The Dual Arrhenius and Michaelis–Menten kinetics model for decomposition of soil organic matter at hourly to seasonal time scales

Decomposition of soil carbon stocks is one of the largest potential biotic feedbacks to climate change. Models of decomposition of soil organic matter and of soil respiration rely on empirical functions that relate variation in temperature and soil water content to rates of microbial metabolism using soil‐C substrates. Here, we describe a unifying modeling framework to combine the effects of temperature, soil water content, and soluble substrate supply on decomposition of soluble soil‐C substrates using simple functions based on process concepts. The model's backbone is the Michaelis–Menten equation, which describes the relationship between reaction velocity and soluble organic‐C and O₂ substrate concentrations at an enzyme's reactive site, which are determined by diffusivity functions based on soil water content. Temperature sensitivity is simulated by allowing the maximum velocity of the reaction (V_max) to vary according to Arrhenius function. The Dual Arrhenius and Michaelis–Menten kinetics (DAMM) model core was able to predict effectively observations from of laboratory enzyme assays of β‐glucosidase and phenol‐oxidase across a range of substrate concentrations and incubation temperatures. The model also functioned as well or better than purely empirical models for simulating hourly and seasonal soil respiration data from a trenched plot in a deciduous forest at the Harvard Forest, in northeastern United States. The DAMM model demonstrates that enzymatic processes can be intrinsically temperature sensitive, but environmental constrains of substrate supply under soil moisture extremes can prevent that response to temperature from being observed. We discuss how DAMM could serve as a core module that is informed by other modules regarding microbial dynamics and supply of soluble‐C substrates from plant inputs and from desorption of physically stabilized soil‐C pools. Most importantly, it presents a way forward from purely empirical representation of temperature and moisture responses and integrates temperature‐sensitive enzymatic processes with constraints of substrate supply.     

Thermodynamic theory explains the temperature optima of soil microbial processes and high Q10 values at low temperatures

Our current understanding of the temperature response of biological processes in soil is based on the Arrhenius equation. This predicts an exponential increase in rate as temperature rises, whereas in the laboratory and in the field, there is always a clearly identifiable temperature optimum for all microbial processes. In the laboratory, this has been explained by denaturation of enzymes at higher temperatures, and in the field, the availability of substrates and water is often cited as critical factors. Recently, we have shown that temperature optima for enzymes and microbial growth occur in the absence of denaturation and that this is a consequence of the unusual heat capacity changes associated with enzymes. We have called this macromolecular rate theory – MMRT (Hobbs et al., 2013 , ACS Chem. Biol. 8:2388). Here, we apply MMRT to a wide range of literature data on the response of soil microbial processes to temperature with a focus on respiration but also including different soil enzyme activities, nitrogen and methane cycling. Our theory agrees closely with a wide range of experimental data and predicts temperature optima for these microbial processes. MMRT also predicted high relative temperature sensitivity (as assessed by Q₁₀ calculations) at low temperatures and that Q₁₀ declined as temperature increases in agreement with data synthesis from the literature. Declining Q₁₀ and temperature optima in soils are coherently explained by MMRT which is based on thermodynamics and heat capacity changes for enzyme‐catalysed rates. MMRT also provides a new perspective, and makes new predictions, regarding the absolute temperature sensitivity of ecosystems – a fundamental component of models for climate change.     

土壤呼吸温度敏感性的影响因素和不确定性

土壤呼吸是陆地生态系统碳循环的重要环节之一, 其对温度升高的敏感程度在很大程度上决定着全球气候变化与碳循环之间的反馈关系。为了深刻理解地下生态过程对气候变化的响应和适应,本文综述了土壤呼吸温度敏感性（Q10）的影响因子及其内在机制,并分析了当前研究存在的不确定性。土壤生物、底物质量和底物供应显著调控着土壤呼吸的Q10值,但研究结论仍然有很大差异。温度和水分等环境因子则通过对土壤生物和底物的影响而作用于土壤呼吸的温度敏感性,一般情况下,随着温度的升高,土壤呼吸的Q10值下降;水分过高或过低时Q10值降低。另外本文从土壤温度测定深度、时空尺度、土壤呼吸不同组分温度敏感性差异、激发效应以及采用方法的不同等几方面分析了温度敏感性研究存在的不确定性。并在此基础上, 指出了未来拟重点加强的研究方向:（1）土壤呼吸不同组分温度敏感性差异的机理;（2）底物质量和底物供应对温度敏感性的交互影响;（3）生物因子对土壤呼吸温度敏感性的影响。     

Does declining carbon‐use efficiency explain thermal acclimation of soil respiration with warming?

Enhanced soil respiration in response to global warming may substantially increase atmospheric CO₂ concentrations above the anthropogenic contribution, depending on the mechanisms underlying the temperature sensitivity of soil respiration. Here, we compared short‐term and seasonal responses of soil respiration to a shifting thermal environment and variable substrate availability via laboratory incubations. To analyze the data from incubations, we implemented a novel process‐based model of soil respiration in a hierarchical Bayesian framework. Our process model combined a Michaelis–Menten‐type equation of substrate availability and microbial biomass with an Arrhenius‐type nonlinear temperature response function. We tested the competing hypotheses that apparent thermal acclimation of soil respiration can be explained by depletion of labile substrates in warmed soils, or that physiological acclimation reduces respiration rates. We demonstrated that short‐term apparent acclimation can be induced by substrate depletion, but that decreasing microbial biomass carbon (MBC) is also important, and lower MBC at warmer temperatures is likely due to decreased carbon‐use efficiency (CUE). Observed seasonal acclimation of soil respiration was associated with higher CUE and lower basal respiration for summer‐ vs. winter‐collected soils. Whether the observed short‐term decrease in CUE or the seasonal acclimation of CUE with increased temperatures dominates the response to long‐term warming will have important consequences for soil organic carbon storage.     

Comparison of several mathematical models for describing the joint effect of temperature and ph on glucanex activity

The aim of the present work was to evaluate with different statistical criteria the suitability of nine equations for describing and optimizing the simultaneous effect of temperature and pH on glucanex activity using two characteristic polysaccharides (curdlan and laminarin) as substrates. The most satisfactory solutions were found with an empirical equation constituted with parameters of practical interest (Rosso model), and a hybrid model between the Arrhenius equation and the mathematical expression generated by the protonation-hydroxylation mechanism (Tijskens model). The joint optimal values of pH and temperature calculated with the Rosso model were obtained at 4.64 and 50°C with curdlan and 4.64 and 48°C using laminarin as substrate.     

Embracing a new paradigm for temperature sensitivity of soil microbes

The temperature sensitivity of soil processes is of major interest, especially in light of climate change. Originally formulated to explain the temperature dependence of chemical reactions, the Arrhenius equation, and related Q₁₀ temperature coefficient, has a long history of application to soil biological processes. However, empirical data indicate that Q₁₀ and Arrhenius model are often poor metrics of temperature sensitivity in soils. In this opinion piece, we aim to (a) review alternative approaches for characterizing temperature sensitivity, focusing on macromolecular rate theory (MMRT); (b) provide strategies and tools for implementing a new temperature sensitivity framework; (c) develop thermal adaptation hypotheses for the MMRT framework; and (d) explore new questions and opportunities stemming from this paradigm shift. Microbial ecologists should consider developing and adopting MMRT as the basis for predicting biological rates as a function of temperature. Improved understanding of temperature sensitivity in soils is particularly pertinent as microbial response to temperature has a large impact on global climate feedbacks.     

Speed it up: How temperature drives toxicokinetics of organic contaminants in freshwater amphipods

The acceleration of global climate change draws increasing attention towards interactive effects of temperature and organic contaminants. Many studies reported a higher sensitivity of aquatic invertebrates towards contaminant exposure with increasing or fluctuating temperatures. The hypothesis of this study was that the higher sensitivity of invertebrates is associated with the changes of toxicokinetic processes that determine internal concentrations of contaminants and consequently toxic effects. Therefore, the influence of temperature on toxicokinetic processes and the underlying mechanisms were studied in two key amphipod species (Gammarus pulex and Hyalella azteca). Bioconcentration experiments were carried out at four different temperatures with a mixture of 12 exposure relevant polar organic contaminants. Tissue and medium samples were taken in regular intervals and analysed by online solid-phase extraction liquid chromatography high-resolution tandem mass spectrometry. Subsequently, toxicokinetic rates were modelled and analysed in dependence of the exposure temperature using the Arrhenius equation. An exponential relationship between toxicokinetic rates versus temperature was observed and could be well depicted by applying the Arrhenius equation. Due to a similar Arrhenius temperature of uptake and elimination rates, the bioconcentration factors of the contaminants were generally constant across the temperature range. Furthermore, the Arrhenius temperature of the toxicokinetic rates and respiration was mostly similar. However, in some cases (citalopram, cyprodinil), the bioconcentration factor appeared to be temperature dependent, which could potentially be explained by the influence of temperature on active uptake mechanisms or biotransformation. The observed temperature effects on toxicokinetics may be particularly relevant in non-equilibrated systems, such as exposure peaks in summer as exemplified by the exposure modelling of a field measured pesticide peak where the internal concentrations increased by up to fourfold along the temperature gradient. The results provide novel insights into the mechanisms of chemical uptake, biotransformation and elimination in different climate scenarios and can improve environmental risk assessment.     

Investigating biological control over soil carbon temperature sensitivity

Understanding the temperature sensitivity of soil respiration is critical for predicting the response of ecosystems to climate change, yet the microbial communities responsible are rarely considered explicitly in studies or models. In this study, we assessed total microbial community composition, quantified bacterial respiration temperature response, and investigated the temperature dependence of bacterial carbon substrate utilization in tropical, temperate, and taiga soils (from Puerto Rico, California, and Alaska). Microbial community composition was characterized using phospholipid fatty acid analysis. Bacterial community respiration on a standardized set of substrates was ascertained using the BiOLOG^™ substrate utilization assay incubated at four temperatures: 4, 12, 28, and 40 °C. First, we found that microbial communities from the three latitudes were compositionally distinct and that the bacterial component of the three communities had markedly different respiration temperature–response curves corresponding with their experienced temperature regimes. We use these data to highlight limitations of widely used temperature–response equations and investigate temperature-dependent patterns of substrate utilization. We found that temperature response, in terms of both respiration rates and substrate use, varied for these bacterial communities independent of substrate quality or quantity interactions such as labile depletion. In contrast to the common assumption of heterotrophic microbial ubiquity, we found that bacterial community differences from these diverse systems appeared to determine both rates of respiration and patterns of carbon substrate usage. We suggest that microbial community composition-specific responses to changing climate may be important in predicting the long-term role of ecosystems in atmospheric CO₂ dynamics.     

Consistent temperature dependence of respiration across ecosystems contrasting in thermal history

Ecosystem respiration is a primary component of the carbon cycle and understanding the mechanisms that determine its temperature dependence will be important for predicting how rates of carbon efflux might respond to global warming. We used a rare model system, comprising a network of geothermally heated streams ranging in temperature from 5 °C to 25 °C, to explore the nature of the relationship between respiration and temperature. Using this ‘natural experiment’, we tested whether the natal thermal regime of stream communities influenced the temperature dependence of respiration in the absence of other potentially confounding variables. An empirical survey of 13 streams across the thermal gradient revealed that the temperature dependence of whole‐stream respiration was equivalent to the average activation energy of the respiratory complex (0.6–0.7 eV). This observation was also consistent for in‐situ benthic respiration. Laboratory experiments, incubating biofilms from four streams across the thermal gradient at a range of temperatures, revealed that the activation energy and Q₁₀ of respiration were remarkably consistent across streams, despite marked differences in their thermal history and significant turnover in species composition. Furthermore, absolute rates of respiration at standardised temperature were also unrelated to ambient stream temperature, but strongly reflected differences in biofilm biomass. Together, our results suggest that the core biochemistry, which drives the kinetics of oxidative respiratory metabolism, may be well conserved among diverse taxa and environments, and that the intrinsic sensitivity of respiration to temperature is not influenced by ambient environmental temperature.     

A theoretical derivation of the Contois equation for kinetic modeling of the microbial degradation of insoluble substrates

Although developed as an empirical model to describe microbial growth on soluble substrates, the Contois equation has been widely accepted for kinetic modeling of insoluble substrate degradation. Yet, the mechanistic basis underlining these successful applications remains unanswered. Unlike soluble substrates that mainly cultivate suspended cultures, microbes cultivated on insoluble substrates have the populations that attach to the substrate surface or remain suspended in the bulk solution, while those attached usually grow faster than those suspended due to their proximity to food resources. This imbalanced growth provides a plausible explanation to the inverse relationship between microbial concentration and their specific growth rate as conveyed in the Contois equation. Based on a theoretical derivation, this study revealed that the Contois equation holds true only when attached microbes substantially obstruct the access of food to their suspended counterparts. On the other hand, when plentiful insoluble substrate surfaces are exposed for cell attachment, the Contois equation will be reduced back to the classic Monod equation.     

Effects of substrate availability on the temperature sensitivity of soil organic matter decomposition

Soil carbon is a major component in the global carbon cycle. Understanding the relationship between environmental changes and rates of soil respiration is critical for projecting changes in soil carbon fluxes in a changing climate. Although significant attention has been focused on the temperature sensitivity of soil organic matter decomposition, the factors that affect this temperature sensitivity are still debated. In this study, we examined the effects of substrate availability on the temperature sensitivity of soil respiration in several different kinds of soils. We found that increased substrate availability had a significant positive effect on temperature sensitivity, as measured by soil Q ₁₀ values, and that this effect was inversely proportional to original substrate availability. This observation can be explained if decomposition follows Michaelis–Menten kinetics. The simple Q ₁₀ model was most appropriate in soils with high substrate availability.     

Effect of temperature on the pathways of NADH-oxidation in broad-bean mitochondria

1. Respiration rates of broad-bean (Vicia faba) mitochondria were studied as a function of temperature. Arrhenius plots of all membrane-bound enzymes, as obtained with saturating substrate concentrations, revealed a break in the lower temperature range. That break was considered to indicate a phase transition of membrane phospholipids, characteristic for chilling-sensitive plants. A second discontinuity at 30°C occurred only with activities linked to energy conservation. — 2. The activation energies for the oxidation of NAD⁺-linked substrates differ between states 3 and 4. State 3 respiration of NAD⁺-linked substrates is the result a superimposition of two branches of electron transport, which can be separated by different sensibilities to rotenone. A characteristic temperature dependency of the respiratory control, as well as a shift of the low temperature break in the Arrhenius plot toward a higher temperature after state 4 to state 3 transition, are calculated to be caused by the superimposition of the two branches. — 3. The temperature dependency of the oxidation of extra-mitochondrial NADH and of succinate differs remarkably from that of the oxidation of matrix-NADH. It has been concluded that the rotenone-resistant oxidation of matrix-NADH and the oxidation of external NADH are mediated via different pathways with individual regulation sites.Abbreviations BSA bovine serum albumin - CCCP carbonylcyanide-m-chlorophenylhydrazone - TPP thiaminepyrophosphate     

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.     

A ligand-induced, temperature-dependent conformational Change in penicillopepsin. Evidence from nonlinear Arrhenius plots and from circular dichroism studies

The effect of temperature on the rate constants of hydrolysis of various substrates by penicillopepsin is dependent on the length of the substrate. For the series Ac-(Ala)m-Lys-Nph-(Ala)n-amide (where Ac- is acetyl- and Nph- is p-nitrophenylalanyl-), where m and n = 0-2, substrates lacking both P'2 and P3 residues give linear Arrhenius plots with an energy of activation of about 55 kJ.mol-1. The Arrhenius plots of substrates in which an alanine residue occupies P'2 show a sharp break at an average transition temperature of 10.5 degrees C. The activation energies are approximately 90 kJ.mol-1 below and approximately 54 kJ.mol-1 above the transition temperature, respectively. For substrates in which P3 is occupied, the average transition temperature is 14.2 degrees C. In this case, the activation energies are 66 kJ.mol-1 below and from 26 to 39 kJ.mol-1 above the transition point. The most probable explanation of these phenomena is that substrate interaction at subsites S3 and/or S'2 of the enzyme induces a temperature-dependent conformational change. Physical evidence for this comes from the observation that the temperature dependence of a CD absorption band at 242 nm of a penicillopepsin-pepstatin complex shows a sharp break that corresponds to those observed in the Arrhenius plots of substrates with alanine at P'2 and P3, whereas the same CD band in the free enzyme is linearly dependent on temperature.     

The carbon quality-temperature hypothesis does not consistently predict temperature sensitivity of soil organic matter mineralization in soils from two manipulative ecosystem experiments

The temperature sensitivity of soil organic matter (SOM) decomposition is a source of uncertainty in models of soil-climate feedbacks. However, empirical studies have given contradictory results concerning the temperature response of SOM fractions, even as the understanding of the chemical nature of SOM is evolving. The carbon-quality temperature (CQT) hypothesis states that more ‘recalcitrant’ SOM should have higher temperature sensitivity. Incubation studies have often shown a negative correlation between soil respiration rates and temperature sensitivity. However, there have been important exceptions to these results which challenge the assumption that older SOM is necessarily more chemically complex. We asked whether we would expect a universal relationship between temperature sensitivity and soil respiration given that SOM decomposition is influenced by factors other than chemical complexity. We examined temperature sensitivity in long-term incubations of four soils representing two biomes and two ecosystem-level manipulations. Soils from a manipulative climate experiment in Pacific Northwest grasslands demonstrated an increase in temperature sensitivity with incubation duration, but soil from a 20-year input manipulation study in a Northeastern forest showed no relationship of temperature sensitivity with either carbon depletion or incubation time. Furthermore, across all four soils, the temperature sensitivity of soil respiration was frequently inconsistent with indices of carbon quality and did not show a negative correlation with soil respiration rate. We conclude that the CQT hypothesis fails to universally capture the temperature sensitivity of SOM decomposition across environmental contexts, consistent with an emerging understanding of the multiplicity of factors that control soil carbon cycling.     

Mutational analysis of m-values as a strategy to identify cold-resistant substructures of the protein ensemble

Characterizing the native ensemble of protein is an important yet difficult objective of structural biology. The structural dynamics of protein macromolecules play key roles in biological function, but the short lifetimes and low population of near-native states of the protein ensemble limit their ability to be studied directly. In part to address such issues, it was shown recently that the cooperative substructures that populate a protein ensemble could be ascertained by NMR methods performed at very cold temperatures. What is presented here is an argument that these same substructures can also be determined by denaturant-induced unfolding studies performed on protein at room temperature. Data supporting this argument are given for Staphylococcal nuclease, chymotrypsin inhibitor 2, and ubiquitin. The observation of an agreement between the thermodynamics of the protein ensemble simulated under very cold temperatures to the apparent sensitivity of the ensemble to chemical denaturants at room temperature also suggests that the overall structural-thermodynamic character of an ensemble is surprisingly robust and preserved even in the presence of strong denaturing conditions.     

On the variability of respiration in terrestrial ecosystems: moving beyond Q10

Respiration, which is the second most important carbon flux in ecosystems following gross primary productivity, is typically represented in biogeochemical models by simple temperature dependence equations. These equations were established in the 19th century and have been modified very little since then. Recent applications of these equations to data on soil respiration have produced highly variable apparent temperature sensitivities. This paper searches for reasons for this variability, ranging from biochemical reactions to ecosystem‐scale substrate supply. For a simple membrane‐bound enzymatic system that follows Michaelis–Menten kinetics, the temperature sensitivities of maximum enzyme activity (V_max) and the half‐saturation constant that reflects the affinity of the enzyme for the substrate (K_m) can cancel each other to produce no net temperature dependence of the enzyme. Alternatively, when diffusion of substrates covaries with temperature, then the combined temperature sensitivity can be higher than that of each individual process. We also present examples to show that soluble carbon substrate supply is likely to be important at scales ranging from transport across membranes, diffusion through soil water films, allocation to aboveground and belowground plant tissues, phenological patterns of carbon allocation and growth, and intersite differences in productivity. Robust models of soil respiration will require that the direct effects of substrate supply, temperature, and desiccation stress be separated from the indirect effects of temperature and soil water content on substrate diffusion and availability. We speculate that apparent Q₁₀ values of respiration that are significantly above about 2.5 probably indicate that some unidentified process of substrate supply is confounded with observed temperature variation.     

Comparative growth of the thermal alga Cyanidium caldarium on nitrate and ammonia at different temperatures

Summary The growth of Cyanidium caldarium on nitrate and ammonia as nitrogen sources was studied at different temperatures from 21 to 54°C.Algal growth occurred at temperatures of 24° C or above when ammonia was the nitrogen source, whereas with nitrate, growth occurred at 30° C or above. The optimum and the maximum growth temperatures were 45 and 54° C respectively on both substrates.Arrhenius plots show that the logarithm of the growth rate is not linear with the reciprocal of absolute temperature, but exhibit sharply defined breaks at 30° C on ammonia and at 40° C on nitrate.It is assumed that below 40° C, when Cyanidium grows on nitrate, the utilization of this substrate represents the master reaction which controls the growth rate of the alga.     

A simple method for measuring fungal metabolic quotient and comparing carbon use efficiency of different isolates: Application to Mediterranean leaf litter fungi

The metabolic efficiency of different microbial groups in carbon source uses and single species storage efficiency is poorly characterised and not adequately represented in most biogeochemical models. It is proposed here a simple approach for an estimation of the metabolic quotient of fungal isolates. The method is based on the values of substrate use (respiration) and growth (biomass production) obtainable for single fungal isolates in vitro using the Phenotype MicroArray? system to test the metabolic performance of fungi on different substrates. As a case study, this carbon-use efficiency method was used to compare a group of leaf litter fungi. The metabolic efforts of single fungal species were measured on 95 different substrates of different complexity. The respiration to biomass ratio showed a high reliability and the possibility of being used as a measurable property of the micro-organisms and an indicator of organism’s performance or fitness.     

Large seasonal changes in Q10 of soil respiration in a beech forest

We analyzed one year of continuous soil respiration measurements to assess variations in the temperature sensitivity of soil respiration at a Danish beech forest. A single temperature function derived from all measurements across the year (Q₁₀ = 4.2) was adequate for estimating the total annual soil respiration and its seasonal evolution. However, Q₁₀'s derived from weekly datasets ranged between three in summer (at a mean soil temperature of 14 °C) and 23 in winter (at 2 °C), indicating that the annual temperature function underestimated the synoptic variations in soil respiration during winter. These results highlight that empirical models should be parameterized at a time resolution similar to that required by the output of the model. If the objective of the model is to simulate the total annual soil respiration rate, annual parameterization suffices. If however, soil respiration needs to be simulated over time periods from days to weeks, as is the case when soil respiration is compared to total ecosystem respiration during synoptic weather patterns, more short‐term parameterization is required. Despite the higher wintertime Q₁₀'s, the absolute response of soil respiration to temperature was smaller in winter than in summer. This is mainly because in absolute numbers, the temperature sensitivity of soil respiration depends not only on Q₁₀, but also on the rate of soil respiration, which is highly reduced in winter. Nonetheless, the Q₁₀ of soil respiration in winter was larger than can be explained by the decreasing respiration rate only. Because the seasonal changes in Q₁₀ were negatively correlated with temperature and positively correlated with soil moisture, they could also be related to changing temperature and/or soil moisture conditions.