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Perspectives in Science (2014) 1, 110–120

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Abbreviations: PE☆This article is p

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REVIEW

Standards for the reporting of kinetic isotopeeffects in enzymology$

Kevin Francis, Amnon Kohenn

Department of Chemistry, University of Iowa, Iowa City, IA 52242-1727, United States

Received 25 February 2013; accepted 19 December 2013; Available online 27 March 2014

KEYWORDSIsotope effects;Standard analysis;Error propagation;Regression;Kinetic isotopeeffects;Graphic presentation

0.1016/j.pisc.2014he Authors. Publismons.org/licenses

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thor. Tel.: +1 319mnon-kohen@uiow

AbstractKinetic isotope effects (KIEs) are a powerful tool in the study of enzymatic mechanism andfunction. Standardization of how data are reported would allow for comparisons of datacollected under different conditions, in different laboratories, or by different assays, and willcontribute to the assessment of their fit to different models and support of quantitative andqualitative conclusions. This paper will provide suggestions and examples as to how KIE datashould be presented in publications of enzyme reaction mechanisms. The importance offollowing the Standards for the Reporting of Enzymological Data committee's recommendationswhen reporting KIE studies are outlined and a particular focus is placed on procedures forcalculating, propagating, and reporting experimental errors. We hope that this paper will beuseful for researchers, authors of scientific papers and presentations, and reviewers of thesepapers alike, and will eventually enhance the impact of KIE studies by assisting in broaderapplication and implications of data.& 2014 The Authors. Published by Elsevier GmbH. This is an open access article under the CC BYlicense (http://creativecommons.org/licenses/by/3.0/).

Contents

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

KIE nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Intrinsic versus observed KIEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Importance of STRENDA recommendations for KIE measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

.02.009hed by Elsevier GmbH. This is an open access article under the CC BY license/by/3.0/).

y surface; PMF, potential mean forcesue entitled “Reporting Enzymology Data - STRENDA Recommendations and Beyond”. Copyright by

335 0234; fax: +1 319 335 1270.a.edu (A. Kohen).

111Standards for the reporting of kinetic isotope effects

Statistical procedures relevant to KIE measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Data fitting and propagating errors in KIE measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Global data regression in compliance with STRENDA requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Concluding remarks and summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Conflict of interest statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Introduction

The utility of kinetic isotope effects (KIEs) as mechanisticprobes of enzymes was recognized as early as 1936 bySüllman and coworkers, who found that the rate of oxygenconsumption decreased by �40% when α-α0-dideuteriosucci-nic acid was used as a substrate for succinate dehydrogenasecompared with unlabeled substrate (Erlenmeyer et al.,1936). The ensuing years saw an increased use of KIEs inthe study of enzyme mechanism (Fisher et al., 1953; Mahlerand Douglas, 1957; Rachele et al., 1955; Rose, 1961; Seltzeret al., 1959), which was revolutionized during the 1970s,largely due to the theoretical developments by Northrop(1975, 1981), Cleland (1975, 1982, 2005), and others. In thepast several decades they have been used to deduce manyaspects of enzyme chemistry including the mechanisms ofhydrogen transfer, oxygen activation and decarboxylation.Examples for all these applications in enzymology can befound in the following references (Fitzpatrick, 2004, 2010;Gadda, 2008; Hay et al., 2008; Klinman, 2007, 2013; Meyerand Klinman, 2005a, 2005b; Lin et al., 2008; Meyer et al.,2008; Nagel and Klinman, 2010; Roth and Klinman, 2003;Roth, 2007; Seltzer et al., 1959; Sikorski et al., 2004;Sutcliffe et al., 2006; Wang et al., 2012), and the followingreviews (Allemann and Scrutton, 2009; Cook, 1991, 1998;Cleland, 2005; Kohen, 2003; Kohen and Klinman, 2014; Kohenand Limbach, 2006; Wang et al., 2012). The increased use ofisotope effects in the study of enzyme function requires astandardization of the ways data are reported and analyzed.This paper will outline protocols for presenting isotope effectdata with a particular focus on the methods for calculatingand reporting error analysis. Detailed accounts of the theoryand uses of KIEs will not be given as they can be foundelsewhere in numerous books and review articles (Cleland,2005; Wang et al., 2012; Cook, 1991; Cook and Cleland, 2007;Kohen and LImbach, 2006).

The Standards for the Reporting of Enzymological Datacommittee (STRENDA) has outlined several requirements forpublishing studies of enzyme structure and function(Apweiler et al., 2010). These guidelines are of specialimportance in studies of isotope effects because the valuesobtained often depend on experimental conditions. Parti-cular emphasis must be placed on whether the reported KIErepresents the intrinsic value on bond cleavage or is anobserved value that might be masked by kinetic complexity(Cook and Cleland, 2007; Northrop, 1981). STRENDA'srequirements that the pH, temperature and substrateconcentration be reported are therefore critical in isotopeeffect studies as each can influence the magnitude andmeaning of the measured KIE (Cook and Cleland, 2007;Cornish-Bowden, 2012; Segal, 1975). Furthermore, thesaturation level of the substrate concentration used should

also be noted (e.g. relative to its Km value) in steady-stateassays or if pre-steady state rates are reported the portionof prebound substrate should be mentioned.

In addition to the general recommendations of STRENDA,proper error analysis is vital when reporting data fromisotope effects. This is especially true for secondary,solvent, equilibrium or heavy atom KIEs since the magni-tudes of these values are quite small and therefore can beobscured by the experimental errors if careful steps are nottaken during the measurement. Even for larger primaryKIEs, though, a rigorous error analysis must be carried outsince biophysical studies on enzymes often involve measure-ments over a range of conditions and the conclusions drawnfrom such studies can be dramatically changed by theuncertainty of the experimental values. One of the probesof quantum mechanical nuclear tunneling in enzymaticC–H activation, for example, relies on measurements ofthe temperature dependence of the KIE (Kohen et al., 1999;Nagel and Klinman, 2006; Sutcliffe et al., 2006; Sutcliffeand Scrutton, 2002; Wang et al., 2012). Temperatureindependent KIEs and the associated isotope effect onArrhenius preexponential factors (Al/Ah, where l and h arethe light and heavy isotopes, respectively) outside the semi-classical limits are taken as evidence for quantum mechan-ical tunneling of the hydrogen isotope (Bell, 1980; Nagel andKlinman, 2006, 2010; Sutcliffe et al., 2006; Sutcliffe andScrutton, 2002; Wang et al., 2012). For KIE data, Arrheniusor Eyring plots, or the isotope effects on their parametersare identical, as all differences in the rate equations dropout of the ratio equation. Yet visual inspection of Arrheniusor Eyring plots, or simple regression to average values, isoften insufficient to determine whether the Al/Ah value iswithin or outside semiclassical limits (i.e., can be explainedwithout invoking nuclear tunneling). Experimental errorshave to always be introduced with even the most sensitiveexperimental methodologies, to enable assessment ofwhether the data can be explained by a certain theoreticalmodel or not. Similarly, comparison of KIEs calculated bycomputer based simulation and experimental data requiresboth a clear indication of certainty in the calculated values,their distribution (e.g., PES vs. PMF calculations) and thestatistical confidence or deviation range of the experimentaldata from their average value. As in these examples, inclusionof error bars in plots of KIE data, and in data fit to anymathematical model, are absolutely required to allow for adetermination of the validity of conclusions drawn from suchstudies. Consequently, errors must also be reported in tablesof rates and KIE data to allow the reader to validate theanalysis and to further use the data in different analyses or forcomparison to new findings. Additionally, clear informationregarding the conditions, attempts to assess intrinsic values,and other data processing or manipulation should be reported

K. Francis, A. Kohen112

for experimental KIEs to be compared to values calculated bycomputer-based simulation, and to be compared to similarmeasurements conducted by other researchers, or the sameresearchers using a different assay. Examples of propagation,calculation and reporting of errors are detailed below.

This paper will begin with general considerations of report-ing isotope effects on enzymes that will include brief descrip-tions of intrinsic versus observed KIEs. This section will befollowed with a general discussion of error analysis and caseswhere the conclusions drawn are stringently dependent on theanalysis and its statistics. Methods for data fitting to theore-tical models by non-linear regression and plotting of data asfunction of different parameters will then be outlined andexamples will be given to illustrate the importance of arigorous error analysis. Finally, the recommendations in thisreport will be summarized in the concluding remarks. It ishoped that the suggestions put forth here will standardize thereporting of data in the field and further the pursuit of ourunderstanding enzymatic catalysis.

General considerations

KIE nomenclature

A reported KIE measurement should be either narrative innature (e.g., H/D KIE on a single turnover rate), or bedenoted as a superscript preceding the rate constant that isdescribed. The superscript should specify the heavy isotopethat was used and the rate constant should be reportedusing STRENDA's requirements (Apweiler et al., 2010). Thus,an oxygen KIE (k16O/k) should be reported as 18Okcat,18O(kcat/Km),

18Okchem, etc. For solvent KIEs the heavysolvent used should be denoted in the superscript, thus aD2O isotope effect should be denoted as D2OkX. In mixedlabeling experiments the isotopic labeling is specified bysubscripts of the general form ki,j, where isotope i is in theprimary position and isotope j is in the secondary position. AkHH/kTH designation, for example, would describe a primaryH/T KIE with hydrogens at the secondary position of bothmolecules, whereas kHH/kTT would indicate a primary H/Tand secondary H/T KIEs in the same measurements.

Intrinsic versus observed KIEs

The isotopic labeling of the substrates can be designed so mostof the measured KIE will reflect a specific kinetic andmechanistic step such as binding or bond cleavage (Agrawaland Kohen, 2003; McCracken et al., 2004; Markham et al.,2004; Schramm, 2007). However, when designing a study ofbond cleavage, for example, kinetic steps such as substratebinding, conformational rearrangements, product release orregeneration of the catalyst still contribute to the rate of theenzymatic reaction and may mask the intrinsic KIE (Cleland,1975, 2005; Kohen, 2003; Northrop, 1975). As described byNorthrop (1975, 1981) and extensively reviewed elsewhere(Cleland, 2005; Cook, 1998; Cook and Cleland, 2007; Kohenand Limbach, 2006) even kinetic steps that are not ratelimiting can decrease the observed KIE from the intrinsicvalue. This behavior is quantitatively expressed by Eq. (1),where KIEobs is the measured KIE, KIEint is the intrinsic isotopeeffect resulting from the cleavage of the labeled bond, Cf and

Cr are the forward and reverse commitments to catalysis(Cook, 1991; Cook and Cleland, 2007; Kohen, 2003; Kohen andLimbach, 2006; Northrop, 1975), respectively and EIE is theequilibrium isotope effect. Naturally, Cf and Cr could becomplex expressions that depend on the system under studyand the conditions of the measurement.

KIEobs ¼KIEintþCfþCrEIE

1þCfþCrð1Þ

The masking of the KIE can sometimes be reduced byusing pre-steady state kinetics (Fierke et al., 1987;Loveridge et al., 2012), changing the pH or temperature(Bahnson et al., 1993; Cook and Cleland, 1981a, 1981b; Kohenet al., 1999), using an alternate substrate (Bahnson et al.,1993; Gadda et al., 2000; Kohen et al., 1999), performing themeasurements at different saturation levels of the secondsubstrate (Fan and Gadda, 2005; Hong et al., 2007), orswitching to methodologies that further expose the intrinsicKIE (Cook, 1991; Sen et al., 2011).

When presenting values of measured KIEs it is critical toreport whether the data represent intrinsic or observedvalues (i.e., KIEobs or KIEint). This is true even if theexperimental questions being addressed do not requirerigorous controls to ensure that the data reflect solely theeffects of isotopic substitution on the kinetic step ofinterest, as different levels of commitment can exposeinteresting mechanistic features such as whether a reactionis concerted or stepwise (Cook et al., 1980; Hermes et al.,1982). Additionally, a deuterium KIE is commonly measuredto determine whether enzymatic C–H bond cleavage is atleast partly rate limiting in the overall catalytic cycle. Insuch an application, a value significantly greater than unityis sufficient to warrant a positive conclusion even if this valueis decreased relative to its intrinsic value. Yet, failing to reportthe value as observed may mislead readers into thinking theresult represents the intrinsic value on bond cleavage. Thiscould then lead to wasted efforts by other research groupswho may want to use the data as a starting point for furtherinvestigations, and particularly mislead theoreticians trying toreproduce this value by computer-based simulation of only thebond-cleavage step. By not specifying that the KIE reported isan observed value, which may be decreased by other kineticsteps, computational efforts may lead to erroneous conclu-sions and superfluous controversies in the field. Hence, a KIEshould always be reported as an observed value, or offer clearexplanation of which efforts have been put forth to onlymeasure or assess intrinsic KIE.

Importance of STRENDA recommendations for KIEmeasurements

In order to create a comprehensive protein structure–function database, the STRENDA committee has put fortha set of guidelines to standardize the results reported fromdifferent laboratories. These guidelines can be found inreference (Apweiler et al., 2010) and were put forth inorder to allow direct comparisons of the wealth of datareported in the literature. STRENDA's recommendations arenot only necessary to achieve the ambitious goal of creatinga universal database, but also for assessing the validity ofconclusions drawn from KIE studies. In this section the

113Standards for the reporting of kinetic isotope effects

importance of reporting experimental conditions of KIEmeasurements will be outlined with an emphasis on howthe results obtained depend on the reaction environment.

STRENDA requires that both the temperature and pH bereported for any enzymatic rate measurement and this isparticularly important in measurements of KIEs. Both tem-perature and pH can effect commitments to catalysis (Cf

and Cr in Eq. (1)) and thus the measured KIE, since many ofthe steps that occur during turnover depend on thesefactors (Cleland, 1982; Cook and Cleland, 2007; Cornish-Bowden, 2012; Kohen and Limbach, 2006). The deprotona-tion of nitroalkanes by nitronate monooxygenase, for exam-ple, exhibits a deuterium KIE of only �4 at physiological pH,but this value is increased to �7.5 at low pH due to anabolishment of the kinetic complexity under alkaline con-ditions (Francis and Gadda, 2006). Similarly, the KIE for thedihydrofolate reductase reaction is completely masked atlow pH due to a large commitment to catalysis of theprotonated substrate, but is sizable at high pH (Fierkeet al., 1987). The kinetic complexity and thus masking ofthe observed KIE is also influenced by temperature asobserved in studies of the hydride transfer reaction cata-lyzed by dihydrofolate reductase (Wang et al., 2006). Evenif measures are taken to assess intrinsic KIE values, the pHand temperature must always be reported because themagnitude of the KIE may very well be influenced andreflect the experimental conditions.

In addition to temperature and pH, the kinetic parameterunder study must be clearly stated, or in case the KIE ismeasured on a rate (i.e., one set of conditions) rather thana rate constant (i.e., KIE on kinetic parameter), substrateconcentrations must be presented. Different mechanisticconclusions can be reached if the KIE is measured fordifferent rate constants such as the steady state secondand first order rates of the Michaelis–Menten model, i.e.,kcat/Km or kcat, respectively, since these parameters reflectdifferent aspects of enzymatic turnover (Cook, 1991; Cookand Cleland, 2007; Cornish-Bowden, 2012; Kohen andLimbach, 2006; Northrop, 1998). It is of course critical tostate whether the measurements were performed understeady-state or pre-steady state conditions and if a continuousor end-point assay was employed. A further consideration isrequired when studying multi-substrate enzymes, since thesaturation level of the unlabeled substrate can often influencethe observed KIE for the labeled one (Cook, 1991; Cook andCleland, 2007; Kohen and Limbach, 2006). Each of thesefactors are critical when determining if the measured KIEreflects an observed value, whether an intrinsic KIE has beenassessed, which step along the catalytic cycle the KIE mayreflect, and for comparing the results from enzymes obtainedfrom different sources or their mutants.

Finally, the raw data used to calculate isotope effectsshould always be presented either in the main text or in thesupplementary information to allow for a critical review ofthe conclusions by the reader, and to enable their use in analternative analysis or for comparison to new data collectedin the future. Conclusions are often drawn from trends inthe KIEs observed with either pH, temperature, or uponsite-directed mutation of the enzyme. Figures or tablesshowing the parameters and their standard deviation orstandard errors obtained from overall fits of isotope effectdata to the relevant equations are often the most effective

and meaningful way of reporting results. While it is typicallyappropriate to exclude the raw data from the main text theresults should be presented as supplemental informationwhenever possible.

Statistical analysis

Introduction

A critical yet often neglected component of reports on KIEsis a clear description of how error analysis was performed.Like any experimental measurement there is a certain levelof uncertainty regarding precision and accuracy whenmeasuring a KIE for an enzymatic reaction. Even in thesimple example of the common non-competitive method,which involves separate rate measurements of both thelight and heavy isotopes, each rate has to be measured byseveral repeats under the same conditions, the errors fromeach measurement (whether from continuous or otherassays) should be propagated when calculating the averagevalue for each set of conditions. Then, the errors associatedwith each rate need to be propagated and reported in theratio of rates between light and heavy isotopologues, i.e.,the KIE. While the competitive method reduces the errorpropagation by directly comparing both the light and heavyisotopes to measure a KIE rather than rates, it also involvesmultiple measurements to assess the confidence in themeasured value. The errors associated with each measure-ment must also be propagated when averaging the KIE.Furthermore, since KIEs are typically more meaningful whenreported for kinetic parameters rather than a single rate,special attention must be paid as to how the raw data are fitto calculate the effects of isotopic substitution. This sectionwill briefly review the relevant equations used to propagateerrors in KIE measurements and will outline the proper waysto present the data using hypothetical examples.

Statistical procedures relevant to KIEmeasurements

The most common procedures and equations used in thestatistical analysis of KIE measurements are listed inTable 1. The derivation and proofs of these expressionscan be found in most common statistics or chemistry text-books (Calcutt and Boddy, 1983; Skoog et al., 1998) and aretherefore not discussed in detail here. Error propagationshould start with the individual rate measurements and theirexperimental errors, and should be carried throughout theentire data analysis whether the results reported are averagedvalues or subject to regression. When reporting the resultsfrom multiple assays the number of independent measure-ments must be clearly stated in the figure or table legend.

The standard deviation (sdev) describes the precision of asingle measurement and thus shows how much variation or“dispersion” exists from the average. For a normal distribu-tion of measurements it is common to report sdev as inTable 1, which describes the deviation from the averagevalue where 68.2% of the measured values are found(i.e., 1s). In cases where higher precision is needed, thedistribution in which 95.4% of the measured values arefound (i.e., 2s) can also be calculated (Calcutt and Boddy,

Figure 1 Fitting of hypothetical rate data. Panel A shows ahypothetical set of rate data as function of [S], fitted to Eq. (2),and Panel B shows the same data as linearized Lineweaver–Burkplot with the same errors but fit to the linearized equation(Eq. (3)). The black lines present fit to the relevant model and theblue and red lines the fit to71s deviation from each average value.

Table 1 Statistical equations for isotope effectmeasurements.

Calculation Example Equation

Addition orsubtractiona

x=a+b+c sx ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2aþs2bþs2c

q

Multiplicationor divisiona

x=a n b/c sxx ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisaa

� �2þ sbb

� �2þ scc

� �2q

Standarddeviationb sdev ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑x2i � ∑xið Þ2=N

� �N�1

r

Standard errorb serr ¼sdevffiffiffiffiN

p

aa, b and c are individual measurements with standarddeviations or errors of sa, sb and sc, respectively, and sx is thestandard deviation or error for x.

bxi is the value of the ith measurement; N is the totalnumber of measurements.

K. Francis, A. Kohen114

1983; Skoog et al., 1998). The reliability of the reportedvalue increases when more experiments are conducted, andfor more than 7 independent measurements this reliabilitycan be estimated from about twice the standard error(a factor known as the 95% confidence interval). Standarderrors (serr) describe the variability of a population of dataand reveal information concerning the reproducibility of themeasurement. For less than 7 independent measurements,it is more meaningful to report standard deviation and thenumber of measurements (N). While either the standarddeviation or error may be appropriate for a given set ofdata, the parameter used should always be clearly notedwhen reporting isotope effects. In addition, one shouldalways state which statistical method was used in theanalysis (i.e. method of least squares, confidence limits)so the reader can determine the meaning of the reporteduncertainty.

Data fitting and propagating errors in KIEmeasurements

The final conclusions drawn from isotope effect studiesrarely arise from a single KIE, but rather from the KIE asfunction of various parameters, i.e., the trend of the datacollected over a range of experimental conditions. KIEmeasurements are often examined as a function of pH(Cook and Cleland, 1981a, 1981b; Francis and Gadda,2006; Gadda et al., 2000), temperature (Kohen et al.,1999; Limbach et al., 2006; Nagel and Klinman, 2006;Roston et al., 2012; Wang et al., 2006), pressure (Hayet al., 2007, 2010, 2012; Pudney et al., 2010), concentra-tion of another substrate (Fan and Gadda, 2005; Hong et al.,2007), or fraction conversion (for competitive KIEs) (Kohenet al., 1999; Sikorski et al., 2004; Stojkovic et al., 2010;Wang et al., 2006), and data are fit to equations represent-ing a theoretical model associated with the function understudy (e.g., the Michaelis–Menten equation for concentra-tion dependence or Arrhenius equation for temperaturedependence). Before computers were readily available, it

had been common to first linearize the equation in question,and then conduct a linear root mean square regression(Calcutt and Boddy, 1983; Skoog et al., 1998) to find theparameters of the model (Segal, 1975). As discussed below(Figure 1) this can lead to erroneous error propagation, andnow that computers and programs that conduct non-linearregressions are readily available, it is always important toconduct non-linear regression to the model under study.Errors that are introduced during the experimental mea-surement must be propagated throughout the data analysisin order for valid conclusions to be drawn from the study.

Fitting the data to the Michaelis–Menten equation, forexample, will have errors associated with kcat, Km and kcat/Km. In a non-competitive assay this will result in individualerrors for both the light and heavy isotope that must bepropagated when calculating the KIEs using the equations inTable 1. Since multiple measurements have to be made, thefinal error must be propagated when reporting the KIEs onthe different parameters. When measuring KIEs as a function ofpH, temperature, pressure, fraction conversion, etc., the errorsassociated with the individual experiments must be carried overto the fits of the data to the relevant equations. The errorsfrom these fits must be reported when presenting the final fits

115Standards for the reporting of kinetic isotope effects

of the data to obtain the isotope effects reported in the study.The procedures for propagating and reporting errors for KIEdata are illustrated in the examples presented below.

Before the widespread availability of software packagesthat conduct non-linear regression, the kinetic parametersof an enzyme were commonly determined through a linearroot mean square regression. Common examples for theseprocedures included plotting 1/[vo] versus 1/[S] (i.e. Line-weaver–Burk plots), constructing Eisenthal, Cornish-Bowdenplots where [S] is plotted on the negative abscissa and vo isplotted on the ordinate, or Hanes–Woolf plots in which the[S]/vo is plotted against [S], where vo is the initial velocityand [S] is the substrate concentration, respectively (Cookand Cleland, 2007; Cornish-Bowden, 2012; Segal, 1975).While each method has its advantages and disadvantages,linear regressions of kinetic data result in an erroneousweighing of errors and as a consequence the value anduncertainty of the determined KIE as illustrated in Figure 1for a hypothetical Lineweaver–Burk plot.

As extensively described elsewhere (Cook and Cleland, 2007;Cornish-Bowden, 2012; Segal, 1975), the Michaelis–Mentenequation (Eq. (2)) can be linearized as shown in Eq. (3), where[E] is the concentration of enzyme, Km is the Michaelis constantand kcat is the turnover number, respectively.

v0½E� ¼

kcat½S�Kmþ½S� ð2Þ

½E�v0

¼ Km

kcat

1½S� þ

1kcat

ð3Þ

Plotting 1/[vo] versus 1/[S] gives a linear line with a slopeof Km/kcat (the reciprocal of the second-order rate constantof the enzyme, kcat/Km), a y-intercept of 1/kcat and anx-intercept of �1/Km. While these values can easily bedetermined without the aid of a computer, they are heavilydependent on the precision of rates determined at thelowest substrate concentrations as illustrated in Figure 1.This is problematic since the precision of the measurementis lowest at low substrate concentrations due the slowerrates and correspondingly small signal changes in the kineticassay employed. As can be seen in Figure 1, small changes inthe rates determined at low substrate concentrations candramatically affect both the slope and intercepts of theLineweaver–Burk plot and thus the kinetic parameters andassociated KIEs determined using this method. This sensi-tivity is overcome when plotting the untransformed dataand using the non-linear Michaelis–Menten equation (Eq. (2))to determine the kinetic parameters. Similar uncertaintiesarise when using alternate methods of plotting enzymekinetic data and should therefore be avoided.

Global data regression in compliance with STRENDArequirements

When isotope effects are measured for a multi-dimensionalmodel the data should be fit globally to equations describingthe kinetic mechanism under study. Common and generalexamples can be expressed as y=F[xi], where xi is more thana single variable, such as multi-substrate enzymes (y=F[S1,S2,…[Si]]), temperature and pressure (y=F[P1,P2,…[Pi]]), etc.The kinetic parameters obtained from these fits should be

used to calculate both the isotope effects on the relevantparameters and their associated errors. The relevant equa-tions used to fit the data should be reported as well as thesoftware package used for the analysis, the regressionmethod, and the specific methods for errors assessment,incorporation, statistical weighing, and propagation. In gra-phic presentation of the data, the individual curves should beplotted using the kinetic parameters obtained from the globalfitting, rather than a single dimensional fit for a specific set ofvariables (e.g., concentration of inhibitor in Figure 2). Inaddition, the statistical confidence of the global fit should bereported either in a table or the figure legend. It is importantto use global fits of the data to determine a KIE, since thevalues obtained from fitting to a model of lower dimension (e.g., fitting to individual curves measured under differentconditions) may not represent meaningful and general para-meters (Cook, 1991; Cook and Cleland, 2007; Cleland, 1963;Kohen and Limbach, 2006). Furthermore, the plots presentedshould be fit using the parameters obtained from the globalfits to allow for a visual inspection of the quality of the data.As illustrated in Figure 2, fitting the rate data at eachinhibitor concentration [I] (colored blue to black for low tohigh [I], respectively) to either non-linear or linearizedequations (Eqs. (2) and (3), respectively) in panels A and Cmay give the false impression that the data fit the modelunder study very well. However, fitting the same data to twodimensional function representing competitive inhibition(Eqs. (4) and (5) and panels B and D, respectively, where [I]is the inhibitor concentration and KI the inhibition constant)indicate poor agreement between data and model. In thisspecific example the experimental conditions did not in factallow for an accurate determination of the kinetic parametersof interest (Francis and Gadda, 2009).

v0½E� ¼

kcat½S�Km 1þ ½I�

K I

h iþ S½ �

ð4Þ

½E�v0

¼ Km

kcat1þ ½I�

K I

� �1½S� þ

1kcat

ð5Þ

The kinetic parameters of an enzyme are first determinedthrough fits of the data to the Michaelis–Menten equation ateach temperature (Figure 3). In this example the assay isran in triplicate for each substrate concentration. Thepractice of fitting the averaged rates at each substrateconcentration as shown in Panel A ignores errors for datapoints at each concentration, and should be avoided.Different regression packages enable weighting errors ateach concentration, which partly alleviates the underestimation of the errors on the parameters, but differentpackages may lead to different errors' assessment as theyuse different algorithms. This method should also bediscouraged from statistical theory point of view becauseit assumes the same Gaussian distribution at very differentsets of data. The proper procedure should be fitting of all ofthe experimental data points to the non-linearized Michae-lis–Menten equation (hyperbola, e.g., Eq. (2)) and using theresulting parameters (e.g., kcat, Km, subscribed) to calcu-late the KIE on each parameter by dividing the value for thelight isotope by that for the heavy isotope (while propagat-ing the errors as described in Table 1). For graphical clarity,the averaged values of the multiple measurements should

Figure 2 Example of a global fitting of kinetic data – rates for single substrate and single inhibitor model. The plots are forpreliminary data testing a presumed competitive inhibition of Williposis markii nitronate monooxygenase by bromide (Francis, K.and Gadda, G. unpublished results). Initial rates were measured using ethylnitronate as substrate in the presence of 0 (black),3 (red), 15 (green) 24 (purple) and 30 (blue) mM inhibitor (KBr) in 50 mM potassium phosphate at pH 7.4 and 30 1C. Panel A showsthe fit of individual sets to a linear line (e.g., Eq. (3)), panel B shows the fit of the data to a linearized equation for a global fit ofcompetitive inhibition (Eq. (5)), Panel C shows the fit to the non-linearized Michaelis–Menten Eq. (2), and Panel D shows the fit of thenon-linearized data to the global fit for competitive inhibition (Eq. (4)). Note that in Panel A the data appear to converge well atthe Y-axis, which would indicate competitive inhibition, while both linearized and non-linearized global fits for the same dataindicate poor agreement with the competitive model (Eq. (4)). Additionally, the inhibition constant (KI) obtained did not fit theoverall trend for anion inhibition of the enzyme as reported in (Francis and Gadda, 2009). The experiment was repeated using abetter distribution of KBr and substrate concentrations to give a more reliable inhibition constant (Francis and Gadda, 2009).

K. Francis, A. Kohen116

be presented in the plot, but the curves plotted should befrom the fit of the data to the global, multidimensionalmodel and its equation, i.e., using the parameters resultingfrom the global fit (Panel D in Figure 3).

To continue this example to KIE calculation, one dividesthe values obtained from the fitting presented above andthe associated errors are propagated using the secondequation in Table 1. While the magnitudes of the KIEs mightbe qualitatively similar whether the regression is conductedcorrectly or not, the wrong conclusions could be reachedregarding differences between KIEs measured at differenttemperatures, for different mutants, or different substratesof the enzyme. Such wrong conclusions could, for example,suggest a significant effect of a mutation on the mechanism,although an appropriate fit and error propagation mightindicate the two variants are actually indistinguishable. Thisis even more critical for measurements of small KIEs, suchas for heavy isotopes (Marlier et al., 2008, 2011; Silva et al.,2005, 2009) or 21 KIEs (Roston and Kohen, 2010), wheresmall differences in values and their statistical distributionare very sensitive to small changes when concluding what isthe location of the enzymatic reaction's transition state.

In some studies, mechanistic details of an enzyme could befurther examined by measuring the KIE as a function of

temperature, i.e., the elucidation of the isotope effects onactivation parameters. Since the KIE on activation parametersare most mechanistically meaningful when calculated forintrinsic KIEs, efforts for estimating KIEint are commonly inplace prior to assessing these KIEs. Activation parameters onKIEobs involve many temperature dependent processes, and thusare hard to interpret. In some cases single turnover rates couldassess intrinsic KIE values (Fierke et al., 1987; Loveridge et al.,2012), but in some cases significant commitment still maskmeasured rates, and triple isotopic labeling methods canfurther assist in assessing intrinsic KIEs (Sen et al., 2011;Wang et al., 2006). For the latter method, the propagation oferrors from the observed KIEs to the intrinsic KIEs is compli-cated by the fact that it involves a numerical calculation. Therelevant numerical procedure (denoted the Northrop methodafter its inventor; Cook, 1991; Northrop, 1975) and detailedexplanation of the statistically appropriate error propagationare presented elsewhere (Cook, 1991; Northrop, 1975; Senet al., 2011; Wang et al., 2006). Fitting KIEs measured atdifferent temperatures to the Arrhenius equation (Eq. (6)),which for KIEs is identical to the Eyring equation, would givevery different values for the isotope effects on the activationparameters (Al/Ah and ΔEa in Eq. (6)) depending on the fittingprocedure used. Furthermore, the correct fitting would

117Standards for the reporting of kinetic isotope effects

commonly result in larger statistical range of possible values,which could be critical when concluding whether the KIE inquestion is within the range of semiclassical theory, or wouldrequire nuclear tunneling (Kohen et al., 1999; Kohen andLimbach, 2006; Nagel and Klinman, 2010; Sutcliffe andScrutton, 2002).

KIE¼ Al

AheΔEa=RT ð6Þ

The above examples, while only covering a very small setof applications, illustrate the vital importance of propercalculation and reporting of error analysis in reports of enzy-matic isotope effects. Recent literature provides numerousexamples where fundamentally different conclusions concern-ing the mechanism of enzymatic reaction would be implied ifthe KIE is temperature dependent or not (Nagel and Klinman,2006; Sutcliffe and Scrutton, 2002; Roston et al., 2012; Wanget al., 2012), or whether Al/Ah is within the semiclassical region(Kohen, 2003; Kohen and Limbach, 2006; Nagel and Klinman,2010; Sutcliffe and Scrutton, 2002; Wang et al., 2012). Tobroaden this picture, one has to remember that each ratemeasurements (continuous assay or not) result in experimentalerror, which has to be propagated to the mutilate calculationsas presented in the hypothetical example presented in Figure 3.That fit leads to parameters, used for the KIE calculations,whose temperature dependence can be used for the calculationof isotope effects on activation parameters (entropy andenthalpy). Each step should involve propagation of errors, thusthe initial underestimation of the errors will propagate and beamplified in every step. Correct propagation from individualrate measurements to the final assessment of errors on the KIEsfor the activation parameters will afford realistic assessment ofthe confidence, and differentiation between comparative stu-dies. For example, effect of mutation on the nature of thechemical step that is isotopically sensitive could be erroneouslyconcluded to be significant if the errors are not propagated in arigorous fashion as demonstrated above. Furthermore, theprocedures discussed are equally applicable to studies of KIEsas a function or pH, pressure, fraction conversion or any otherexperimental variable used to study enzyme-catalyzed reac-tions via KIEs. These examples demonstrate how the under-standing of enzyme catalysis could be seriously hampered bynot applying a rigorous statistical analysis of the data.

Figure 3 Deuterium KIEs for the hypothetical enzyme Ease.Panel A shows a plot of the averaged values of triplicatemeasurements for protiated (black) and deuterated (red)substrates, where the lines show the fit to Eq. (2). Panel Bshows a fit of all of the data points collected to the sameequation. Panel C shows the appropriate presentation of the

Concluding remarks and summary

In certain studies, qualitative findings such as whether a KIE isat all measureable for a specific labeling pattern can lead tothe correct mechanistic conclusion regarding whether certainchemical step is partly rate limiting or not. However, manystudies require careful estimation of quantitative values andtheir errors to draw a meaningful mechanistic conclusion. It ishoped that the guidelines put forth in this paper will standar-dize the reporting of KIEs in enzymology. As a quick reference,the suggestions outlined above are summarized below:

average values at each concentration and their sdev, but thecurve is from panel B, i.e., fit to all the experimental data

1. points. The table demonstrates that fitting the averaged valuesartificially deflates the associated sdev on the parameters,which will lead to even more substantial error deflation whenthe isotope effects for these parameters is calculated.

A KIE should be reported as an observed experimentalvalue under a specific set of conditions that need to bespecified. In case where efforts were carried out toassess the intrinsic KIE value, the methodology and therigorous controls examined have to be provided.

K. Francis, A. Kohen118

2.

STRENDA's requirements for reporting enzyme data(Apweiler et al., 2010) should be followed. Thus, thepH, temperature, substrate concentrations, and otherrelevant conditions should be reported and the assaydescribed in sufficient details to assess the exact natureof the data.

3.

It should be stated if the kinetic measurements werecarried out under steady state or pre-steady stateconditions, if a continuous or end point assay wasused and any other specific details regarding thekinetic assay should be noted or referenced. Also,the kinetic parameter that the KIE is reporting on mustbe specified.

4.

Kinetic data as function of changing conditions (tempera-ture, pH, pressure, fraction conversion, etc.) should befitted non-linearly and globally where all the experimentaldata points are used for regression (rather than averagingdata for each condition set prior to fitting to the appropriatefunction).

5.

The raw data collected in the study should be reported ineither the main text or supporting information.

6.

Error propagation should start with the individual ratemeasurements and be propagated throughout the dataanalysis.

7.

Error bars are required in all plots of isotope effect data,and the standard deviation or error must be reported forall experimental values presented in tables or text.

Conflict of interest statement

None of the authors have any conflict of interest.

Acknowledgments

This work was supported by NIH R01 GM65368 and NSFCHE0133117.

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