Real-time measurement of metabolic rate during freezing and thawing of the wood frog, Rana sylvatica: implications for overwinter energy use

Ectotherms that overwinter without feeding are wholly dependent on their body energy reserves to fuel winter metabolism, as well as development, activity and reproduction in the spring. For example, reproductive output of female goldenrod gall flies is determined by lipid reserves remaining in the spring (Irwin and Lee, 2000). Because metabolism of ectotherms (and many hibernating mammals) is determined by the ambient temperature, overwinter energetics can mediate the relationship between environmental conditions and the persistence and performance of populations, and therefore the geographic distribution of animals (Humphries et al., 2002). Overwinter energy use is determined not only by direct temperature–metabolic rate relationships, but also by physiological thresholds, which can also influence energy use; for example, lower critical temperature signals have been shown to increase energetic costs of thermoregulation in mammals (Humphries et al., 2002), and metabolic suppression associated with ice formation reduces overwinter energy consumption in insects (Marshall and Sinclair, 2012). Thus, identifying these thresholds, and the magnitude of their effects, is an important component of understanding the energetics of overwintering.

Some frogs, turtles and lizards are freeze tolerant, surviving internal ice formation as part of their overwintering strategy (Storey and Storey, 1992). The freezing process is usually initiated by contact with external ice; however, ice-nucleating agents have been found in the skin of the brown tree frog, Litoria ewingii, and in the blood and gut of the wood frog, Rana sylvatica (Wolanczyk et al., 1990; Lee and Costanzo, 1998; Rexer-Huber et al., 2011). In R. sylvatica, the best-studied freeze-tolerant vertebrate, ice formation initiates a signalling cascade that leads to the production of a variety of stress-related proteins and the mobilisation of glycogen from liver reserves. Glycogen is cleaved into glucose, which acts as a cryoprotectant (Layne and Lee, 1995; Storey and Storey, 1996; Storey, 2004; Storey, 2008). Once freezing is initiated, maximal ice formation takes 24 h or more in R. sylvatica (Lee et al., 1992), during which cardiac function can continue for more than 12 h (Costanzo et al., 1993). Although ventilation ceases as ice content in the body increases, frogs may also respire cutaneously until freezing ceases circulation to the skin. Unfrozen overwintering frogs probably primarily catabolise lipids [cf. frogs overwintering in water (Tattersall and Ultsch, 2008)], but once the frog is completely frozen, metabolism is largely anaerobic, and is mainly fuelled by carbohydrates (Storey and Storey, 1986). Cardiovascular function of R. sylvatica is re-established within 1 h of thawing, with recovery of breathing and hind leg reflexes taking longer (Layne and First, 1991). During thawing, glucose is cleared either directly from the blood or after reabsorption from the bladder, and converted back to glycogen in the liver (Storey and Storey, 1986; Costanzo et al., 1997).

The production, distribution and re-sequestration of carbohydrate cryoprotectants have energetic costs. The metabolic rate of frogs is higher after thawing (Layne and Kefauver, 1997; Layne, 2000; Voituron et al., 2009), suggesting that the energetic cost of freezing and thawing likely includes additional costs beyond the simple effect of temperature on metabolic rate, such as repair of accumulated damage, re-establishment of osmotic and ionic gradients, and re-synthesis of damaged proteins. Metabolic rate in frozen frogs may be suppressed due to high concentrations of solutes, reduced cellular volume and accumulated urea (Muir et al., 2008). To date, measurements of metabolism associated with low temperature in freeze-tolerant amphibians and reptiles have been conducted with closed-flow systems and/or at static temperatures (Voituron et al., 2002a; Voituron et al., 2009), which means that the direct metabolic costs of the freezing and thawing processes are unknown.

Real-time measurement of metabolic rate with temperature (or other) changes is possible using both direct calorimetry (Hansen et al., 2006) and respirometry (Lighton and Turner, 2004). Sinclair et al. (Sinclair et al., 2004) measured metabolic rate in a freeze-tolerant tineid caterpillar, concluding that freezing and thawing in this insect did not have an energetic cost. The release of a large amount of CO₂ associated with the onset of freezing was hypothesised to be caused by the compression of the tracheal system with ice expansion in the body, rather than by an increase in metabolism or change in CO₂-buffering capacity of the haemolymph.

Voituron et al. (Voituron et al., 2002b) predicted that freeze tolerance should be favoured over freeze avoidance as an energy conservation strategy; however, an important assumption of this model is that any direct costs of a freezing event are offset by energy savings when frozen. Thus, a model of overwinter energy costs would need to include not only the temperature effects on metabolic rate, but also the energetic costs of freezing and thawing, the degree to which metabolic rate is suppressed when frozen, and some consideration of the substrates used to fuel metabolism during winter. Total depletion of carbohydrate reserves will prevent the production of glucose cryoprotectants, leading to death if the frog freezes. Depletion of lipid energy reserves also has potential fitness consequences, as R. sylvatica does not feed before breeding in the early spring (K.B.S., unpublished). Thus, the energy reserves remaining at the end of winter are all that is available to fuel energetically costly activities associated with reproduction, including locomotion, calling, amplexus and egg production (Irwin et al., 2003; McLister, 2003). A winter energy budget has not previously been developed for any overwintering, freeze-tolerant vertebrate, but such a model would allow a test of the assumptions of Voituron et al. (Voituron et al., 2002b).

Here we use open-flow respirometry to measure CO₂ release (as a proxy to metabolic rate) in R. sylvatica during a short freeze–thaw cycle. We determine the cost of freezing and thawing, and use these values to parameterise a numerical simulation of overwinter energy use and freeze–thaw based on microclimate temperatures from two locations over a single winter. This allows us to partition the utilisation of carbohydrate and lipid energy reserves, and to determine the relative importance of freezing tolerance to the overwinter energetics of this species.

Microclimate temperatures were recorded hourly with iButton DS1922L Thermochron data loggers (Maxim-Dallas Semiconductor, Sunnyvale, CA, USA) placed on the ground beneath 2–5 cm of leaf litter and attached to a steel peg with a length of non-conductive string. The data loggers were placed in a woodlot near Ottawa dominated by black walnut (Juglans nigra), ash (Fraxinus spp.) and cherry (Prunus spp.). Temperatures were recorded at two locations ~30 m apart in the 2008–2009 winter. The data logger site is within 60 km of the site where frogs were collected, and wood frogs overwinter underneath leaf litter in forests such as this (Regosin et al., 2003; Baldwin et al., 2006) and have been present in all such woodlots that have been investigated (K.B.S., personal observation). For the purposes of numerical simulation (below), we used data from 1 November to 16 April to represent winter, as during our recordings, this period encompassed all instances of sub-zero microclimate temperatures. The soil data loggers were supplemented with an unshielded data logger at 2 m on the north-facing side of a nearby tree (‘canopy temperature’), which was expected to approximate meteorological air temperature observations (with the exception that it is exposed to some solar radiation; see supplementary material Fig. S1 for a detailed comparison).

Male Rana sylvatica LeConte 1825 were collected from woodlands near Ottawa. Autumn-collected frogs were collected in the second week of October 2010, held on crushed ice and transferred to Carleton University. Spring-collected frogs were collected at breeding ponds on 10–11 April 2011, kept in coolers on snow and transferred to Carleton University. All frogs were given an initial wash in a tetracycline bath, then placed in plastic boxes with a bed of damp sphagnum moss and held in an incubator at +3°C. Frogs were transferred to the University of Western Ontario in containers cooled with ice packs in mid-January (autumn-collected) or mid-April (spring-collected) 2011. Prior to being used in experiments, frogs were held in groups of 10 with moist sphagnum moss in 2.6 l plastic containers in the dark at +4±1°C. After experiments, frogs were held individually on a moist paper towel in 720 ml plastic containers at +4±1°C. Laboratory experiments were conducted under University of Western Ontario animal care guidelines, protocol AUP-2010-016.

Respirometry was conducted in an 85 cm³ acrylic chamber sealed at each end with an aluminium plug. A channel was milled into the underside of the chamber to reduce its thickness and allow freezing of the frog to be monitored with three 36 AWG Type-T thermocouples (Omega, Laval, QC, Canada) applied to the outside of the bottom of the chamber. The thermocouple that gave the clearest signal of freezing (and was therefore positioned closest to the frog) was used in analyses of each data set. A fourth, reference thermocouple was placed on top of the chamber; this reference thermocouple allowed us to detect deviations between the trajectory of bath and chamber temperatures and thus identify freezing and melting events. Thermocouples were connected to a TC2000 and recorded via a UI2 analog–digital interface (both Sable Systems International, Las Vegas, NV, USA). Activity was monitored with a Sable Systems AD-1 infrared activity detector. The chamber containing the frog, the reference thermocouple and an identical reference chamber (used as a baseline) were then placed into a plastic bag and submerged in the bath of a refrigerated circulator (Proline RP3530, Lauda, Wurzburg, Germany) containing 50:50 ethylene glycol:water (v/v).

Dry, CO₂-free air was directed through either the baseline chamber or the chamber containing the frog by a BL-2 baseline unit (Sable Systems International) at ~46 ml min⁻¹ [controlled by a mass flow valve (Sierra Instruments, Monterey, CA, USA) and measured by an SS3 sub-sampler (Sable Systems International)]. The air was pre-cooled before entering the baseline chamber by being passed through a 172 cm×6.2 mm copper coil tube submerged in the bath fluid. Water vapour was scrubbed post-animal with magnesium perchlorate, and CO₂ emission was then determined with a CA-10 CO₂ analyser (Sable Systems International). All instruments were interfaced to a computer using a UI2 AD interface (Sable Systems International), and data were acquired at 1 s intervals using Expedata software (Sable Systems International).

Frogs were weighed (Mettler PE 300, Columbus, OH, USA) and a silver iodide paste (1:4 AgI:water, v:v) was applied to the bottom of both hind feet to inoculate freezing before they were placed in the respirometry chamber at +4°C for 130 min (autumn-collected frogs) or 190 min (spring-collected frogs), which included a 20 min baseline recording. They were then cooled at 0.1°C min⁻¹ to 0°C, and from 0 to −2.4°C at 0.05°C min⁻¹. Frogs were held at −2.4±0.1°C for 12 h, and warmed to +4°C at 0.5°C min⁻¹, after which they were held at +4°C for 7.5 h (spring-collected frogs) or 6.5 h (autumn-collected frogs), followed by another baseline recording.

All statistical comparisons were made of CO₂ emission, and means ± s.e.m. are reported throughout. All statistical analyses were conducted in R v.2.13 (R Development Core Team, 2010). CO₂ and were ln-transformed and tested for homoscedasticity using Levene's test for homogeneity of variance in the lawstat package in R (Hui et al., 2008). Comparisons between means were conducted using ANCOVA with initial body mass as a covariate, and temperature of crystallisation (T_c) and body mass were compared among spring- and autumn-collected frogs using Welch's t-tests.

We predicted overwinter energy consumption from microclimate data using a combination of empirical data and assumptions supported by the literature (Fig. 2). We used the CO₂ emission traces to derive a temperature– relationship, and also identified three periods during cooling, freezing and thawing when was substantially in excess of that expected from this relationship. These were: (1) an increase in during cooling, but before the initiation of ice formation (which we henceforth call the ‘cooling threshold’); (2) an increase in upon freezing; and (3) an increase in during thawing (Fig. 1). We assumed that lipid was the main fuel source when the frogs were unfrozen [as is the case for all dormant frogs that have been studied (Fitzpatrick, 1976; Long, 1987; Tattersall and Ultsch, 2008)], but that metabolism during freezing, thawing and while frozen was fuelled by carbohydrate (Storey and Storey, 1986). We then used this simulation to predict CO₂ production from microclimate data (see Marshall and Sinclair, 2012) from the microhabitat temperature recordings, and calculated expected total overwinter carbohydrate and lipid consumption (Fig. 2). We varied each of the parameters in our model in turn to determine the sensitivity of the conclusions to our assumptions.

Because the Q₁₀ estimated during cooling (7.97) was unusually large, we repeated this to obtain coefficients assuming a Q₁₀ of 2.0, which is at the low end expected for biochemical reactions (Hochachka and Somero, 2002). For our modelling, we expected (from most other biological systems) that thermal sensitivity would be less than 8.0 at higher temperatures, so we assumed a Q₁₀ of 2.0 at temperatures higher than an arbitrary threshold of +4°C, and a Q₁₀ of 7.97 at temperatures of +4°C and below. We explored the impact of these assumptions in our sensitivity analyses. From our empirical data, we obtained the average CO₂ production at the cooling threshold (prior to ice formation) of 104.6 μl CO₂ frog⁻¹ event⁻¹ at an average threshold temperature of +1.03°C. From our empirical data we estimated the additional CO₂ production associated with the freezing event to be 565 μl CO₂ frog⁻¹ freezing event⁻¹ and an additional 564 μl CO₂ frog⁻¹ freezing event⁻¹ associated with thawing. We assumed that any drop in temperature below the mean T_c would result in the full energetic cost of freezing, and the energetic cost of thawing was applied only when the temperature increased above the mean temperature where the melt endotherm ended (−0.16°C).

Previous studies have suggested that metabolic rate is depressed beyond direct temperature effects when frozen (Voituron et al., 2009; Marshall and Sinclair, 2012; Zhang and Storey, 2012), but using the Q₁₀ of 7.97, we estimated a CO₂ production of frogs frozen at −3.5°C (9.588×10⁻⁵ ml CO₂ min⁻¹ g⁻¹) that was the same order of magnitude as that observed empirically (2.450×10⁻⁵ ml CO₂ min⁻¹ g⁻¹), so we did not employ any freeze-related depression of metabolism in our main simulation, likely leading to overestimates of energy use while frozen. However, we did explore the consequences of this assumption in our sensitivity analyses. Previous studies have indicated that while frozen, R. sylvatica is dependent on carbohydrate metabolism (Storey and Storey, 1986), and we assumed that, when unfrozen, lipid stores provide the main fuel source (Fitzpatrick, 1976; Long, 1987; Tattersall and Ultsch, 2008). We assumed that carbohydrates were the fuel source during bursts of CO₂ production in cooling, freezing and thawing, and that carbohydrates provided all metabolic fuel when the frogs were frozen. To calculate total lipid consumption, we assumed a respiratory quotient (RQ) of 0.7 and that 2 ml of oxygen is consumed per milligram of lipid oxidized. Total carbohydrate consumption was calculated assuming an RQ of 1.0 and that 0.84 ml of oxygen is consumed per milligram of carbohydrate oxidized. Total energy use was calculated by converting substrate mass to kJ, assuming 17 kJ g⁻¹ carbohydrate and 39 kJ g⁻¹ lipid.

We calculated CO₂ production for each hour of temperature recording, assuming that the temperature remained the same for that hour (see also Marshall and Sinclair, 2012; Williams et al., 2012), and that a frog's body temperature is equilibrated with that of its surrounding microhabitat (this comprises the base model). We then identified events where the temperature dropped below the ‘cooling threshold’, and freeze–thaw events using an approach based on that of Sinclair (Sinclair, 2001), but implemented in R (code available from the authors upon request) (see also Marshall and Sinclair, 2012), and applied the metabolic costs of those events as described above. Frogs were assumed to freeze any time the temperature dropped below the freezing threshold, and to thaw any time the temperature increased above the melting point, and we scaled most of our predictions for a 7.1 g frog (the mean mass of the frogs we used).

We explored the sensitivity of the results of the model to our assumptions and estimated parameters. First, we explored the impact of our assumptions about Q₁₀, and also our assumptions about a change in Q₁₀ at threshold temperatures. We used a Q₁₀ of 4.0 (Voituron et al., 2009); a change to a Q₁₀ of 1.5 above +4°C; a threshold for Q₁₀ change of 0 and 8°C; and a Q₁₀ of 2.0 or 7.97 without a threshold change. Second, we modified the costs of freezing and thawing, and made the freezing and melting points more conservative (shift of T_c to −0.8°C, and melting point to −0.6°C). Finally, we introduced a depression of metabolic rate when frozen to 50, 5 or 0.5% of the value calculated from our equation.

Body mass was allometrically related to at +4°C with an exponent of 0.744±0.305 (F_1,10=5.97, P=0.035), and was retained as a covariate in subsequent analyses. CO₂ emission by frogs during cooling, freezing and thawing was qualitatively similar for all individuals (N=12), and an example trace is shown in Fig. 1C. Upon cooling from +4°C, CO₂ production decreased (Q₁₀=7.97±0.39) until a threshold of 1.03±0.1°C was reached, when CO₂ production increased markedly. This CO₂ increase was not associated with increased activity (apart from ventilation), and we call it the ‘pre-freeze increase’ in CO₂ production. This pre-freeze increase released a mean of 104±17 μl CO₂ frog⁻¹ event⁻¹, and the maximum (0.73±0.049 μl CO₂ min⁻¹ g⁻¹) was always lower than subsequent maxima during freezing. Freezing was readily detected by the thermocouples, and was accompanied by a further sharp increase in , to a mean maximum of 1.11±0.11 μl CO₂ min⁻¹ g⁻¹. Accounting for the projected baseline decline in CO₂ production associated with decreasing temperature, the increase in CO₂ production with freezing amounts to 565±85 μl CO₂ frog⁻¹ freezing event⁻¹. Ventilation was identifiable as regular inflections of the CO₂ trace (Fig. 1). Ventilation ceased 76.9±8.8 min (range: 24–150 min) after the initiation of the exotherm (Fig. 1), but CO₂ emission remained elevated for 465±20 min after the start of freezing, and some activity (presumably movement of the frog stimulated by expansion of ice) occurred after the cessation of breathing in some cases. While frozen, remained stable at 0.174±0.020 μl min⁻¹ frog⁻¹ (Table 1).

Upon rewarming, increased rapidly (Fig. 1). The beginning of thawing was identifiable by a deflection of the frog temperature, and began at −0.16±0.01°C. Thawing took 150.4±8.2 min to complete, and ventilation resumed 93.6±12.3 min after the completion of thawing. The total CO₂ production associated with thawing from the beginning of rewarming to the resumption of ventilation was 564±75 μl CO₂ frog⁻¹ freezing event⁻¹.

The temperature of crystallisation was lower in autumn-collected frogs than in frogs collected in spring (Table 1). There was no significant difference between body mass of frogs collected in autumn and spring (Table 1); however, the autumn-collected frogs lost less mass during the respirometry run (Table 1), probably because the respirometry runs were approximately 5 h shorter for the autumn- versus spring-collected frogs, resulting in less evaporative water loss.

Microclimate temperatures for the 2008–2009 winter (1 November–16 April) from the Ottawa region are shown in Fig. 3 and summarised in Table 2. The buffering effect of leaf litter and snow reduced the amplitude of microclimate temperature fluctuations compared with air temperatures, but the leaf litter temperatures were also increased on clear days due to solar radiation (Fig. 3; supplementary material Fig. S1). Although the mean air temperature was only slightly lower than the means recorded in the leaf litter (Table 2), the minimum temperature recorded in air (−30.7°C) was much lower than the minimum temperature measured in the leaf litter (−5.4°C at location 2). Snow cover meant that most of the freeze–thaw cycles in the leaf litter were confined to the spring and autumn (Fig. 3). Microclimate data show mean predicted lengths of freeze–thaw cycles (14–17 h) similar to the freezing exposures used in the present study. However, the maximum length (76 h) was substantially longer than that used in our experiments.

Our model and the microclimate recordings predict that, in the leaf litter, frogs would have experienced as many as 23 freeze–thaw cycles in the winter we observed, and would have spent 6–8% of the winter frozen (Table 2). The longest single period a frog was predicted to be frozen lasted 76 h (Table 2). Comparison of the leaf litter and air temperatures indicate that the microclimate is considerably buffered compared with air temperatures (Table 2). Calculation of predicted frog freeze–thaw events from air rather than microclimate temperatures suggests a higher number of freeze–thaw cycles, longer periods spent frozen and an increased length of freeze–thaw cycles in air compared with leaf litter.

Using our base model (assuming no cost to freezing and thawing), we predicted that frogs would use 1.5–1.6 kJ g⁻¹ over the winter (Fig. 4). The total predicted energy use was increased by <10% when the cost of freezing and thawing and the ‘pre-freeze increase’ of metabolism were included (Fig. 4). Most of the energy use was during the spring and autumn, when a lack of snow cover resulted in more extreme temperature fluctuations, including high temperatures, which result in disproportionately high energy use due to Jensen's inequality (Ruel and Ayres, 1999; Williams et al., 2012) (Figs 4, 5). Using our assumptions about fuel sources, a 7.1 g frog would be expected to consume 0.28 to 0.37 g lipid and 0.05 to 0.12 g carbohydrate per winter (Table 3).

Sensitivity analyses (Table 4) identify several assumptions of our model that have an impact on our estimates of the number of freeze–thaw cycles and overwinter energy use. Increasing the T_c from −1.36 to −0.8°C increased the number of freeze–thaw cycles and time spent frozen by ~20%, which had a comparable impact on predicted winter carbohydrate consumption. Lowering the melting point from −0.16 to −0.6°C had no impact on the predicted number of freeze–thaw cycles, although it did reduce the time spent frozen by 7%, which therefore slightly increased lipid consumption and reduced carbohydrate consumption. When T_c was increased to −0.8°C and melting point decreased to −0.6°C, the number of freeze–thaw cycles increased by 39%, but the time spent frozen decreased by only 7%. Consequently, this scenario led to <1% lipid savings, but a 26% increase in predicted carbohydrate consumption relative to the base model.

We observed a high Q₁₀ (7.97) of during cooling from +4°C, so our base model assumed a shift to a lower thermal sensitivity (Q₁₀=2.0) above a specific threshold (+4°C). Decreasing the threshold at which Q₁₀ increases from +4 to 0°C increased the predicted overwinter lipid consumption by 31%, but raising that threshold to +8°C increased the predicted lipid consumption by only 4%, so the high Q₁₀ we observed results mainly in a suppression of metabolic rate at these temperatures. Neither change in Q₁₀ threshold affected the predicted carbohydrate consumption (Table 4). Changing Q₁₀ to a constant value of 2.0 increased both lipid and carbohydrate consumption by ~40%, and using a Q₁₀ of 7.97 throughout increased our prediction of lipid consumption by 137%. Assuming that metabolic rate is depressed when the frog is frozen decreases predicted carbohydrate consumption by 17–33%, the value increasing as the magnitude of the depression was increased (Table 4).

Previous studies of metabolism in freeze-tolerant vertebrates (e.g. Voituron et al., 2002a; Voituron et al., 2009) have employed a closed-system approach that does not allow the patterns of metabolic changes to be observed, nor does it allow the direct estimation of the metabolic costs of the freezing and thawing processes. Here we show that CO₂ production by R. sylvatica during freezing and thawing is dynamic. In particular, we noted an increase in CO₂ production during cooling before the onset of freezing, an additional increase in CO₂ production coincident with ice formation, and an ‘overshoot’ of CO₂ production following thawing.

The increases in CO₂ production associated with cooling, freezing and thawing were not associated with increased movement (Fig. 1). Furthermore, although electrical noise prevented us from making quantitative measurements, oxygen consumption increased in tandem with at each of these points (B.J.S. and J.R.S., unpublished observations), which suggests that the increase in reflects an increase in metabolism, rather than a change in the CO₂-buffering properties of the blood. Note that an increase in CO₂ production is in the wrong direction to simply reflect a shift in fuel use from lipid to carbohydrate during this pre-freeze period (Sinclair et al., 2011). We observed the same qualitative pattern of changes in in frogs that were collected at the beginning and end of the winter, and also in frogs that were frozen a second time (N=2, data not shown), which suggests that this is a repeatable pattern in this species. It will be valuable to measure metabolism in real time in other species for which freezing is associated with mobilisation of glucose [e.g. lizards and earthworms (Costanzo et al., 1995; Holmstrup et al., 1999)]to determine whether the increased CO₂ production with freezing and thawing is a general pattern.

The large increase in we observed during cooling (but prior to ice nucleation) was surprising because signal transduction that triggers cryoprotectant synthesis is only initiated by ice nucleation (Storey and Storey, 1985), and R. sylvatica held between 0 and −2°C did not mobilise glucose or increase heart rate until ice formation was initiated (Storey and Storey, 1985; Layne et al., 1989). Thus, it does not appear that the observed pre-freeze increase in is associated with preparatory physiological processes that are directly linked to known cryoprotection. However, this increase was observed in all frogs, was initiated at above-zero temperatures and was not accompanied by a change in physical activity by the frog. A similar pre-freezing increase in metabolic rate was observed using closed-system respirometry in Rana arvalis (Voituron et al., 2009), but these authors also observed an increase in plasma glucose during this time. The increase we observed is unlikely to be due to a threshold response to water loss, as it was dependent on temperature, rather than time in the chamber, and is unlikely to be due to preparatory mobilisation (but not circulation) of glucose from glycogen in the liver, as that process is energetically inexpensive and does not begin until after nucleation. Although we always observed this pre-freeze increase in metabolism at approximately the same temperature in each frog, future real-time measurements of metabolism during cooling from different starting temperatures will be necessary to determine whether this increase is a response to rapid cooling per se, or a response to a specific temperature threshold. In particular, we note that transient receptor potential (TRP) channels are sensitive to changing temperatures, rather than absolute temperature (Voets et al., 2004), so there is a possibility that this mechanism could mediate a metabolic rate to temperature change. Clearly, further work on the dynamic responses of freeze-tolerant vertebrates during the cooling process is necessary to fully understand any preparatory processes.

A release of CO₂ coincident with freezing has been reported in an insect (Sinclair et al., 2004), but in that case the volume of CO₂ released was consistent with expulsion of air from the tracheal system, and in any case, freezing is thought to be largely passive in freeze-tolerant insects (Zachariassen, 1985). In R. sylvatica, we detected a sharp increase in that was clearly initiated with ice formation, and that persisted beyond the cessation of active ventilation. It is likely that once ventilation ceased, we were observing cutaneous gas exchange, which accounts for a significant proportion of respiration in terrestrial frogs (Feder and Burggren, 1992), and also diffusive exchange with the lungs via the nares. We hypothesise that the increase in associated with freezing reflects the increased metabolism associated with the production and distribution of cryoprotectants, the costs of the physiological and molecular responses to ice formation, as well as a slight increase in metabolic rate associated with the heat released during ice crystallisation (Layne et al., 1989; Storey and Storey, 1996).

The final increase in we observed was during thawing, specifically in the period after the temperature of the frog began increasing, indicating that all of the ice had melted. This increase in probably reflects the increase in ATP turnover needed to reactivate physiological functions, repair any freeze-induced damage and restore homeostasis (e.g. ion gradients may need to be restored to reactivate nerve transmission and muscle contractility), as well as initiate glucose clearance from the blood and bladder and the resynthesis of liver glycogen (Storey and Storey, 1986; Layne and First, 1991; Costanzo et al., 1997). This period also includes a recovery phase from the hypoxia/anoxia and ischemia stresses experienced by tissues when frozen. Thus, the overshoot will also include the initial costs of processing anaerobic end products (lactate, alanine) that accumulated when frozen, and the costs of macromolecular repair or replacement to redress damage accrued during the freeze–thaw event (Storey and Storey, 1986; Storey and Storey, 1996). It is unlikely that ice formation was maximal after the 12 h cold exposure we applied (Lee et al., 1992), so it may be possible to further investigate the nature of the post-thaw increase in metabolism by manipulating the length of the frozen period, which would allow the cost of thawing to be parsed from the costs incurred while the frog is in the frozen state.

We calculated a Q₁₀ of 7.97 during cooling from +4 to +1°C. This Q₁₀ was consistent with the observed low when frozen, and is a little larger than that calculated from measurements presented for R. arvalis [~4.5 (Voituron et al., 2009)] but is orders of magnitude lower than the abrupt drops in observed to coincide with chill coma onset in insects (Sinclair et al., 2004). The Q₁₀ we measured is nevertheless high – ‘typical’ biological values are 2.0–3.0 (Withers, 1992) – and suggests that the period of cooling below 4°C could include active metabolic suppression, rather than simple Arrhenius effects. Thermal sensitivity of metabolism may change across important biological thresholds (MacMillan et al., 2012), and the Q₁₀ of 7.97 that we measured would be very unusual if it occurred over the whole range of biological temperatures (and, as revealed by our sensitivity analyses, would result in very high energy expenditure at higher temperatures). Therefore, we included a threshold shift in Q₁₀ in our model to reflect the likelihood that thermal sensitivity of metabolism is lower at higher temperatures. We have modelled this shift as a threshold, but it could also be a curvilinear relationship, which would not alter our conclusions. Our assumption of a decrease in the thermal sensitivity of metabolism at higher temperatures was the model parameter with the greatest influence on predicted overwinter lipid use, and therefore on energy use overall. At the extreme, assuming that Q₁₀ is a constant 7.97 more than doubled our estimate of overwinter lipid consumption. Conversely, assuming a much lower thermal sensitivity was predicted to increase both lipid and carbohydrate consumption moderately, the latter because of the lack of metabolic rate suppression at low temperatures.

Our predictions of freezing and thawing in the field suggest that frogs may spend the majority of the winter unfrozen, and that there is inter-location (and undoubtedly inter-annual) variability in the frequency of freeze–thaw events, even within a small geographic area. The number of predicted freeze–thaw cycles is strongly influenced by the temperature of crystallisation used in the model. We used a T_c of −1.4°C (derived from our empirical measurements); however, frogs in the wild will be in contact with ice in frozen soil or leaf litter, which will nucleate freezing at temperatures up to 1°C warmer (Lee and Costanzo, 1998). A higher T_c will increase the number of predicted freeze–thaw cycles, and thus the expected energetic costs associated with freezing, in a linear fashion. However, our sensitivity analyses show that increasing T_c from −1.4 to −0.8 in our model increased the number of freeze–thaw cycles by only ~20% (Table 4), which is within the range of variability we observed between locations (Table 3). Therefore, a higher T_c in nature would not substantially alter our conclusions. In addition, we did not place a time constraint on the criteria for identifying a freeze–thaw event. Ice formation and melting take many hours (Fig. 1) (Lee et al., 1992), yet the shortest of the freeze–thaw events we identified was only 1 h. Although it is probable that the costs of freezing and thawing would be lower for shorter events (especially when ice content is low), it is also likely that a certain level of threshold costs exists. Frogs trigger cryoprotectant synthesis within 2 min of nucleation (Storey and Storey, 1985), and the majority of the threshold increase in freezing we observed occurred in the short period after the initiation of ice formation (Fig. 1), suggesting that the initial metabolic costs associated with freezing will have energetic consequences regardless of the amount of ice formed. Manipulating the length of freezing events will allow a finer analysis of the factors that determine variation in the costs of freeze–thaw, and whether short freezing events represent reduced or increased metabolic costs. Variation in intensity of cold exposure has an impact on post-thaw locomotor responses (Layne and Rice, 2003), so it is possible that exposure to higher or lower temperatures would also modify metabolic responses during and after thawing. Future work could also examine the impacts of different minimum temperatures on energetic responses.

In our model, we have assumed that unfrozen overwintering frogs consume mainly lipid, while they consume carbohydrate when frozen and during the freezing process. The latter assumption is supported by the observed accumulation of lactate and alanine as glycolytic end products while frogs are frozen (Storey and Storey, 1986). Although we assume that this transition is a step function, it is quite likely that there will be a period of fuel-use transition from lipid to carbohydrate during the freezing process, and a similar transition during and after thawing. While such transitions could modify the absolute amount of lipid and carbohydrate consumed, they would not substantially alter the conclusion that freeze–thaw thresholds are a primary driver of winter carbohydrate consumption. It is also possible that the pre-freeze increase in that we observed could be fuelled by lipid. The pre-freeze increase accounted for a very small amount of overwinter energy consumption in our model (Fig. 4), so we do not expect our conclusions to be altered by metabolic substrate at this threshold. Future fine-scale investigations into the nature of fuel use during these transitions will be necessary to test our assumptions.

Assuming limited protein catabolism and/or gluconeogenesis from protein or other sources over winter, the dichotomy between carbohydrate use when frozen and lipid use when unfrozen means that wood frog energy stores are separated into two pools that respond differently to winter thermal conditions. This is exemplified in our sensitivity analyses, where shifts in some parameters (for example, those that modify the number of freeze–thaw cycles) have a large impact on predicted carbohydrate consumption while leaving predicted lipid consumption largely unchanged. By contrast, thermal sensitivity of metabolism will disproportionately change lipid consumption because it is more important at above-freezing temperatures due to the effects of Jensen's inequality (Ruel and Ayres, 1999) (Table 4).

It has been predicted that the energy savings of being frozen may be a primary advantage of freeze tolerance (Voituron et al., 2002b). Comparison of predicted energy use at the two locations is useful because at Location 2 frogs would have experienced more freeze–thaw cycles and spent more time frozen. This difference meant that there was an increase in predicted carbohydrate consumption by frogs at Location 2, but there was no concomitant decrease in predicted lipid consumption. Thus, in this case, the importance of freeze tolerance in energetic savings would depend upon the relative abundance of lipid and carbohydrate reserves, the thermal sensitivity of unfrozen metabolism and the temperatures experienced in the unfrozen state. Metabolic depression when frozen can save significant amounts of energy (Irwin and Lee, 2002; Voituron et al., 2002a; Marshall and Sinclair, 2012) but our sensitivity analyses suggest that metabolic depression when frozen will reduce predicted overwinter carbohydrate consumption by less than one-third, even if metabolism is suppressed by 99.5% (Table 4). This is likely because a significant portion of overwinter carbohydrate consumption occurs as a result of the threshold costs of cooling, freezing and thawing (Fig. 4), which are not modified by metabolic rate depression when frozen. Therefore, if our measurements of metabolic rate during freezing and thawing are representative, it appears that the energetic costs of an active freezing process have the potential to outweigh any energy savings advantages of being frozen, and that freeze tolerance probably evolved as a response to selective pressures other than energy conservation.

Rana sylvatica collected from the same location as our individuals have approximately 150 mg carbohydrate g⁻¹ liver in the autumn and 120 mg carbohydrate g⁻¹ liver in the spring (Storey and Storey, 1984; Storey and Storey, 1987). Assuming that the liver is 12% of the frog's body mass in autumn and 2.4% in spring (K.B.S., unpublished), and that the liver contains the majority of the frog's store of carbohydrate that fuels overwinter metabolism, we can estimate consumption of 112 mg of carbohydrate in a 7.1 g frog over the course of a winter. Our model predicts overwinter carbohydrate consumption in the region of 44–56% of this value (Table 3), suggesting that our estimates are conservative, but supporting the general form of the model. In particular, this calculation does not account for stores of glycogen in other tissues (Storey and Storey, 1984), which likely fuel a portion of overwinter metabolism as well as metabolic activity in the spring. Lipid stores are variable among individuals (K.B.S., unpublished), but predictions of overwinter lipid consumption could, in future, be tested using non-invasive techniques on individuals, for example with quantitative magnetic resonance spectroscopy (Guglielmo et al., 2011). The stoichiometry underlying our predictions of carbohydrate consumption assumes aerobic respiration throughout the winter. Although gas exchange is possible across the skin and mucosal membranes, frozen frogs accumulate anaerobic end products, which will be fuelled by carbohydrate metabolism, but not reflected immediately in CO₂ release (Storey and Storey, 1984; Storey and Storey, 1986). This anaerobic metabolism will not be included in energy consumption in our model, unless the increase in metabolism during and after thawing is reflective of the catabolism of anaerobic end products accumulated when the frog was frozen. Thus, our assumptions may lead to an underestimate of carbohydrate consumption.

Finally, we point out that our microclimate recordings are only an approximation of frog temperature. Our woodlot location is slightly warmer than the temperatures recorded at a nearby meteorological station, while snow cover and the effect of insolation on leaf litter temperature suggest that meteorological measurements would be a poor approximation of frog temperature (supplementary material Fig. S1). Also, our measurements assume that there is no thermal inertia in the frogs' cooling and warming rates. This thermal inertia may be particularly important during the endothermic stage of ice melting, which means that any brief periods of thawing may not lead to the frog thawing completely. We did not explore whether there are additional energetic consequences for partial thawing or re-freezing. We suggest that future studies may aim to obtain a better estimate of the temperatures actually experienced by the frogs, either by housing data loggers in models matched for the thermal mass of the animal (e.g. Hertz, 1992), or by implanting data loggers in overwintering frogs (e.g. Rausch et al., 2008).

The present results and predictions from our model can be used to illustrate some important potential impacts of winter climate change on R. sylvatica, and other species that have an active response to internal ice formation. Either higher temperatures or a reduction in precipitation could decrease the depth or persistence of the snow pack and lead to an increase in freeze–thaw cycles (Henry, 2008), resulting in increased carbohydrate consumption over the winter. The timing of these freeze–thaw cycles is important: if there are more freeze–thaw cycles during the early winter, due to a delay in the accumulation of snow cover, this could lead to a premature reduction in carbohydrate reserves, and thus depletion of both metabolic fuel and cryoprotectants. Such a scenario would be accompanied by greater exposure to high temperatures, leading also to higher lipid consumption. Changing autumn conditions (for example, a shift in the timing of winter snow accumulation in the Ottawa location where our frogs were collected) could lead to increased carbohydrate consumption due to an increase in the number and frequency of freeze–thaw cycles, as well as an increase in lipid consumption because of warmer non-freezing conditions. Similar implications of climate change for overwinter energy use are also predicted to have an impact on some capital-breeding insects, such as overwintering butterflies (Williams et al., 2012a; Williams et al., 2012b) and hibernating mammals (Humphries et al., 2002). In the case of R. sylvatica, many of our predictions may be tested through field studies across a wider geographical area representing a range of winter temperatures and snow cover situations.

Thanks to Jan Storey and two anonymous referees for insightful comments on an earlier version of the manuscript.

 
• Q₁₀

  thermal sensitivity coefficient

 
• RQ

  respiratory quotient

 
• T

  temperature

 
• T_c

  temperature of crystallisation

 
• 

  rate of carbon dioxide production