Rapid-equilibrium rate equations for the enzymatic catalysis of A + B = P + Q over a range of pH

Enzyme-catalyzed reductase reactions in particular are characterized by large changes in the binding of hydrogen ions Δ(r)N(H). This is a thermodynamic property of the reaction that is catalyzed. For example, in the ferredoxin-nitrite reductase reaction, there is an increase of eight in the binding of hydrogen ions for every molecule of nitrite reduced to ammonia H(2)O. If these hydrogen ions are consumed in the rate-determining reaction, the limiting velocity is proportional to [H(+)](8). This would make it practically impossible to determine the kinetic parameters. This article shows that when n hydrogen ions are consumed in reactions preceding the rate-determining reaction the limiting velocity is not proportional to [H(+)](n) and may only vary with pH according to the pK's of the enzyme-substrate complex that produces products. Rapid-equilibrium rate equations for ordered A + B → products are derived for two mechanisms in which a single hydrogen ion is consumed prior to the rate-determining reaction. Rate equations are tested by calculating velocities for the minimum number of velocity measurements required to estimate the kinetic parameters and using these velocities to estimate the kinetic parameters.

We briefly review the role of the triple-α reaction in astrophysics and discuss the uncertainties associated with the determination of the reaction rate. We summarize the results of three recent experimental studies of the breakup of the Hoyle state in 12C into three a particles, and we show how these results eliminate an often overlooked source of uncertainty in the determination of the triple-α reaction rate. Finally, we contemplate whether improved studies of the breakup of the Hoyle state can teach us something about the structure of the Hoyle state.

The effects of pH on the rates of enzyme-catalyzed reactions are very important because they yield information on the pKs of acidic groups in the enzymatic site and the various enzyme-substrate complexes. But many enzyme-catalyzed reactions produce or consume hydrogen ions in a way that cannot be explained with pKs. These pH effects extend over the whole pH range of interest. In investigating these effects, the rapid-equilibrium assumption is especially useful because a large number of chemical reactions have to be taken into account. In these calculations, all of the reactions up to the rate-determining reaction are treated with biochemical thermodynamics. Kinetic studies make it possible to determine the number of hydrogen ions consumed in the rate-determining reaction, a number that can be in the range of 0-8. It is shown that the experimental limiting velocity of the forward reaction V(fexp) is equal to 10(npH)V(f), where n is a negative integer and Vf varies with pH in the way determined by the pKs of the enzyme-substrate complex that reacts in the rate-determining reaction. A computer program for the initial reaction velocity makes it possible to investigate the rapid-equilibrium kinetics of enzymatic mechanisms that involve the consumption of hydrogen ions.

The "area" and the "slope" determination of reaction rates from the ion arrival-time spectrum of Tyndall drift tubes are generally thought to yield identical results. They are shown to be different when lateral diffusion and the difference in ion temperature between the parent and the daughter species are taken into account. Both methods yield only an apparent, instead of the real, rate of the ion-molecule reactions. The apparent rate determined from the area method is usually much closer to the real rate than that determined from the slope method. Formulas and diagrams are provided in order to estimate whether the area method of rate determination is sufficiently accurate for the purpose of an experiment. The dependences of the apparent rate on the radius of the drift tube, $\frac{E}{{P}_{0}}$, the initial ion distribution, and the collector size are discussed. One important conclusion is that the exact solutions from the transport equations are not necessary in an appreciable number of situations for fairly accurate determination of reaction rates, provided that the area method is used. The relevance of this analysis to other methods of data analysis in drift tubes is discussed. A method for a relative-abundance calibration of a mass spectrometer is suggested.

The influence of rotational excitation on vibration-chemistry-vibration-coupling

The chemical oxidant permanganate (MnO(4)(-)) has been shown to effectively transform hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) at both the laboratory and field scales. We treated RDX with MnO(4)(-) with the objective of quantifying the effects of pH and temperature on destruction kinetics and determining reaction rates. A nitrogen mass balance and the distribution of reaction products were used to provide insight into reaction mechanisms. Kinetic experiments (at pH ∼ 7, 25 °C) verified that RDX-MnO(4)(-) reaction was first-order with respect to MnO(4)(-) and initial RDX concentration (second-order rate: 4.2 × 10(-5) M(-1) s(-1)). Batch experiments showed that choice of quenching agents (MnSO(4), MnCO(3), and H(2)O(2)) influenced sample pH and product distribution. When MnCO(3) was used as a quenching agent, the pH of the RDX-MnO(4)(-) solution was relatively unchanged and N(2)O and NO(3)(-) constituted 94% of the N-containing products after 80% of the RDX was transformed. On the basis of the preponderance of N(2)O produced under neutral pH (molar ratio N(2)O/NO(3) ∼ 5:1), no strong pH effect on RDX-MnO(4)(-) reaction rates, a lower activation energy than the hydrolysis pathway, and previous literature on MnO(4)(-) oxidation of amines, we propose that RDX-MnO(4)(-) reaction involves direct oxidation of the methylene group (hydride abstraction), followed by hydrolysis of the resulting imides, and decarboxylation of the resulting carboxylic acids to form N(2)O, CO(2), and H(2)O.

Influences of heat transport on the determination of reaction rates using the temperature scanning plug flow reactor

Elements, Atoms, and Electrons Matter and Elements Atoms Atomic Structure Isotopes The Periodic Table Electron Structure of Atoms Covalent Bonding and Molecules Interactions between Atoms Covalent Bonds Are Formed by Sharing Outer Electrons Formulae of Compounds Covalent Bonds Formed by Combining Atomic Orbitals Single Overlap, the Sigma-Bond Double Overlap, the Pi-Bond Molecules with s- and p-Bonds Hybrid Molecular Orbitals Forces Within and Between Molecules Ionic Bonding Polar Covalent Bonds Dipole-Dipole Forces The Hydrogen Bond van der Waals Forces The Hydrophobic Effect Coordinate Bonds Chemical Reactions Rates of Reaction Factors Affecting Rate of Reaction Rate Equations Integrated Forms of Rate Equations Zero-Order Reactions Integrated Form of the Zero-Order Rate Equation First-Order Reactions The Integrated Form of the First-Order Rate Equation Second-Order Reactions Integrated Forms of Second-Order Rate Equations Pseudo-First-Order Reactions Reversible Reactions Equilibrium Water The Water Molecule Ice Water Solutions The Mole Concept Calculating Molar Masses Molarity Colloidal Solutions Diffusion and Osmosis Acids, Bases, and Buffers Ionisation of Water The Hydrogen Ion Acids and Bases Strong Acids and Strong Bases Weak Acids and Weak Bases Ka and Kb Relationship between Ka and Kb pH, pOH, pKw, pKa, pKb Solutions of Weak Acids and Bases Salts and Salt Hydrolysis Buffer Systems Calculating the pH Values of Buffers Indicators Titrations Gases Pressure Measurement of Pressure Ideal Gas Laws Partial Pressures Solubility of Gases Diffusion in Gases Aliphatic Carbon Compounds Simple Molecules Containing Carbon Organic Compounds Alkanes and Alkyl Groups Alkenes Alcohols Thiols Aldehydes and Ketones Carboxylic Acids Amines Lipids, Sugars, and Linkages between Reactive Groups Fatty Acids Esters Glycerol Esters Hemiacetals and Hemiketals Simple Sugars Chirality in Simple Sugars Straight-Chain Sugars Spontaneously Form Rings Sugar Hydroxyls Can Be Chemically Modified Sugars Are Joined Together by Glycosidic Bonds Aromatic Carbon Compounds and Isomerism Benzene Bioactive Aromatic Compounds Isomerism Structural Isomerism Chain, Positional, and Functional Group Isomerism Tautomerism Stereoisomerism Geometrical Isomerism Optical Isomerism Organic and Biological Reaction Mechanisms Reactive Sites and Functional Groups Describing Reaction Mechanisms Bimolecular Nucleophilic Substitution Electrophilic Addition to a Nonpolar Double Bond Elimination to Form an Alkene Nucleophilic Addition to a Polar Double Bond Free Radical Reactions Carbon-Carbon Bond Formation in Biosynthesis Sulphur and Phosphorus The Electron-Shell Structure and Valency of Phosphorus and Sulphur Sulphur The Thiol Group and Thiol Esters Phosphate, Pyrophosphate, and Polyphosphate Phosphate Esters The Role of Phosphate Esters and ATP in Cellular Energy Metabolism Oxidation and Reduction Reactions Oxidation Is Linked to Reduction The Chemical Changes in the REDOX Process Splitting REDOX Reactions Standardising REDOX Half-Reactions Predicting Electron Flow Free Energy and Standard Reduction Potentials Redox Reactions and Nonstandard Conditions Metals in Biology General Properties of Metals in Biology Some Properties of Alkali Metals The Alkaline Earth Metals Transition Metals Role of Metal as Oxygen Carrier Metals Facilitate Biocatalysis The Role of Metal Ions as Charge Carriers The Toxicity of Metals Energy The First Law of Thermodynamics Units of Energy Measurement of Energy Internal Energy, U, and Enthalpy, H Calorimetry Hess's Law Enthalpies of Formation The Second Law of Thermodynamics Free Energy Interaction of DeltaH with TDeltaS Reactions and Equilibrium DeltaG and Equilibrium Activation Energy The Effect of the Temperature on Reaction Rate The Arrhenius Equation Catalysis Enzyme Catalysis Kinetics of Enzyme Reactions Finding Vmax and KM Light Light Is Part of the Electromagnetic Spectrum Wavelength and Frequency The Quantum Theory of Light The Absorption of Light The Relationship between Light Absorption and Concentration The Spectrophotometer The Fate of Absorbed Light Appendix: Derivations of Equations Index

A major result of the various genome programs has been an accumulation of complete genomic sequences and their associated annotation. These resources are extremely valuable to various fields of biology, not least metabolism and metabolic modelling. As these complete sequences have started appearing they have been used to derive lists of metabolic reactions that are catalysed by enzymes whose genes are identified in the genome sequence. These metabolic "reconstructions" are further interpreted as metabolic networks and several analyses can be derived from them. In the case of the popular model organism Saccharomyces cerevisiae the metabolic reconstruction is fairly advanced in terms of completeness and sophistication [2, 1].

The reaction rate of starch hydrolysis catalyzed by a glucoamylase covalently bound to chitin particles was measured in a Differential Fixed-Bed Reactor (DFBR). Under selected test conditions the initial reaction rate may represent biocatalyst activity. Some aspects which influence measurement of the initial reaction rate of an immobilized enzyme were studied: the amount of desorbed enzyme and its hydrolytic activity, the extent of pore blockage of the biocatalyst caused by substrate solution impurities and the internal and external diffusional mass transfer effects. The results showed that the enzyme glucoamylase was firmly bound to the support, as indicated by the very low amount of desorbed protein found in the recirculating liquid. Although this protein was very active, its contribution to the overall reaction rate was negligible. It was observed that the biocatalyst pores were susceptible to being blocked by the impurities of the starch solution. This latter effect was accumulative, increasing with the number of sequential experiments carried out. When the substrate solution was filtered before use, very reliable determinations of immobilized enzyme reaction rates could be performed in the DFBR. External and internal diffusional resistences usually play a significant role in fixed-bed reactors. However, for the experimental system studied, internal mass transfer effects were not significant, and it was possible to select an operational condition (recirculation flow rate value) that minimized the external diffusional limitations.

Simultaneous decompositions of nitrous oxide

This approach uses a set of algebraic linear equations for reaction rates (the method of steady-state stoichiometric flux balance) to model the purposeful metabolism of the living self-reproducing biochemical system (i.e. cell), which persists in steady-state growth. Linear programming (SIMPLEX method) is used to derive the solution for the model equations set (determining reaction rates which provide flux balance at given conditions). Here, we demonstrate the approach through the mathematical modeling of steady-state metabolism in Saccharomyces cerevisiae mitochondria.

A theory of double potential step chronoamperometry (DPSCA) is developed for the reversible follow-up reactions represented as Ox+ne\ightleftarrowsRed, Red\oversetk\undersetkK\ightleftarrowsZ, where k and K are the rate and the equilibrium constants of the follow-up chemical reaction, respectively. DPSCA is applied to investigate the kinetics of aquation reaction of [Co(edma)2]0 (edma: ethylenediamine-N-acetate), which is produced by electrolytic reduction of [Co(edma)2]+ in the range of pH 1.5 to 10.5. At pH<4.5, the aquation reaction of [Co(edma)2]0 is irreversible. The rate of aquation reaction is accelerated by hydrogen ions and approaches an upper limiting value (2.1×103s−1). At pH>4.5,on the other hand, the hydrogen ions do not substantially contribute to the aquation and thus the rate approaches a lower limiting value (4.7×102s−1), which is in good agreement with that obtained in neutral region (4.5<pH<7), where the reverse (complex formation) reaction must be taken in to consideration. Above pH 7, the[Co(edma)2]0 species exists as main species in the solution and thus the kinetic behavior of the aquation is not observed. It is demonstrated that DPSCA is a useful method for kinetic studies of the dissociation-association reactions of labile complexes.

Efficient acquisition of iron (Fe) in graminaceous plant species relies on the synthesis and release of phytosiderophores, which are low-molecular weight chelators with functional carboxy-, amino- and hydroxy-groups for hexadentate metal coordination (Sugiura & Nomoto 1984). Metal-phytosiderophores formed in the rhizosphere are subsequently taken up by YS1-type membrane proteins, that energize root uptake by the cotransport of metal-phytosiderophores with protons (Schaaf et al., 2004). As Fe(III)-phytosiderophores dominate Fe(III) chelation over hydroxide formation in the pH range between 3.5 and 8.5 (von Wirén et al., 1999) and as they are mainly found in root exudates or the xylem sap (Kawai et al., 2001), phytosiderophores may adopt a major role in extracytosolic Fe chelation. Nicotianamine (NA), which occurs in all higher plants, is structurally similar to phytosiderophores and serves as a precursor in their biosynthetic pathway. Fe trafficking within the plant has been shown to have a strong dependency on NA; this has been demonstrated by severe symptoms of Fe deficiency in mutant or transgenic plant lines with low NA levels (Ling et al., 1999; Takahashi et al., 2003). NA has been shown to chelate not only Fe(III) but also Fe(II) (Benešet al., 1983), in particular at higher pH values, which may allow its function as an intracellular Fe(II) scavenger thereby protecting the cell from Fe(II)-mediated oxidative damage (von Wirén et al., 1999). The occurrence of phytosiderophores and NA in graminaceous plant species thus raises the question whether Fe(III) may undergo a chelate exchange from phytosiderophores to NA, as proposed by von Wirén et al. (1999). These authors concluded on the basis of titration and capillary electrophoresis studies that the phytosiderophore deoxymugineic acid (DMA) chelates Fe(III) preferentially at more acidic pH values (pH 3–6), while NA is a more competitive chelator at pH values > 6. Reichman & Parker (2002) reanalysed the previously published data and claimed to have identified information which partially rejects the above hypothesis and has important implications for Fe physiology and transport in plants. The two aspects which were the subject of criticism were (i) the competition between NA and DMA for Fe(III) at pH 7.0, and (ii) the relative affinity of NA for Fe(II) and Fe(III). We address these two aspects in sequence. By considering the formation of a single negatively charged complex [Fe(III)-DMA(H−1)]−, along with the neutral complex [Fe(III)-DMA]0, Reichman & Parker (2002) calculated a speciation plot, in which Fe(III)-DMA formation dominated over the pH range 2.5–9, thus prohibiting the occurrence of an Fe(III)-NA complex, when NA was present at equimolar concentrations (Reichman & Parker, 2002, Fig. 2B). It was then concluded that DMA outcompetes NA over the entire physiologically relevant pH range, in contrast to that proposed by von Wirén et al. (1999). Since the analysis of chelate formation reported by von Wirén et al. (1999) was based on experimentally determined pKa values and iron(III) affinity constants, we first reassessed the pKa values for both NA and DMA and also determined the affinity constants for Fe(III) by potentiometric titration. Our previously determined values of the Fe(III) affinity constants were based on spectrophotometric analysis of competition studies with maltol. Employing chemically synthesised compounds the same sequence of pKa values for both NA and DMA was obtained as previously reported (von Wirén et al., 1999) (Table 1). DMA has four measurable pKa values whereas NA has five. This difference is due to the terminal amino group of NA, that protonates at a pKa of 7.73, while the terminal hydroxyl group of DMA does not dissociate even at very high pH values (Table 1, Fig. 1a). There are different protonation states for both NA-Fe(III) and DMA-Fe(III) complexes and these possess different net charges, namely for DMA [Fe(III) DMA]0, [Fe(III) DMA(H−1)]− and [Fe(III) DMA·(H−1)OH]2–. We have now measured the equilibrium constants relating to each of these species for both NA and DMA by potentiometric titration as previously reported (von Wirén et al., 1999) (Table 1). With DMA we found evidence for the protonated species [Fe(III) DMA]0 over the pH range 2–7 which agrees with the earlier data produced by von Wirén et al. (2000). We found no evidence for the hydroxylated species [Fe(III) DMA·(H−1)OH]2–. We also investigated the possibility of dimer formation of the type reported for HEDTA (Gustafson & Martell, 1963) and EDTA (Schuger et al., 1969; 1972) and could find no evidence for the existence of such species at µm concentrations and below. This analysis is in agreement with the electrophoretic determination of Fe(III)-DMA species that showed a gradual shift from the negatively charged to the neutral species when lowering the pH from 7 to 5 (von Wirén et al., 2000, Fig. 3). Unfortunately, this latter study was apparently not considered by Reichman & Parker (2002). Thus the speciation plot for Fe(III)-DMA is relatively simple with the two Fe complexes [Fe(III) DMA·(H−1)]1– and [Fe(III) DMA]0 dominating over the pH range 2–8 (Fig. 1b). The pKa value for this deprotonation process is 6.3. (a) Structures of deoxymugineic acid (DMA) and nicotianamine (NA). Superscript numbers indicate the assignment of the pKa values given in Table 1. (b)–(d) Computer simulations of the pH dependence of the Fe(III) complexes of NA and DMA: (b) 1 µm Fe +10 µm DMA (= L); (c) 1 µm Fe +10 µm NA (= L′); (d) 1 µm Fe +10 µm DMA (= L) +10 µm NA (= L′). With NA there are three major Fe(III) species. As derived from the binding constants (Table 1) and the associated speciation plot, [Fe(III)-NA·H]1+ dominates at pH 2–6, while [Fe(III)-NA]0 dominates over the pH range 6–9 (Fig. 1c). This is consistent with with the neutral charge of the Fe(III)-NA complex at pH 7.0 when determined by paper electrophoresis (von Wirén et al., 1999). The hydroxylated species [Fe(III)-NA·(H−1)]1– is only present at more alkaline pH values (above 8.0). As with DMA we could find no evidence for the existence of dimer complexes at concentrations below 1 µm. The affinity constants of both NA and DMA for Fe(III) have been determined by two independent methods, namely potentiometric titration and spectrophotometric analysis of the competition of each ligand with maltol. As there are several Fe(III) complex species for NA and mugineic acid (MA), the competition analyses give an apparent formation constant (KFe3+). With these Fe(III) affinity constants it is possible to calculate the pFe3+ values independently. Both pairs of values are in good agreement (Table 2). On the basis of this new conductiometric data (Table 1) we have recalculated the speciation of Fe(III) in the simultaneous presence of NA and DMA. Consideration of the negatively charged [Fe(III)-DMA(H−1)]1–, that was omitted in von Wirén et al. (1999), will effectively decrease the relative competitiveness of Fe(III)-DMA over Fe(III)-NA. Over the 5.5–8.5 pH range it is clear that NA is predicted to dominate the co-ordination of Fe(III) (Fig. 1d), which supports the earlier analysis reported by von Wirén et al. (1999), where both DMA species have not been considered separately. A major point of Reichman & Parker's (2002) criticism pertained to the experimental approach made by von Wirén et al. (1999), in which capillary electrophoresis was employed to verify the relative ability of NA to form Fe(II) or Fe(III) complexes. Reichman & Parker (2002) raised the issue that Fe(III)-NA complexes were not detected by capillary electrophoresis, by virtue of the rapid formation of Fe(III)-hydroxides. This difference, however, is clearly indicated in Fig. 5 of von Wirén et al. (1999), where it is demonstrated that the pFe3+ value for NA at pH 7.4 is only marginally greater than the Fe(III)-hydroxide solubility curve, whereas the corresponding pFe2+ value is very well resolved from the Fe(II)-hydroxide solubility curve. Thus, although the affinity constant for Fe(III) is larger than that for Fe(II) (1018.4 vs 1012.8, respectively), competition with the hydroxide anion at pH 7.4 is much more effective for Fe(III) than for Fe(II). Since Fe(III)-hydroxide formation can certainly occur in the cytoplasm, our experimental conditions properly reflect the situation in planta and correctly emphasize the fact that Fe(II) possesses a relatively higher stability when complexed by NA. Reichman & Parker (2002) developed another argument based on theoretically derived redox potentials of NA-complexed Fe(II) and Fe(III) which led to the conclusion that thermodynamic considerations can satisfactorily explain the high stability of Fe(II), while kinetic aspects as in von Wirén et al. (1999) are not needed. This statement turns out to be purely speculative. First, Reichman & Parker's (2002) computation of redox potentials considered [Fe(III)-DMA]1– and [Fe(III)-DMA·OH]2– as the most important complexes, which is in contrast with the predicted and experimentally determined species at neutral pH (von Wirén et al., 2000). Second, Reichman & Parker's (2002) theoretically derived reduction potentials do not agree with experimentally derived values from Sugiura & Nomoto (1984), as they indicate in their correspondence 'the reasons for this discrepancy are not known'. Third, kinetic considerations are of outmost importance when the formation of DMA complexes with different metal ions are observed. For example, the efficient formation of Cr(III)-DMA complexes is severely restricted by its slow kinetics. Thus, metals that undergo faster complex formation will dominate even if their formation constants are weaker (Hider, 1984). Until such time as there is better consistency between theory and experiment, we believe that arguments based on redox potentials associated with a complicated series of equilibria cannot provide definitive conclusions. On the basis of the concepts presented herein, the transfer of Fe(III) from DMA to NA would appear to be possible. However the kinetics of the movement of Fe(III) from one hexadentate siderophore to another is exceedingly slow (Hider, 1984) and, therefore, as previously suggested by von Wirén et al. (1999) and Sugiura & Nomoto (1984), reduction to Fe(II) before transfer to NA would appear to be a likely mechanism. The important point that emerges from this debate is that both von Wirén et al. (1999) and Reichman & Parker (2002) agree that NA form stable Fe(II) complexes. To avoid further speculation on metal speciation in plant extracts, future investigations should definitely focus on the direct chemical analysis of metal chelates. Such an analysis has recently been performed with yeast subjected to Ni toxicity, where Ni(II)-NA complexes were detected (Vacchina et al., 2003). As demonstrated recently, NA complexes with Ni(II), Fe(II) and Fe(III) form suitable substrates for membrane transport mediated by the metal phytosiderophore transporter ZmYS1 (Schaaf et al., 2004). Thus apparent Fe deficiency symptoms as observed in the NA-deficient tomato mutant chloronerva (Ling et al., 1999) are likely to be related with an intracellular maldistribution of Fe (Becker et al., 1995). Such a role is further supported by an immunochemical localization of NA in vacuoles (Pich et al., 2001). Another sharp contrast to the conclusion by Reichman & Parker (2002) that Fe-NA is unlikely to be employed for long-distance Fe transport, is the finding that NA deficiency in transgenic tobacco plants resulted in malnutrition of flowers with metal micronutrients including Fe. Again, this was best explained by an involvement of NA in intra- and intercellular Fe trafficking (Takahashi et al., 2003). Furthermore, recent studies on a ZmYS1 homolog from Arabidopsis, AtYSL2, indicated that nicotianamine-chelated Fe(II) is a suitable substrate for AtYSL2. Since AtYSL2-GFP fusion proteins are mainly located in the plasma membrane of vascular cells in roots (DiDonato et al., 2004), there is a high probability for Fe(II)-NA acting as an endogenous mobile Fe binding form. Taken together, in addition to the physico-chemical characterization of Fe-NA chelates, there is plenty of evidence from physiological and genetic studies that further indicate a role of NA in Fe trafficking, also in graminaceous species where DMA and NA occur in parallel (Becker et al., 1995; Pich et al., 2001; Bereczky et al., 2003; Takahashi et al., 2003; Schaaf et al., 2004). NA chelation and subsequent transport or compartmentation offers an attractive opportunity for plant cells for short- and long-distance transport of Fe and other essential metals and to decrease the immediate toxicity of Fenton-reactive free metals or simply to support their tissue and cellular distribution. In view of all this experimental evidence, Reichman & Parker's (2002) criticisms would appear to be unfounded. We thank Prof Dr T Kitahara and Prof Dr S Mori, (University of Tokyo, Japan) for the supply of NA and DMA. We thank the DFG Bonn for financial support to NVW (Grant WI 1728/6-1); the BBSRC for financial support to RCH; and CREST (Care Research for Evolutional Science and Technology) of Japan Science and Technology Corporation to EY.

Reaction rates are usually identified at laboratory scale, by comparing measured concentrations with those of the corresponding mathematical models. However, laboratory-scale reaction rates may not necessarily reflect the reactive transport scenarios at the field scale. Thus, a major challenge for field-scale modeling is the determination of reaction kinetics and rates. The conventional inversion of reaction rates relies on optimization approaches that require expensive computation to obtain the gradient of objective functions. In this manuscript, we present a combined simulation–emulation approach for calibrating the first-order reaction rates at the field scale. A number of sample points are adaptively selected to represent the high-dimensional parametric space including dimensions of reaction rates. Correspondingly, reactive transport models are generated and executed for constructing response surfaces of objective functions. Taking the advantage of smooth response surfaces, optimization of reaction rates is efficiently performed. For several benchmark cases, the advantage of using global sensitivity analysis and uncertainty quantification of the objective functions in terms of uncertain reaction rates is demonstrated.