Multicomponent determinations using addition-generated reagent profiles and partial least squares...

Analytica Chimica Acta 535 (2005) 287–295

Multicomponent determinations using addition-generated reagentprofiles and partial least squares regression

Rosa Garcıaa, Guillermo Lopez-Cuetob, Miren Ostraa, Carlos Ubidea,∗a Departamento de Qu´ımica Aplicada, Facultad de Qu´ımica, Universidad del Pa´ıs Vasco, Apdo. 1072, 20080-San Sebasti´an, Spain

b Departamento de Qu´ımica Anal´ıtica, Facultad de Ciencias, Universidad de Alicante, Apdo. 99, 03080-Alicante, Spain

Received 12 May 2004; received in revised form 30 November 2004; accepted 30 November 2004Available online 7 January 2005

Abstract

The use of addition-generated reagent profiles is proposed for multicomponent determinations when the reactions between the reagent andanalytes are slow. The oxidation of cysteine, methionine and homocysteine with dichromate in acidic medium has been used as the chemicalsystem for experimental verification of some theoretical suppositions. The methodology tries to make the most of the differences in the kineticb l data whent e reagenti oncentrationso inations( ted to be ofg l interest oft©

K ares regress

1

tRchpa[Ad

s re-ss ofationedfasts-

ition-ied

romeoreti-ex-

eter-peri-filesner-

0d

ehaviour. The continuous addition of dichromate (the reagent) to the sample including the amino acids provides the experimentahe visible signal from dichromate is followed along time with a diode array spectrophotometer. The whole signal-time profile for ths then used to characterize the sample, and partial least squares regression (PLSR) has been applied as calibration algorithm. Cf amino acids between 10−4 and 10−3 M have typically been used. In the present case, mean errors increase from individual determbetween 2 and 5%) to binary (between 4 and 8%) and ternary mixtures (between 6 and 13%). This tendency can be expeceneral application. Some validation with pharmaceutical products has been accomplished. A critical discussion on the practica

his application is finally included.2004 Elsevier B.V. All rights reserved.

eywords:Reagent profiles; Dichromate; Cysteine; Methionine and homocysteine determination; Multicomponent determination; Partial least squ-ion

. Introduction

When a reagent (R) is added, at a constant rate, to a reac-ion mixture where an analyte (A) is present, and the reaction

+ A→ P (product) is slow, the variation of the reagent con-entration with time shows a characteristic profile[1] whichas been namedreagent profile[2]. This kind of profiles wereroposed years ago for kinetic studies of fast bromination re-ctions, where bromine was obtained by electrogeneration

1], but they do not seem to have been used much ever since.relatively recent paper proposed their use for analytical

eterminations in chemical systems moving to equilibrium,

∗ Corresponding author. Tel.: +34 943018211.E-mail address:[email protected] (C. Ubide).

after handling the whole profile with partial least squaregression (PLSR) as calibration algorithm, and regardlewhether the reagent is obtained either by electrogeneror by continuous addition[2]. The technique has also provto be useful for multicomponent determinations whenreactions are involved[3]. The experimental set up is esentially the same as in the so called continuous-addof-reagent (CAR)[4], but the latter has only been applto signals obtained from the products of slow reactions[5],whilst in the case of the reagent profiles only signals fthe reagent are used. The present paper presents a thcal evaluation of the analytical possibilities that can bepected by using reagent profiles for multicomponent dminations when slow reactions are involved. Some exmental validation is also made. The use of reagent prooriginated either by continuous addition or continuous ge

003-2670/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.aca.2004.11.077

288 R. Garcıa et al. / Analytica Chimica Acta 535 (2005) 287–295

ation of the reagent is a non-conventional way of getting reac-tion profiles that, together with the use of PLSR, show someadvantages:

• It can be used with rather fast reactions, because the lowconcentration of the reagent slows down the reaction rate[1] and reactions going to completion in few seconds inbatch originate useful reaction profiles for both kinetic andanalytical purposes[2].

• Reagents that give strong experimental signals are allowedbecause the reagent is always in deficit along the reaction,its concentration is low and there is no danger of detectorsaturation. This may give an extra opportunity to reagentssuch as MnO4−, Cr(VI), Br2, organic reagents etc., and canbe applied to both photometric and electroactive reagents.

• Unstable and/or hazardous reagents may be generated insitu and consumed immediately.

• The possibility of choosing the reagent concentration andits addition/generation rate can, probably, allow to changein some extension the concentration range to be deter-mined.

• The use of whole spectrum calibration methods, such asPLSR, allows the use of the whole reaction profile as an-alytical signal, regardless the signal comes from reagent,analyte, products or any mixture of them. In the latter case,a higher mixed signal is generated that may result in im-

ibleences

• ities,etics

R inp ac-t ionals high-p ctor,lk tp pro-fi two-d ainsa es).S beena pur-p madet ipleso

einew temt theor idw ta ion-i ionsa of the

Scheme 1.

cell function is considered[11]; homocysteine (hcy) seems tobe related to nutritional deficiencies that may originate renalfailures or cardiovascular diseases[12] and the importanceof its determination in biological samples has recently origi-nated a review of methods[13]. The three amino acids havea sulphur centre (Scheme 1) that can easily be oxidized, andthey all are related becausehcy is formed as intermediate inthe metabolism ofmetto cys[13]. PLSR is used for the de-termination of the above-mentioned amino acids, includingbinary and ternary mixtures. Some pharmaceuticals are alsoincluded in the validation.

We have been unable to find examples about the use ofreagent profiles for multicomponent determinations either inthe case of slow reactions or when the reaction rate is slowedby restricting the availability of a reagent. The oxidation ofcysandmetby dichromate belongs to the first case, the ox-idation of hcy belongs to the second one. The term “slow”is used here to indicate those reactions whose rate constantcan be determined experimentally with standard laboratoryequipment.

2. Experimental

2.1. Reagents

andu hout.

ep urica inoa ds(

2

St asua ntin-u lett-P andb ededf elayt stantt d.A where[

proved sensitivity. In any case, signals from the visregion are usually preferred because spectral interferfrom the UV region are then avoided.The use of PLSR makes irrelevant whether absortivrate constants, etc. are known or not. The reaction kinmay even obey an apparent variable reaction order.

Multivariate calibration methods, in general, and PLSarticular are getting popularity in the daily analytical pr

ice because they are well suited to handle three-dimensignals such as those obtained from evolutionary data:erformance liquid chromatography–diode array dete

iquid chromatography–mass spectrometry[6] or reactioninetics followed at several wavelengths[7]. In the presenaper three-dimensional signals are obtained (reactionles at several wavelengths) but they are handled asimensional signals (in the data matrix each row contll the spectra that correspond to a sample at different timome other multivariate calibration methods could havepplied, but PLSR is specially designed for calibrationoses; the reason is that the variable reduction step is

o get as good prediction power as possible. The princf PLSR have already been given elsewhere[8,9].

The oxidation of cysteine, methionine and homocystith dichromate in acidic medium is the chemical sys

hat has been used here to validate the afore-mentionedetical purposes. Cysteine (cys) is a non-essential amino acith antioxidant properties that can be used as detoxican[10]nd is frequently present in vitamin preparations; meth

ne (met) is an essential nutrient whose oxidation reactre getting greater consideration as far as the regulation

-

All the chemicals were of analytical-reagent gradesed as received. Doubly distilled water was used throug

Dichromate solution (10−1 M) was prepared from thotassium salt (Merck) and dissolved in 2.0 M sulphcid (Riedel-de-Haen); the solution was stable. Stock amcid solutions (10−1 M) were prepared daily from the soliFluka).

.2. Apparatus

A 100 ml reaction vessel of a Metrohm Model 716 DMitrino autoburette with continuous magnetic stirring wsed. The temperature was kept constant (25± 0.2◦C) withcirculation water-bath thermostat. The solution was coously carried to a diode-array spectrophotometer Hewackard HP 8452A, furnished with a 1.0 cm flow cell,ack to the vessel with a peristaltic pump. The time ne

or the solution to reach the detector was about 10 s (dime). A Peltier control accessory HP 89090 to keep conhe temperature in the cell holder (25± 0.2◦C) was also use

scheme of the measuring device has been given else3].

R. Garcıa et al. / Analytica Chimica Acta 535 (2005) 287–295 289

2.3. Computers, software and data processing

The absorbance versus time data from the spectropho-tometer was treated with the UNSCRAMBLER version 7.5software package (Camo A/S, Trondheim, 1999), which al-lowed the application of principal component analysis (PCA),principal component regression (PCR) and PLSR calibration.Unless otherwise stated all the data were mean-centred be-fore the chemometric treatment[14]. The number of latentvariables, LV, to be used with PLSR was chosen to minimizethe error of prediction calculated by means of the statisticrelative error (RE):

RE = 100

√√√√∑m

i=1(Ci − Ci)2

∑mi=1C

2i

(1)

whereCi andCi are the estimated and added analyte concen-trations, respectively, for the samplei. RE can be applied toboth the calibration (REcal) and the validation (REval) sets.These sets were defined before any data processing and re-mained unchanged along the work. The calibration modelwas constructed by applying the cross-validation procedure(leave-one-out method); then the model was applied to theprediction set and REval was calculated for different numberof LVs. The number of LVs of the model must be carefullyc tedb aret hel td -i isp calp ienceat read.

f boutw goodt errori istic(

R

wo .

2

oa and5 ed.T backt set to

0 between 250 and 500 nm. The dichromate solution wasthen added (this point was taken as zero time) at a rate of0.08 ml min−1. Unless otherwise stated, the reaction was fol-lowed between 250 and 500 nm at 6 nm intervals, and onespectrum was acquired every 6 s for 500 s (this means 3530data points for every run). After 500 s the volume in the vesselhad increased in 0.67 ml approximately. Because the initialvolume was 52 ml, the final change of volume represents a1.3% increment. This made volume corrections unnecessary.

2.5. Procedures for commercial samples

Policolinosil (Laboratorios Medea, S.A., Barcelona,Spain) was taken into solution by shaking two pills with 25 mlof 1 M H2SO4 overnight. The solution was filtered troughfilter paper Albet 150 (Filabet, S.L., Barcelona, Spain) andtaken to 100 ml with some more 1 M H2SO4. Aliquots of 2 mlwere taken to the reaction vessel and treated as for syntheticsamples.

Aminoveinte(Laboratorios Madariaga, Madrid, Spain) isa cloudy liquid with some solid in suspension. A volume of15 ml was spun at 4000 rpm for some 10 min. An aliquot of10 ml of the liquid, still cloudy, was dialyzed through a tubingmembrane MWCO 12–14.000 Da with 55 ml of 1 M H2SO4during 3 h. An aliquot of 50 ml of the dialyzed solution wasta as fol-l e.T di andm

nepH bet1 so-l for1 tot es

m thec inoa

3

3k

ht -t cessd e theer in

hosen; if a number too low is taken, errors will be originay non-modelled systematic effects, but if too many LVs

aken, errors will be due to over-fitting (noise modelling). Towest number of LVs for which the value of REval does noiffer significantly from the minimum value of REval, accord

ng to anF-test with a probabilityP= 0.25, was chosen. Throbability level is not very common in the daily analytiractice, but it was proposed based on previous expers a compromise between under- and over-fitting[15]. The

est gives reasonable results and its use is very widespModels were evaluated using the REval value, that is in

act a relative residuals mean. It gives not only an idea ahich model predicts better results, but also about how

he predicted results are. To obtain an idea of the relativen the resolution of a mixture as a whole, a similar statthe relative error for a mixture, REm) can be used:

Em = 100

√√√√∑m

i=1∑p

j=1(Ci − Ci)2

∑mi=1

∑p

j=1C2i

(2)

herep is the number of analytes in the sample. REm hasnly been applied here to the prediction (validation) set

.4. Procedure for synthetic samples

A total volume ofxml (maximum 2 ml) of the amincid solutions was placed in a 100 ml reaction vessel2− xml of the 1 M sulphuric acid solution were then addhe solution was pumped to the spectrophotometer and

o the vessel for about 3 min and the absorbance was

aken to the reaction vessel and 2 ml of 1 M H2SO4 weredded. The same procedure as for synthetic samples w

owed to find the concentration ofmetout of the membranhe concentration ofmet in the original sample was foun

n the way explained under “Determination of cysteineethionine in samples” (see ahead).Pilfood (Laboratorios Serra Pamies, Reus, Spain). O

ill was shaken overnight with some millilitres of 1 mol l−1

2SO4. The solution was filtered through filter paper Al50 and taken to 100 ml with some more 1 M sulphuric

ution. The solution, still cloudy, was spun at 4000 rpm0 min. An aliquot of 7 ml of the clear solution was taken

he reaction vessel and 45 ml of 1 M H2SO4 were added. Thame procedure as for synthetic samples was followed.

In any case the concentration of amino acid (cysand/oret) in the acidic solution of samples was calculated from

orresponding calibration model prepared from pure amcid solutions.

. Results and discussion

.1. Oxidation of amino acids: stoichiometry andinetics

The oxidation reactions ofcys,metandhcydepend on bothe oxidant and the reaction conditions[10]. The stoichiomery of the reactions considered was studied in batch in exichromate. Reaction mixtures were allowed 500 s beforxcess dichromate was determined at 350 nm (Fig. 1). Theesults obtained are inTable 1. In the time scale shown


Fig. 1. Reaction profiles for the reaction between 1.096× 10−3 mol l−1

Cr2O72− and 1, 1.01× 10−3 mol l−1 cys; 2, 1.00× 10−3mol l−1 met; 3,

1.04× 10−3 mol l−1 hcy. 4, no reductant present (blank). Sulphuric acid,1 mol l−1; temperature, 25◦C; ionic strength, 1; wavelength, 350 nm. Batchconditions, hand mixing. The break of the time axis shows the second slowreaction (see text).

Fig. 1, and up to 500 s, reactions go apparently to comple-tion, but the slope of traces 1–3 at longer times, althoughslight, should be considered a real effect to which the scaleof the graph (up to 500 s) cannot do justice. In fact, when re-action mixtures are incubated for longer periods of time (forinstance 24 h,Fig. 1), different stoichiometric relations arefound showing that, in the three cases, a very slow secondreaction sets in. That is, the values inTable 1should be con-sidered as apparent “short term” stoichiometries. The errorin stoichiometry ofhcy is significantly larger than the othertwo amino acids. This is probably related to the fact that thesecond reaction is more significant in the case ofhcy(Fig. 1).Oxidation products were not identified.

The study of the reaction kinetics in all the three cases,through integrated forms of the rate law[16], is strongly hin-dered because of the second slow reaction that sets in. Inthese cases, the use of initial rates would be an acceptablealternative, but during the time of mixing (about 3s) a sig-nificant percent of reaction is lost (Fig. 1) and initial ratescannot be measured. However, using the first stages of re-action experimentally measured, for different initial aminoacid concentrations (in excess amino acid), an apparent sec-

Table 1Stoichiometry (in excess dichromate) and estimated values of the second or-der rate constant (in excess amino acid) for the reactions between dichromatea

S-

t

ond order rate constant of the rate law

Rate= −d[Cr2O72−]

dt= k[amino acid][Cr2O7

2−] (3)

can be obtained and used with comparison purposes exclu-sively. The results found are given inTable 1. In addition, ithas been noticed that the behaviour ofmetseems to be closeto Eq.(1), whilst the behaviour ofhcyseems to be rather farfrom it, the case ofcysbeing halfway between the others.This is probably the reason why the error estimate is smallerfor metand higher forhcy.

3.2. Reaction conditions

To oxidize amino acids several oxidants that show ab-sorption bands in the visible region were tried in the 1–10pH range, viz., Fe(CN)6

3−, Mo(CN)83−, W(CN)83−, Br2,Cr2O7

2−, MnO4− and Ce(IV). In general, the higher is the

acidity the faster is the reaction rate, but the contrary hap-pens with Fe(CN)63−. Bromine gives fast reaction rates.Mo(CN)83− and W(CN)83− give very slow reaction rates andonly in acidic medium. MnO4− gives useful reaction profilesin acidic medium, but it was discarded because it tends togenerate MnO2 deposits along the flow system. Cr2O7

2− andCe(IV) behave similarly; they both generate useful reagentp 4+ ift db n pri-m muchc ter inh er-c ctedb cleard d sul-p fectss and5 ratew andv nt

Ft ne,9t

nd cysteine, methionine and homocysteine

Amino acid �[amino acid]/�[Cr2O7

2−]anb Rate constant

(mol−1 l s−1)cnb

Cysteine 1.9 (0.2) 5 13d (2) 6Methionine 3.0 (0.2) 4 9e (1) 5Homocysteine 2.6(0.5) 5 140f (35) 3

tandard deviations are given in parenthesis. H2SO4, 1.0 M;T, 25◦C.a Initial concentration ratioR= [amino acid]0/[Cr2O7

2−]0 ranging beween 0.76 and 2.4.b Number of samples.c [Cr2O7

2−]0, 2× 10−4 mol l−1.d [cys]0 ranging between 2.0 and 10× 10−3 mol l−1.e [met]0 ranging between 0.5 and 4.0× 10−2 mol l−1.f [hcy]0 ranging between 0.8 and 2.5× 10−3 mol l−1.

rofiles in acidic medium (Ce precipitates basic saltshe acidity is not high enough), but Cr2O7

2− was preferreecause solutions are stable, the potassium salt is its owary standard, has a suitable equivalent weight and is

heaper than Ce(IV) salts. Because the reaction is fasigh acidic solutions, hydrochloric, sulphuric, nitric and phloric acids were tried as reaction medium. HCl was rejeecause reactions are much slower in that medium. Noifferences were found among the other three acids anhuric acid was chosen. The concentration of acid afignificantly the reaction rate and acidities between 0.1.0 M were tried. For the three amino acids the reactionas very slow when the acid concentration was 0.1 Mery rapid when it was 5.0 M.Fig. 2 shows some reage

ig. 2. Effect of acidity on the reagent profile for the dichromate-cysreac-ion. Sulphuric acid/mol l−1: 1, 0.1; 2, 1.0; 3, 2.0; 4, 3.0; 5, 5.0. Cystei.09× 10−4 mol l−1; dichromate (0.1 mol l−1) flow rate, 0.08 ml min−1;

emperature, 25◦C; ionic strength, 1; wavelength, 350 nm.


profiles for the oxidation ofcysat several acidities. Similarbehaviour is obtained formetandhcy. A value between 1.0and 2.0 M was considered optimum, so 1.0 M sulphuric acidwas finally chosen. Ionic strength (1 approximately, owingmainly to sulphuric acid) and temperature (25◦C) were fixedwithout optimization.

3.3. Individual determinations, binary and ternarymixtures

Taking into account the rate constant values inTable 1,some restrictions can be foreseen in the kinetic determina-tion of cys, met and hcy using conventional batch mixingprocedures. For instance, the rate constant forhcy is ratherhigh, and over 50% reaction is missed during the time of man-ual mixing. This means that initial rates cannot be measured.The values of the rate constants forcysandmet (kcys andkmet) are so close that mixtures of these amino acids cannotbe resolved by the usual kinetic methods of determination[17]. On the other hand, the reaction products do not absorbin the near UV region, so the CAR methodology with reagentmonitoring is the most obvious choice to follow the reactionkinetics.Fig. 3 shows some typical reagent profiles for thereaction between dichromate and different concentrations ofmet. Similar profiles are found forcysandhcy, but differencesda usedw bra-t SR,r eticc LSRm ghern n bea in thec na inedb hro-m ouldi in-

F d1 1.Fs h,3

clude spectral interferences. Because spectral discriminationis not possible above 250 nm, the use of several wavelengthsdoes not provide extra discriminating power but some kindof error compensation. So the use of the 250–500 nm inter-val, in this case, can be useful to evaluate the discriminatingpower of reagent profiles based exclusively on kinetics andstoichiometry. PCR was also tried as calibration algorithm.In line with some other precedents[19], results did not dif-fer significantly from those obtained with PLSR in the caseof individual determinations and binary mixtures. However,for ternary mixtures mean relative errors ranged between 10and 20% when PCR was used. So PLSR was maintained forcalibration.

The possibilities provided by kinetics and stoichiometryfor the resolution of binary mixtures can be suspected fromFig. 4. During the first part of reaction, profiles depend mainlyon kinetics (the kinetic region), and high rate constant valuesgenerate profiles close to thex-axis in this region. During thefinal part of reaction (the stoichiometric region), the profile is

Fig. 4. Reagent profiles for binary mixtures ofcys, met and hcy. Pro-file 1, blank in all figures (no analyte present). Concentrations arein mol l−1. (a), (cys+met) mixtures: 2, 2.00× 10−4 cys+ 9.72× 10−4

met; 3, 10.0× 10−4 cys+ 1.96× 10−4 met. (b) (met+hcy) mixtures:2, 0.93× 10−4 hcy+ 9.82× 10−4 met; 3, 9.59× 10−4 hcy+ 0.98× 10−4

met. (c), (cys+hcy) mixtures: 2, 0.96× 10−4 hcy+ 9.62× 10−4 cys; 3,9.64× 10−4 hcy+ 0.96× 10−4 cys. Other conditions as inFig. 3.

ue to different rate constants and stoichiometries (Table 1)re found. The whole reagent profile obtained can beith determination purposes if a proper method of cali

ion is used. Multivariate calibration methods, such as PLelate the whole profile (whatever it is a spectrum, a kinurve, etc.) to the concentration of analyte. Moreover, Pay deal with non-linear chemical systems by using a hiumber of latent variables (LV). PLSR calibration can eveble to model interferences, whenever they are includedalibration set of samples[18]. In this work PLSR has beepplied to the spectrophotometric reagent profiles obtaetween 250 and 500 nm, where only the reagent (dicate) absorbs. The use of wavelengths under 250 nm w

nclude some spectral discrimination, but it would also

ig. 3. Typical reagent profiles for the reaction between dichromate anmet., nometpresent (blank). Methionine/10−4 mol l−1: 2, 2.91; 3, 14.7; 4, 29.low rate of 0.1 mol l−1 dichromate, 0.08 ml min−1; initial volume, 52 ml;ulphuric acid, 1 mol l−1; temperature, 25◦C; ionic strength, 1; wavelengt50 nm.


Table 2Concentration ranges and relative errors found in the determination ofcys, met, hcyand their binary and ternary mixtures

Sample LV No. of samples Concentration range (×104 mol l−1) RE (%) REm (%)

cys met hcy cys hcy met

cys 2 5a 0.98–11.7 1.73b 2.92–8.78 2.5

met 2 4a 2.91–19.4 0.23b 4.85–14.6 4.4

hcy 3 5a 1.92–19.2 2.64b 2.89–16.4 3.2

cys–met 4–3 15a 0.97–10.0 1.93–19.4 7.7 7.812b 1.00–10.0 1.96–19.4 10.2 5.7 7.1

cys–hcy 4–5 15a 0.96–9.63 0.96–9.62 2.8 3.912b 0.96–9.61 0.96–9.62 4.1 8.8 6.5

met–hcy 4–4 16a 0.97–9.77 0.97–9.64 6.6 9.012b 0.97–9.77 0.97–9.74 5.9 8.6 7.4

cys–met–hcy 7–8–7 57a 0.97–9.76 1.92–19.4 0.96–9.71 13 9.1 6.316b 0.97–9.69 1.94–19.3 0.96–9.68 18 13 8.8 11

Individual determinations: wavelength variables, 350 nm; time variables, 3–400 s every 6 s. Binary mixtures: wavelength variables, 250–500 nm every 6 nm;time variables, 3–500 s every 6 s. Ternary mixtures: wavelength variables, 250–500 nm every 6 nm; time variables,cysandmet, 250–500 s every 6 s;hcy, 3–250 severy 6 s.

a Samples of the calibration set.b Samples of the validation set.

dictated not only by kinetics but also by stoichiometry. Bet-ter possibilities can be expected for thehcy–cys(Fig. 4b) andhcy–met(Fig. 4c) mixtures than for thecys–metmixture. InTable 2the results found for individual determinations andbinary and ternary mixtures ofcys, met and hcy are sum-marized. The errors increase from individual to binary andternary mixtures, as it could be expected. The REm valuesare similar for the three binary mixtures. Nevertheless, theway in which the REm value is calculated does not allow tosee that, as a whole,cysis not properly resolved in its mix-ture withmetand a mean error around 10% is obtained (thehigh value of the mean error comes mainly from the lowerconcentrations ofcys). This agrees with the fact thatkcysandkmet are quite similar. So, in general, some care should betaken with the interpretation of the statistics REm when it isused.

The number of latent variables (LV) gets higher as thecomplexity of the sample increases (Table 2). It goes fromtwo for the individual determination ofcysandmettill eightfor metin the ternary mixture. This can be considered accord-ing to forecasts because some LV will always be necessaryto model the kinetic behaviour of the system, as far as it isinfluenced by the way in which the reagent is added. In fact,the reagent is in deficit all along the reaction and this makesthe analytes to be in competence for it. This kind of antag-o t willn

itlys cipalc eb tht ce

of non-linearities, the score matrix should reproduce, withsome rotation, the concentration matrix[20], but this is notthe case and the score matrices are completely deformed.Moreover, there are significant differences betweenFig. 5bandFig. 5e on one side, andFig. 5h on the other. The ex-plained variance by the second principal component, PC2,in Fig. 5b (3.8%) andFig. 5e (3.0%) is clearly higher thanthat explained inFig. 5h (1.3%); or in other words, the in-formation contained in PC2 is higher in the case ofFig. 5band e (hcypresent) than in the case ofFig. 5h (hcyabsent).When the loading values of the variables for PC2 are exam-ined (Fig. 5c, f and i), it can be deduced that the informationcontained in PC2 can be separated into two parts: beforeand after variable 2000 approximately (300 s). Whenhcy ispresent the information contained in PC2 comes mainly fromvariables before 300 s, whereas ifhcy is absent the variationin PC2 comes mainly from variables after 300 s. This reflectsthe fact thathcyis the analyte that mainly gives reaction withCr(VI) before 250–300 s, owing to the higher rate constant.After that time the loading values of PC2 are similar for thethree mixtures. All this has consequences in the ternary mix-ture as it is explained next. When some attention is paid totime variables (Table 2) it can be seen thathcy (the fast an-alyte) needs the early time variables (under 250 s), when themost of its reaction is taking place. Consequently,cysandm 0 so n.

ohts net-w ve-

nism generates an inherent non-linear behaviour thaeed some modelling through extra latent variables.

The non-linearity of the chemical system can be explichown when a variable reduction process, such as prinomponent analysis (PCA), is done.Fig. 5 shows the threinary concentration matrices (Fig. 5a, d and g) together wi

he two-first-score matrices (Fig. 5b, e and h). In the absen

et are modelled with the late time variables (from 25n), whenhcyoxidation has practically gone to completio

Mean errors forcysandhcy, in ternary mixtures are toigh to be acceptable most of the times (Table 2), so the

ernary mixture is not satisfactorily resolved, and onlymethows mean errors under 10%. When artificial neuralorks (ANN) were used as calibration algorithm no impro


Fig. 5. Binary mixtures. First column: concentration matrix (underlined numbers correspond to the validation sets). Second column: the two first scores matrix(PC2 vs. PC1). Third column: loading values of PC2. First row:cys–hcymixture. Second row:met–hcymixture. Third row:cys–metmixture.

ment was obtained. Some improvement could be tried byintroducing spectral discrimination through the use of wave-lengths under 250 nm, but the risk of signal interferencesshould not be ignored.

3.4. Accuracy, precision, and effect of foreign aminoacids

When multivariate methods are used for multicomponentdeterminations, the calibration models must be robust enough

to be valid for a long period of time, otherwise they would beof no practical use. Because of it, several months after cali-bration, accuracy and precision[21] were empirically testedagain for individual amino acids and for thecys–metmix-ture. Results are inTable 3. Measurements for every samplewere taken in, at least, three sessions along 4 or more days.The precision values are similar to those shown inTable 2.However, a systematic error formet, in the lowest concen-tration level, can be found forP= 0.05 (2.92 and 3.14 differsignificantly for that probability level).

Table 3Accuracy and precision in the determination ofcys, metandhcy

Sample Amino acid n Taken Found Concentration (×104 mol l−1)

Error (%) R.S.D. (%)

cys cys 10 6.78 7.02 3.5 3.3met met 7 2.92 3.14 7.5 5.7

met 8 9.84 9.98 1.4 2.9hcy hcy 8 9.80 9.58 2.2 5.3cys–met cys 9 9.17 9.28 1.2 3.4

met 9 18.2 18.6 2.2 5.1


Some selectivity can be expected in the determina-tion of cys, met and hcy by the use of dichromate asreagent because very few amino acids, apart from thosehaving a sulphur centre, give reaction with dichromatein acidic medium. A species was considered to interferewhen the analyte concentration found differed from the ex-pected one more than twice the standard deviation at thatlevel of concentration. When analytes were at a concentra-tion of 10−3 M, tyrosine, glutamine, hystidine, lysine andglycine did not show any apparent reaction with dichro-mate even at concentration levels of 10−2 M. Only cys-tine and tryptophan interfere at such a high concentrationlevel, but they do not show interference at a concentration of10−3 M.

3.5. Determination of cysteine and methionine inpharmaceuticals

The resolution of thecys–metmixture is more difficultthan the resolution of binary mixtures withhcypresent, mostprobably because the rate constant values forcysandmetare quite similar (Table 1). Commercial samples withhcyare not very common; so, the application of the proposedmethodology to the resolution of thecys–met mixture ina commercial sample was considered an interesting chal-lc aceu-t , butt -f sultsa nthsa atesw 4 orm ft wave-lw cen-t hed f them romtai darda ownm cen-t utionb -b alytec trap-o theu

andt eat-m by them

Table 4Determination ofcysandmetin some pharmaceuticals

Sample Amino acid Content (mg) R.S.D. (%)

Reported Found

Policolinosila cys 12.5 13.1b,c 3.8Aminoveinted met 66.6 65.1e,f 5.8g

Pilfoodh cys 80 87f,i 1.8met 200 205f,i 4.8

a Reported content per pill (in Spanish in the original):acidos ri-bonucleicos, 10 mg; peptidos hepaticos, 10 mg; orotato de lisina, 25 mg;glutamato de arginina, 25 mg;acido tioctico, 2.5 mg; vitamina B15, 5 mg;orotato de colina, 50 mg; fosfolıpidos puros e colina, 25 mg; cisteına clh,12.5 mg; mesoinositol, 25 mg; vitamina B1 (NO3), 5 mg; vitamina B2 clh,2.5 mg; vitamina B12, 20 mcg; vitamina P.P., 10 mg; pantotenato de calcio,2.5 mg;acido folico, 0.05 mg; sacarosa, 132 mg; otros excipientes.

b Ten replicates.c PLSR model defined with three LV. Wavelength variables: 270, 300, 350

and 380 nm. Time variables, 1–400 s every 2 s.d Reported content per 100 ml (in Spanish in the original): cianocobal-

amina (vit B12), 0.2 mg; colecalciferol (vit D3), 33,333 UI; piridoxina clh(vit B6), 1.7 mg; tiamina clh (vit B1), 4.2 mg; riboflavina (vit B2), 1.7 mg;mesoinositol, 8.3 mg;acido folico, 4.2 mg; nicotinamida, 8.3 mg; pantote-nato de calcio, 5.0 mg; biotina, 0.17 mg;acidop-aminobenzoico, 8.3 mg;lisina, 16.7 mg; metionina, 66.6 mg; glicina, 5.0 mg; histidina, 4.2 mg;acidoglutamico, 4.2 mg; CaHPO4, 365.0 mg; benzoato sodico, sorbato potasico yotros excipientes, hasta 100 ml.

e Regression line of the standard addition method (see text) made witheight points.

f The PLSR model inTable 2was used.g Calculated from the regression line[22].h Reported content per pill (in Spanish in the original):dl-metionina,

200 mg;d(+)-Cisteına HCl, 80 mg;l-Cistina, 25 mg; Extracto seco de mijo,20 mg; Pantotenato calico, 2.5 mg; Riboflavina (sodio fosfato) (VitaminaB2), 0.5 mg; Piridoxina (clorhidrato) (Vitamina B6), 0.7 mg; Biotina (Vi-tamina H), 0.05 mg; Alfa-Tocoferol Acetato (Vitamina E), 3 mg; Estearatomagnesico c.s. y Sılice coloidal anhidra c.s.

i Four replicates.

4. Overall evaluation and conclusions

The unconventional way in which reagent profiles are ob-tained has allowed to resolve properly binary mixtures whoseapparent rate constants ratio is lower than 2. This is not possi-ble when classical kinetic methods are used. Ternary mixturesare more difficult to resolve and higher errors are obtained,though determinations can probably be useful most of thetimes.

However, a question stays: what is the practical interest ofthis application? It has been written elsewhere[23]: “The useof uncatalyzed reactions for determination of single speciesis to be avoided if an adequate non-kinetic method (equilib-rium or static) is available, since little is gained in sensitivityor accuracy. . .”. Nevertheless, this does not apply to multi-component determinations. The methodology here exposedtries to make the most of the discriminating ability of reac-tion kinetics for mixtures of 2–3 components. In these cases,when applicable, methods using reaction profiles can be analternative to methods that make use of previous separationssuch as chromatography or electrophoresis, because no pre-vious separation is needed and the instrumentation and the

enge. The individual determination ofcysandmet in twoommercial products was also accomplished. Pharmical products cannot be considered complex matriceshose used in this paper are not simple (Table 4) and can ofer some validation for the proposed methodology. Rere in Table 4. Measurements were taken several mofter the PLSR calibration models were made. Replicere measured in at least two different sessions alongore days. In the case ofPolicolinosil, the complexity o

he sample made necessary the use of more than oneength to get good results. In the case ofAminoveintedialysisas strictly necessary to get a clear sample. The con

ration of met found after applying the PLSR model to tialyzed solution corresponds to the concentration out oembrane. Obviously, this concentration is different f

he original one because the analyte (met) is distributed innd out of the membrane. To find the concentration ofmet

n the original sample, a methodology similar to the standdition method was applied. That is, different and knetamounts (between 0 and 200% of the expected con

ration) were added to several aliquots of the spun solefore dialysis. Once themetconcentration out of the memrane was determined for each spiked aliquot, the anoncentration in the original sample was obtained by exlation of the found versus added concentration plot insual way.

Taking into account the composition of the matricesaking into account that very simple, if any, previous trent was used, good agreement to the values reportedanufacturer was obtained in any case.


chemometric approach used are simple. The practical detec-tion limits obtained in this work (around 10−4 M) are notlow, but this should not be considered of general applica-tion. In fact, the limit of detection will depend on both thechemical system and sensitivity and precision of the instru-mental technique used to follow the progress of reaction.If, for instance, spectrophotometry is used, a reagent withgood spectrometric features may be required to achieve anappreciable analytical sensitivity, but the use of PLSR makessensitivity to depend on the chemical system as a whole(reagent, products, stoichiometry, kinetics, etc.) and not onlyon the reagent, because the whole profile is used as analyticalsignal.

The proposed methodology can be considered a newapproach to multicomponent determinations using kineticmethods of determination, but more validation is obviouslyrequired.

Acknowledgements

The authors acknowledge financial support from MCyT,Spain (project BJU2000-0263-C02-02).

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