic rate should be paralleled by structural changes) (Weibel et al., 1991;1992;Seymour et al., 2004;2005;Runciman et al., 2005;Canals et al., 2005;Figueroa et al., 2007;Canals et al., 2007).

SAMPLE AND METHODS
Fifteen adult males (Mb = 54.4 ± 17.3 g) and 15 adult females (Mb = 37.7 ± 7.6 g) of Phillotis darwini were trapped in Quebrada de la Plata (coordenadas).The animals were transported to the laboratory, where they were kept in pairs at room temperature with food (sunflower seeds and Champion R rabbit food) and water ad lib.After mating, pregnant females were maintained in individual cages (40x40x20 cms) in climatic chambers and randomly assigned to one of two temperature treatments.One group was maintained at low energetic requirements for thermoregulation at a constant temperature of 30 ± 2º C (warm acclimated group) and a second group maintained at high energetic requirements for thermoregulation, 15 ± 2º C (coldacclimated group), about 10° C below the lower limit of thermoneutrality for this species (Bozinovic et al., 1988).After the offspring were born, three or four unrelated individuals were selected for each environmental condition at days: 1 (neonates), 7, 14, 21 and 60 (adult).
The lung volume, the alveolar surface density and the thickness of the alveoluscapillary barrier were measured by means of water displacement and the stereological method in optical and electronic transmission microscopy, respectively.
From these structural measurements, the morphometric oxygen diffusion capacity (tissue) was estimated using , where D t O 2 is the oxygen diffusion capacity of the alveolo-capillary barrier (tissue) and κ is Krogh's diffusion coefficient κ = 4.1 • 10 -10 cm 2 s -1 mbar -1 = 4.1 • 10 -12 cm 2 • s -1 • Pa -1 (Gehr et al., 1981).AS d is the alveolar surface density, Vp is the parenchymal lung volume and τ h is the harmonic mean thickness of the blood-gas barrier.The total air-erythrocyte oxygen diffusion capacity was estimated with D L O 2 ≈ D t O 2 / 10, a reasonable estimator derived from the ratio D L O 2 /D t O 2 (Canals et al., 2005).
In all animals maximal oxygen consumption was determined in an openflow respirometer system (Sable Systems).All measurements were made during the resting phase (8 to 18: 00 hours) of the species.Using the oxygen conductance and maximal oxygen consumption during ontogeny reported by Canals et al. (2009a;b), we estimated the gradients of partial pressure between air and blood (ΔPO 2 ) necessary to sustain the maximum metabolism of each animal from ΔPO 2 = VO 2max / D L O 2 .Because the usual values of ΔPO 2 in mammals are around 7.5 kPa or 60 mmHg, the ratio between this value and that necessary to satisfy maximum oxygen consumption was used as a crude estimate of the safety factor associated with oxygen diffusion.We used a non-parametric ANOVA to estimate safety factors.Other methodological details are reported in the cited articles (Canals et al., 2009 a;b)

RESULTS
The gradients of partial pressure between air and blood (ΔPO 2 ) necessary to sustain the maximum metabolism of each animal were close to the usual values in young mammals (7.5 kPa or 60 mmHg), but in adults ΔPO 2 needs were lower (Table 1),.
The ratio between this value and the value necessary to satisfy maximum oxygen consumption provides a crude estimate of the safety factor (Sf) associated with oxygen diffusion.Estimated safety factors of young individuals of both groups were very close to unity; and in one group it fell below one.This suggests that the respiratory system design is strictly linked to maximum capacities during ontogeny, as suggested by symmorphosis.Safety factors were not affected by the acclimation temperature (F 1,21 = 1.002, p = 0.328).However, we found differences among age groups (F 4,21 = 3.13, p = 0.036).Multiple comparisons revealed that safety factors of adults were different from those of all other groups, while other groups did not show significant differences (Table 1, Figure 1).

DISCUSSION
From an evolutionary point of view, several objections have been proposed to symmorphosis.For example, i) organisms perform different functions, not just one; consequently constraints are pervasive from reaching a single optimal solution; ii) biological materials have limitations related to their own histories; iii) energetic efficiency is not necessarily what selection maximizes; iv) environments are always changing and selection cannot follow the rhythm of that change; and vi) genetic drift operates in all populations and can be an important factor in determining the phenotype (Garland, 1998;Bacigalupe and Bozinovic, 2002).
The authors who proposed the symmorphosis hypothesis were surprised when they observed that the diffusing capacity of the lung was only partly adjusted to maximal oxygen capacity both in adaptative and allometric variation (Taylor and Weibel, 1981;Weibel et al., 1991;1992), so species of great body size had excess diffusing capacity, whereas smaller species did not.For example, while the safety factors of small animals are small, they can reach values as high as 6 in some artiodactyls of large size (Table 2).Safety factors of other biological structures vary between 1 and 10, most of them being between 1.3 and 6 (Diamond, 1988).Alexander (1998) proposed that the presence of safety factors contradicts the material economy proposed in the hypothesis of symmorphosis, but is consistent with optimization of organs and organisms whether the role of natural selection is incorporated.A safety factor with both low energetic cost and minimum fail probability would be favored by natural selection (Alexander, 1998).The same author showed theoretically that in a system composed of a chain of organs, the probability of failure of the entire chain can be minimized by i) increasing the value of the safety factor of a particular organ instead of another and ii) increasing the value of the safety factor of the organ with lowest predictability (Alexander, 1997).
The advanced results during the ontogeny of P. darwini agree the symmorphosis hypothesis, in a similar way that do the studies of Seymour et al. (2004Seymour et al. ( , 2005) ) and Runciman et al. (2005) in birds.They found that altricial pelicans and precocial turkeys have a parallel allometry between VO 2max and DLO 2 , consistent with the concept of Symmorphosis during development.The variability found in VO 2max and DLO 2 was attributable to age differences between the experimental groups, but there is some residual variability attributable to individual or possible sex differences among individuals.While the latter variable was not controlled, TABLE 1 Mass specific oxygen diffusion capacity (D L O 2 /m b ) maximum metabolic rate (VO 2max ) (from Canals et al. 2009a,b), required alveolo-capillary gradient of partial oxygen pressures (ΔPO 2 = VO 2max / D L O 2 ) and safety factor (Sf = 7.5kPa/ ΔPO 2 ) in individuals of different ages of Phyllotis darwini acclimated to two environmental temperatures, 15° and 30° C from gestation).Values expressed as average ± 1 standard deviation.Asterisks denote significant differences among groups after the posteriori Tukey test.Our results also showed that in the adult stage the safety factors were greater than 2, which suggests that in this stage animals developed a structure greater than that required by the maximum capacities (see also Gehr et al., 1981;Taylor and Weibel 1981;Taylor et al., 1996;Weibel et al., 1991;1992 for studies in other mammal species).On the basis of Bohr's equation, comparisons between animals of different size are justified; since D L O 2 should be proportional to VO 2max based on the strong assumption that ΔPO 2 is independent of body size.When this is not the case, larger animals may have lower ΔPO 2 than smaller animals, and then the safety factor in adults could be overestimated.However there is no empirical evidence to support that ΔPO2 varies with body mass (Weibel, 1983).
Our results are consistent with an excess of D L O 2 in adults because during postnatal development there is a stage of high energetic requirements that necessarily implies a large refinement of respiratory capacities, leading to a full adjustment between structure and maximal capacity (i.e. a safety factor close to unity).But this refinement is maintained consistently in both experimental groups (15 °C and 30 °C) in the adult age, in spite of a decrease in energetic requirements per unit of mass.This phenomenon results in an excess of structure which constitutes a safety factor that appears to protect P. darwini from the transient challenges of highly energetic environmental demands.In this sense, a high safety factor in the respiratory system of adults could be a consequence of the symmorphosis that operates during ontogeny and does not provide support to a rejection of this hypothesis.This result suggests that symmorphosis should always be tested during organism development, in which structural design may be commensurate with functional needs from regulated morphogenesis.

Figure 1 :
Figure 1: Estimated safety factor of lungs in Phyllotis darwini during development at two environmental temperatures, 15° (cold) and 30° C (warm).The solid line represents a perfect adjustment of morphometric oxygen diffusion capacity to the maximal oxygen consumption for a usual alveolus-capillary gradient of partial oxygen pressures (7.5 kPa).