Calorespirometry of terrestrial organisms and ecosystems.

Methods xxx (2014) xxx–xxx

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Calorespirometry of terrestrial organisms and ecosystems Lars Wadsö a,⇑, Lee D. Hansen b a b

Building Materials, Lund University, Box 118, 221 00 Lund, Sweden Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA

a r t i c l e

i n f o

Article history: Received 9 September 2014 Received in revised form 20 October 2014 Accepted 21 October 2014 Available online xxxx Keywords: Calorimetry Efficiency Oxygen Carbon dioxide Growth Thornton’s constant

a b s t r a c t Calorespirometry is the simultaneous measurement of heat and gas exchange from biological systems. Such measurements can be used to assess fundamental properties of many different types of systems from small ecosystems to isolated tissues. Techniques for calorespirometric measurements on terrestrial (non-aquatic) samples are described. Methods and models for evaluation of carbon conversion efficiencies, growth rates, and responses to environmental variables from calorespirometric measurements are described. A realistic model of the system under study is essential in the evaluation. Calorespirometry allows testing of models for tissues, individual organisms, and ecosystems. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Calorespirometry is the simultaneous measurement of heat and gas exchange. Such measurements can be made to assess overall values of fundamental parameters in biological systems. A system can be a single whole organism (for example an insect), part of an organism (for example a leaf cut from a plant), or a microcosm containing many organisms (for example a soil sample). The heat measurements are made in a calorimeter and the system under study is what is inside the calorimetric ampoule. Calorimetry and respirometry can be done separately, as was done by Lavoisier and Laplace [1] and Crawford around 1780 [2] (Lavoisier and Laplace were probably first [3]). However, it is advantageous to perform simultaneous calorimetry and respirometry instead of combining measurements made on living organisms or tissues at different times or on different samples. Therefore, we limit this discussion to calorespirometry, the simultaneous measurements of heat and gas exchange. The biochemical details of respiration are immensely complex, but can to an ever increasing extent be revealed by studies at the protein and gene level. However, it is also necessary to use methods that characterize biological systems on a higher level, i.e. as complete, functioning systems, and calorespirometry is such a method. The measured parameters (heat and gas exchange rates) ⇑ Corresponding author. E-mail addresses: [email protected] (L. Wadsö), [email protected] (L. D. Hansen).

are fundamental properties of biological systems and can be used to infer characteristics such as growth rates, carbon conversion efficiencies, and response to environmental variables. Fig. 1 is a schematic of an aerobic biological system from the point-of-view of calorespirometry, i.e. the flow of matter and energy through a biological system. To emphasize the flow aspect we use the terms Rq (J s1 = W), RO2 (mol s1) and RCO2 (mol s1) for the rates of heat, oxygen and carbon dioxide. Note that RO2 and RCO2 are equivalent to the terms OUR (oxygen uptake rate) and CER (carbon dioxide evolution rate), respectively. Calorespirometry has been used on many different types of biological systems, see for example the following references dealing with mammalian tissue [4], insects [5], plant tissues [6], mammalian cells [4], aquatic microorganisms [7], mold fungi [8], soil [9] and fish [10]. Calorespirometry is mainly used for biological systems, but similar methods have also been employed for non-biological systems. There are for example studies of abiotic degradation of a herbicide [11] and the reaction in a Zn-air battery [12] in which simultaneous calorimetry and respirometry was done (carbon dioxide in the first case and oxygen in the second). Calorimetry on its own is a worthwhile method for studying biological systems. Illustrative examples are studies of the influence of salinity on respiration rates in different barley cultivars [13], influence of anti-browning substances on metabolic activity of potatoes [14], and quantification of thermal inactivation of tomato cells [15]. However, the observed effects cannot be related to metabolic parameters or other functions when only heat is measured, as is often possible from calorespirometric measurements.

http://dx.doi.org/10.1016/j.ymeth.2014.10.024 1046-2023/Ó 2014 Elsevier Inc. All rights reserved.

Please cite this article in press as: L. Wadsö, L.D. Hansen, Methods (2014), http://dx.doi.org/10.1016/j.ymeth.2014.10.024

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L. Wadsö, L.D. Hansen / Methods xxx (2014) xxx–xxx

O2

R

Rq O2

Biological system RCO2

heat CO2

Fig. 1. Schematic of an aerobic, steady-state biological system and the rates measured in calorespirometry, emphasizing the organism or tissue as a complete, functioning system.

Some common concepts used in the discussion of the overall activity of biological systems in this paper are: Aerobic and anaerobic refers to metabolism with and without free oxygen. Aerobic metabolism is also called respiration. A biological sample – especially if it is composed of different types of organisms – can simultaneously have aerobic and anaerobic metabolic components. Many calorimetric measurements have been performed on organisms in aquatic environments, but this paper focuses on organisms and systems in air, and we call these systems terrestrial. Catabolic processes degrade molecules, releasing energy that can be used by anabolic processes to build new biomass. Both are necessary, catabolic processes supply the energy and ATP to catalyze and drive anabolic processes, but it is advantageous for individual organisms under most circumstances and for industrial biochemical processes including crop production to have a low catabolic fraction, i.e., high efficiency. Growth vs. maintenance is a conceptual division into biological activity that makes new tissue and activity that maintains the state of the old tissue. All organisms have maintenance, but only growing organisms have growth. However, at present there is no method for measuring these processes separately because they involve the same metabolic pathways. Thus, only overall efficiency is discussed in this paper. Steady-state biological systems do not change their state with time, although there is mass and energy flow through them (dynamic steady-state); unsteady-state systems change their constitution by growing, storing metabolites, or autolysis (self-digestion). Steady-state is typical of non-growing tissue, for example adult animals (that have reached their final size), vegetables under dark storage and microorganisms under harsh conditions where growth is not possible. All consumed substrate is then converted to carbon dioxide in the process of maintenance. Note that we here use the term steady-state for a type of biochemical behavior of a biological system; there is also a physical steady-state criterion that needs to be fulfilled in calorespirometric measurements, for example that the produced carbon dioxide is released and measured. The nomenclature used is given in Table 1. 2. Methods This paper is about different ways to measure the rates shown in Fig. 1 and how these can be used to gain information on the underlying processes and properties of a biological system. In this sense, calorespirometry is the science of gaining information about the inner workings and functions of a black/gray box system from externally measured parameters. We can, for example, investigate the division of energy and nutrients between growth and reproduction. However, critical to successful evaluation of calorespirometric measurements is the choice and testing of a relevant model of the biological system. Calorespirometric measurements can be made in different ways, depending on the biological system of interest. Table 2 gives an overview of the possibilities. In all methods, the heat rate is

Table 1 Nomenclature. Rates are defined as positive in the directions of the arrows in Fig. 1. Enthalpies follow the thermodynamic sign convention (negative for exothermic processes). Note that J s1 = W. Symbols DabsH DTH m MB p R RCB RCO2 RO2 RRG Rq t T V x

a b

c e

Enthalpy of absorption of carbon dioxide by absorbent Thornton’s constant (about 455 103; see Section 3) Dry sample mass Molar mass of biomass per carbon atom Pressure Gas constant (8.314) Rate of carbon biomass accumulation Rate of carbon dioxide production (CER) Rate of oxygen consumption (OUR) Relative (specific) growth rate Heat production rate Time Temperature Ampoule volume See footnote (c) in Table 3 See footnote (f) in Table 3 Eq. (9) Carbon oxidation number Carbon conversion efficiency (CCE)

Indices B S 0 1

J mol1 J mol1 g g mol1 Pa J mol1 K1 mol s1 mol s1 mol s1 g g1 s1 J s1 = W s K m3 1 1 1 1 1

Biomass Substrate Without absorbent With absorbent

Table 2 Different ways to make calorespirometric measurements. Primary results written in bold are directly measured as rates; non-bold results are given by the time derivative of a concentration sensor signal. Method of measurement

Primary result

Heat rate

CO2 rate

O2 rate

IC IC IC IC IC IC IC

CO2 sensor – CO2 sensor abs., ext. abs., ext. abs., int. abs., int.

– O2 sensor O2 sensor – P sensor – P sensor

Rq, Rq, Rq, Rq, Rq, Rq, Rq,

RCO2 RO2 RO2, RCO2 RCO2 RO2, RCO2 RCO2 RO2, RCO2

IC = isothermal calorimetry. abs. = absorbent (NaOH solution). ext. = removable vial with absorbent. int. = absorbent vial can be opened and closed in ampoule. P = thermal power. p = pressure.

measured in an isothermal calorimeter, either a heat conduction or power compensation calorimeter. The main difference is in the method of measuring the gas exchange rate which can be done with sensors that measure gas concentration or with a carbon dioxide absorbent. The latter can be combined with a pressure sensor, as is done in Warburg respirometry [16–18]. Different gas sensors have been employed in calorespirometry. To be useful for in-situ measurements in calorimetric ampoules, such sensors must be small and produce a negligible or constant heat rate. Oxygen can be measured in the aqueous phase with an oxygen electrode, for example a Clark electrode [19]. In the gas phase, oxygen can be measured by optical sensors [12], paramagnetic sensors [19], etc. and carbon dioxide by IR sensors [20,21]. Gas composition can also be measured by gas chromatography and mass spectroscopy, but these methods require removing a sample of the head-space gas from the calorimetric vessel, which is difficult to do without disturbing the heat measurement [22]. Gas phase oxygen and carbon dioxide sensors are often too large for calorimetric ampoules, and may also have other disadvantages,



like the need for frequent calibrations, high heat production and consumption of the measured species (the Clark electrode consumes oxygen). Although we will certainly see an increased use of gas sensors in calorespirometry devices in the future, at present, sensor based calorespirometry is not as easy for terrestrial systems as is the calorimetric carbon dioxide absorbent method with/without pressure measurements. We will therefore focus on the absorbent method in this paper. In the method developed by Hansen, Criddle and co-workers (see for example Refs. [6,23]), a calorespirometric measurement is started by measuring the heat production rate of only the biological sample (index 0). When stable signals have been reached, an absorbent vial is added and the measurement is continued (index 1). The carbon dioxide absorbent is usually a 0.4 M NaOH solution with a water activity close to many biological materials (normal saline solution). The reaction enthalpy for the reaction (Eq. (1))

CO2 ðgÞ þ 2OH ðaq; 0:4 MÞ ! CO2 3 ðaqÞ þ H2 OðlÞ

ð1Þ

is DabsH = 108.5 kJ mol1 CO2 [23]. The NaOH concentration can be increased or decreased to match the water activity of the sample, but the value of DabsH must be changed accordingly. Refs. [24,25] give data from which water activity and carbon dioxide absorption enthalpy for aqueous solutions of NaOH can be calculated. The heat production rate in this second step with the absorbent present (Rq1) is the sum of the metabolic heat production rate and the heat production rate from reaction of the produced carbon dioxide with the absorbent. As the metabolic heat production rate from the sample is known from the measurement without absorbent (Rq0), the carbon dioxide production rate can be calculated using DabsH. The measurement is usually continued without absorbent to correct for any drift in the rates and as a check that the sample has not changed during the measurement, cf. Fig. 2. For aerobic systems, the thermal power typically rises by about 20% when the absorbent is added. Rates of heat and carbon dioxide production from the sample (Rq and RCO2) can then be calculated from the calorimetric measurements without and with the absorbent (Eqs. 2 and 3):

Rq ¼ Rq0 ; RCO2 ¼

ð2Þ

Rq1 Rq0 : Dabs H

ð3Þ

R

q1

Heat production rate

Rq0

0

1

0

0 0

40 80 Time / min

120

Fig. 2. Schematic description of a calorespirometric measurement with a carbon dioxide absorbent. These measurements are usually done in three parts of equal duration without (0), with (1) and without (0) absorbent. To remove the influence of a sloping baseline, a linear interpolation between the two heat production rate values without absorbent (black markers) can be made; then both Rq0 and Rq1 can be determined at the end of the second part (white markers).

3

The minus sign on the enthalpy is needed because we define rates as positive according to Table 1 and Fig. 1, while the thermodynamic sign convention is used for the enthalpy. In aerobic systems oxygen consumption is approximately balanced by production of carbon dioxide, so a pressure sensor typically shows little or no change in pressure when no CO2 absorbent is present. With CO2 absorbent present, the pressure decreases at a rate proportional to the oxygen consumption rate. The oxygen consumption rate can then be calculated by the ideal gas law (Eq. (4)),

RO2 ¼

V dp1 ; RT dt

ð4Þ

where dp1/dt is the time derivative of the pressure with the absorbent present. The difference between the oxygen consumption and the carbon dioxide production rates can be evaluated from pressure measurement without absorbent (Eq. (5)),

RO2 RCO2 ¼

V dp0 : RT dt

ð5Þ

Although this difference is often small as dp0/dt usually is near zero, this measurement can be used as a check on the gas exchange rates or it can be used to calculate RO2 from RCO2 from the calorimetric measurement. A difficulty with this method is determination of V, the gas volume, which is equal to the ampoule volume minus the sample volume and any additional materials added such as a NaOH vial. The correction can be made either from knowledge of the sample mass and density or by measuring the pressure change when a known volume of gas is injected into the ampule. Calorespirometric measurements can be made on aquatic as well as terrestrial biological systems, but there are two differences in the way measurements are made. Firstly, the absorbent method is not suitable for aqueous systems because the dissolved carbon dioxide does not readily leave the liquid phase. Secondly, as oxygen diffusion in water is slow, unstirred liquid cultures easily become anoxic and even stirred cultures can have problems with oxygen transfer from the gas phase to the liquid [26–28]. In terrestrial systems this is much less of a problem as gas diffusion in air is comparatively rapid. However, gas diffusion resistance inside large pieces of tissue may present a problem [29]. The above described absorbent method is easy to use and can be implemented in any calorimeter. However, there are disturbances when the vial of absorbent is inserted or removed from the calorimeter ampoule. To avoid this disturbance, it is possible to use two calorimeters: one for the sample and one for the absorbent [8,23,26] with the ampoules connected by a tube to allow for gas exchange. However, because the two calorimeters must be thermally isolated, the tube between the sample vessel and the absorbent vessel tends to be rather long, and thus has a high diffusive resistance. Another option is to use two calorimeters and have a flow of carbon dioxide free air through the sample vessel and into the absorbent vessel [30]. The difficulty with this method is avoiding evaporation or condensation of water if the humidity of the air does not exactly match the equilibrium humidity of the sample and absorbent. A third option is to have an absorbent vial in the ampoule that can be opened and closed without opening the calorimeter ampoule [31]. Isothermal heat conduction calorimeters can be slow in their responses due to the thermal inertia of the sample and ampoule. This is, for example, seen when an ampoule is inserted into a calorimeter as the inserted ampoule is unlikely to be at exactly the same temperature as the calorimeter. This slow response is quantified in terms of a time constant [32], that typically ranges from about 100 s for small vessels/samples to >1000 s for large aqueous samples. The time for the calorimetric measurement to reach a steady state is typically defined as six time constants (99.8% of the process completed). The slow response can to some extent be


4


corrected by the Tian equation [31,32] that calculates the true heat production rate from the instrument signal. One of the main advantages of using isothermal calorimetry for kinetic measurements is that the rate of heat production (which is proportional to the rate of the studied process) is measured directly. Thus, taking the derivative of the data with the consequent loss of the most significant digit is not necessary. Note that all heat rate measurements in Table 2 are printed in bold – signifying a direct measurement of rate – while most of the gas exchange rate measurements are not. When a carbon dioxide absorbent is used, the carbon dioxide rate is also directly measured. When pressure or concentration is measured, the time derivatives have to be used to obtain rates, causing increased noise and uncertainty. We here list common general problems in calorespirometric measurements (partly taken from Ref. [33]): (1) Not using the proper amount of tissue [33]. Use of too much tissue leads to a fast depletion of oxygen and absorbent. Use of too little tissue gives low signal-to-noise ratio. (2) Not using the proper tissue [33] can lead to the wrong conclusions. For example, if plant growth rate is to be calculated, measurements should only be made on the tissues where cells are actively dividing or expanding. To compare different organisms, these must be in comparable states of development. (3) Failure to seal the ampoule [33] leads to evaporation of water with a large endothermic heat effect. Small leaks can produce a constant, endothermic heat effect and consequently a smaller apparent metabolic heat rate that is in error. (4) Microbial contamination [6] usually appears as a rapid exponential rise in the heat rate that should not be confused as a heat rate from the sample, i.e. calculated growth rates must be consistent with prior knowledge of the growth rate. (5) Confusing latent heat effects during thermal equilibration of the calorimeter with heat effects from sample metabolism. Time constants of calorimeters vary widely and must be taken into account when planning an experiment or analyzing rate data. The Tian equation can sometimes be used to correct for the time constant. (6) Short term measurements of gases can be in error because of outgassing or retention of carbon dioxide [34]. Some specific problems with sensors are: (1) Pressure-sensor data needs to be differentiated to obtain a rate; this can give rise to significant noise. (2) Drift in sensors makes it necessary to do frequent calibrations. (3) Non-linear sensor output makes it necessary to do multipoint calibration. (4) Hysteresis in sensors. (5) Condensation of water into pressure sensors is a common problem if the sensor is colder than the sample ampoule. Finally, some problems that can be encountered when using the absorbent method for CO2 rate measurements: (1) Sometimes difficult to find consistent levels of heat production rate to use in evaluation [23]. (2) Long equilibrium time from thermal equilibration of absorbent vial and contents. (3) Difference in water activity between sample and absorbent solution causes transfer of water from sample to absorbent solution or from absorbent solution to sample. (4) Absorption of CO2 by basic media or sample.

(5) Samples sensitive to O2 and/or CO2 concentrations, and/or pressure sensitive samples. The O2 concentration necessarily continuously decreases and CO2 builds up during a measurement in a sealed ampoule. Metabolism of most plant tissues is relatively independent of oxygen pressure until oxygen is nearly depleted [6,35], and it is possible to use elevated oxygen concentrations [6] with most plant tissues. Most plant tissues are also insensitive to CO2 concentration up to at least 10%. However, CAM plant respiration is sensitive to CO2 concentration [36] and some organisms and tissues are sensitive to O2 concentration and total pressure [37]. Some plant tissues also produce metabolic inhibitors that slow or stop respiration as these build up in a sealed ampoule [38,39]. Many aquatic organisms are sensitive to ammonia from waste products that may increase during a measurement. (6) Use of too little or too dilute absorbent solution. NaOH solutions must be properly prepared and stored or the hydroxide ion is depleted by reaction with CO2 or other acids in the air. (7) Absorbent solution must not come in contact with the sample as this will give large heat effects [33]. 3. Thornton’s rule Thornton’s rule is central to calorespirometry and indirect calorimetry (the calculation of heat rates from measurements of gas exchange). Thornton’s rule states that the enthalpy of all oxidation reactions of organic compounds by oxygen is approximately constant when expressed as heat per mole of oxygen. Thornton’s original paper [40] from 1917 showed that the enthalpy of combustion of different organic compounds were rather similar and had a mean value of 444 kJ mol1 [41]. Slightly different values have been published and used in the biocalorimetric literature; for example 430 to 480 kJ mol1 ‘‘for a variety of substrates and conditions’’ [4], 469 kJ mol1 for glucose metabolism [42], 453 kJ mol1 for herbivorous animals [43], and 455 ± 15 kJ mol1 as a generally applicable value for compounds in living systems [44]. We call this value Thornton’s constant, give it the symbol DTH and use 469 kJ mol1 for carbohydrates and 455 kJ mol1 for other substances or when the substance is unknown. Three problems with Thornton’s rule should be mentioned. First, heats of combustion of some organic compounds differ significantly from the rule, for example nitrogen containing compounds [40] and peroxides [45]. This is normally not a problem in calorespirometry, with the exception that adjustments may need to be made for some nitrogen containing compounds (e.g. urea and ammonia). Second, Thornton’s constant is dependent on the state of the involved compounds. For example, the value is different if the consumed oxygen comes from the liquid phase or from the gas phase. However, the heats of solution of oxygen and carbon dioxide are small (about 12 kJ mol1 [4]) so this typically is not a major issue (see Gnaiger and Kemp [4] for examples of how the value can differ when different states occur). Third, Thornton’s rule is only valid for aerobic processes that use O2 as the oxidant. Anaerobic processes do not consume oxygen and an enthalpy given as joules per mole oxygen then has no meaning. However other oxidants, such as the nitrate ion, follow a similar rule, but the constant of proportionality differs. Note that Thornton’s rule is a useful statement about the enthalpy of chemical reactions involving oxygen, but measurements on biological processes do not necessarily give this enthalpy because there can be, and often are, other thermally active processes at the same time [4,46]. Thornton’s rule is only applicable if all processes are aerobic or if we want to determine the presence of thermally active anaerobic components (then the oxygen



consumption does not equal the heat multiplied by Thornton’s enthalpy). Thornton’s rule can then be used to assess the amount of heat from the anaerobic component by a comparison between measured and calculated (with Thornton’s rule) oxygen consumption rates [47]. Indirect calorimetry, in which heat production rate is calculated from oxygen uptake rates, is invalidated by such processes. 4. Why do calorespirometry instead of only respirometry? It is relevant to ask why we should combine calorimetry with respirometry instead of only doing respirometry. From the viewpoint of indirect calorimetry, Rq and RO2 are proportional to each other (Thornton’s rule) and their ratios with RCO2 are only influenced by the oxidation state of the substrate. However, as we discuss in this paper, these simple proportionalities are often not true, and then the set of three different measurables Rq, RO2 and RCO2 can be used to extract more information. Calorimetry is in many respects a simple technique and the results are highly reproducible. It also has the advantage that it directly measures the rate of, in our case, heat and carbon dioxide. Isothermal calorimeters are sensitive instruments for measuring heat production rate. Many instruments work in the sub-microwatt range and make highly reproducible measurements; for example Criddle et al. [6] found a standard deviation of 5% of the heat production rates for replicates of corn seedling from a single inbred line. Calorimetric carbon dioxide measurements can also be very sensitive; a heat production rate of 5 lW produced by the absorbent corresponds to about 50 pmol s1 CO2 [23]. Pressure measurements and gas sensors are usually less sensitive, especially as we have to take the time derivative of these signals to get rates. 5. Interpreting Rq, RO2 and RCO2 The measured rates (Rq, RO2, RCO2) and the ratios of these rates contain information on the metabolism of the sample under study. The rate-ratios have been given different – sometimes confusing – names in the literature. For example, the measured ratio Rq/RO2 is often called the calorespirometric ratio and is compared to calculated/tabulated values of its theoretical counterpart, the oxycaloric equivalent [4] (Thornton’s constant). Note also that Rq/RCO2 and Rq/RO2 can have widely different values [6]. The heat production rate Rq can be seen as wasted energy from the biochemical processes, but it is a necessary part as the release of ‘‘waste heat’’ from the catabolic reactions needed to drive the biochemical processes. There is different information in RO2 and RCO2. In relation to Rq, the former can tell us whether the metabolism is fully aerobic and steady-state (Thornton’s constant), while the latter contains information about the balance of catabolism and anabolism. Nearly all of the metabolic heat is produced by oxidative reactions of catabolism, while carbon dioxide is produced by both catabolism and anabolism [48], and in rapidly growing tissues with carbohydrate substrate, most of the CO2 comes from near thermally neutral disproportionation reactions of organic compounds. The ratio between carbon dioxide production and oxygen consumption is referred to as the respiratory quotient, RQ [34]. For steady-state systems this non-calorimetric value is only a function of what substrate that is being used. It is, for example, 1.0 when a carbohydrate is combusted to carbon dioxide and about 0.85 and 0.7 for the combustion of proteins and lipids, respectively. However, the steady-state assumption is probably not true in most cases, and if it is known what substrate is being metabolized, deviations from the steady-state value can be used to quantify the non-steady-state part. There are principally two reasons for such

5

deviations: growth and production/consumption of storage compounds. Quite deviating values of RQ may be found if an organism synthesizes lipid storage compounds. One study [49] did for example find that geese metabolizing grain had an RQ of 1.33 as a significant part of the grain was converted to lipids, so RQ was the sum of one part carbohydrate combustion (RQ = 1) and one part lipid production from carbohydrate (RQ > 1). The ratio of heat production to oxygen consumption Rq/RO2 can be compared with Thornton’s constant DTH. At steady-state, for aerobic processes Rq/RO2 DTH, and for anaerobic processes Rq/RO2 = 1. For a mixed aerobic–anaerobic process at steady-state the value of Rq/RO2 gives an indication of the fraction of anaerobic metabolism. Finally, the ratio of heat production to carbon dioxide production Rq/RCO2 can be seen as a simple measure of efficiency [33] as it is an approximate measure of the rate of catabolism over the rates of catabolism plus anabolism. A low value of Rq/RCO2 thus indicates that relatively little energy is lost from catabolism. This ratio typically has values in the range 200–500 kJ mol1 [33]. It should be noted that all measurements have uncertainties and when we combine measured parameters such as the rates discussed here, these uncertainties will increase.

6. Evaluating calorespirometric results Calorespirometry involves three components: the measurement, the evaluation of rates, and the further evaluation of metabolic parameters (efficiency, etc.). The first two components can be made in different ways – as was discussed above – and are in general quite straightforward, but further evaluation of metabolic parameters is complicated by the need to decide on a model with which to interpret the data [45]. There is no general evaluation model as the measurements give fewer parameters than there are unknowns in the general case. We thus need to make assumptions to be able to interpret our calorespirometric results, and if we make the wrong assumptions we will not get a valid result. However, modeling results can usually be tested for consistency with other data on the system. If we know/assume that our system is fully aerobic and that the substrate is carbohydrate, the evaluation is comparatively easy. Most other cases are more complex and need to be handled by suitable models and assumptions. One important aspect of a model is the overall chemistry involved. As examples of such chemical models we can take two examples of glucose consuming systems. A system with only maintenance (non-growing) could be modelled as (Eq. (6))

C6 H12 O6 þ 6O2 ! 6CO2 þ 6H2 O;

ð6Þ

while for a growing system we need to take nitrogen and formed biomass into account [50] (Eq. (7)):

aC6 H12 O6 þ bO2 þ cNHþ4 ! CH1:8 O0:5 N0:2 þ dCO2 þ eH2 O þ f Hþ :

ð7Þ

These two systems clearly differ in level of complexity and also in how an evaluation is made. An important parameter for the second case is the state of the formed biomass. This can be taken into account by introducing a factor DBH, which is the difference in the heat of combustion of biomass and the substrate. Unfortunately, this enthalpy can have values in the range 10–100 kJ mol(C)1 [45], so its value has to be assessed for each specific case. In some cases it is known what substrate is used – for example in glucose amendment experiments with soils – while in other cases it is known what the composition of the biomass is (the above example is a general formula for bacterial biomass from Ref. [51]). As another example, heats of combustion and thus oxidation states of vegetative plant matter, are approximately constant [52].


6


For the continued discussion we here introduce two concepts: carbon conversion efficiency and oxidation number. The (substrate) carbon conversion efficiency e is the fraction of the consumed (substrate) carbon that ends up as new structural (non-storage) biomass. Carbon conversion efficiencies can vary from 0 for systems that do not produce any new biomass to 0.9 for systems with efficient production of new biomass [45]. Carbon conversion efficiencies can in many cases be calculated from calorespirometric measurements. Oxidation number c is the number of electrons that an element has lost with respect to the state of the pure element (that by definition has c = 0). The carbon oxidation number is a useful concept in calorespirometry as it connects the stoichiometry of carbon containing molecules (substrate, biomass, carbon dioxide) with the heat of combustion. (Note that the symbol c is also used for the related concept degree of reduction [53]). In organic compounds the oxidation numbers of hydrogen and oxygen are always +1 and 2, respectively, while carbon can have oxidation numbers from 4 to +4. A complication is that nitrogen can have widely different oxidation numbers (3 in ammonium NH+4 to +5 in nitrate NO 3 ). If the oxidation state of nitrogen in substrate and biomass is unknown it can either be assumed that the contribution of nitrogen is insignificant or that the oxidation state of nitrogen in both substrate and biomass is the same. A similar – but smaller – problem is sulfur [54]. Other compounds and elements are either not subject to redox reactions (e.g. Ca2+) or occur in too small amounts to be significant. These conditions make it possible to calculate the carbon oxidation number of any compound containing only carbon, hydrogen and oxygen. Examples of such numbers in different types of compounds are: hydrocarbons c = 4, carbohydrates c = 0, and carbon dioxide c = +4. Typical values for proteins and lipids are 1 and 1.8, respectively [45]. Biomass can have different oxidation numbers, for example depending on whether it contains lipid storage tissue. A typical value for non-storage tissue is 0.25 [45]. For organic compounds, the carbon oxidation number is a measure of how much oxygen that a substance can react with, and, hence, the heat that is available from such a reaction (cf. Thornton’s rule). Hydrocarbons like methane (CH4) are energy-rich; carbohydrates like sugars (C6H12O6) are intermediate, and carbon dioxide (CO2) is maximally oxidized and is a waste product that contains no usable energy for aerobic catabolic processes. Calorespirometric results can be used to increase our knowledge of an aerobic system, but doing so requires a stoichiometric model that links the measured rates, Rq, RO2 and RCO2, to other properties of the system such as growth rate and efficiency. The overall reaction of aerobic metabolism can be represented as the sum of two reactions with variable weightings as shown in Table 3. Based on these reactions, the three measured parameters Rq, RO2 and RCO2 can be divided into reactions that use O2 and reactions that produce structural biomass. The enthalpy change for each of these reactions can be written in units of joules per mol oxygen, per mol carbon dioxide, and per mol carbon of substrate and biomass. All of these relations are given in Table 3. Note that Thornton’s constant is central as it is used in all of the enthalpy relations. The assumptions made in this model of aerobic metabolism are, first, the oxidation state of nitrogen does not change, second, minor compounds make negligible contributions to metabolic heat and CO2 rates, and third, reactions not involving O2 or CO2 make negligible contribution to the measured heat rate. The model in Table 3 allows calculation of two properties of an aerobic system that are otherwise difficult and time consuming to measure, the substrate carbon conversion efficiency (e) and the relative growth rate RRG. The overall reaction is the sum of the two reactions shown in Table 3 when multiplied by the appropriate factors, i.e. by 1 e and e, where e is a fraction between 0 and 1. Note

that 1 e is the fraction of carbon that is oxidized to CO2 in oxidative phosphorylation (catabolism) to provide the ATP to catalyze anabolic reactions plus any CO2 produced by disproportionation reactions that reduce substrate to biomass; e is the fraction of substrate carbon that is converted into structural biomass in anabolic reactions. Solving for this efficiency in terms of measured parameters (for example by solving RCO2/RO2 = (1 e)/x for e) gives (Eq. (8)):

e¼

b ; bþ1

ð8Þ

where b is defined by Eq. (9):

b¼

4 cB cS

Rq 4 cS : RCO2 DT H 4

ð9Þ

Once e is known, the growth rate in terms of moles carbon biomass produced per time unit can then be calculated by Eq. (10):

RCB ¼ RCO2

e 1e

:

ð10Þ

This can then be used to calculate the relative growth rate by Eq. (11):

RRG ¼

e MB RCO2 ; ð1 eÞm

ð11Þ

where MB is the average molar mass of the biomass per carbon atom and m is the dry mass of the sample. The average molar mass can be calculated if an average stoichiometry of the biomass is known. The stoichiometry given in Eq. (7) above gives MB = 12.012.05 = 2 4.6 g mol1. It should be noted that the calculations made in Eqs. (8)–(11) can be made using only the respirometric rates, but the heat production rate makes it possible to check the assumptions of steady-state and aerobic metabolism. Therefore calorespirometry can generate much more solid data than only respirometry. Further, Rq can be measured more accurately and easier than the gas rates, particularly O2 rates, and calorimetry provides a better way to measure CO2 rates than sensors. A general problem with the model in Table 3 is that the three measured parameters are not simply related to the variables cS and cB, and this system of equations cannot be solved without simplifying assumptions or auxiliary data on these two variables. However, if we believe that a system follows the aerobic model in Table 3, the table can be used to interpret measured data. Consider the examples given in Table 4. In the first case we know or assume the substrate is carbohydrate with cS = 0 and can then conclude that we have a steady-state system with no growth. In the second case, assumptions about both cS and cB allow calculation of the carbon conversion efficiency and a growth rate. In the third case the measured data cannot be reconciled with reasonable values of cS and cB, so we conclude that the model is incorrect; probably because there is another reaction with significant heat output. The fourth case in Table 4 possibly indicates a non-growing system with lipid as the substrate, but other possibilities exist. These four examples show typical ways in which the aerobic calorespirometric model can be used to relate the measured rates to system properties. For many real systems, the problem with the necessary assumptions is not serious because reasonable values can be assigned to cS and cB from well-known information, e.g. vegetative tissues in plants commonly use sucrose as the substrate (cS = 0) and the composition is relatively constant with cB = 0.25 [52]. There are also multiple ways of determining cB, four such methods are discussed in Ref. [55].


7


Table 3 Overview of a stoichiometric model of strictly aerobic metabolism. Based on Ref. [45], but with somewhat changed nomenclature. For simplicity, water is not shown in the reactions. Reaction

Overall b,c

CO2 production 4c C S þ 4 S O2 ! CO2

Biomass productiona cS O2 ! C B C S þ cB 4

DTH = 455 ± 15 4cS DT H 4 4cS DT H 4

DTH = 455 ± 15 Not defined cB cS DT H 4

Stoichiometry

CS + xO2 ? eCB + (1 e)CO2

DH, kJ/mol O2d DH, kJ/mol CO2c,e

DTH = 455 ± 15 x 1e DT H

DH, kJ/mol CSc

xDTH

Respiratory quotient, RQ = mol CO2/mol O2c

1e x

–

–

Rq RO2c RCO2c

aR q aRO2

(1 a)Rq (1 a)RO2 0

Heat production rate, J/s or Wf O2 consumption ratef CO2 production rate

RCO2

a

When the substrate is more reduced than the biomass produced, cB–cS > 0, and this reaction represents the actual oxidation process. When the substrate is more oxidized than the biomass produced, cB–cS < 0, and the reduction of substrate actually takes place by loss of CO2, not by loss of O2. However, as long as the overall reaction is correct, the separation into two reactions can be done in any way that does not violate stoichiometry. Writing the reaction in the way shown leads to a useful result, while writing the reaction with CO2 as a product makes it impossible to separate the two sources of CO2. Note that storage compounds are included in CS, not in CB, when the separation is made in this way. b c d e f

These reactions define the carbon conversion efficiency (e or CCE). cS . x ¼ ð1 eÞ 44cS þ e cB 4 Note that this enthalpy is the theoretical counterpart of Rq/RO2. Note that this enthalpy is the theoretical counterpart of Rq/RCO2. a ¼ 1x e 44cS .

Table 4 Examples of calorespirometric data (Rq, RO2 and RCO2) and conclusions that can be drawn by introducing different assumptions. Rq/mW

RO2/nmol/s

RCO2/nmol/s

Assumptions

Conclusion

1.0 1.0 1.0 1.0

2.2 2.2 2.8 2.2

2.2 2.8 2.8 1.5

cS = 0 cS = 0, cB = 0.25 cS = 0, cB = 0.25

e = 0 (steady-state, only maintenance) e = 0.77 (growth)

Steady-state

7. Examples of applications of calorespirometry Fig. 3 shows calorespirometric results from the literature that represents different aspects of such measurements. Fig. 3A shows an example of the type of calorespirometric measurement discussed in this paper. The measurement was made on two small insects; convenient study objects in isothermal calorimeters. The measured heat production rates were about Rq0 = 150 lW and Rq1 = 200 lW, so the carbon dioxide production rate RCO2 = 0.46 nmol s1, and the ratio Rq/RCO2 = 325 kJ mol1 (Eqs. (2) and (3)). Fig. 3B gives an example of a measurement on plant root tissue from which the carbon conversion efficiency has been evaluated [56] as a function of the temperature and the relative growth rate. Fig. 3C is from a measurement on glucose amended soil [57], a complex sample that is a microcosm of different organisms. From 3 to 10 h the heat production rate shows an exponential increase indicating growth of microorganisms. The ratio Rq/RCO2 is quite constant during the exponential phase, but then drops to significantly lower values, indicating a change of metabolic paths. Simultaneous calorimetry and oxygen consumption measurements make it possible to test whether an aerobic organism also has an anaerobic metabolic component. Fig. 3D gives the result of an experiment on an aqueous (non-terrestrial) system: eggs and larvae of a fish [58]. The ratio Rq/RO2 was determined at different ages in a calorimetric flow-through ampoule where the oxygen consumption was calculated from the difference between two oxygen sensor measurements. The mean Rq/RO2-value is close to Thornton’s constant (a significant part of the spread in the data is probably noise) indicating that the organism is strictly aerobic. Note that Thornton’s constant is not a strict constant, but can vary at least ± 15 kJ mol1 for different carbon sources (see [4,58] and the

Aerobic assumption probably not true as Rq/RO2 > DTH cS = 1.8 (lipid substrate)

present paper for a further discussion of this). A similar study is described in Ref. [47]; but comes to the conclusion that a significant portion of the metabolic heat was from anaerobic metabolism by the normal anabolic reactions involved in growth of the organism. Fig. 3E gives two examples of carbon conversion efficiency profiles as a function of temperature [59]. Calorespirometry is probably the only technique by which this type of results can be obtained within reasonable times. It is clearly shown that cabbage and tomato are adapted to totally different temperature regions. Such profiles should be useful in the discussion of organism adaption and what happens when the environment changes, for example if there is a shift to higher temperatures. Calorespirometry should also be able to give input to ecological models, for example those of Metabolic Theory of Ecology (MTE) [60] in which the central equation for how a factor B is a function of body mass M and temperature T is written (Eq. (12)):

B ¼ B0 f 1 ðMÞf 2 ðTÞ:

ð12Þ

In MTE, the second function is the Arrhenius equation, but this could be exchanged for temperature functions measured by calorespirometry, either related to rates or efficiency. The last example in Fig. 3F gives an example showing that calorespirometry can be used to follow changes in metabolic pathways as a function of time [31]. The shoot of white clover (Trifolium repens) contains photosynthetically produced substrate at the start of the measurement, and as this is consumed and decreases in amount, the activity of the sample also decreases. Most samples behave like this during calorespirometric measurements. The Penicillium mold growing on bread – a nutrient rich medium – is not limited by substrate availability, and therefore metabolizes at a rather constant rate. The carrot (Carota dauca)


8


B

0.8 150 0.6 100

0.4

50

0 0

50 100 Time / min

C

0.5 Relative spec. growth rate

1

D

520

Rq/RCO2 / kJ mol−1 Rq/RO2 / kJ/mol

500 400 300

q

200 100

1 0.8

Rq / μW g−1 5

10 Time / h

F cabbage tomato

ε 0.4 0.2 10 20 30 Temperature / °C

480 460 440

0

0.6

0 0

500

420 15

Heat prod. rate / mW

0 0

E

13 and 21 °C 25 °C

0.2

0 0

R and Rq/RCO2

1

200

ε

Heat prod. rate / μW

A

40

2

4 6 Time / days

8

0.5 clover 0.4 carrot 0.3 0.2 mold 0.1 0 0

2

4 Time / h

6

Fig. 3. Examples of calorespirometric measurement results. (A) The heat production rate of two convergent lady beetles Hippodamia convergens at 25 °C measured with the method described above (Fig. 2) [5]. (B) Carbon conversion efficiencies for Eucalyptus globulus root parts calculated from calorespirometric measurements at different temperatures (the two lower temperatures gave indistinguishable results). Drawn as a function of the relative growth rate (molC molC1 day1) [5]. (C) Results from calorespirometric measurements on a soil sample [9]. Two measurements with similar soil samples were made in parallel, one with and one without a carbon dioxide absorbent. (D) Measurements of Rq/RO2 for fish egg and larvae (turbot, Scophthalmus maximus) [58]. The gray bar indicates the time of hatching. (E) Measurement of carbon conversion efficiency as a function of temperature for cabbage and tomato [59]. (F) Heat rates from calorespirometric measurements as a function of time on three samples. Only Rq is shown here in order to show how the rates often change during a measurement [31].

was cut into small pieces before the measurement. Because of metabolic repair (wound healing) processes that start within a few hours after wounding, the rate of metabolism increases. As is seen from the above examples, calorespirometry has a wide area of use for studying complete, functioning biological systems of different types.

8. Conclusions Calorespirometry – the simultaneous measurement of heat and gas exchange rates – is an interesting method for the study of complete, functioning biological systems. However, to give correct results a valid evaluation model for the system under study has to be used. In the present paper we discuss the absorbent method for terrestrial calorespirometry and we exemplify the evaluation of such measurements with a model for strictly aerobic metabolism. Calorespirometry has the potential to both validate the evaluation model chosen and to generate – if the model is appropriate – for example carbon substrate conversion efficiencies and growth rates. The evaluation can also be performed with only respirometry, but respirometry cannot validate the model chosen, and it is probable that assumptions about steady-state and aerobic metabolism are incorrect in many cases. Calorespirometry is thus a preferable method.

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