Estimation of Instantaneous Gas Exchange in Flow-Through Respirometry Systems: A Modern Revision of Bartholomew's Z-Transform Method

Flow-through respirometry systems provide accurate measurement of gas exchange over long periods of time. However, these systems have limitations in tracking rapid changes. When an animal infuses a metabolic gas into the respirometry chamber in a short burst, diffusion and airflow in the chamber gradually alter the original signal before it arrives at the gas analyzer. For single or multiple bursts, the recorded signal is smeared or mixed, which may result in dramatically altered recordings compared to the emitted signal. Recovering the original metabolic signal is a difficult task because of the inherent ill conditioning problem. Here, we present two new methods to recover the fast dynamics of metabolic patterns from recorded data. We first re-derive the equations of the well-known Z-transform method (ZT method) to show the source of imprecision in this method. Then, we develop a new model of analysis for respirometry systems based on the experimentally determined impulse response, which is the response of the system to a very short unit input. As a result, we present a major modification of the ZT method (dubbed the ‘EZT method’) by using a new model for the impulse response, enhancing its precision to recover the true metabolic signals. The second method, the generalized Z-transform (GZT) method, was then developed by generalizing the EZT method; it can be applied to any flow-through respirometry system with any arbitrary impulse response. Experiments verified that the accuracy of recovering the true metabolic signals is significantly improved by the new methods. These new methods can be used more broadly for input estimation in variety of physiological systems.     

Metabolic and water loss rates of two cryptic species in the African velvet worm genus Opisthopatus (Onychophora)

Velvet worms (Onychophora) are characterised by a dearth of mechanisms to retain water, yet recently identified cryptic species are located in areas with seemingly different climates. Using flow-through respirometry, this study determined the metabolic, water loss and cuticular water loss rates of two cryptic species of Opisthopatus cinctipes s.l. from locations that differ in their current climate. When controlling for trial temperature and body mass, velvet worms from the drier and warmer site had significantly lower water loss rates than the wetter and cooler site. Mass-corrected metabolic rate and cuticular water loss did not differ significantly between the two sites. The scaling exponent for the relationship between log metabolic rate and log body mass for O. cinctipes s.l. declined with an increase in temperature from 5 to 15 °C. Females in the two cryptic Opisthopatus species had higher metabolic, water loss and cuticular water loss rates than males, which may represent the increased energetic demands of embryonic growth and development in these viviparous taxa.     

Influence of respirometry methods on intraspecific variation in standard metabolic rates in newts

Standard metabolic rate (SMR) is both a highly informative and variable trait. Variation in SMR stems not only from diverse intrinsic and extrinsic factors, but also from the use of diverse methods for metabolic measurements. We measured CO(2) production (VCO(2)) and oxygen consumption rates (VO(2)) using two flow-through respirometry modes, continuous and intermittent (stop-flow), to evaluate their potential contribution to SMR variation in Alpine newts, Ichthyosaura alpestris. Both respirometry modes yielded similar and repeatable VCO(2) values. Although VO(2) was highly repeatable, continuous respirometry produced lower VO(2) than the intermittent method. During intermittent measurements, the total number of activity bouts was higher than during continuous respirometry trials. Statistical correction for disparate activity levels minimized variation in oxygen consumption between respirometry modes. We conclude that use of either method of flow-through respirometry, if properly applied, introduced less noise to SMR estimates than a variation in activity levels.     

Flight energetics and dispersal capability of the fire ant, Solenopsis invicta Buren

Experiments were conducted to estimate the flight capabilities of fire ant (Solenopsis invicta Buren) alates. These experiments were designed to: (1) quantify energetic expenditure during fixed flight; (2) characterize metabolic substrates of male and female alates; (3) estimate flight speed of male and female alates; and (4) quantify wingbeat frequency and water loss of females during flight. Flying males (in closed-system respirometry) increased metabolic rate approximately 38.4-fold over resting rate. Females increased metabolic rate approximately 51-fold (closed-system respirometry) and 48-fold (flow-through respirometry) over resting rate. Female alates had a mean respiratory quotient (RQ) of 0.999, indicating reliance on carbohydrates. The mean RQ of males was significantly lower (0.867). The flight speed of females on a circular flight mill averaged approximately 0.7 m s(-1), and increased with temperature but decreased with increasing body mass. The flight speed of males was 43% greater (approximately 1.0 m s(-1)) and increased linearly with temperature and increasing body mass. Female alates lost an average of 1.8 mg water h(-1) during flight. A simple energetics model, combined with previous work on the nutrient content of S. invicta and patterns of CO(2) release observed in this study, indicate that the flight capability of S. invicta female alates is limited to <5 km in the absence of wind.     

Standard and digestive metabolism in the banded water snake, Nerodia fasciata fasciata

Estimating energy costs by respirometry is fundamental to many studies of the ecology, behavior and evolution of reptiles. However, traditional respirometry procedures seldom incorporate objective techniques for removal of outliers from estimates of metabolic parameters. We demonstrate how computer-automated respirometry equipment, which records many respiratory measurements over short intervals, can be coupled with mathematical procedures to produce robust estimates of pre- and post-prandial metabolism in banded water snakes (Nerodia fasciata fasciata). Standard metabolic rate of N. f. fasciata was estimated to be 1.21 ml O2/h (mass = 30.21 +/- 0.74 g) at 25 degrees C. After ingestion of a fish equaling 20% of their body mass, snakes exhibited a fivefold increase in metabolic rate with peak O2 consumption rate (VO2) reaching 6.5 ml O2/h. Total cost of digestion was 5.44 kJ, equivalent to approximately 21% of the energy in the meal. Repeated measurements of metabolism in the same individuals revealed that our methods yielded similar results, even when individuals exhibited different patterns of VO2 variation between respiratory trials. Our results underscore the importance of obtaining many VO2 measurements, coupled with objective removal of outlier values from estimates of metabolic rate, especially when metabolic values are to be interpreted in a comparative context.     

Ecological implications of body composition and thermal capabilities in young antarctic fur seals (Arctocephalus gazella)

In comparison with other homeotherms, young recently weaned marine mammals in high latitudes face exceptional energetic demands when foraging and thermoregulating. Lipids are an important source of energy and a major component of insulation that allows them to meet these demands. To examine the role of lipid stores in a high-latitude pinniped, we measured the body composition and thermoregulatory capabilities of Antarctic fur seal (Arctocephalus gazella) pups and yearlings by using flow-through respirometry and hydrogen isotope dilution. From these data, we constructed a model to examine the importance of postweaning fasting capability in free-ranging young fur seals. Resting metabolic rates were different for pups and yearlings measured in 0.6 degrees C water, 10.3 degrees C water, and ambient air; however, mass and percent lipid as covariates accounted for the different metabolic responses in pups and yearlings for all treatments. The estimated lower critical temperature for combined pups and yearlings was 14.4 degrees C, 10 degrees -15 degrees C above water temperatures normally experienced by Antarctic fur seals. Modeling predicted that a weaned fur seal pup would survive at sea from 9.8 to 36.2 d before succumbing to starvation. The most likely maximum travel distance within this time constraint suggests that food resources close to the natal rookery are important to first-year survival for this species.     

The effects of mass and age on standard metabolic rate in house crickets

Abstract. This study employed flow-through respirometry to measure the oxygen consumption rates (VO₂) of inactive male house crickets, Acheta domesticus L. (Orthoptera: Gryllidae), and to quantify the effects of body mass and adult age on standard metabolic rate (SMR). The Vo₂ increased with male body mass at a rate similar to that found in other studies of insect aerobic metabolism. The data reported in this study are combined with published data from other species of Orthoptera to generate a consensus allometric relationship between SMR and body mass for the Order. In general, the Orthoptera expend 2–3 times the energy per unit of body mass when inactive as compared to other arthropods, such as tenebrionid beetles, ants and spiders. Possible explanations for this substantial difference are discussed. By contrast to body mass, mass-specific Vo₂ decreased with increasing male age. This age effect has previously been reported for mammals but is not well established for insects, and its implications for the preference of cricket females for older mates is discussed. As energy expended for metabolic maintenance comprises 78% of a male cricket's daily energy budget, changes in SMR may have a substantial effect on the energy available for reproduction.     

Artificial selection on metabolic rates and related traits in rodents

Artificial selection experiments are potentially powerful, yetunder-utilized tool of evolutionary and physiological ecology.Here we analyze and review three important aspects of such experiments.First, we consider the effects of instrumental measurement errorsand random fluctuations of body mass on the total phenotypicvariation. We illustrate this with the analysis of measurementsof oxygen consumption in an open-flow respirometry set-ups.We conclude that measurement errors and fluctuations of bodymass are likely to reduce the repeatability of oxygen consumptionby about one third. Using published estimates of repeatabilityof metabolic rates we also showed that it does not tend to declinewith increasing time between measurements. Second, we reviewdata on narrow sense heritability (h²) of metabolic rates inmammals. The results are equivocal: many studies report verylow (     

Energy expenditure, body-weight and foraging performance of Storm Petrels Hydrobates pelagicus breeding in artificial nesting chambers

Many avian species, such as Storm Petrels Hydrobates pelagicus, are intolerant of disturbance at the nest, which complicates the collection of data relating to metabolic rate and the use of body reserves during incubation. I describe the design of an artificial nest chamber, which is simple and inexpensive to construct and facilitates the collection of such data. Eighty-one nest chambers situated in a large colony of breeding Storm Petrels had high occupancy rates (29/81 in each of 2 years), and the breeding success of birds nesting in boxes was similar to that of pairs nesting in natural crevices. Direct measurement of carbon dioxide production using standard respirometry techniques and estimations of metabolic rate based on the rates of mass loss during incubation indicated close agreement between the two methods of estimating energy consumption. Assuming the metabolic requirements during incubation are furnished entirely from stomach oil, 76% of the daily mass lost represented stomach oil catabolism. The duration of incubation shifts was unrelated to the body mass, and presumably to body reserves, of Storm Petrels on arrival at the nest. Shifts were usually terminated by the return of the foraging partner. The body mass of birds returning from foraging was relatively constant and was unrelated to the amount of time spent foraging at sea, indicating that the decision rule to return from foraging was the acquisition of a threshold level of body mass (about 31 g). There was a negative relationship between the duration of foraging trips and the body mass of Storm Petrels at departure from the nest and a positive relationship between trip duration and the net mass gain at sea. The use of nestboxes based on the design described here would have a wide variety of applications in facilitating data collection for many cavity-or burrow-nesting species which are sensitive to disturbance.     

Measuring the efficiency of sound production

Sound production efficiency is a complex phenotypic trait that incorporates biochemical and mechanical events beginning with substrate oxidation and ending with the radiation of sound. Its accurate measurement is significant in understanding the mechanisms and energetics underlying acoustic signaling and sexual selection. I show that in the short-tailed cricket Anurogryllus arboreus Walker, acoustic performance is apparently the same in acoustic free fields and in the reverberant conditions of a respirometry chamber. I present three methods for simultaneous and nearly simultaneous determination of calling metabolic rate and acoustic power output. The new methods yielded metabolic rates 3%-6% lower than matched controls using traditional flow-through respirometry (mean=8.1 mW); however, none of theses differences were statistically significant. I also evaluate four methods for determining the efficiency of sound production. The means of an individual's efficiencies calculated using these methods vary between 0.50% and 0.60%, with no statistically significant differences between the methods. I conclude with a critical evaluation of these techniques.     

Quantitative genetic variation of metabolism in the nymphs of the sand cricket, Gryllus firmus, inferred from an analysis of inbred-lines

Compared with morphological and life history traits, quantitative genetic variation of metabolic and related traits in animals has been poorly studied. We used flow-through VCO(2) respirometry and simultaneous activity measurement on nymphs of the sand cricket (Gryllus firmus) from inbred lines to estimate broad-sense heritability of four metabolic variables. In addition, we measured a number of linear dimensions in the adults from the same inbred lines. There were significant multivariate effects of inbred lines for all traits and broad-sense heritability for physiological traits was 4.5%, 5.2%, 10.3% and 8.5% for average, resting, minimum and maximum CO(2) production in nymphs, respectively. Though the MANOVA indicated significant genetic variation among inbred lines in adult morphology, the broad-sense heritabilities were relatively low ranging from 0-18%. Our results indicate that the heritabilities of metabolic measures are large enough to potentially respond to selection.     

Aerobic metabolism of American alligators, Alligator mississippiensis, under standard conditions and during voluntary activity

We measured the rate of consumption of oxygen by alligators in a dry metabolic chamber and in a tank of water where they were free to dive and surface at will at 10-35 degrees C, a range spanning most of the body temperatures experienced by alligators in nature. Neither the standard metabolic rate nor the rate of oxygen consumption during one hour of sustained, voluntary activity varied with body mass, month of the year, duration of fasting before measurement, or experimental condition (terrestrial vs aquatic). Voluntary diving is not accompanied by any reduction in standard metabolic rate; these results and those of others suggest that the "diving reflex" of alligators is probably employed only in emergencies. Spontaneous activity for one hour is accompanied by a 1.9-4.4 fold rise in oxygen consumption; this factorial increase is less than that for other reptiles induced to maximal activity for brief intervals. Both standard and active oxygen consumption rise significantly with body temperature.     

In vitro control analysis of an enzyme system: Experimental and analytical developments

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, C_LDH and C_pump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.     

Mass transfer effects on DNA hybridization in a flow-through microarray

The goal of this study is to assess the influence of mass transfer phenomena on DNA hybridization kinetics in a flow-through, porous microarray for fast molecular testing. We present a scaled mathematical model of coupled convection, diffusion and reaction in porous media, which was used to simulate hybridization kinetics and to analyze the influence of convective transport on the reaction rate. In addition to computer simulations, we also present experimental data of hybridization collected on our microarray system for different flow rates. The results reported in this paper provide for a better understanding of the interaction between reaction and mass transfer processes during flow-through hybridization and suggest criteria for system design and optimization.     

Construction of a low cost and highly sensitive direct heat calorimeter suitable for estimating metabolic rate in small animals

Although the concept of a metabolic rate is readily understood, actual measurement of metabolism has proved much more difficult. The numerous strategies for estimation of metabolic rate all result in an incomplete accounting. Respirometry or gas exchange is the most widely used approach but mostly ignores the anaerobic component. Here, we describe a readily-built and low cost direct heat calorimeter that may be coupled with standard respirometry equipment to provide a more complete portrait of metabolism. The device is sensitive and provides a predictable measurement of heat flow from an organism.     

Inter-sexual differences in resting metabolic rates in the Texas tarantula, Aphonopelma anax

Intra-specific variation in life history and mating strategies can lead to differences in energy allocation and expenditure in males and females. This may, in turn, explain large-scale evolutionary patterns. In this study, I investigated the effects of body mass, temperature and sex on resting metabolic rates (RMRs) in sexually mature male and female tarantulas (Aphonopelma anax (Chamberlin)), a species that exhibits extreme inter-sexual differences in life history after reaching sexual maturity. RMRs were measured as rates of CO(2) production in an open-flow respirometry system at 20, 25, 30 and 35 degrees C. These temperatures are typical to what this species experiences under natural conditions. In addition, a respiratory quotient (RQ) of 0.92 was calculated from rates of CO(2) production and O(2) consumption in a closed, constant-volume respirometry system. As expected, RMRs increased with increasing temperature and body mass. However, after adjusting for the influence of body mass, males had substantially higher metabolic rates than females at each temperature. This higher metabolic rate is proposed as an adaptive strategy to support higher energetic demands for males during their active, locomotory search for females during the mating season.     

Resting metabolic rate can vary with age independently from body mass changes in the Colorado potato beetle, Leptinotarsa decemlineata

Temperature and mass dependency of insect metabolic rates are well known, while less attention has been given to other factors, such as age. Among insect species that experience seasonal variation in environmental conditions, such as in temperate latitudes, age may also have indirect effects on the metabolic rate. We examined the effect of age on the resting metabolic rate of Leptinotarsa decemlineata during 11 days after adult emergence by using flow-through respirometry. Age had a significant mass-independent effect on metabolic rate of beetles. A twofold increase in metabolic rate occurred during the first 2 days of adult life after which metabolic rate decreased with age relatively slowly. Ten day-old adult beetles had a metabolic rate similar to newly emerged beetles. The beetles have to be able to complete their development and prepare for overwintering during the relatively short favourable summer periods. Therefore, the observed pattern in metabolic rate may reflect physiological changes in the pre-diapause beetles adapted to temperate latitudes.     

Basal rate of metabolism and temperature regulation in Goeldi's monkey (Callimico goeldii)

Basal rate of metabolism (BMR) and temperature regulation are described for Goeldi's monkey (Callimico goeldii), a threatened New World primate species of the family Callitrichidae. Measurements were conducted on sleeping individuals during the night, using a special nestbox designed to serve as a respirometry chamber, such that test animals remained undisturbed in their customary surroundings. Oxygen consumption was measured at ambient temperatures between 17.5 and 32 degrees C for 10 individuals with an average body mass of 557 g. Average BMR was 278+/-41 ml O(2) h(-1), which is lower than the value predicted on the basis of body mass. Individual differences in BMR were significant even when body mass was accounted for. Body temperature was measured in five individuals below thermoneutrality and averaged 36+/-0.3 degrees C. The corresponding thermal conductance averaged 29.3+/-2.2 ml O(2) h(-1) degrees C(-1), which is similar to the expected value. The metabolic and thermoregulatory patterns observed in C. goeldii resemble those of the closely related marmosets and tamarins. Low BMR is presumably associated with limited access to energy resources and may be directly linked with phylogenetic dwarfing in the family Callitrichidae.     

Open-flow respirometry under field conditions: How does the airflow through the nest influence our results?

Open-flow respirometry is a common method to measure oxygen-uptake as a proxy of energy expenditure of organisms in real-time. Although most often used in the laboratory it has seen increasing application under field conditions. Air is drawn or pushed through a metabolic chamber or the nest with the animal, and the O₂ depletion and/or CO₂ accumulation in the air is analysed to calculate metabolic rate and energy expenditure. Under field conditions, animals are often measured within the microclimate of their nest and in contrast to laboratory work, the temperature of the air entering the nest cannot be controlled. Thus, the aim of our study was to determine the explanatory power of respirometry in a set-up mimicking field conditions. We measured O₂ consumption of 14 laboratory mice (Mus musculus) using three different flow rates [50 L*h⁻¹ (834 mL*min⁻¹), 60 L*h⁻¹ (1000 mL*min⁻¹) and 70 L*h⁻¹ (1167 mL*min⁻¹)] and two different temperatures of the inflowing air; either the same as the temperature inside the metabolic chamber (no temperature differential; 20 °C), or cooler (temperature differential of 10 °C). Our results show that the energy expenditure of the mice did not change significantly in relation to a cooler airflow, nor was it affected by different flow rates, despite a slight, but significant decrease of about 1.5 °C in chamber temperature with the cooler airflow. Our study emphasises the validity of the results obtained by open-flow respirometry when investigating energy budgets and physiological responses of animals to ambient conditions. Nevertheless, subtle changes in chamber temperature in response to changes in the temperature and flow rate of the air pulled or pushed through the system were detectable. Thus, constant airflow during open-flow respirometry and consequent changes in nest/chamber temperature should be measured.     

Glucose oxidation and nonoxidative glucose disposal during prolonged fasts of the northern elephant seal pup (Mirounga angustirostris)

Elephant seal weanlings demonstrate rates of endogenous glucose production (EGP) during protracted fasts that are higher than predicted on the basis of mass and time fasting. To determine the nonoxidative and oxidative fate of endogenously synthesized glucose, substrate oxidation, metabolic rate, glycolysis, and EGP were measured in fasting weanlings. Eight weanlings were sampled at 14 days of fasting, and a separate group of nine weanlings was sampled at 49 days of fasting. Metabolic rate was determined via flow-through respirometry, and substrate-specific oxidation was determined from the respiratory quotient and urinary nitrogen measurements. The rate of glucose disposal (Glu((R)(d))) was determined through a primed, constant infusion of [3-(3)H]glucose, and glycolysis was determined from the rate of appearance of (3)H in the body water pool. Glu((R)(d)) was 1.41 ± 0.27 and 0.95 ± 0.21 mmol/min in the early and late fasting groups, respectively. Nearly all EGP went through glycolysis, but the percentage of Glu((R)(d)) oxidized to meet the daily metabolic demand was only 24.1 ± 4.4% and 16.7 ± 5.9% between the early and late fasting groups. Glucose oxidation was consistently less than 10% of the metabolic rate in both groups. This suggests that high rates of EGP do not support substrate provisions for glucose-demanding tissues. It is hypothesized that rates of EGP may be ancillary to the upregulation of the tricarboxylic acid cycle to meet high rates of lipid oxidation while mitigating ketosis.