Chapter 2

INTRODUCTION

The need for a mechanistic model of isoprene emission to predict future levels of emission has been highlighted by the key role that isoprene plays in atmospheric chemistry (Trainer et al., 1987; Chameides et al., 1988; Monson et al., 1991a) and the magnitude of global isoprene emissions, which are estimated to be of a similar order to biogenic methane production (Zimmerman et al., 1978; Rasmussen and Khalil, 1988; Monson et al., 1991a). The synthesis of isoprene from dimethylallyl pyrophosphate (DMAPP) by isoprene synthase is dependent upon light and is highly temperature sensitive (Tingey et al., 1979; Sanadze, 1991; Monson and Fall, 1989; Monson et al., 1992; Sliver and Fall, 1995). Emission rates are closely linked with carbon metabolism and ATP levels within the leaf (Loreto and Sharkey, 1990; 1993). Considering the high temperature dependency of isoprene emission, which would be expected to cause emission rates to rise in a warming climate, together with the potential of isoprene to increase atmospheric concentrations of ozone, PAN, CO and methane, there is a need to predict the effect of putative global warming conditions on isoprene emission rates (Monson et al., 1991a).

In the past, the inventory approach has been used to estimate present day canopy and ecosystem emissions of isoprene, by empirically scaling up emission rates measured at the leaf-level, using knowledge of leaf area dynamics and community species composition (Monson et al., 1991a), for examples see Lamb et al. (1987), Rasmussen and Khalil (1988), and Anastasi et al. (1991). This method has recently been improved by the inclusion of the empirical algorithm model of leaf isoprene emission rates of Guenther et al. (1991; 1993) (see Guenther et al., 1994; Geron et al., 1995). Although the model of Guenther et al. (1993) only considers the light and temperature dependency of isoprene emissions, it can predict the diurnal variations in hourly averaged emissions to within 35%. Humidity and atmospheric CO2 conditions, the two other driving variables included in the model of Guenther et al. (1991), only play a minor part in predicting instantaneous isoprene emission rates from leaves under present day conditions. Thus, the inhibition of isoprene emission rates at high Ci are not simulated by the improved model of Guenther et al. (1993), and the previous model of Guenther et al. (1991) could not predict the exponential decline in emission rates at high CO2 concentrations, as reported by Loreto and Sharkey (1990) (Figure 2.1). Therefore, as increased atmospheric concentrations of CO2 are expected to occur concurrently with global warming (Watson, 1990), it is apparent that a more robust, process-based approach to simulating isoprene emission rates might be more appropriate for the formulation of air quality policies for the future.

The rate of synthesis of isoprene will be controlled by the rate of the slowest reaction within its synthetic pathway, known as the "limiting rate" or the "rate-determining factor" (Lawlor, 1990). The rate of isoprene synthesis is suggested to depend on the minimum rate of the supply of carbon in the form of phosphoglyceric acid (PGA) or pyruvate, the rate of phosphorylation to supply the ATP needed for the conversion of PGA/pyruvate to DMAPP and the amount and in vivo activity of the enzyme isoprene synthase (Loreto and Sharkey, 1990; 1993; Sharkey et al., 1991a; Monson et al., 1992; Delwiche and Sharkey, 1993; Kuzma and Fall, 1993).

The overall aim of this chapter is to formulate a process-based model to enable the prediction of isoprene emission rates from leaves under future environmental conditions, and is to be accomplished by the following objectives. First, to construct and present a mechanistically-rich model of isoprene emission, using the findings of the most recent research on isoprene synthesis within the leaf, exploring the relationship between photosynthesis, photorespiration and isoprene emission during the construction of the model.

Second, to test the model against published data, using the relationships between rate of isoprene emission (Fiso) and photon flux density, concentration of carbon dioxide ([CO2]) and temperature. Third, to evaluate the coefficients and parameters of the model using sensitivity analysis. Fourth, to use the model to predict the effects of rising temperature and elevated [CO2] on leaf isoprene emission rates, both singly and in combination, thus simulating emission rates under conditions of putative global warming. Finally, the increased knowledge gained during model construction of the relationship between of photorespiration and isoprene synthesis is discussed.

2.2.1 Outline of model structure

The mechanistic model proposed for leaf isoprene emission rates is based on the determination of the limiting rate for each of the three processes known to control isoprene production: 1) the rate of supply of carbon for the isoprene molecule skeleton, 2) the rate of supply of ATP by phosphorylation, and 3) the rate of the reaction catalysed by isoprene synthase (Loreto and Sharkey, 1990; 1993; Sharkey et al., 1991a; Monson et al., 1992; Delwiche and Sharkey, 1993; Kuzma and Fall, 1993). The interrelationships between model driving and state variables, constant parameters and rate processes are illustrated in the relational diagram, Figure 2.2. Although there are four rate processes illustrated in the model diagram, the rate of the intermediate pathway for the conversion of pyruvate to DMAPP is assumed to be controlled by the rate of ATP production from phosphorylation, and is not itself considered to control the rate of isoprene synthesis.

The driving variables are carbon dioxide and oxygen partial pressures, light, temperature and humidity. The partial pressures of carbon dioxide and oxygen drive isoprene synthesis by driving photosynthesis and photorespiration. Light, in addition to driving photosynthesis and photorespiration, also drives phosphorylation rates, via the electron transport chain, and is assumed to affect isoprene synthase activity via the provision of Mg2+ and optimum pH within the chloroplast. Temperature drives the rate of the isoprene synthase catalysed reaction, and plays a major role in controlling isoprene emission rates (Monson et al., 1992). Temperature also affects the rates of both photosynthesis and photorespiration, and affects their response to [CO2] (Long, 1991). Humidity has a relatively minor effect on rates of leaf isoprene synthesis, as stomatal conductance does not influence emission rates (Fall and Monson, 1992). Under low light conditions, humidity may have a minor effect on rates of isoprene synthesis via the effects of stomatal conductance on carbon dioxide uptake. Throughout this thesis, water is assumed to be non-limiting.

The state variables are the amount of carbon for the skeleton of isoprene, represented in the diagram by pyruvate, together with the amounts of ATP, ADP, DMAPP and isoprene. The amount of the carbon to be used for isoprene that is synthesised within the chloroplast affects the rate of the intermediate conversion pathway forming DMAPP. The effects are both direct, through the supply of the amount of substrate for the conversion pathway, and indirect, via the feedback effects on rates of phosphorylation and ATP production. The feedback effect is mediated by the reversal of sensitivity of photosynthesis and pyruvate production, to carbon dioxide and oxygen concentrations. The concentration of ATP has the potential to limit the rate of conversion of pyruvate to DMAPP. The amount of DMAPP affects the rate of the isoprene synthase reaction directly by substrate supply, and may have a feedback effect on the conversion rate of carbon substrate to DMAPP. Due to the high volatility of isoprene and the lack of stomatal control over its emission from the leaf, isoprene is assumed not to accumulate within the leaf to levels high enough to cause a feedback effect on isoprene synthase activity.

The amount of the two principal enzymes controlling isoprene production, Rubisco and isoprene synthase, included in the model as constants, are affected by growth conditions such as temperature, light and nitrogen. The amount and activity of Rubisco and isoprene synthase affect the rates of photosynthesis and photorespiration, and isoprene synthesis from DMAPP, respectively (Harley et al., 1994). Another constant included in the model is the species-specific emission magnitude constant, representing the quantity of isoprene "typically" emitted by the species. Species have been divided into the four categories of high, medium, low and non-emitters by Evans et al. (1982) and Guenther et al. (1994).

The determination of which one of the three potentially controlling steps is limiting the rate of isoprene emission, requires the dynamic calculations of carbon flux through Rubisco. The flux of carbon was determined by the equations of Farquhar et al. (1980), which were obtained from the existing WIMOVAC model (Windows Intuitive model of Vegetation Response to Atmosphere and Climate Change) (Humphries and Long, 1995). WIMOVAC is a plant leaf and canopy photosynthesis software package written in Microsoft Visual Basic. It is a modelling system designed to provide easily accessible leaf and canopy models of photosynthesis in order to allow simulation of the effects of global climate change on vegetation. WIMOVAC is subdivided into defined interacting modules, which allows the easy development of models of leaf and canopy photosynthesis (Figure 2.3). The programming code of the model is written in the object oriented Visual Basic language format, but with strings of text large enough to allow variables to be given self explanatory names, and with Windows oriented graphics to allow user-friendly control of input variables and design of simulated results. The structure and inherent flexibility of WIMOVAC, which allows a wide variety of users, not just modellers and computer programmers, together with its versatility and wider application to leaf, canopy and ecosystem levels of organisation, were the main considerations in choosing this method of programming the isoprene emission module. The modular structure, for example, allowed the newly constructed mechanistic leaf isoprene emission module to be easily integrated with the existing module of Farquhar's biochemical model of leaf photosynthesis, required to calculate both the flux of carbon through the Rubisco and the availability of ATP, represented by the reversal of sensitivity of photosynthesis to carbon dioxide and oxygen.

The rate determined to be limiting isoprene synthesis is multiplied by a species dependent coefficient, s s, to represent the species specific magnitudes of isoprene emission. The present isoprene module is based on the work conducted on aspen (Populus tremuloides Michx.) by Monson and Fall (1989), which supplied the most comprehensive measured data of the temperature dependence of isoprene emission, central to the control of emission rates. Plants can be divided into four categories of emitter, according to magnitude of emissions measured (Evans et al., 1982). The high, medium, low or non-emitter categories have been evaluated as emitting 70± 35, 35± 17.5, 14± 7 and <0.1 µgC g-1h-1, respectively, at a leaf temperature of 30oC and at a photon flux density (PFD) of 1000 µmol m-2 s-1 (Guenther et al., 1994). However, aspen (Populus tremuloides), red oak (Quercus rubra), eucalyptus (Eucalyptus globulus Labill.) and velvet bean (Mucuna pruriens), all classified as belonging to the high emitter category, vary considerably in their light saturated emission rates.

Therefore, the species dependent coefficient is included to allow scaling of the aspen emission rates to individual species, within the leaf emission module, by multiplication of a scaling factor corresponding to the ratio of magnitudes of leaf emissions of the species concerned. The species dependent scaling factor was included in the model for later use, for example, within future canopy isoprene emission rate models where species composition data is available. Due to a lack of data, the coefficient was not used within the models presented in this thesis.

2.2.2 The supply of carbon for the molecular skeleton of isoprene

The source of carbon for isoprene production is closely linked to the photosynthetic carbon reduction pathway (Sharkey et al., 1991a; Delwiche and Sharkey, 1993; Loreto and Sharkey, 1993). The precursor of isoprene, dimethylallyl pyrophosphate, is thought to be produced by the mevalonic acid pathway from acetyl CoA, although the exact pathway for the conversion of carbon, in the form of pyruvate, to DMAPP is uncertain (Sharkey et al., 1991a). For example, it has not been determined whether the isomer of DMAPP, isopentenyl pyrophosphate (IPP), is formed within the chloroplast, or is imported from the cytosol. Although Sharkey and co-workers could suggest five conceivable sources of carbon, by tracing the possible paths of carbon to isoprene backwards from isoprene to photosynthetic carbon pools, the most likely pathway is thought to be from pyruvate formed directly from Rubisco carboxylation and oxygenation. Pyruvate is produced by such reactions about 1% of the time (Andrews and Kane, 1991; Sharkey et al., 1991a).

Although the experiments of Hewitt et al. (1990) have ruled out a direct relationship between isoprene emission rates and photorespiration under relatively low ambient CO2 partial pressures (450 µbar or less), an indirect link between isoprene emission rates and photorespiration, such as via production rates of the substrate DMAPP, is not ruled out. If the rate of isoprene emission from a leaf is assumed to reflect the rate of flux of carbon through both the photosynthetic and photorespiratory pathways, this would explain the light dependence of isoprene emission; the presence of magnesium ions and pH of 8 in the stroma, which are conducive to isoprene synthase activity and are present during photosynthesis; the inhibition of emissions of isoprene only in air concurrently depleted in both CO2 and O2; the lack of a CO2 compensation point in the relationship between Fiso and Ci; and the good correlation found between PGA concentration and isoprene emission rates at low CO2 concentrations.

Therefore, at least phenomenologically, isoprene emission appears to be related to carbon flux through Rubisco, and the link could be the small amount of pyruvate that is formed as a by-product of Rubisco catalysed reactions (Andrews and Kane, 1991; Sharkey et al., 1991a). The pyruvate may then be converted to IPP and DMAPP via the mevalonic acid pathway (Sharkey et al., 1991a). Whatever the exact path is, as isoprene synthesis can occur when either Rubisco carboxylation or oxygenation occurs, it is assumed for the purposes of this model, that both photosynthesis and photorespiration provide the skeletal carbon for isoprene synthesis within the leaf, and therefore the amount of carbon for isoprene formation can be represented mathematically by taking a small percentage of the flux of carbon through RubP carboxylation and oxygenation. It is further assumed that, as PGA is formed by both carboxylation and photorespiration, and as the rate of labelling of the carbon molecules of isoprene by 13C closely follows the pattern of the rate of labelling of PGA, the carbon for isoprene synthesis can be represented mathematically by a percentage of the PGA synthesised (Delwiche and Sharkey, 1993). This provides a basis for calculating the flux of carbon through Rubisco, which is represented by the additional rates of photosynthesis and photorespiration in the ratio 2:3, as each carboxylation reaction produces two molecules of PGA and each CO2 evolved in photorespiration involves the production of three molecules of PGA.

Only a fraction of the carbon assimilated by photosynthesis is used in isoprene formation, typically between 1 and 2% at temperatures of between 25 and 30oC. The exponential relationship between the fraction of carbon assimilated used in isoprene formation and leaf temperature (T) must, for now, be modelled empirically (Monson et al., 1991a).

2.2.3 Phosphorylation and the availability of ATP

Under elevated [CO2] or low light conditions, where the supply of carbon is not limiting, the reduction in rates of isoprene synthesis is found to be highly correlated with ATP content (Monson and Fall, 1989; Loreto and Sharkey, 1993). ATP limitation of isoprene synthesis is thought to be effective at the levels of the enzymes mevalonate kinase, phosphomevalonate kinase, or pyrophosphatemevalonate kinase (Loreto and Sharkey, 1993). Two molecules of ATP are required for the pyrophosphorylation of mevalonic acid to IPP within the process which converts pyruvate to IPP. Thus, isoprene synthesis can be assumed to be highly sensitive to phosphorylation at high Ci, due to both the requirement of phosphate for DMAPP formation, and the effects low phosphate levels have on the pH of the stroma. It is assumed for the purpose of the model that ATP limitation effects on isoprene synthesis may be considered extreme, and thus can be represented by a reversal of the sensitivity of photosynthesis to intercellular concentrations of carbon dioxide and oxygen, as found under the extreme photosynthesis feedback-limited conditions, caused by high rates of photosynthesis, at high Ci (Sharkey, 1985; Sharkey et al., 1991a). Feedback limitation of photosynthesis is caused by high rates of CO2 assimilation, which produce such large quantities of phosphorylated products that the capacity of the chloroplasts to convert these products to starch or sucrose is exceeded and inorganic phosphate is not released, causing reduced phosphate levels in the stroma, which limit ATP production and alters the pH of the stroma (Sharkey et al., 1991a). Sharkey's model to predict the insensitivity of photosynthesis to Ci and Oi, using the limitation of triose phosphate utilisation (TPU) however, cannot predict the reversal of the sensitivity, as the ratio of A at 21% O2 to A at 3% O2 never exceeds 1 (Sharkey, 1985). Thus, a new model equation is constructed to predict the reversal of sensitivity, using the ratio of intercellular oxygen and the addition of oxygen by carboxylation, to intercellular CO2 and the addition of CO2 by rates of dark respiration and photorespiration ((Oi+Vc)/(Ci+Vpr+Rd)). The reversal of sensitivity of isoprene formation to [CO2] and [O2] could also explain the apparent relationship between photorespiration and isoprene emission under high CO2 partial pressure, not necessarily apparent under the lower [CO2] conditions used in the experiments of Hewitt et al. (1990). Thus, it is assumed that the rate of conversion of pyruvate to IPP and DMAPP is controlled by the limiting rate of phosphorylation (Figure 2.2).

2.2.4 Isoprene synthase activity

The third process that controls the rate of isoprene production is the catalysed elimination of pyrophosphate from DMAPP to form isoprene, which occurs within the chloroplast, and is controlled by the amount and activity of the enzyme isoprene synthase (Sanadze, 1991; Mgaloblishvili et al., 1978; Silver and Fall, 1991; 1995). Isoprene synthase has been detected in leaves of velvet bean (Mucuna pruriens), aspen (Populus tremuloides) and willow (Salix alba), all isoprene-emitters, but has not been extracted from any non-isoprene emitting plants (Kuzma and Fall, 1993; Silver and Fall, 1991; 1995). The temperature sensitivity of isoprene emission rates parallel the in vitro temperature dependency of isoprene synthase, which suggest isoprene production rates are controlled by the in vivo activity of the enzyme (Monson et al., 1992). Further evidence of control of isoprene production by this enzyme is given by a rise in isoprene synthase activity in parallel with isoprene emission during leaf development (Kuzma and Fall, 1993).

Isoprene synthase has a high temperature optimum varying from 38oC to 45oC, according to growth temperature (Monson et al., 1992; Silver and Fall, 1995). The presence of magnesium ions and a pH of 8 are required for efficient catalysis (Silver and Fall, 1995). Both the presence of magnesium ions and a pH of 8 are provided by the chloroplast stroma during photosynthesis. Thus isoprene synthase is most active when stromal conditions are signalling the occurrence of photosynthesis.

Phenomenologically, the temperature dependence of isoprene synthase activity closely parallels the simple Arrhenius temperature-dependent relationship for an enzyme which can exist in both an active and an inactive state, taken from Thornley and Johnson (1990). This equation was parameterised to fit the data of Monson and Fall (1989) for the temperature sensitivity of isoprene emission rates of aspen, until values for the parameters of in vivo enzyme kinetics of isoprene synthase can be established. Current in vitro determinations are thought to be flawed by the extraction techniques (Silver and Fall, 1995).

2.2.5 Summary

To summarise, the model of leaf isoprene emission rates is based on the knowledge that isoprene emission from a leaf requires carbon for the skeletal structure of isoprene, is dependent on ATP supply in the stroma and is correlated with the temperature dependency of the isoprene synthase reaction (Loreto and Sharkey, 1990; 1993; Monson et al., 1992). Assumptions made for the purpose of modelling leaf isoprene emission rates are that the carbon required for isoprene formation is derived from both photosynthesis and photorespiration, and that the rate of conversion of pyruvate to IPP is dependent on the rate of phosphorylation. Therefore, the model is based on the premise that the rate of isoprene emission from a leaf is determined by the availability of carbon, the availability of ATP and the temperature dependency of the activity of isoprene synthase rate reaction.

2.3.1 Model overview

The isoprene emission rate is calculated as the limiting rate of the three processes known to control isoprene production, the rate of supply of pyruvate (Wisoco), the rate of supply of ATP by phosphorylation (Wisop) and the rate of the reaction catalysed by isoprene synthase (Wisomax), multiplied by a species dependent coefficient, s s, and subsequently converted from units of µmolC m-2 s-1 to units of nmol m-2 s-1 (Equation 2.1, Table 2.1). This method assumes the absence of large pools of substrates within the synthesis process, a method similarly employed within the well-validated model of Farquhar et al. (1980) (Long, 1991). The isoprene emission rate sub-model was integrated into the model of Humphries and Long (1995). The carbon dioxide assimilation module is required to calculate the rates of carboxylation.

2.3.2 Carbon dioxide assimilation model

In order to calculate the rates of carbon flux through Rubisco, the mechanistic biochemical equations of leaf carbon dioxide assimilation rates (A) were used (Farquhar et al., 1980; Farquhar and von Caemmerer, 1982) (Equations A.1-A.10, Table A, Appendix I, p.196). The Farquhar model equations, which are listed in Table A, as they are common to more than one chapter, have been widely used and validated (Long, 1985; Long and Drake, 1991; Harley et al., 1992). The equations are described in Long (1991) and Evans and Farquhar (1991). To calculate the rate of assimilation, which is required to calculate stomatal conductance and Ci, dark respiration is deducted from the product of the minimum of the three limiting rates of carboxylation and the fraction 1-G */Ci (Equation A.1). The other part of the fraction, G */Ci, represents the fraction of RubP activity that is photorespiration. The term G * is the CO2 compensation point of photosynthesis in the absence of dark respiration (Rd), which is dependent on the Michaelis-Menten constants and maximum rates of carboxylation and oxygenation, and the intercellular concentration of oxygen (Equation A.2).

Table 2.1: Model equations to calculate leaf photorespiration and isoprene emission rates. Equation 2.10 is adapted from Thornley and Johnson (1990). Definitions of the symbols used are listed in Appendix II.

The intercellular concentrations of oxygen and carbon dioxide are calculated for a temperature of 25oC by Equations A.3 and A.4, respectively. The parameters of Farquhar et al. (1980) were for a leaf temperature of 25oC, which have been corrected for the appropriate temperatures relative to 25oC, both for Rubisco kinetic Michaelis constants response and for the varying solubility's of CO2 and O2 (Equation A.5) (Jordan and Ogren, 1984; Linke, 1965; Kaye and Laby, 1973; Long, 1991). The three limiting rates of carboxylation consist of the RubP saturated rate of carboxylation (Wc), the RubP limited rate of carboxylation (WJ) and the phosphorylation limited rate of carboxylation (Wp). Equations A.6 and A.7 are used to calculate (Wc) and (WJ). The two-step calculation of Evans and Farquhar (1991) is used for the relationship between irradiance and potential rate of electron transport (Equations A.8 and A.9). Firstly, the irradiance usefully absorbed by photosystem II (I2) is related to the incident irradiance (I0), where f is the dimensionless coefficient of the fraction of light not absorbed by functional photosynthetic pigments and r is the reflectance. The potential rate of electron transport can then be related to the light-saturated rate of electron transport (Jmax), the absorbed irradiance and the curvature factor (q c) of the assimilation/light response relationship. Finally, the stomatal response is described by the phenomenological equation of Ball et al. (1987) as modified by Harley et al. (1992) (Equation A.11). A definition of symbols are listed in Appendix II.

Thus, the equations listed in Table A (p.196) were used to calculate the values of the parameters required for the equations of the mechanistic isoprene emission model (rates of carboxylation, dark respiration, intercellular CO2 and O2 concentrations, and leaf temperature) which were already incorporated into the plant leaf and canopy photosynthesis software package WIMOVAC (Humphries and Long, 1995).

2.3.3 The rate of pyruvate formation in the stroma

To simulate the limiting rate of pyruvate formation in the stroma (Wisoco), the flux of carbon through Rubisco (FPYR) is multiplied by the parameter h , which represents the fraction of carbon assimilated that is lost as isoprene (Equation 2.2, p.42). The data of Monson and Fall (1989) was used to find h . Their data for the dependence of isoprene emission rates on leaf temperature was fitted to the exponential relationship: h = Exp(bT+a) (Equation 2.3) (Figure 2.4). Dark respiration is deducted from the flux of carbon through Rubisco, to give the rate of pyruvate formation (FPYR) (Equation 2.4). As RubP carboxylation produces two molecules of PGA and photorespiration produces three molecules of PGA, the relationship between Vc and Vpr is calculated in the ratio 2:3, although the calculation of G * (Equation 2.13), reduces the effective production of PGA to 1.5 molecules from photorespiration, due to the requirement of two molecules of glycine for each serine molecule produced, and thus two molecules of RubP for each CO2 evolved. The flux of carbon is dependent upon the rates of RubP carboxylation (Vc) and concurrent photorespiration (Vpr). The calculation of carboxylation rates (Vc) is described by Equation 2.5, which requires the determination of the minimum rates of the RubP saturated rate of carboxylation (Wc); the RubP limited rate of carboxylation (WJ) and the phosphorylation limited rate of carboxylation (Wp) (Equations 2.6-2.14). Photorespiratory rates are determined by the fraction of assimilation and dark respiration that is not photosynthesis, represented by Equation 2.15, using the fraction G */Ci in place of 1-G */Ci in the assimilation rate relationship of Equation A.1. Photorespiration (Vpr) requires the determination of the minimum rates of the RubP saturated rate of carboxylation (Wc); the RubP limited rate of carboxylation (WJ) (Equations 2.5-2.13), together with the phosphorylation limited rate of photorespiration (Wop) (Equation 2.16). The latter equation was adapted from the phosphorylation limited rate of carboxylation, by replacing the fraction (1-G */Ci) with (G */Ci), in order to prevent the inconsistent occurrence of a CO2 compensation point in the Fiso/Ci relationship. Thus, the supply of pyruvate for isoprene synthesis is the product of h and the flux of carbon through Rubisco (FPYR) (Equation 2.2).

2.3.4 Phosphorylation limitation of DMAPP production

The limitation of isoprene production under high Ci conditions, assumed to be limited by rates of phosphorylation and ATP availability, as represented by Equation 2.17, where the reversal of the sensitivity of photosynthesis to Ci and Oi is represented by the factor ((Oi+Vc)/(Ci+Vpr+Rd)). As this phenomenon was first noticed to affect photosynthetic rates, the ratio Vc:1.5Vpr is used to represent the ratio of photosynthesis to photorespiration. Therefore, the product of h , the percentage of carbon assimilated used for isoprene, and (Vc+1.5Vpr)-Rd is multiplied by ((Oi+Vc)/(Ci+Vpr+Rd)) to determine the potentially limiting rate of phosphorylation to isoprene synthesis (Equation 2.17, p.42).

2.3.5 Temperature dependency of isoprene synthase reaction rate

The third potential rate limitation of isoprene production is the activity of isoprene synthase. Here the enzyme reaction rate is simulated by a simple Arrhenius temperature-dependent relationship for an enzyme which can exist in both an active and an inactive state, taken from Thornley and Johnson (1990) (Equation 2.18). The parameter values of the equation given in Thornley and Johnson were adjusted slightly to give simulations that describe the temperature response of isoprene emission rate from aspen (Populus tremuloides Michx.). The data shown is of emissions from two different experiments, together with the model simulation curve (Figure 2.5).  

2.3.6 Model validation

In order to test the model, the results of simulated isoprene emission rates were compared with those published in the literature, under comparable experimental conditions. As the published data of measured isoprene emission rates come from a variety of sources, using a variety of species and using inherently different experimental protocols, the results for testing model behaviour are presented as a percentage of the maximum emission rates. The finding that plant growth conditions such as light and nitrogen levels can also alter the magnitude of isoprene emissions further supports the use of this method of presenting the results (Harley et al., 1994). The data used for model validation testing are from Loreto and Sharkey (1990); Sharkey et al. (1991b); Monson et al. (1991b) and Monson et al. (1992). The leaves used in the published research were from red oak (Quercus rubra), aspen (Populus tremuloides), eucalyptus (Eucalyptus globulus Labill.) and velvet bean (Mucuna pruriens).

The magnitude of isoprene emissions further supports the use of this method of presenting the results (Harley et al., 1994). The data used for model validation testing are from Loreto and Sharkey (1990); Sharkey et al. (1991b); Monson et al. (1991b) and Monson et al. (1992). The leaves used in the published research were from red oak (Quercus rubra), aspen (Populus tremuloides), eucalyptus (Eucalyptus globulus Labill.) and velvet bean (Mucuna pruriens).

For clarity, as the data for model testing simulations were collected from a number of sources, the values of driving variables used together with the species tested and the references where the data was obtained, are set out in Table 2.2. The values of the driving variables are those recorded for the specific experiments. Where humidity was not given it was assumed to be 70% RH. Values of other model variables were common to more than one chapter (Table 2.3 and Appendix II, p.203).

2.3.7 Sensitivity analysis

A sensitivity analysis of the two main model coefficients was conducted to determine their effects on model simulations of isoprene emission rates under varying environmental conditions. The coefficient h , which affects both the rate limited by carbon supply and the rate limited by phosphorylation, and the coefficient niso, which affects the rate limited by isoprene synthase capacity, were first reduced and then increased by both 10% and 50% for the initial sensitivity analysis, to gain an insight to how these two coefficients affect the relationships between rates of isoprene emission and light, [CO2] and temperature. The standard conditions chosen for the sensitivity analysis were a PFD of 1000 µmol m-2 s-1, ambient [CO2] of 350 µmol mol-1 and a leaf temperature of 25oC.

For a more detailed analysis, using the same standard conditions, the values of Vc, Vpr, Rd, Oi and Ci were also altered by 10%, assumed to be sufficient to reflect general trends, and the percentage change in predicted values of chosen parameters was noted. The chosen parameters were the quantum yield of isoprene emission (f iso), calculated as the initial slope of relationship between Fiso and PFD, and the light saturated rate of isoprene emission at carbon dioxide concentrations of 350 (Fiso[CO2]=350) and 650 µmol mol-1 (Fiso[CO2]=650).

Table 2.3: Values of model parameters used in leaf isoprene emission model simulations.

 emission at carbon dioxide concentrations of 350 (Fiso[CO2]=350) and 650 µmol mol-1 (Fiso[CO2]=650).

 2.3.8 Prediction of leaf isoprene emission rates under increased temperature and elevated [CO2] conditions

The model was used to predict the interactive effects of elevated [CO2] and rising temperatures on leaf isoprene emission rates, by simulating emission rates under conditions of putative global warming. In order to simulate the interactive effects of rising temperatures and [CO2], leaf emission rates of isoprene at 1000 µmol m-2 s-1 were simulated over a range of atmospheric [CO2] from 0 to 700 µmol mol-1, at three different temperatures. The temperatures were the assumed normal, of 25oC, together with 26 and 27oC to simulate a rise of 1 and 2oC.

The model was used to simulate the light response of isoprene emission rates at very high and low [CO2], 1382 µmol mol-1 (1400 µbar) and 148 µmol mol-1 (150 µbar), respectively, corresponding to data of Loreto and Sharkey (1990). Finally the effects of higher temperatures and elevated [CO2] on the light response of isoprene emission were simulated, both individually and then in combination. The temperatures used were 25 and 27oC and the [CO2] were 350 and 650 µmol mol-1.

2.4.1 Model simulation tests

2.4.1.1 Response of isoprene emission rates to photon flux density

The simulated results agreed well with all three sets of measured data used to test model simulations of the response of isoprene emission to light, except at the transition between light-limitation and light-saturation, where a lower convexity than simulated is observed. For example, the simulation closely agreed with reported emission rates for Eucalyptus globulus (Figure 2.6), but the difference in convexity between simulated and observed data in the simulation for the second set of data for Quercus rubra, resulted in a greater than twenty percent overestimation of simulated isoprene emission rates, at a PFD of 1000 µmol m-2 s-1 (Figure 2.7). The simulation of the response of isoprene emission rates of Mucuna pruriens to light at two temperatures predicted the proportionate increase in the isoprene emission light saturated rate from 26 to 34oC well, but again, due to the greater convexity of the simulated data at the transition between light-limitation and light-saturation, the model overpredicted the emission rate by approximately 20%, at the lower light level of 500 µmol m-2 s-1 (Figure 2.8).

The greater convexity of model simulations is due to limitation in the model by isoprene synthase activity, which, if removed would give Fiso/light curves of a similar shape to CO2 assimilation/light curves.

2.4.1.2 Response of isoprene emission rates to CO2 concentrations

The first two sets of data, to test model simulations of the response of isoprene emissions to carbon dioxide concentrations, are from Loreto and Sharkey (1990). The response is well correlated at the relatively high light level of 700 µmol m-2 s-1 for the response of emissions from Q. rubra up to Ci concentrations of nearly 1600 µmol mol-1. The "plateau" of maximum isoprene emission rates for a Ci between 150 and 400 µmol mol-1, the decline in emissions at high Ci and the inhibition of Fiso at Ci less than 100 µmol mol-1, are all closely mimicked. However, the model underestimates Fiso within the 150 to 400 µmol mol-1 range of Ci under the relatively low light conditions of 180 µmol m-2 s-1 and 80 µmol m-2 s-1 (Figure 2.9).

The simulated data of the response of isoprene emission from Q. rubra to Ci, at the higher light level of 1500 µmol m-2 s-1, follows the general trend of the measured data, except the model does not predict the unexpected dip in the isoprene emission rates measured at Ci of 280 µmol mol-1 (Figure 2.10). The model predicts the reduced emission rate at Ci of less than 60 µmol mol-1, although the minimum value of Fiso near zero Ci is overestimated by the model simulation.

The predicted change in Fiso with Ca loosely follows the pattern of data measured by Sharkey et al. (1991b), for the response of isoprene emission of Q. rubra and P. tremuloides to [CO2] at a light level of 900 µmol m-2 s-1 (Figure 2.11). However, evidence to support the predicted decline in isoprene emission at high Ca is ambiguous. For example, the variability in the data points of the predicted "plateau" of Fiso values for P. tremuloides, between approximately 60 and 450 µmol mol-1, make it difficult to determine whether or not the data point at Ci of approximately 720 µmol mol-1 reflects the predicted decline in isoprene emission rates at high Ci. In addition, the predicted decline at high Ci is not evident in the measured data of Q. rubra (Figure 2.11). The predicted low emission rate at Ci of less than 60 µmol mol-1 is observed, although the minimum value of Fiso near zero Ci is underestimated for P. tremuloides. The model does not predict minor variations between the isoprene emission responses of different species.

2.4.1.3 Response of isoprene emission rates to temperature

The predicted response of isoprene emission rates to temperature is closely correlated with the data measured by Monson et al. (1992) for M. pruriens up to 44oC, despite the use of a different plant species to that used for model construction (Figure 2.12). The difference between the predicted and measured isoprene emission rates at an extremely high temperature of 50oC results from the assumption that the enzyme isoprene synthase is inactivated by such high temperatures.

2.4.2 Sensitivity analysis

Changing h by 10% caused changes in the light response curve at light levels of less than approximately 500 µmol m-2 s-1 (Figure 2.13a). Changes due to carbon availability were also evident in the [CO2] response, Figure 2.13b, causing a 10% change in the emission rate at zero [CO2], also causing a change in the extent of the [CO2] "plateau". Changes via phosphorylation limiting rates were apparent at high [CO2] (Figure 2.13b). Altering the value of h by 10% had negligible effects on the temperature response of isoprene emission (Figure 2.13c). The increases in light and [CO2] responses are augmented by a 50% increase in h , but a 50% reduction causes a dramatic decrease in the response of Fiso to light, [CO2] and temperature.

The marked effects on the response of Fiso to light, ambient [CO2] and temperature to a 10% alteration in niso, the isoprene temperature coefficient, were enhanced by a 50% change (Figure 2.14a, b and c). The light saturated rates of isoprene emission were affected, increasing by 10% with a 10% increase of niso (Figure 2.14a). Fiso under the range of Ca from approximately 50 to 400 µmol mol-1 were affected, as was extent of the plateau, particularly at high Ci (Figure 2.14b). The changes were, as expected, reflected in the temperature responses (Figure 2.14c). These results, together with those of the more detailed sensitivity analysis are presented in Table 2.4.

A 10% change in carboxylation rates (Vc) results in a similar 10% change in both the quantum yield of isoprene emission and a slightly greater change in isoprene emission rates under elevated [CO2], but no change at ambient [CO2] of 350 µmol mol-1 (Table 2.4). A 10% alteration in rates of both photorespiration and dark respiration were found to have only a small effect on Fiso, under low light conditions and high [CO2]. A 10% change in intercellular oxygen concentrations had an approximately 9% effect on both the quantum yield of isoprene emission and Fiso at elevated [CO2]. A 10% change in Ci under low light conditions causes an effect in the opposite direction on the quantum yield of isoprene emission, but no effect at light saturated rates, either at ambient or elevated [CO2] (Table 2.4).

Table 2.4: The percentage change in predicted quantum yield of isoprene emission, (f iso); and light saturated isoprene emission rates at Ca of 350 and 650 µmol mol-1 (Fiso[CO2]=350 and Fiso[CO2]=650, respectively), with a 10% change in the value of the model parameters listed. Standard conditions were PFD = 1000 µmol m-2 s-1; [CO2] = 350 µmol mol-1; and T = 25oC, and nc denotes no change.

 2.4.3 Isoprene emission rates under high temperature and elevated [CO2]

Increase in temperature from 25oC to 27oC is predicted to cause a 37.6% increase in isoprene efflux at [CO2] of 350 µmol mol-1 and 42.3% increase at [CO2] of 650 µmol mol-1 (Figure 2.15). An increase in [CO2] from 350 to 650 µmol mol-1 is predicted to cause a 11.2% decrease in emission rate at 25oC, and 8.1% decrease at 27oC (Figure 2.15). Thus, a concurrent increase in temperature of 2oC and increase in [CO2] from 350 to 650 µmol mol-1 would, according to the model, cause an overall increase in isoprene emission of 26.4%, at an isoprene emission light saturating rate of 1000 µmol m-2 s-1.

The model slightly underestimates the emission at low Ca, at very low light levels of between 0 and 200 µmol m-2 s-1, and overestimates Fiso under high Ca at high light levels, when tested against the data of Loreto and Sharkey (1990) (Figure 2.16). An increase in temperature of 2oC, from 25 to 27oC at both ambient and elevated [CO2] is predicted to cause a dramatic increase in the rates of isoprene emission (Figure 2.17). However, increasing carbon dioxide concentrations at present day temperatures are predicted to cause a decrease in Fiso, particularly at low light levels. Meanwhile, a concurrent increase in atmospheric [CO2] with rising temperature is predicted to reduce the quantum yield of isoprene emission and increase the light level at which light saturated maximum isoprene emission rates are reached.

DISCUSSION

The first objective of this chapter, to construct a mechanistically-rich model, has been achieved by basing the model on the three potentially limiting processes underlying isoprene synthesis, namely, pyruvate supply to provide the substrate of isoprene carbon, ATP supply for phosphorylation to DMAPP, and the rate of isoprene synthesis from DMAPP, controlled by the temperature dependency of the active enzyme isoprene synthase. Mechanistic methods were used wherever possible to calculate the rates of the three potentially limiting rate processes. For example, the limiting rate of carbon availability, represented by the flux of carbon through RubP carboxylation and oxygenation, uses the well validated biochemical mechanistic model equations for photosynthesis (Farquhar et al., 1980; Farquhar and von Caemmerer, 1982). The isoprene emission model is based on the findings collected from most recent research into isoprene synthesis and emission, and include the biochemical analysis of isoprene synthesis, as well as data of emission rates measured at the leaf level (Loreto and Sharkey, 1990; 1993; Delwiche and Sharkey, 1993; Monson et al., 1992; Kuzma and Fall, 1993; Silver and Fall, 1991; 1995). The use of the limiting rates of pyruvate production in the stroma and ATP availability, known to limit isoprene synthesis, together with the temperature dependency of the isoprene synthase reaction, provides a comprehensive predictive model of isoprene emission rates from a leaf, which can be used to simulate the effects of environmental conditions on isoprene emission rates, via the effects on these limiting rates.

The second objective, to test the results of model simulations under changing light, carbon dioxide concentrations and temperature conditions against published data, was achieved by comparing predicted emission rates with the data from three different papers, Loreto and Sharkey (1990); Monson et al. (1991b) and Monson et al. (1992), which found the model to mimic the proportionate change in leaf isoprene emission rates with changing environmental conditions (Figures 2.6 to 2.12). This generally good correlation is in spite of the fact that the measured data was for a different species to that on which the model was based, namely, Populus tremuloides. However, absolute quantities were not so accurately predicted. Other small variations between model simulations and measured data include: 1) the greater convexity of light response model simulations, due to limitation in the model by isoprene synthase activity, which, if removed would give Fiso/light curves of a similar shape to CO2 assimilation/light curves, 2) the underestimation of Fiso under low light conditions, Figure 2.9, 3) the lack of evidence to support the predicted decline in isoprene emission at high Ca in Figure 2.11, due to the scatter of data points, and 4) the underestimated minimum emission rate predicted for P. tremuloides at a Ci of 0 µmol mol-1, Figure 2.11, due to the inability of the model to predict minor inter-species variations of isoprene emission response.

The third objective, to evaluate the two main model coefficients, niso and h , together with the parameters Vc, Vpr, Rd, Oi and Ci by sensitivity analysis was conducted by comparing the values of predicted quantum yield, and light saturated rates at ambient and elevated [CO2] when values of the coefficients and parameters were changed by 10%. The results of the sensitivity analysis showed that the most important coefficient under high light and ambient [CO2] conditions is niso, the temperature coefficient. Under low light levels, for example, during the early morning, the combination of conditions of increasing Vc, decreasing Ci and increasing Oi would be expected to increase the quantum yield of isoprene emission.

The fourth objective, to predict changes in leaf isoprene emission rates with future climate change was achieved by the simulation of rates under conditions of [CO2] increased to 650 µmol mol-1, and temperatures increased from 25 to 27oC. From Figure 2.17 it is apparent that isoprene emissions are predicted to increase under putative global warming conditions at higher light levels, of above approximately 600 µmol m-2 s-1, but to decrease at light levels lower than 600 µmol m-2 s-1.

Due to the mechanistically-rich basis of the model presented here, the model has theoretical advantages over the best empirical models of isoprene emission rates, those of Guenther et al. (1991; 1993). The models of Guenther et al. provided a method to simulate some of the interactive effects of environmental conditions on isoprene emission rates and the model of Guenther et al. (1993) could predict the diurnal variations in hourly averaged emissions to within 35%, and so could be used for the estimation of isoprene emission rates as part of the inventory method. However, the model could not be confidently used for predictive purposes under changing climate conditions, partly due to the lack of a mechanistic basis, and partly due to the lack of a [CO2] effect. The mechanistic model presented here may be better placed to predict the interactive effects of climate change on rates of isoprene emission to the atmosphere, due to its higher mechanistic and phenomenological content.

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