The response of soil biochemical processes to changing temperature (T) is critical for predicting daily, seasonal and annual variation of biological cycling of nutrients and carbon (C). Soil biochemical processes are strongly temperature dependent in two broad ways: (i) Intrinsic – the direct effect of temperature on microbial metabolism which is largely driven by enzymatic kinetics; and (ii) Extrinsic – indirect effects, such as through temperature controls on substrate solubility and diffusion, and freezing and thawing (Davidson & Janssens, 2006; Conant et al., 2011). Extrinsic effects are highly context specific in that they vary between soils and climates, whereas intrinsic effects are directly dependent on enzyme-catalysed biochemical reactions. While extrinsic effects are extremely important, the focus of the work presented here is primarily on intrinsic effects.
A wide range of different mathematical models of biochemical responses to changing temperature in soils have been proposed (Lloyd & Taylor, 1994; Kirschbaum, 2000; Davidson & Janssens, 2006; Tuomi et al., 2008; Sierra, 2012). Many of these models are based on the Arrhenius function, but this function does not predict an optimum temperature (Topt) above which the rate declines (Fig. 1a). The decline in the rate of activity in biological systems above Topt has been attributed to enzyme denaturation at higher temperatures coupled with complex regulatory temperature responses in the cell. Corkrey et al. (2012) modelled these effects on the basis of a single ‘master enzyme’ where the complex negative effects above Topt are rolled into an enzyme denaturation term. However, enzyme denaturation is not a coherent explanation in soil systems as enzyme denaturation generally occurs at higher temperatures than those that are commonly observed in soils. For example, the well-studied soil bacterium Bacillus subtilis has an optimal growth temperature of 39 °C and a typical enzyme from Bacillus subtilis has an unfolding (denaturation) mid-point temperature of 59 °C (Ruller et al., 2008).
A second poorly explained observation is that the relative temperature sensitivity of ecosystem biological reactions is greatest at low temperatures and declines as temperature increases. Relative temperature sensitivity has frequently been calculated as the Q10 for biological processes; Q10 is the ratio of rates determined 10 °C apart (Conant et al., 2011; Sierra, 2012). Empirical measurements show high values of Q10 at low temperatures and declining Q10 values as temperature increases (e.g. for respiration (Del Grosso et al., 2005; Hamdi et al., 2013; Kirschbaum, 1995)). Despite recognizing that relative temperature sensitivity is not constant with increasing temperature, a number of global climate models simply fix Q10 at 2 or 1.5 or assign fixed Q10 for different C pools (summarized in Friedlingstein et al. (2006)). While this may be a reasonable first approximation for relative temperature sensitivity, a theoretical basis for changing Q10 is needed to place models on a stronger footing. The development of any underpinning theory would need to account for changing relative temperature sensitivity and particularly for declines in Q10 from a mean value of ~4.8 at 0 °C to ~2 above 25 °C as recently reported by Hamdi et al. (2013) in a synthesis of 68 studies of respiration.
We have recently developed a thermodynamic theory of the temperature dependence of enzyme reaction rates and microbial growth rates (Hobbs et al., 2013). We have called this ‘Macromolecular Rate Theory (MMRT)’ as it takes into account critical thermodynamic properties of biological macromolecules and specifically those of enzymes. At the heart of the theory is the fact that the activation energy (EA from the Arrhenius equation) of enzyme-catalysed reactions is theoretically temperature dependent. The temperature dependence of EA arises from a large, negative change in heat capacity associated with enzyme-catalysed reactions. This change in heat capacity results in negative curvature in a temperature vs. rate plot and directly predicts a Topt for enzymatically driven processes in direct contrast to the standard Arrhenius function (Fig. 1a). Furthermore, MMRT accounts for the decline in reaction rates above Topt without the need to invoke enzyme denaturation at modest temperatures. This theory also specifically predicts high Q10 values at low temperatures for enzymes (Fig. 1b and c).
Here, our objective was to apply MMRT to soil biochemical data, to test whether this approach could sensibly explain observed temperature responses of soil processes including Topt and the decline in Q10 with increasing temperature. First, we summarize the theoretical basis of MMRT. Second, we fit the derived equations to the observed temperature response curves of individual soil processes from studies drawn from the literature and compare derived physical parameters to those known from enzyme studies (Hobbs et al., 2013). Lastly, we use this framework to demonstrate that the theory predicts that Q10 will decline with increasing temperature, comparing the resulting curve with soil respiration data sets collated by Hamdi et al. (2013).