J. Phys. Chem. 1980, 84, 2567-2575
FHT = (fl - fJh1
(B.6)
(fl - f2) satisfies ecl 34, and, therefore, the combination
* N
fjprop= (fl - f J would fit as an "absorber" 'with linearly independent rates.
QLS
Glossary matrix of measured absorbanses averaged absorbance matrix; A, = (1/N) C;='=,Alk r principal component estimate of A weighted absorbance matrix eigenvector matrix of S , concentration matrix estimated concentration matrix concentration vector of absorber j dcl/dt M-analysis estimate of 8, using 81pro proposed concentration profile for aisorber j normalized concentration profile of absorber i in a two-absorber experiment limiting concentrationprofiies that define a solution band for 8,' in a two-absorber experiment static spectra matrix estimated static spectra matrix static spectrum vector of absorbgr j M-analysis estimate of fl, using flprop proposed static spectrum for absorber j normalized static spectrum of absorber i in a twoabsorber experiment limitins static spectra that define a solution band for f,' in a two-absorber experiment S-analysis estimate of fl, using fjprop vector relating fJto S-analysis eigenvectors in eq 34 least-squares estimate of g,! using f concentration matrix used in S analysis, defined by eq 2!3 weighting matrix for wavelength dependence of measurement error variance weighted ciecond moment matrix (Nlp)M,1'
2587
essential rank of M, number of consecutive spectra number of wavelength channels number of absorbers least-squares loss function for using tjprop to estimate uj weighted sample covariance matrix essential rank of S, weighting matrix for time dependence of measurement error variance rotation matrix that relates M-analysis eigenvectors to F least-squares estimate of uj, using rotation matrix that relates M-analysis eigenvectors to c least-squares estimate of vi, using 8jprop diagonal matrix used to define fij~sin eq 17 diagonal matrix used to define QjLS in eq 19 wavelength dependence of ab; in the error model expressed by eq 2 time dependence of qj2 in the error model expressed by eq 2 eigenvalue matrix of M, matrix of random measurement errors eigenvalue matrix of S , variance of the i j t h measurement error eigenvector matrix of Mw ith eigenvector of Mw eigenvector matrix of Mw' ith eigenvector of SY diagonal matrix defined by eq 6 unit vector
References and Notes (1) Air Products and Chemicals, Inc., Box 538, Allentown, PA 18105. (2) R. N. Cochran and F. H. Horne, Anal. Chem., 49, 846 (1977). (3) W. H. Lawton and E. A. Sylvestre, Technometrlcs, 13, 617 (1971). (4) I. M. Warner, E. R. Davidson, and G.D. Christian, Anal. Chem., 49, 2155 (1977). ( 5 ) R. N. Cochran, F. H. Horne, J. L. Dye, J. Ceraso, and C. H. Suelter, J. Phys. Chem., foilowina paper. (6)R. N. Cochran, Ph.D. Discehation, Michigan State University, East Lansing, MI, 1977.
Principal Component Analysis of Rapid Scanning Wavelength Stopped-Flow Kinetics Experiments on the Liver Alcohol Dehydrogenase Catalyzed Reduction of p-Nitroso-N,N-dimethylaniline by 1,4-Dihydronicotinamide Adenine Dinucleotide R. N. Cochran,' F. H. Horne,* J. L. Dye, J. Ceraso,* Department of Chemistty, Michigan State University, East Lansing, Mlchigan 48824
and C. H. Suelter Depaifment of Biochemistty, Michigan State University, East Lansing, Michigan 48824 (Received: June 15, 1979; In Final Form: May 12, 1980)
Principal component analysis (PCA) is used to identify the spectra and concentration-time profiles of the reactants and two of the intermediates in the liver alcohol dehydrogenase catalyzed reduction of p-nitroso-N,N-dimethylaniline by 1,4-dihydronicotinamide adenine dinucleotide. It is shown that at least two other absorbing intermediates are involved in the reaction, but their spectra and time behavior cannot be uniquely determined from the data at hand. This application of PCA to data obtained by scanning stopped-flow absorbance methods shows how such data can be used to obtain mechanism-independent information about transient species. Introduction In this paper we apply the method of principal component analysi&4 to a scanning stopped-flow study of the horse liver alcohol dehydrogenase (LADH) catalyzed reduction of the substrate analogue p-nitroso-N,N-di0022-3654/80/2084-2567$01 .OO/O
methylaniline (NDMA) by 1,4-dihydronicotinamide adenine dinucleotide (NADH). Previous studiess8 have shown that this reaction is spectrally complex. LADH is a dimeric enzyme with one active site per monomer subunit whose transient behavior during catalysis has been extensively 0 1980 American Chemical Society
2568
The Journal of Physical Chemistry, Vol. 84, No. 20, 1980
Cochran et al.
TABLE I: Initial Conditions for the Rapid Scanning Stopped-Flow Experiments and Essential Ranks Obtained by PCA [LADH1O,a expt 1 2 3
mixing order NADH + (LADH t NDMA) (NADH t NDMA) t LADH (NADH + NDMA) t LADH (NADH t NDMA) + LADH
4
PM
7.4 7.4 18.6 7.4
[NADH],, PM 15.0 15.0 15.0 6.0
[NDMAI,, PM 13.4 13.4 13.4 13.4
essential ranksb
m 5 5 5 6
s 4 4 4 5
a Active site concentration using two active sites per molecule and based upon total absorbance at 280 nm. Minimum number of linearly independent absorbers ( m )and minimum number which change independently with time (s).
studied with aromatic substrates."15 Dunn and Bernhard6 proposed the following reaction for the LADH-catalyzed reduction of NDMA by NADH:
A transient absorption at -330 nm was attributed to off-enzyme s p e c i e ~ .Later, ~ Dunn et ala8wrote the overall stoichiometry as
-
.u (CH3)zNON//
t 2NADH t H'
LADH
,' \ (->
(CHd2N
NH2 t zNAD+ t H20
(2)
The aromatic nitroso compound NDMA was used because of its intense chromophore at 440 nm (€440 = 3.54 X lo4 M-l cm-l). The LADH-catalyzed reduction of NDMA by NADH was considered analogous to the corresponding reduction of aldehydes5 because the nitroso group of NDMA is isoelectronic with the carbonyl group of aldehydes. We now report a study of the spectral and kinetic behavior of the substrates, products, and transient intermediates in the LADH-NDMA-NADH reaction system. The broad-banded absorbance spectra of substrates, enzyme, and products, as well as those of suspected intermediates: make this system spectrally complex: NDMA (A, = 440 nm), NADH (Amsxl = 260 nm, Am& = 340 nm), LADH (Amsx = 280 nm), NAD' (Amm = 260 nm), and final = 255 nm). Dunn and Bernhard5observed product(s) (A, that the decay of absorbance at 330 nm, which they attributed to the 340-nm absorbance band of NADH, was not correlated to the decay of absorbance at 440 nm, which they attributed to NDMA. Since the decay at 330 nm was much slower than at 440 nm, they hypothesized an absorbing intermediate at 330 nm. Schack and Dunn6 observed absorbance growth and decay at 555 nm, which they attributed to yet another intermediate, later postulated to involve a radical cation.8 Suelter et al.' observed in four replicate scanning stopped-flow experimentsthat the decay portions of the absorbance-time profiles at 330,350, and 360 nm had different first-order decay parameters. They suggested the presence of two intermediates absorbing in this region in addition to NADH. Suelter et al.' also observed the growth and decay of absorbance at 51G550 nm similar to that reported by Schack and Dunn6 and Dunn et al.8 These observations of spectral complexity and the occurrence of possible transient intermediates, and especially the previous lack of a systematic mechanism-independent means of sorting out these intermediates, prompted the development of statistically weighted principal component analysis (PCA).a4 In this paper we show how PCA can be used to sort out the various absorbing
species by applying it to a few selected experiments. A later paper will deal with the assignments of species and the kinetics of the reactions and will show that the overall system is too complex to be described by a single stoichiometry. Experimental Section The buffer system used for all solutions was 0.05 M Na2Pz07(Mallinckrodt Analytical Reagent) made with quartz-distilled H20 and titrated to pH 8.75 with 6 N HCl (Mallinckrodt Analytical Reagent). Horse liver alcohol dehydrogenase was purchased as a crystalline suspension from the Boehringer Mannheim Corp. The enzyme precipitate obtained after centrifugation was dissolved in 10 mL of pH 8.75 buffer and dialyzed against three 2000-mL portions of pH 8.75 buffer to remove the ethanol and other low molecular weight impurities. The dialyzed 10-mL LADH solution was diluted to 30 mL with pH 8.75 buffer to make the LADH stock solution, which was stored at 0 "C until used in the kinetics measurements. The specific activity of the LADH stock solution in the reduction of NDMA by NADH was determined to be 10 f 2 mol of NDMA/s per mole of catalytic sites of LADH at pH 8.75 and 24 "C. This specific activity is substantially lower than that obtained by Dunn and Bernhard5 under the same conditions as well as by Suelter et al.7and in later experiments in this lab.16 While this may have an effect on the interpretation of the results, it does not affect the main objective of the present paper which is to demonstrate the application of principal component analysis to a spectrally complex system. This view is strengthened by the observation of essentially the same results in later experiments. The coenzyme 1,4-dihydronicotinamide adenine dinucleotide was obtained from P. L. Biochemicals as Chromatopure Coenzyme-1 (DPNH). NDMA was purchased from Aldrich Chemical Co. as Aldrich-Analyzed N,N-dimethyl-p-nitrosoaniline. NADH and NDMA were used without further purification! The concentrations of the LADH, NDMA, and NADH stock solutions were calculated from absorbancesmeasured on a Cary Model 17 spectrophotometer, using e280 = 3.53 X lo4 M-l cm-l for LADH,17 €340 = 6.22 X lo3 M-l cm-l for NADH,18and cU0 = 3.54 X lo4M-' cm-l for NDMA.5 The initial concentrations of these species in the kinetics experiments were computed from dilutions of stock solutions. The kinetic measurements were performed on a modified rapid scanning stopped-flow absorbance spectrometerlg originally described by Papadakis et a1.20 This instrument was modified to minimize volumes of reactants. The interface of the spectrometer to a PDP8I computer is described by Coolen et a1." Table I summarizes the four sets of initial conditions used for the rapid scanning kinetics experiments described in this paper. For simplicity, we refer to each set of initial conditions as an "experiment". Replicate runs were performed for each set of initial conditions, and the results were reproducible to within the random noise among
Enzyme Application of Principal Component Analysis
The Journal of Physical Chemistry, Vol. 84, No. 20, 1980 2589 &33
TABLE 11: Correspondence between Channel Number ( m )and Wavelength m h/nm m h/nm 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
274.6 27 5.2 275.9 276.8 277.9 279.2 280.0 282.3 284.1 286.1 288.3 290.8 293.4 296.3 299.4 302.8 306.4 310.3 314.4 318.9 323.7 328.8 334.3 340.2
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
346.5 353.2 360.3 367.9 376.7 384.6 393.8 403.4 413.6 424.3 435.5 447.2 459.4 47 2.0 484.9 498.0 511.3 524.6 537.6 550.4 562.6 574.0 584.4
replicate experiments. Experiment, 2 repeats the initial concentrations of experiment 1, but with NADH and NDMA premixed in one pushing syringe instead of LADH and NDMA. This was done to determine whether LADH and NDMA react without NADH in a way that measurably alters the course of the reaction after NADH is added. Experiments 3 and 4 have NADH and NDMA premixed in one syringe. Individual static (i.e., time-independent) spectra of LADH (7,4pM), NADH (18.6 pM), and NDMA (5.36 pM) were measured in the stopped-flow spectrometer with the same instirumental settings as for the kinetics experiments and used as spectral shape functions for suspected absorbem in the PCA of experiments 1-4. All experiments listed in Table I were performed with scans covering the vvavelength range 275-584 nm with 47 wavelength channels per scan and 37.5 scans per second. The correspondence between channel numbers and wavelength is given in Table 11. Ten groups of spectra were collected with six spectra per group and a grouping factor of 2.20v21Each experiment was completed at 23-24 "C, the ambient temperature of the laboratory. Details of absorbance, time, and wavelength calibrations for these experiments are given elsewhere.22
Results Each scanning kinetics experiment gives a three-dimensional surface of absorbance vs. wavelength and time. Figure 1shows the absolute absorbance-wavelength-time surface A for experiment 1. Note that the 61 consecutive spectra in Figure 1 ,are equally spaced and that the scale for the time axis is geometric in time. This is because the data collection software averages a number of measured scans and stores the average as a single consecutive spectrum. The number of measured scans averaged into each stored spectrum is increased with time during the reaction (see ref 21 for details). The last spectrum in each experiment was taken after the absorbance monitored on a storage oscillosco~pewas observed to be constant. In 'Figure 1the elapsed time between the next-to-last spectrum and the last spectrum was 300 s. Figure 1 is dominated by large constant absorbances that obscure the progress of the reaction. The dynamics of the change of absorbance with time and wavelength are better illustrated for experiment 1 by the difference surface ( A
WAVELENGTH (nm)
Figure 1. Measured absolute absorbance surface for experiment 1. The solvent background has been subtracted.
Figure 2. Measured experimental difference surface for experiment 1. The difference (A - A ) reflects changes in absorbance with time at each channel.
- A), shown in Figure 2. The data shown in Figure 1 are replotted in Figure 2 after subtracting the average of all 61 consecutive spectra from each spectrum. This difference surface, ( A - A ) , would be a horizontal plane if absorbance did not change with time during an experiment. Assignment o f Weights. A cursory examination of Figure 2 shows more random noise at short wavelengths and early times than at long wavelengths and late times. Cochran and Horne3 proposed a weighting scheme that accounts for the imbalance of signal/noise with wavelength and time in principal component analysis. The scheme assumes an error model in which u ~ .the ~ ,variance of the i, jth measurement error, is given 6y 0;; = xizj where x i and zj describe the variation of the root mean square (rms) noise with wavelength and time, respectively. Application
The Journal of Physical Chemistry, Vol. 84, No. 20, 1980
2570
0.02
Cochran et al.
assigned by the equation L, = u1/2x;1/2 with the arbitrary constant a set to unitye3 The rms noise decreases with time as the number of scans averaged into each stored spectrum increases. Since the number of scans averaged into the jth spectrum is g(ni-l) where nJis the group number and g is the grouping factor,2l the time dependence of the noise is expected to be given by eq 4. However, eq 4 assumes no digital error and no
0.01 Z]
= g(l-n,)
(4)
contributions from noise components of substantially lower frequency than the scan repetition rate. Examination of the rms noise levels as a function of time showed that no reduction of zI occurred after spectral averaging of eight measured scans per stored spectrum. Therefore, eq 4 was used only for the first four groups of spectra, after which z . was assumed to be constant. The time weights, TI,were then assigned by eq 5, with the arbitrary constant b set to unitye3
ul
+ .c 3
a,
u 0.011 C
e z
n
a 2
TJ = b1/2ZJ-1/2
v
X-
0.00~
O.OO( IO 20 30 40 WAVELENGTH CHANNEL
I
50
Flgure 3. Standard deviation of random errors (x,”*) vs. wavelength channel number at various absorbance levels obtained by insertion of neutral density filters to give nominal absorbances of (A) 1.2, (6) 0.7, and (C) 0.0.
of the weighting scheme requires an assessment of the experimental noise with respect to both time and wavelength. The variation of experimental noise with wavelength was estimated from a separate series of experiments, as previously ~uggested,~ in which 63 consecutive scans were collected with buffer in both of the sample paths to give a nominal nonzero absorbance. The wavelength dependence of the noise, x i , was estimated from scatter about the mean absorbance for each wavelength channel by means of eq 3. Figure 3 shows x t / 2 vs. wavelength channel 63 Xi
= (1/62)
2 (Aik - Ai)’
k=l
(3)
i at three absorbance levels covering the range of absorbances used in these experiments. Note that x L 1 l 2varies with absorbance as well as with wavelength channel i. The rising noise in the UV region reflects the lower light intensity at short wavelengths, while the peaks near channels 30 and 40 result from fluctuations caused by xenon lamp “spikes” in these regions. Although the weighting scheme does not have enough degrees of freedom to fully account for the variation of noise with three independent variables (wavelength, time, and absorbance), the variation with absorbance was approximated by choosing for xL1l2in each kinetics experiment the value for the nominal absorbance level closest to the mean absorbance measured at channel i in the kinetics experiment. With this approximation, L,, the wavelength weight for the ith wavelength channel, was
(5)
Number of Absorbers. The first step in principal component analysis is to determine for each experiment the minimum total number of absorbers, m, and the minimum number of absorbers, s, whose concentrations change with time. The numbers m and s are defined as the minimum number of eigenvectors (the essential ranks) of the matrices M, and s,, respectively, that are required to reconstruct the experimental absorbance surface to within its random experimental error^.^ It is important to note that the term “absorber” may, in fact, refer to several species, if there is linear dependence of their concentration-time profiles (in M analysis), rates (in S analysis), or Nonabsorbing species, spectra shapes (in M or S anal~sis).~ of course, do not contribute to either analysis. Two criteria were used to determine how well the experimental surfaces were fit by reconstructed surfaces: (1) visual comparison of the reconstructed and experimental surfaces, and (2) examination of the weighted residual surface as previously de~cribed.~ For a fit to within random experimentalerrors, points in the weighted residual surface should fluctuate randomly about zero, and the value of the function [Q,/(N- r ) ( p- r ) ] ,the weighted residual sum of squares divided by the degrees of freedom, should be approximately unity. The weighted residual sum of squares Q, is given by3 eq 6. P N Qr
=
C C L,Tl[ail(r)- ALII2
1=1 ]=1
(6)
Principal component analysis involves a determination of the minimum number of absorbers in an experiment. For experiment 1 the number of eigenvectors of M, was increased from one by unit increments until the reconstructed difference surface matched the experimental surface to within its random errors. For one, two, three, and four eigenvectors, the reconstructed and experimental surfaces did not match, and the weighted residual surfaces were nonrandom. The values of [ Q , / ( N- r ) ( p - r ) ] were 657, 260,84, and 10.6 for, respectively, one, two, three, and four eigenvectors. A minimum of five eigenvectors was required to reconstruct the surface (Figure 4A) to within the random errors of the experimental surface. The weighted residual surface (Figure 4B)fluctuates randomly about zero, and [ Q , / ( N - r ) ( p - r ) ] = 2.2 for five eigenvectors. When more than five eigenvectors were used, [Q,/ ( N - r)(p- r ) ]continued to decrease (it is by definition zero when the number of eigenvectors used equals the number of wavelength channels), but the improvement in
The Journal of Physical Chemisfry, Vol. 84, No. 20, 1980 2571
Enzyme Application of Principal Component Analysis
x 0 0 0
0
ooo 0 0
0
" 5nml
I
x x x x x i 00000
O x, 47
WAVELENGTH CHANNEL
15a4nmi
(A) 6
W L
8 LT + 5.0
-
am
9
a
Q
3 8 z? 0.0
[I
0
c"I P
!i
ai
-100-
Flgure 4. (A) Reconstructedexperimental difference surface assuming five absorbers in experiment 1. This should be compared with the experimental difference surface given in Figure 2. (6) Weighted residual surface assumWlg five tabsorbers in experiment 1.
reconstructing the experimental surface involved fitting the random experimental errors themselves. Therefore, experiment 1has a iminimum of five linearly independent absorbers. The essential ranks, m and s, determined for experiments 1-4 are summarized in Table I. Experiments 1-3 gave five linearly independent absorbers, of which at least four changed concentration with time. Experiment 4 gave six linearly indepenldent absorbers, of which at least five changed concentration with time. Spectrum of Each Absorber. The measured static spectra of NDMA, ILADH, and NADH were fitted to the M- and S-analysis eigenvectors of experiments 1-4. A measured static spectrum that fits the M-analysis eigenvectors may be counted as belonging to one of the m linearly independent absorbers of that experiment. If a measured static spectrum fits both the M- and S-analysis eigenvectors, it may be counted as belonging to an absorber whose concentration changed with time and whose rate was linearly independent of the rates of the other absorbers. The M-analysis fit of NDMA to experiment 1is shown in Figure 5A. The spectrum of NDMA approximately fits
,
l215nrn)
WAVELENGTH CHANNEL
47
15a4nmi
:B) Figure 5. M-analysis fit of the shape of the measured NDMA static spectrum to (A) experiment 1 and (6) experiment 4: X = measured spectrum; 0 = calculated spectrum. The vertical scale is in arbitrary absorbance units; the horizontal scale is linear in channel number (see Table 11). Note that the misfit in experiment 1 caused by the simultaneous decay of NADH and NDMA occurs largely in the region of NADH absorbance as expected. Of course, the absence of a contribution from NADH in the static spectrum of NDMA results in systematic misfis at other wavelengths since the calculated spectrum is the best overall fit to the data.
the data except for a shoulder in the calculated spectrum centered at approximately 340 nm. (See Table I1 for the correspondence between wavelength and channel number.) Similar results were obtained for NDMA in experiments 2 and 3. These results suggest that the concentration profile of NDMA in experiments 1-3 is linearly dependent on the concentration profile of another species with an absorbance maximum at 340 nm. In experiment 4 NDMA fits the M-analysis eigenvectors without a shoulder at 340 nm in the calculated spectrum (Figure 5B). The measured static spectrum of LADH does not fit the M-analysis eigenvectors for any of the experiments. This suggests either that LADH undergoes an absorbance shift during the reaction or that the time dependence of the absorbance due to LADH is linearly dependent on the concentration profile of one or more of the other absorbers. NADH has two absorbance maxima, one at 260 nm from its adenine moiety and one at 340 nm from its nicotinamide moiety. Since only the long wavelength tail of the 260-nm band is accessible by the scanning spectrometer and since product and enzyme both absorb in this region, only the 340-nm absorbance was fitted to the M-analysis eigenvectors of experiments 1-4. Although the 340-nm band does not fit experiments 1-3, it does fit experiment 4. Thus, the 340-nm band of NADH may be counted as one of the six independent absorbers in experiment 4. Since NDMA and the 340-nm band of NADH fit both the M- and S-analysis eigenvectors of experiment 4, they have
2572
The Journal of Physical Chemistty, Vol. 84, No.
Cochran et ai.
20, 1980
TABLE 111: Essential Ranks Obtained from Wavelength Subspaces I-IV and Information Obtained by Two-Absorber Analysis of Experiment 1 subspace
wavelength range, nm
essential ranks m s
absorbers presenta
information obtained
I
275-299
1, 2
I1 I11
solution bands only; absorbers are linearly dependent
299-376 316-4 1 2
3, 4
IV
412-584
4, 5
+ IT1 I + I11 + IV
static spectra and concentration profiles static spectrum and concentration profile of absorber 5
215-299and316-462 376-584 215-299and316-584 275-584
3-5 1-5 1-5
I
I11 t IV I
+ I1 + I11 + IV
complete static spectra of absorbers 3-5
a Absorbers 1 and 2 have linearly dependent concentrations and could not be resolved; absorber 3 is an intermediate with a peak at 403 nm and a shoulder near 320 nm; absorber 4 results from NDMA and NADH whose concentrations are linearly dependent; absorber 5 is an intermediate with peaks at 230 and 540 nm.
linearly independent rates in this experiment. Since the absorbance of NADH shifts from 340 to 325 nm when it is bound to LADH,5 it might seem appropriate to use the static spectrum of this complex as one of the absorbers. This was tried in earlier experiments, but the fit was poor, indicating that the NADH-bound chromophore is not an independent absorber. As noted later, however, one of the independent absorbers has a peak at 320 nm, and another has a pronounced shoulder in this region. Therefore, it is possible that NADH bound to the enzyme has an absorbance which is coupled to one or more of the other species present. These results strongly indicate that the 340-nm band of NADH contributes to experiments 1-3 as an absorber whose concentration is linearly dependent on the concentration of NDMA but as an independent absorber in experiment 4. This interpretation is consistent with the following observations: (A) NADH (340 nm) fits experiment 4, but not experiments 1-3. (B) Experiment 4 has six linearly independent absorbers, whereas experiments 1-3 have only five. (C) In experiments 1-3, the concentration profile of NDMA appears to be linearly dependent on the concentration of an absorber near 340 nm, whereas, in experiment 4, NDMA fits as a linearly dependent absorber. For observation (C) we note that in experiments 1-3 the ratio of initial concentrations [NDMA],/ [NADHIo is close to unity (0.89), whereas in experiment 4 the ratio [NDMA],/[NADH], is 2.3. This suggests that the fast initial disappearance of both NDMA and NADH occurs in a 1:l stoichiometric ratio which would couple the two spectra in experiments 1-3 but not in experiment 4. Subspace Analysis and Concentration Profiles. Measured static spectra did not provide enough information to resolve the spectra of the independent absorbers or their concentration-time profiles in experiments 1-4. Therefore, experiment 1 was further analyzed for wavelength subspaces which contain fewer than five absorbers. Table I11 summarizes the essential ranks m and s determined for four subspaces I-IV. The results lead to the following conclusions: (1)The two absorbers in subspace I (275-299 nm) have linearly dependent rates ( m = 2, s = 1). (2) Subspaces I11 (376-472 nm) and IV (472-584 nm) have absorbers in common, but the two absorbers in subspace I do not absorb in I11 or IV. (3) Subspaces I, 111, and IV are two-absorber subspaces that, together, contain all five linearly independent absorbers. By separately resolving subspaces I, 111, and IV, using the two-absorber simplifications of the preceding paper,4 N
we could obtain the static spectra and concentration profiles of three of the five linearly independent absorbers for the whole experiment. We illustrate this by applying the two-absorber simplification to subspace 111. Just as the determination of the minimum number of absorbers in an experiment does not require prior information about the spectra of the species present or about the reaction mechanism, the fact that neither absorbance nor concentration can be negative provides mechanismindependent upper and lower bounds to the individual spectra and concentration profiles in a two-absorber regionB4If the two absorbers have well-separated spectral features and distinct temporal behavior, the limits will be close together, while strongly overlapping spectra and/or nearly linearly dependent time behavior will lead to less well-defined spectra and concentration profiles. Figure 6 shows the solution bands (regions between upper and lower bounds) for the normalized static spectra and concentration profiles of the two absorbers in subspace 111. For example, Figure 6A shows the solution bands for the normalized static spectrum of absorber 3. The spectrum of this absorber (an intermediate) must fall on or between fiL'and fiH',symbolized by L and H, respectively." Note that L and H cross, and thus L is not always less than H. The sjmple requirement that absorbances and concentrations cannot be negative permits us to conclude that the absorbance maximum of absorber 3 is between 385 and 403 nm while that of absorber 4 lies between 424 and 459 nm. In fact, for this region we can use spectra to further identify the species involved as described below. The measured static spectrum of NDMA fit the Manalysis eigenvectors as the second absorber in subspace I11 (Figure 7A). (Note that this subspace does not include the region of NADH absorption.) In a two-absorber subspace, when the static spectrum of one absorber is known, the concentration-time profile of the other absorber can be computed dire~tly.~ Figure 7B shows the concentration profile of absorber 3 (one of the intermediates) computed from the static spectrum of NDMA. Missing in this analysis is the absorption spectrum of absorber 3 and the concentration-time profile of NDMA. However, solution bands for the concentration profiles in subspace I11 show that the concentration of absorber 4 (NDMA) does not change significantly during the last 16 consecutive spectra, whereas the concentration of absorber 3 changes during this time. Moreover, an S analysis of the last 16 spectra in subspace I11 gives an essential rank of one, which supports the observation that only one absorber
Enzyme Application of Principal Component Analysis B 8
B
a
W
B
H
m
a
H
L
B
9
H
H H
L
L
38
30
(472nm)
WAVELENGTH CHANNE:L (A)
!385nml
1
38
30
!385"rn)
147Pnm)
WAVELENGTH CHANNEL
(A) H
H H
"0
00
H
00
G G G
0
I
H
SPECTRUM NUMBER 1 -
30 !385"rn)
WI~VELENGTH CHANNEL ( B)
(472nml
Figure 6. Solution bandsJor normalized static spectra in subspace 111 of experiment 1: L 4:; H = (A) absorber 3; (B) absorber 4 (see text for details). f
(5)
38
ti;
is changing concentration. By using the fact that the concentration of NlDMA is constant (and probably zero) in the last 16 spectra, we obtained the shape of the static spectrum of absorber 3 in subspace I11 from eq 7, where il = L-lB,,, (7)
B(l)is the first eigenvector of S,.4 The concentration profile of NDMA was then computed directly from the static spectrum of the intermediate. By these techniques, which utilize the two-absorber simplifications, subspace I11 was completely resolved into its static spectra and concentration profiles. Analysis of subspace I gave only the solution bands for the static spectra and concentration profiles of its two absorbers and could not be further resolved from the data. Subspace IV shares, one absorber (the tail of the NDMA absorption) with subspace 111. The last four wavelength channels (550-584 nm) in subspace IV gave nearly identical upper and lower bounds for the concentration profile of the absorber which is not shared with subspace 111. The lower bound cIL' was arbitrarily chosen as the concentration profile of this absorber. Table I11 summarizes the information obtained by analyzing subspaces I, 111, and IV. Cohplete resolution of experiment 1 into the static spectra and concentration profiles of its five independent absorbers would require evaluation of the elements of either the matrix U or the matrix V, defined in the preceding paper.4 The concentration profiles of absorbers 3,4, and 5, determined from subspaces 111 and I[V, were fitted to the M-analysis eigenvectors of the whole experiment in order to estimate three of the five columns of V. The four possible com-
M-analysis fit of that portion of the measured NDMA spectrum which lies in subspace 111of experiment 1: X = measured; 0 = calculated. Note that since NADH does not absorb in this region the fit of the NDMA spectrum alone is satisfactory. (B) Concentration profile of absorber 3 in subspace I11 of experiment 1 as obtained by using the NDMA spectrum in this region. Vertical scale in arbitrary Concentration unks; horizontal scale linear in channel number (see Table 11). The time scale corresponds to that in Figure 1. Figure 7. (A)
binations of upper and lower bounds for concentration profiles of absorbers 1 and 2 were used to estimate four combinations for the first two columns of V. Thus, four estimates of V were obtained, correspondingto each of the four permutations of known concentration profiles for absorbers 3-5 with the extrema for absorbers 1 and 2. Equation 13 of the preceding paper4 was used to obtain an estimated rotation matrix U corresponding to each estimate of V, and eq g4 was used to obtain from each U an estimated set oE five static spectra for the whole experiment. Two of the four combinations of concentration profiles gave large negative absorbances in the static spectra of absorbers 1 and 2 and were therefore rejected. The other two combinations gave positive absorbances for absorbers 1and 2. All four combinations gave the same set of static spectra for absorbers 3, 4, and 5. Thus, the estimated static spectra of absorbers 3, 4, and 5 were insensitive to the uncertainties of concentration profiles for absorbers 1 and 2. Figure 8A shows the static spectra, and Figure 8B the concentration-time profiles obtained for absorbers 3, 4, and 5 in experiment 1. Absorber 4 has the spectral shape of NDMA with a 340-nm shoulder due to linear dependence between the concentration profiles of NDMA and the 340-nm band of NADH. The static spectra obtained from experiment 1 were fitted to experiments 2-4 to obtain concentration profiles for absorbers in these experiments. In each case the
2574
The Journal of Physical Chemistry, Vol. 84, No. 20, 1980
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Cochran et al.
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(5) Figure 8. (A) Spectra of absorbers 4, 3, 5 (top to bottom) in experiment 1 as deduced by PCA of the entire absorbance-wavelength-time surface. The vertical scales give the correct relative absorbances, but the spectra are displaced for clarity. The horizontal scale is linear in channel number (see Table 11). (6) Relative concentration-time profiles of absorbers 4, 3, 5 (top to bottom) in experiment 1. Note that the fast phase growth of absorber 3 matches the decay of absorber 4 but that the growth of absorber 5 lags behind. The relative concentration of each absorber is scaled to a maximum value of unity. The curves are displaced vertically for clarity. The last point shown corresponds to a time of 500 s.
concentration profiles of absorbers 3, 4, and 5 were insensitive to the static spectra used for absorbers 1and 2. In experiment 4 the 340-nm band of NADH was taken as the sixth independent absorber, and the measured static spectrum of NDMA was used for absorber 4. Experiment 2, which had the same initial concentrations as experiment 1, but a different order of mixing, gave concentration profiles superimposable on those from experiment 1. The concentration profiles obtained for experiments 3 and 4 are shown in Figure 9. Discussion Independently of any mechanistic hypotheses and of any assumptions about spectral shapes, weighted principal component analysis reveals that in the range 275-584 nm experiments 1-3 have at least five linearly independent absorbers, of which four have linearly independent rates, while experiment 4 in the same wavelength range has at least six linearly independent absorbers, of which five have
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Figure 9. (A) Relative concentration-time profiles of absorbers 4, 3, 5 (top to bottom) in experiment 3. Except for absorber 5, the fast phase was complete after one scan under these conditions. The last point Relative concentration-time profiles shown corresponds to 500 s. (6) of absorbers 4, 3, 5 (top to bottom) in experiment 4. The concentration of absorber 6 (NADH) drops to zero during the inltial fast phase which lasts for only 3-4 spectra. The relative concentrationof each absorber is scaled to a maximum value of unity. The curves are displaced vertically for clarity.
linearly independent rates. Application of the methods presented in the preceding paper4 gives the static spectra and concentration profiles for three absorbers in experiments 1-3 and for four absorbers in experiment 4. In experiments 1-3, where the initial concentration of NDMA (13.4 pM) and NADH (15.0 ELM)are almost equal, the 440-nm band of NDMA and the 340-nm band of NADH appear together as one absorber, absorber 4. This is because the concentrations of NDMA and NADH rapidly decay together to near-zero concentration in these experiments. In contrast, NDMA and NADH make separate contributions to experiment 4 (as absorber 4 and absorber 6, respectively). In experiment 4, where the initial concentration of NDMA (13.4 pM) is much greater than the initial concentration of NADH (6.0 pM), NADH still decays rapidly to zero as it did in experiments 1-3, but NDMA decays biphasically. The total decay of NADH is complete by the end of the rapid first portion of the biphasic NDMA decay. This suggests that the rapid portion of the NDMA
Enzyme Application of Principal Component Analysis
decay and the entire rapid decay of NADH in experiment 4 correspond to the same fast process as the concomitant decays of NDMA and NADH in experiments 1-3. The slow portion of the biphasic NDMA decay in experiment 4 is then a step that occurs after NADH has decayed to zero concentration. I t was considered likely that the slower portion of the NDMA decay in exlperiment 4 resulted from recycling of NAD+ by an impurity such as ethanol. This was ruled out in later experiments in two ways: (A) NDMA was incubated with LADH, and the buffer used in the kinetics experiments in the presence of NAD'. The decay of NDMA was orders of magnitude slower than the slower portion of the biphasic decay observed in the kinetics experiments. (B) When (NDMA),/(NADH), > 2 decay of absorbance due to NDMA stopped after the slower phase and showed no change over a period of several minutes. These experiments confirm that while the stoichiometry of the enzymatically catalyzed reaction may be 1:1, further reactions involving intermediates can occur. On the basis of additional experiments, to be described in a separate paper, W I Dconclude that off-enzymehydrolysis reactions and reactions of NDMA and NADH with intermediates can occur. That the chemistry of probable intermediates can be complex is indicated by the studies of Tongz3and others.24 Absorber 3 has thLe same static spectrum in experments 1-4. It is the combination of a band with a peak at 403 nm and a shoulder near 320 nm. There is a striking difference between the behavior of absorber 3 in experiments 1-3 and in experiment 4. In experiments 1-3, absorber 3 grows rapidly as NDMA and NADH decay to zero, and then absorber 3 slowly decays to zero. In experiment 4, absorber 3 grows rapidly during the fast NADH decay and the rapid portion of' the biphasic NIIMA decay, but then, instead of slowly-decaying as in experiments 1-3, absorber 3 continues a slow growth corresponding to the slow portion of the NDMA decay. Absorber 5, whiclh also has the same static spectrum in all four experiments, is a combination of a 320-nm band and a 540-nm band. Absorber 5 accounts for most of the absorbance changes at 540 nm and can thus be identified as the intermediate hypothesized by Schack and Dunn6 and Suelter et aL7 to account for the growth and decay of absorbance at 500-550 nm. Note that the growth of this absorber lags behind the decay of NDMA as observed by Dunn et al.8 Visual examination of the spectra in subspace IV after the decay of absorption due to NDMA is complete shows that the 540-nm band of absorber 5 has two peaks as reported by Dunn et aL8 but the overlap with the NDMA absorption tail and the noise level at early times cause these details to be obscured in the average spectra. (The shape of reconstructed peaks involves use of all of the data.) Principal component analysis gives the new information that in these experiments the 540-nm intermediate also has a band at 320 nm. This could represent
The Jodrnal of Physical Chemistty, Vol. 84, No. 20, 1980 2575
two absorption bands of a single species or two species that grow and decay together under the conditions used in these experiments. These four experiments cannot be used to identify the intermediates completely. However, with the information about spectra obtained here, the application of PCA to a larger number of experiments with various initial conditions should be able to tell us much about the nature of the intermediates. Subsequent measurements to be described in a separate paper have shown that the intermediates, with the possible exception of absorber 3 (403nm peak), occur off enzyme and appear to be associated with various species produced by partial reduction of NDMA as suggested by Dunn et ala8 It appears that absorber 3 may be affected by inactive enzyme since the position of the peak is slightly different when fully active enzyme is used.
Acknowledgment. This research was supported by NSF Grant No. PCM 76-18905. The assistance of David Carr is gratefully acknowledged. References and Notes (1) (2) (3) (4) (5)
(6) (7) (8)
(9) (10) (11) (12) (13) (14) (15)
(1 6)
(17) (18) (19) (20) (21) (22) (23) (24)
Air Products and Chemicals, Box 538, Allentown, PA 18105. Dow Chemical Co., Mldland, MI 48640. R. N. Cochran and F. H. Horne, Anal. Chem., 49, 846 (1977). R. N. Cochran and R. H. Horne, J. Phys. Chem., precedlng paper. M. F. Dunn and S. A. Bernhard, Biochemistry, 10, 4569 (1971). P. Schack and M. F. Dunn, "Abstracts of Papers", 8th Meeting of the Federationof Ewopean Biochemical Societies, Amsterdam, 1972, no. 303. C. H. Suelter, R. B, Cooien, N. Papadakis, and J. L. Dye, Anal. Biochem., 69, 155 (1975). M. F. Dunn, P. Schack, S. C. Koerber, A. M.J. Au, G. Saliman, and R. G. Morris, 2nd International Symposium on Pyridine NucieotideDependent Dehydrogenases, Konstanz, Germany, March 27-April 1, 1977. S. A. Bernhard, M. F. Dunn, P. L. Luisi, and P. Schack, Biochemistry, 9, 185 (1970). J. T. McFarhnd and S. A. Bernhard, Biochemistry, 11, 1486 (1972). P. L. Luis1 and R. Favilla, Biochemisfry, 11, 2303 (1972). P. L. Luisi and E. Bignetti, J . Mol. Biol., 88, 653 (1974). M. Hadorn, V. A. John, F. K. Meir, and H. Dutler, Eur. J. Biochem., 54, 65 (1975). K. Tatemoto, Arch. Biochem. Biophys., 166, 16 (1975). C. F. Weidlg, H. R. Halvorson, and J. D. Shore, Biochemistry, 16, 2916 (1977). One of the referees has suggested that the low activity might be due to the presence of CT, an inhibitor for this enzyme. This Is considered unlikely since it was shown by C. H. Reynolds and J. S. McKinleyMcKee [€or. J . Biochem., 10, 474 (1969)l that CI-at pH 7.4 has K, = 23 mM and interacts competitively with NADH to a group with p K = 9.0. H. Sund and H. Theorell in "The Enzymes", Vol. 7, P. D. Boyer, H. Lardy, and K. Myback, Eds., 2nd ed., Academic Press, New York, 1960, p 25. P. L. Biochemicals, Circular No. OR-10, Milwaukee, WI, 1973. G. Ho, Ph.D. Dissertation, Michigan State University, East Lansing, MI, 1976. N. Papadakis, R. B. Coolen, and J. L. Dye, Anal. Chem., 47, 1644 (1975). R. B. Coolen, N. Papadakis, J. Avery, C. G. Enke, and J. L. Dye, Anal. Chem.. 47. 1649 (1975). R. N. Cochran, Ph.D. Dissertation, Michigan State University, East Lansing, MI, 1977. L. K. J. Tong, J. Phys. Chem., 58, 1090 (1954). J. F. Corbett, J. Chem. SOC. B, 213 (1969).
