Statistical methodology for the detection of small changes in distances by EXAFS: Application to the antimalarial ruthenoquine

Article abstract of DOI:10.1021/jp301811r

Antimalarial compounds ruthenoquine and methylruthenoquine were studied by X-ray absorption spectroscopy both in solid state and in solution, in normal (aqueous or CH₂Cl₂ solutions) and oxidative (aqueous solution with H₂O₂, either equimolar or in large excess) conditions, to detect small changes in the coordination sphere of the ruthenium atom. Since changes in the EXAFS spectra of these compounds are quite subtle, a complete procedure was developed to assess the different sources of uncertainties in fitted structural parameters, including the use of multivariate statistic methods for simultaneous comparison of edge energy correction ΔE₀ and distances, which can take into account the very strong correlation between these two parameters. Factors limiting the precision of distance determination depend on the recording mode. In transmission mode, the main source of uncertainty is the data reduction process, whereas in fluorescence mode, experimental noise is the main source of variability in the fitted parameters. However, it was shown that the effects of data reduction are systematic and almost identical for all compounds; hence, they can be ignored when comparing distances. Consequently, for both fluorescence and transmission recorded spectra, experimental noise is the limiting factor for distance comparisons, which leads to the use of statistical methods for comparing distances. Univariate methods, focusing on the distance only, are shown to be less powerful in detecting changes in distances than bivariate methods making a simultaneous comparison of ΔE₀ and distances. This bivariate comparison can be done either by using the Hotelling's T² test or by using a graphical comparison of Monte Carlo simulation results. We have shown that using these methods allows for the detection of very subtle changes in distances. When applied to ruthenoquine compounds, it suggests that the implication of the nonbinding doublet of the aminoquine nitrogen in either protonation or methylation enhances the tilt of the two cyclopentadienyls. It also suggests that ruthenoquine and methylruthenoquine are, at least partially, oxidized in the presence of H₂O₂, with a small decrease in the Ru-C bond length and increase in the edge energy.

Full text of DOI:10.1021/jp301811r

Article
pubs.acs.org/JPCA
Statistical Methodology for the Detection of Small Changes in
Distances by EXAFS: Application to the Antimalarial Ruthenoquine
Emmanuel Curis,*,† Faustine Dubar,‡ Ioannis Nicolis,† Simone Benazeth,† and Christophe Biot¶
́
†Laboratoire de biomathem
Descartes, Paris, France, Universite
́
atiques, Plateau iB2, Dep
Lille Nord de France
Lille 1, UCCS, UMR CNRS 8181, 59652 Villeneuve d’Ascq Cedex, Lille, France
Lille Nord de France, Universite Lille 1, UGSF, CNRS UMR 8576, IFR 147, 59650 Villeneuve d’Ascq Cedex, Lille,
́ ́ ́ ́
artement Sante publique et biostatistiques, faculte de Pharmacie, Universite Paris
́
‡Universite
́
¶Universite
France
́
́
ABSTRACT: Antimalarial compounds ruthenoquine and
methylruthenoquine were studied by X-ray absorption spec-
troscopy both in solid state and in solution, in normal
(aqueous or CH2Cl2 solutions) and oxidative (aqueous
solution with H2O2, either equimolar or in large excess)
conditions, to detect small changes in the coordination sphere
of the ruthenium atom. Since changes in the EXAFS spectra of
these compounds are quite subtle, a complete procedure was
developed to assess the different sources of uncertainties in
fitted structural parameters, including the use of multivariate statistic methods for simultaneous comparison of edge energy
correction ΔE0 and distances, which can take into account the very strong correlation between these two parameters. Factors
limiting the precision of distance determination depend on the recording mode. In transmission mode, the main source of
uncertainty is the data reduction process, whereas in fluorescence mode, experimental noise is the main source of variability in
the fitted parameters. However, it was shown that the effects of data reduction are systematic and almost identical for all
compounds; hence, they can be ignored when comparing distances. Consequently, for both fluorescence and transmission
recorded spectra, experimental noise is the limiting factor for distance comparisons, which leads to the use of statistical methods
for comparing distances. Univariate methods, focusing on the distance only, are shown to be less powerful in detecting changes in
distances than bivariate methods making a simultaneous comparison of ΔE0 and distances. This bivariate comparison can be
done either by using the Hotelling’s T2 test or by using a graphical comparison of Monte Carlo simulation results. We have
shown that using these methods allows for the detection of very subtle changes in distances. When applied to ruthenoquine
compounds, it suggests that the implication of the nonbinding doublet of the aminoquine nitrogen in either protonation or
methylation enhances the tilt of the two cyclopentadienyls. It also suggests that ruthenoquine and methylruthenoquine are, at
least partially, oxidized in the presence of H2O2, with a small decrease in the Ru−C bond length and increase in the edge energy.
Some hints for a correct estimation of distances and their
comparisons are presented in the reports of the Standards and
Criteria Committee.1,2 Usually, precision is considered to be
around 0.01 Å for distance determination, and 0.001 Å for
distances comparisons. For mineral crystals such as oxides,
methods were developed to allow a very precise determination
and comparison of distances, with an accuracy ranging from 2 ×
10−4 Å (20 fm)3 to 10−5 Å (1 fm).4 Such a precision was
achieved by using third-generation synchrotron sources with a
high beam stability, especially in energy; some of the
approaches use differential EXAFS.4,5 Analysis involves taking
into account thermal expansion of the crystal; hence, studies at
different temperatures and introducing special parameters
known as cumulants.3,6
INTRODUCTION
■
X-ray absorption spectroscopy is well suited to study the local
environment of the metal atom in bioinorganic compounds,
both in solid state and in solution. It can give insights on the
degree of oxidation of the metal atom through the edge energy
and on the distance between this atom and the atoms of its first
coordination shell. However, although good precision is
generally assumed for distances, there is, to our knowledge,
no standardized procedure to determine if distances or edge
energies obtained for two samples are, indeed, different. In fact,
the question is complex for two reasons: First, these values are
obtained through a fitting procedure involving also Debye−
Waller factors, and a straight comparison using standard errors
or confidence intervals of these parameters does not take into
account the correlation between them. Second, uncertainties in
these values not only come from experimental noise, but also
from various sources such as the choice of the initial values in
the fit process, the EXAFS oscillation extraction procedure, etc.
Received: February 23, 2012
Revised: May 16, 2012
Published: May 18, 2012
© 2012 American Chemical Society
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The aim of this paper is to present a potential procedure for
handling such comparisons for bioinorganic compounds in
solution or in solid state. For such compounds, the thermal
expansion approach cannot be used, since they are not in
crystalline form. Our procedure is based on the use of suited
statistical tools and Monte Carlo simulations. This procedure
will be illustrated on samples of ruthenoquine (RQ) and its
methyled derivative, methylruthenoquine (Me-RQ) (Chart 1)7
Synthesis of RQ and Me-RQ Dichlorydrate Salts. RQ or
Me-RQ (0.500 g, 1 mmol) was dissolved in anhydrous
dichloromethane (5 mL). Gaseous HCl (obtained by reaction
of H2SO4 on NaCl) was bubbled into this solution until
precipitation of the dichlorydrate salt. The precipitate was
filtered (RQ, 0.552 g, 1 mmol; Me-RQ, 0.574 g, 1 mmol).
Sample Preparation for XAS Experiments. Preparation
of Solid Samples. Using a mortar, RQ (or Me-RQ, RQ·2HCl,
Me-RQ·2HCl) (10 mg, 20 μmol) or ruthenocene (10 mg, 40
μmol) and boron nitride (10 mg, 400 μmol) were mixed and
ground to a fine powder. The powder was then transferred in
Evacuable Pellet Dies. The pellet was made with a load of 2
tons and a pellet diameter of 6 mm.
Chart 1. Chemical Structures of Ferroquine (FQ),
Ruthenoquine (RQ), and Methylruthenoquine (Me-RQ)
Preparation of Solution Samples. For dichloromethane
solutions, RQ (2.4 mg, 5 μmol) or ruthenocene (1.2 mg, 5
μmol) was dissolved in dichloromethane (1 mL) for a final
concentration of 5 mM. The analysis was performed on a fresh
solution.
For aqueous solutions, RQ·2HCl, or Me-RQ·2HCl (2.8 mg,
5 μmol) was dissolved in distilled water (1 mL) for a final
concentration of 5 mM. The analysis was performed on a fresh
solution.
Equimolar aqueous solutions of RQ, or Me-RQ, and H2O2
were prepared from 20 μL of 30% aqueous H2O2 dissolved in
19.98 mL of distilled water. In 1 mL of this solution, 6.6 mg (11
μmol) of RQ or Me-RQ was dissolved for a final concentration
of 11 mM.
Solutions of RQ or Me-RQ with an excess of H2O2 were
prepared by dissolving 6.6 mg of RQ or Me-RQ in 1 mL of a
solution obtained by mixing 150 μL of 30% aqueous H2O2 in
19.85 mL of distilled water.
The RQ solution in HEPES was prepared by mixing 4 mL of
distilled water, 5 mL of a solution of 5.5 mg (11 μmol) of RQ
in 10 mL DMSO (solution A), and 1 mL of a solution of 25 mg
(100 μmol) HEPES (solution B) in 5 mL of distilled water for a
final RQ concentration of 5.5 mM.
The hemine solution in HEPES (solution 4) was prepared by
mixing 4 mL of distilled water, 1 mL of solution B, and 5 mL of
a solution of 8 mg (12 μmol) of hemine in 10 mL of DMSO.
The equimolar solution of RQ and hemine was prepared by
mixing 1 mL of the RQ solution in HEPES and 1 mL of the
hemine solution in HEPES for a final RQ concentration of 2.75
mM.
The solution of RQ with an excess of hemine was prepared
by mixing 1 mL of the RQ solution in HEPES and 2 mL of the
hemine solution in HEPES for a final RQ concentration of 1.83
mM.
XAS Experiments. Data Recording. Spectra were recorded
on the SAMBA beamline (SOLEIL synchrotron, Saint-Aubain,
France), at the K-edge of the ruthenium (22.1 keV). A
ruthenium foil spectrum was recorded for energy calibration.
To avoid saturation of the ionization chambers (in transmission
mode) and of the fluorescence detector (in fluorescence
mode), an aluminum filter had to be added; its thickness was
adapted to have a beam intensity as high as possible,
maintaining the linearity of the detectors.
Solid state samples (RQ, Me-RQ, RQ·2HCl, Me-RQ·2HCl,
and ruthenocene) spectra were recorded on pellets in
transmission mode with two ionization chambers. The edge
region was recorded with a constant energy scale step (pre-
edge, 5 eV step; acquisition time, 1 s/point; edge, 0.5 eV, 1 s/
point; postedge, 1 eV, 1 s/point), whereas the EXAFS region
was recorded with a constant k-scale step (assuming an edge
in solid state and solutions. Since the cyclopentadienyl ligands
are tightly bound to the ruthenium atom and are quite rigid,
only very small changes in Ru−C distances are expected, even if
the oxidation state of the ruthenium changes, thereby giving a
higher challenge to the procedure.
We selected ruthenoquine, the cold tracer of the antimalarial
ferroquine,8 as a case study because of the need to gain insights
into its structure. Recently, we performed a feasibility study on
single erythrocytes infected by the HB3 strain of Plasmodium
falciparum.9 We showed that the drugs can be detected and
mapped by X-ray fluorescence in a parasite exposed to
concentrations that are comparable to dosages of ferroquine
in clinical assays.10 Moreover, the present study enables us to
compile a library of reference spectra that will be used as a basis
in further X-ray imaging experiments in which micro-XANES
measurements will give insights into the localization and
chemical state of RQ in the parasite. We also included
methylruthenoquine (Me-RQ, Chart 1) in this study.
Last, there are still some questions about the behavior of
ruthenoquine in an oxidative environment, as may be found in
the digestive vacuole of the parasite. Electrochemical oxidation
of ruthenocene leads to complex species that may involve
dimerization11,12 and in which the oxidation state of the
ruthenium core is not clear; the same difficulties are then
expected for RQ and related compounds. Fine studies of the X-
ray absorption edge and of the ruthenium−carbon distances
may give insights on this question. For this reason, experiments
were made with RQ and Me-RQ in aqueous solutions with
either H2O2 or hemine, the hemoglobin degradation product
that is present in the digestive vacuole, as the oxidative agent, to
be close to biologic conditions.
MATERIALS AND METHODS
■
Sample Preparation. RQ = ruthenoquine, RQ·2HCl =
dihydrochloride salt of ruthenoquine (by protonation of the
amine groups), Me-RQ = methylruthenoquine, Me-RQ·2HCl =
dihydrochloride salt of methylruthenoquine.
Synthesis. RQ and methylruthenoquine Me-RQ were
synthesized as previously reported.7,13 Boron nitride and
ruthenocene were purchased at Sigma Aldrich.
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energy of 22 117 eV) with the acquisition time being increased
from 2 to 4 s/point to get a constant signal/noise ratio after k2
weighting. All spectra were recorded at least three times.
Solution samples (RQ in CH2Cl2, RQ in H2O + HCl, Me-
RQ in H2O + HCl, RQ in H2O + H2O2, Me-RQ in H2O +
H2O2, and RQ and hemine in HEPES buffer) spectra were
recorded in fluorescence mode using a seven-element
germanium detector. Potential spectrum distortion induced
by self-absorption was estimated using the approach previously
described14 using the LASE software, which was written by one
of us,15,16 based on the solid state sample spectra, and it was
found to be negligible for such diluted solutions. Spectra were
recorded using the same energy grid as above, with an
acquisition time of 4 s in the edge region and from 4 to 8 s in
the k-scale region; each sample was recorded at least three
times.
ature20 and the ruthenoquine crystal structure22 and used in
FEFF 8.2.23,24 When using the crystal structure of ruthenocene,
FEFF generates numerous scattering paths because of slight
differences in distances in the crystal; such paths were averaged
in LASE before fitting. The resulting model was fitted to both
filtered and unfiltered data, and path selection was made to
have the best fit with the simplest model.
Since only single scattering from the first coordination shell
leads to a significant contribution for the EXAFS oscillations
after this path selection step, the following parameters were
finally fitted, using reference phase and amplitudes: RC, the
average distance of the 10 carbon atoms from this first
2
coordination sphere; σC , the associated Debye−Waller factor;
2
ΔE0, the correction of the edge energy and S0 , the amplitude
correction factor to account for multielectronic transitions. The
fitted equation was then
Data Analysis. All EXAFS analyses were made using the
LASE software. Background absorption was removed using
either a Victoreen model (transmission) or a straight line
(fluorescence); edge energy was taken at 22 126 eV (inflection
point of the ruthenocene edge) for all spectra to ensure a
comparable k-scale. EXAFS oscillations were extracted using a
polynomial smoothing in E and k-spaces, controlled to
minimize the very short distance peak of the Fourier transform.
For all analyses, spectra were averaged after background
removal and error bars propagated throughout EXAFS
oscillation extraction and Fourier transform using previously
published results.17 These unfiltered EXAFS oscillations were
then fitted to obtain structural parameters values. All fits were
made both on averaged spectra and on individual spectra, on
unfiltered EXAFS oscillations, to investigate the effect of the
extraction itself on parameters values.
2
2 NCA(k′)
C
χ(k) = S0
e−2k σ 2 sin 2kR + Φ(k′)
(
)
C
RCk
where NC = 10 is the number of carbon atoms in the first
coordination shell of the ruthenium atom; A(k′) and Φ(k′) are
the electronic phases and amplitudes, including the mean free
path, either computed by FEFF or extracted from the reference
(RQ pellet) spectrum, and corrected for the different edge
energy, with k′ = (k2 + 2(me/ℏ)ΔE0)1/2 (me being the electron
mass and ℏ the reducted Planck constant, expressed in suitable
units). Least-square estimates are used, with a minimization
procedure based on stepwise gradient optimization, with
analytical computation of the derivatives and no constraint.
Initial values for these parameters were ΔE0 = 0 eV, RC
=
2.1880 Å, and σC = 0 Å2, corresponding to the values used to
extract experimental phases and amplitudes. Influence of the
initial values was checked by randomly selecting n′ = 1000
random alternative initial values uniformly in the 3-dimensional
box [ΔE0 , ΔE0 ] × [RC , RC ] × [σC 2, σC 2] and
2
Unfiltered k2-weighted EXAFS oscillations were analyzed
without weighting by the experimental errors (since acquisition
conditions ensure constant error with k2 weighting) between k
= 4 and 14 Å−1. Fitted parameter uncertainties and correlations
were estimated through the Monte Carlo procedure previously
described:18 n = 1000 random unfiltered spectra were generated
based on a normal distribution with expectation equal to the
average of the experimental, unfiltered EXAFS oscillations, and
a diagonal covariance matrix, with diagonal values taken as the
experimental squared standard deviation on each experimental
point, as obtained when averaging the experimental spectra. As
shown before,17 unfiltered spectra have uncorrelated data
points, but this is not true for spectra after Fourier-transform
filtering (either used for noise removal or for peak selection).
Each of these random n spectra was fitted, leading to a set of n
fitted parameter values, then studied using standard statistical
methods. Fits were performed using either reference,
experimental phase and amplitude, or theoretical phases and
amplitudes.
Reference, experimental phase, and amplitude were extracted
from the ruthenocene pellet spectrum by filtering the Fourier
transform peak corresponding to the first coordination sphere,
the back Fourier transform leading to raw phase and amplitude
of the corresponding EXAFS spectrum. There, raw phase and
amplitude were distance-corrected using the average Ru−C
distance (2.188 Å) found in the several available ruthenocene
crystal structures,19−21 then used to fit experimental EXAFS
spectra of other compounds.
min
max
min
max
min
max
comparing the fit results.
Statistical Procedure. All statistical analyses were made
using the R software, version 2.14,25 and a set of scripts written
by one of us. After the fit procedure presented above, several
sets of parameter values were available for each compound,
including the distances to be compared. A two-step procedure
was used to make these comparisons.
First, the various sources of parameter estimate variability
were explored. To evaluate the influence of experimental noise
(“random errors”), the same model was fitted on the average
experimental spectrum, on each individual spectrum, and on
the filtered spectrum. To evaluate the influence of initial values
in the fit process, several initial values were used, and the fit
results were compared. To evaluate the influence of the data
reduction steps, data reduction was made several times, and the
results were compared. All these comparisons relied on both
graphical comparisons of the Monte Carlo simulation results
and numerical inspection of the results. For clarity, details on
these method are presented below, together with the results.
Second, suited statistical comparison procedures were applied.
These procedures were either univariate procedures, with direct
comparisons of the distances only, or multivariate procedures,
comparing the whole set of parameter estimates.
Univariate procedures were of two kinds. First, the usual
analysis of variance (ANOVA) and subsequent multiple
comparison procedures were applied when distance estimation
distributions could be considered as approximately normal
To generate theoretical phases and amplitudes, including
multiple scattering paths, a structural model was built from the
most recent ruthenocene crystal structure at ambient temper-
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Figure 1. EXAFS (left) and its Fourier transform (right; black is the imaginary part, red is the modulus) for solid ruthenoquine. Continuous line,
experiment; squares, model. EXAFS oscillations are k2-weighted and shown with associated experimental error bars. Fourier transform was made
with a Gaussian apodization function; its error bars are shown on the imaginary part.
Table 1. Structural Parameters for Each Compound, After Fitting the Single-Shell, Single Scattering Model with Experimental
a
Phases and Amplitudes Extracted from the Reference Compound EXAFS Spectrum on the Unfiltered EXAFS Oscillations
fitted structural parameters
solid state samples (pellets); transmission mode
solution samples; fluorescence mode
104 σC (Å2)
solution
ΔE0 (eV)
RC (Å)
104 σC (Å2)
2
2
compound
ΔE0 (eV)
RC (Å)
ruthenocene
RQ
−0.35(10)
0.31(1)
2.1896(7)
2.1889(1)
2.1869(8)
1.3(4)
−6.4(2)
0.8(3)
no solution studied
H2O
−0.33(111)
0.36(150)
0.18(190)
0.79(149)
0.79(232)
−0.78(371)
−6.30(419)
−0.34(64)
−0.69(125)
−0.77(166)
2.1857(82)
2.1641(110)
2.1684(138)
2.1753(103)
2.1654(162)
2.1796(271)
2.2159(321)
2.1857(45)
2.1771(92)
−0.6(5)
6.9(60)
d
b
RQ·2HCl
−0.48(10)
H2O2 1:1
H2O2 1:15
7.0(80)
b
CH2Cl2
−6.1(72)
−3.8(83)
−4.1(150)
−5.6(145)
−0.6(30)
3.4(52)
HEPES
HEPES + hemine 1:1
HEPES + hemine 2:1
H2O
Me-RQ
−0.06(5)
−0.18(8)
2.1872(4)
2.1866(7)
−3.2(4)
−4.1(3)
d
c
Me-RQ·2HCl
H2O2 1:1
c
H2O2 1:15
2.1764(123)
8.0(70)
a
b
c
Number in parentheses gives the standard deviation, after Monte Carlo simulation. Visual comparison in Figure 3, left. Visual comparison in
Figure 3, right. Visual comparison in Figure 4.
d
(parametric method). The principles of the analysis of variance,
which can be seen as a generalization of the Student’s T test,
can be found in numerous statistics courses and will not be
given here; see for instance, refs 26−28. Second, and especially
when the parametric analysis of variance assumptions were not
met, nonparametric analysis of the Monte Carlo results was
proposed. This analysis is based on the properties of
nonparametric prediction intervals.29 Let us assume, as a null
hypothesis, that the two sets of parameters come from the same
distribution (have the same theoretical value). Then, the first
sample of n values obtained by the Monte Carlo simulation can
be used as a 1 − (2/(n + 1)) prediction interval for the second
set, that is, an interval that has probability 1 − (2/(n + 1)) to
contain a single value of the second set. Since values of the
second set are independent, the probability that all the n′ values
of the second set are outside this interval (that is, the
probability of no overlap between the two sets of values) is then
(2/(n + 1))n′. With n = n′ = 1000, this is a probability of about
10−2699, completely negligible. Hence, the hypothesis that
parameter values for two samples are the same can be ruled out
if the two Monte Carlo set of values for these two samples do
not overlap. This concept can be adapted to estimate a p-value
in the case of partial overlap: assuming that the k smaller and
the k larger values of the first set are omitted, the probability for
the second set to completely lay outside this reduced first set is
(2(k + 1)/(n + 1))n′.
Multivariate procedures applied were the equivalents of the
univariate ones, using multivariate analysis of variance
(MANOVA) and Hotelling’s test when data were multidimen-
sionally normally distributed, and nonparametric approaches
when otherwise, using prediction regions instead of prediction
intervals. Details about multivariate procedures can be found in
refs 30 and 31, for instance.
In addition, when several samples are to be compared,
multiplicity correction may be required; for instance, here, with
15 samples to be compared, one should use α = (0.05/(15 ×
14/2)) ≈ 4.7 × 10−4 instead of 0.05 to perform the test
(Bonferroni correction). Note that even with this correction,
the complete nonoverlapping of two clouds of points still leads
to reject the null hypothesis of similar parameter values.
RESULTS AND DISCUSSION
■
EXAFS Data Analysis. As expected, all recorded spectra
lead to very similar spectra, in agreement with the common
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ruthenocenic core of all compounds. The Fourier transform
shows a single peak, around 1.7 Å (uncorrected for phase shift;
Figure 1). Fitting the structural model using scattering paths
generated by FEFF 8.2, only single scattering on the first
coordination shell (10 carbon atoms at around 2.21 Å) was
necessary to reproduce this first peak of the Fourier transform
and the EXAFS oscillations to a good extent (Figure 1). To
reproduce secondary peaks of the Fourier transform, models
including multiple scattering paths were built. Such models
only slightly improve the overall fit; however, they lead to an
inconsistent set of structural parameters for these shells, such as
abnormally high (>0.5 Å2) or low (<10−4 Å2) Debye−Waller
factors or inconsistent distances. This probably results from
complex interferences between various multiple scattering
paths, as already observed.18 Since adding these paths makes
the fit process unstable without changing the first shell
parameters values, to allow comparisons between the results,
all subsequent fits were made using reference phases and
amplitudes to avoid the biases due to the theoretical
approximations made.
oscillations. Obviously, the fit on the filtered spectrum should
be almost perfect (to the precision of the computer); the
difference between the two fits will then give the contribution
of all model imperfections (distortions due to Fourier filtering,
mainly) to the parameter value precision. This comparison
leads to Δ(ΔE0) = −0.37 eV, ΔRC = 0.00162 Å and Δ(104σC )
2
= 1.5 Å2. These results give a lower bound for the precision of
the parameters; fitting using theoretical electronic parameters
would lead to even higher lower bounds, since all theoretical
assumptions will also limit the precision of fitted values. These
bounds are well below the uncertainties for fluorescence
spectra; however, they are higher than the Monte Carlo
estimated statistical uncertainties for transmission spectra
(Table 1). This observation is in agreement with the well-
known fact that noise is not the limiting factor in transmission
mode experiments3,4
To note, fitted distances are shifted toward higher values
(ΔRC > 0), which is coherent with the lack of the high-R
contributions to the spectrum when filtering the first peak of
the Fourier transform; in that case, one can expect a similar bias
for any fit using the same phases and amplitudes on structurally
close compounds, as with the ruthenoquine family compounds
here. To check this point, for each of the solid state samples,
phases and amplitudes of the first peak were isolated from the
average transmission spectra using the same procedure and
were used to fit the corresponding unfiltered EXAFS
oscillations. Results of these fits are given in Table 2. As can
This single-scattering, single-shell model was fitted to all
experimental data sets. The results are given in Table 1, and
these values, which differ slightly from one compound to
another, are the values for which the question is raised “How to
compare them?”.
Since the fluorescence mode operated on dilute solution
samples leads to higher noise than the transmission mode,
statistical uncertainties are, as expected, much higher for
fluorescence spectra than for transmission spectra. For
fluorescence spectra, a quick glance at the fitted values and at
the statistical uncertainties suggests that the results are not very
different; for transmission spectra, however, differences in the
distances are much higher than the statistical uncertainties. The
aim of the procedure presented below is to obtain more reliable
answers than would be obtained through this simple
comparison applied to this family of compounds but in a way
that can easily be generalized to any family of closely related
compounds.
Table 2. Fitted R Values on Unfiltered EXAFS Oscillations,
Using Phase and Amplitude Extracted from the First Peak of
a
the Corresponding Fourier Transform, with RC = 2.1880 Å
Me-
compound
ruthenocene
2.1896
RQ
RQ·2HCl Me-RQ
2.1905 2.1899
RQ·2HCl
fitted RC (Å)
2.1913
2.1910
a
Results are for solid state samples only, recorded in transmission
mode.
Assessing the Source of Variability. There are two main
sources of uncertainties in the fitted parameters: systematic
errors and statistical errors. Systematic errors, or biases, are
associated with any unverified assumption during the experi-
ment recording, the data analysis procedure, or the modeling of
the data. Statistical errors are basically due to the noise. They
have different consequences for distances determination and
comparison: systematic errors preclude obtaining a correct
distance value. However, since they are deterministic, they do
not change from one spectrum to another if all assumptions
made are the same; that is, experiments and analyses are made
under the same conditions, and the model is the same for
similar enough compounds. Consequently, they tend to vanish
when taking the difference between two results and do not
preclude, to a certain extent, making comparisons. Conversely,
statistical errors affect not the exactness of the results, but its
precision; hence, they are the key factor to limiting
comparisons of the distances, assuming systematic errors
vanish, as said before.
be seen here, the bias is similar, and always positive, for all
spectra and is around 0.0025 0.0007 Å (mean and standard
deviation). This result suggests that, for estimating absolute
distances, this bias is the factor limiting the precision. However,
when comparing distances,the difference between the two
estimated distances will almost cancel out this bias, and the
precision is then ∼0.0007 Å, rounded to 0.001 Å, comparable
to statistical uncertainties.
Bias Induced by the Extraction Process. A second
source of uncertainty is the extraction process used to obtain
the (unfiltered) EXAFS oscillations to be fitted. To assess its
influence, for each compound, EXAFS oscillations were
obtained either from the average spectrum or from each of
the three recorded spectra; each of these EXAFS oscillations
was fitted, and the results were compared. Typical results are
shown in Figure 2. As can be seen, both for transmission and
fluorescence mode, variations between individual spectra
(including extraction effects) are comparable with the variability
estimated by the Monte Carlo procedure. In addition,
performing data reduction several times, slightly changing the
data reduction parameters, led to very similar results. For this
reason, they are not discussed further.
Bias (Systematic Errors) Introduced by the Model
Itself. The incorrectness of the fitted model itself is one of the
major systematic errors in EXAFS analysis. To assess its
influence, the fit of the ruthenocene pellet spectrum using
experimental phases and amplitudes from ruthenocene itself
was compared between the filtered and unfiltered EXAFS
Influence of the Initial Values in the Fit Procedure.
Since the EXAFS equation is strongly nonlinear relative to its
parameters, the choice of the initial values may have a
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Figure 2. Fitted ΔE0 and RC values obtained from various procedures. Left: fit for RQ in pellet (transmission mode). Right: fit for RQ in aqueous
solution (fluorescence mode). Black circles: Monte Carlo simulations for estimating statistical uncertainties. Red triangles: changing the initial values.
Blue crosses: fit on individual spectra, instead of average. See text for comments.
Figure 3. Comparisons of two-dimensional variability of the (RC, ΔE0) parameter couple obtained from Monte Carlo simulation. Left: results for RQ
in CH2Cl2 (black) and in equimolar H2O2 (red). Right: results for Me-RQ in equimolar (black) and 1:15 (red) H2O2.
significant influence on the fit results. To assess the importance
of this choice, after each fit and using the initial values given in
the method (expected to be the “best” initial values, owing to
the obtention mode of phases and amplitudes), 1000 sets of
alternative initial values were randomly selected in the
parameter space, and the fit was performed again with these
new initial values. Some of these fits were clearly worse than the
reference one, with a residual sum of square higher than 10
times the reference residual sum of square; others led to
obviously unrealistic distances, close to 2.5 Å. These fits
(corresponding to 0−12.1% of the fits) were removed before
analysis of the results.
Typical results of changing initial values, considering only
valid fits, are presented in Figure 2. Here again, for fluorescence
mode spectra, the effect is much lower than the statistical
uncertainties estimated by the Monte Carlo procedure; for
transmission mode spectra, however, results are more difficult
to interpret.
somewhere inside the valley; the noise in the spectrum creates
small bumps in the valley, preventing the algorithm from
finding the “best” minimum. Values of the residual sum of
squares ξ2 are very close. To select a “correct” minimum, the
behavior of the fitted parameters distribution can be a hint: for
a real minimum, the fitted parameters should be at the center of
the cloud of the Monte Carlo simulations, and ideally, this
cloud should look like an ellipsis. This is the case here for the
fitted values obtained starting from the ideal values. Making
Monte Carlo simulations using initial values leading to one of
these other local minima (gray circles on the figure, generated
for the green fitted values) shows that, although the residual
sum of squares is not statistically different, this secondary
minimum is not the real one, since it does not have this
ellipsoidal shape and is not even centered on the fitted values!
Statistical Comparison of the Distances. Comparison is
straightforward for fluorescence mode spectra, since, as shown
above, statistical uncertainties are the major source of variability
in fitted values. Hence, comparisons can be made directly on
the Monte Carlo simulation results. Furthermore, the cloud of
Monte Carlo simulated values is very close to an ellipsis,
coherent with the hypothesis of a multivariate Gaussian
(normal) distribution for fitted parameters.
It seems that the very strong correlation between ΔE0 and RC
leads to a valley in the surface of the minimized function, ξ2 =
i=1ki4(χexp(ki) − χ(ki))2, where n is the number of
n
∑
experimental points and χexp(ki) is the experimental spectrum.
According to the choice of the initial values, the fit converges
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For transmission spectra, comparisons using statistical
uncertainties should be taken with more care because of
other factors cited above.
• Me-RQ and Me-RQ·2HCl in pellets are different from
Me-RQ in H2O2 (both 1:1 and 1:15; p < 0.0007), with a
slightly longer distance for the latter.
• RQ with hemine in excess is different from all solid-state
compounds (ruthenocene, RQ, RQ·2HCl, Me-RQ, and
Me-RQ·2HCl; p < 0.0003).
Direct Comparison. Direct comparison of distances is then
straightforward using Student’s T test for comparing two
distances, or one-way analysis of variance with subsequent all
pairwise comparisons when more distances are to be compared.
Using this approach, the only significant differences in distances
are among the solid state samples, leading to two sets of groups
of compounds: (1) ruthenocene and RQ and (2) RQ·2HCl,
Me-RQ, and Me-RQ·2HCl.
Solution spectra cannot be distinguished by this approach;
however, the equimolar RQ-H2O2 spectrum is significantly
different from the second group of compounds and from RQ.
These differences are consistent with small changes in the
orientation of the cyclopentadienyl rings binding the ruthenium
atom, the two cycles being almost parallel in ruthenocene and
RQ, but being slightly tilted in RQ·2HCl, Me-RQ, and Me-
RQ·2HCl. Such a structural change was observed in the crystal
structure of the equivalent iron compounds, ferroquine32 and
protonated ferroquine.7
• RQ with equimolar hemine is different from RQ in
pellets (p < 0.0002).
• RQ in pellets is different from Me-RQ and Me-RQ·2HCl
pellets and Me-RQ in H2O2 (both 1:1 and 1:15; p <
0.0003).
The graphical procedure is less conservative and more
powerful, so it gives a better classification of the compounds.
From this approach, it appears that
• Ruthenocene is different from all other compounds,
except maybe the Me-RQ pellet, for which there is a
slight overlap of the two clouds. Ruthenocene seems to
have slightly larger distances.
• RQ (pellet) is also different from all other compounds,
with slightly larger distances and higher ΔE0.
• RQ·2HCl (pellet), however, is comparable to RQ in
CH2Cl2 and RQ and Me-RQ H2O solution, but presents
higher distances than other solutions and shorter
distances than Me-RQ and Me-RQ·2HCl pellets.
• RQ in CH2Cl2 and in H2O are almost identical; both are
barely distinguishable from RQ with hemine (both 1:1
and 1:2). They have longer distances than RQ and Me-
RQ in H2O2 (both 1:1 and 1:15).
Comparison Also Using ΔE0. It is well-known that the
ΔE0 and RC values obtained by fitting are strongly correlated,
and Figure 2 confirms these strong correlations. Consequently,
simply comparing the distances without taking into account the
changes in fitted ΔE0 values will artificially increase the
standard error on distances.
For this reason, comparisons of RC values taking into account
the ΔE0 values were made. The importance of this correction is
illustrated in Figure 3: when clouds representing each
parameter variability are superimposed (as on the right),
there is no difference between the fitted parameter values; when
they do not superimpose (as on the left), parameters do differ,
but in both cases, the projection on the two axes masks this
difference. This effect is a well-known consequence of
correlation in multivariate studies. To correct for this, we
propose two methods.
First, the graphical comparison of the fitted parameters
obtained after the Monte Carlo simulation is an easy way to
distinguish between clouds of values clearly overlapping or not,
as exemplified in Figure 3. However, interpretation is more
difficult in the case of partial overlapping, since determining
which prediction region must be used to estimate p-values is
not straightforward.
• RQ and Me-RQ in H2O2 (both 1:1 and 1:15) cannot be
distinguished and present shorter distances than Me-RQ
and RQ in H2O.
• Me-RQ (pellet) has longer distances than Me-RQ·2HCl
(pellet).
• Comparison of RQ in water, RQ in H2O2, and RQ in
HEPES shows that RQ in HEPES is similar to RQ in
H2O2 and different from RQ in water, but distance
comparison is difficult because of the high noise level of
RQ in HEPES spectra. Unexpectedly, RQ in HEPES
leads to results very similar to RQ in H2O2 with or
without hemine.
Taken together, these results suggest that, in the presence of
H2O2, something occurs in solution that tends to shorten the
Ru−C distance. This would be coherent with oxidation (partial
or complete) of the ruthenium atom. However, there is no net
change in the Fourier transform of the RQ or Me-RQ in the
presence of H2O2, as would have been expected in the case of
the formation of a Ru−Ru bond, since Ru is a heavy atom that
would lead to an important EXAFS signal. This suggests that
this dimerization either does not occur with H2O2 or that only a
small amount of RQ is oxidized in such conditions.
Whereas spectra of RQ in HEPES with hemine would
suggest an oxidation of RQ by the hemine, the unexpected
result that RQ would be also oxidized in HEPES alone
precludes this interpretation. In fact, a few papers mention that
HEPES is able to generate H2O2 when exposed to light,33,34 but
that this effect would be mediated via a coupling with riboflavin
present in cell culture media.35 There is no riboflavin in our
solutions; however, the irradiation with the X-ray beam is much
more intense than a usual source light. Moreover, ruthenoquine
has several aromatic rings, especially the aminoquinolone part,
which is known to absorb and fluoresce in visible light. Hence,
we assume that the results observed for RQ in HEPES are the
Second, one can use a Hotelling’s T2 test to simultaneously
compare the fitted parameters values for two compounds,
corresponding to a two-sample MANOVA. This test is a
multidimensional version of the Student’s T test and presents
the same limitations, that is, assuming normality and a similar
variance-covariance matrix between the two samples. Such
conditions are met for the compounds given in Figure 3: the
two clouds look like ellipses (normality) with parallel axes
(same correlation) and similar extension (same variances), but
this is not always the case. This test should be performed on the
fitted parameters obtained by fitting the model on individual
spectra (testing on Monte Carlo simulation results would
artificially increase the sample size; hence, the test power).
Despite limitations of the multiplicity correction, when
applied to our experimental data and fit results, the Hotelling
T2 test finds the following differences:
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consequence of H2O2 generation by HEPES under X-ray beam,
maybe by coupling with the aminoquinolone part of the
ruthenoquine itself.
In addition, quite interestingly, RQ·2HCl, Me-RQ, and Me-
RQ·2HCl exhibit a clear bimodal pattern for the (RC, ΔE0)
distribution (Figure 4) that was not found for any other fit but
limitations are, indeed, the limiting factor for distance
determination, as with our example, a limit of 0.003 Å.
However, for distance comparisons, this effect does not play the
major role. Consequently, for distance comparisons, the same
statistical methods as above are also adapted.
The main contribution of this work is the introduction of
simultaneous comparison of distances and edge energy
correction using either Hotelling’s T2 test or graphical
comparison of Monte Carlo results. As we have shown, using
such methods strongly enhances the ability to detect changes in
distances as small as 0.001 Å as a consequence of taking into
account the strong correlation between ΔE0 and the distance.
Tools for applying these methods are included in our LASE
software15 for the Monte Carlo simulations and as a template R
script, available from the author, for further analyses.
Applications of the methodological developments to
ruthenoquine and related compounds suggest that the
nonbinding electron doublet of the nitrogen atom linking the
aminoquinolone to the ruthenoquinium may be involved in the
orientation of the two cyclopentadienyl groups. Indeed, either
its protonation or its methylation lead to changes in distances
that may be related to an increase of the tilt between the plane
of the two rings. In addition, results suggest a partial oxidation
of the ruthenium atom in aqueous solution in presence of
H2O2, either directly introduced or generated in situ in HEPES
solutions.
Figure 4. Fit results and Monte Carlo simulations for RQ·2HCl
(black) and Me-RQ·2HCl (red). A bimodal pattern clearly exists.
Despite this, these distributions clearly do not overlap, suggesting a
longer distance and smaller ΔE0 for Me-RQ·2HCl.
AUTHOR INFORMATION
■
has the same shape for these three compounds. Previous work
on the interpretation of such bimodal patterns in Monte Carlo
simulations suggests that there may be a combination of two
distances in these compounds.18 Hence, this bimodal pattern
might also be a consequence of the tilt of the two
cyclopentadienyl ligands, leading to two sets of distances, too
close to be distinguished by using two different scattering paths,
but different enough to let the fit converge toward one or the
other according to the noise pattern.
Corresponding Author
*E-mail: emmanuel.curis@parisdescartes.fr.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
These experiments were carried out thanks to the acceptance of
two proposals at SOLEIL: 20090133 and 20090602. We thank
the team of the SAMBA beamline at SOLEIL, especially
CONCLUSION
Step
experiments.
́ ́
hanie Belin and Valerie Briois, for their help in these
■
Precise determination and comparisons of distances between a
metal atom and its first coordination sphere are often some of
the aims of X-ray absorption studies, with a generally admitted
rule of thumb that the precision is around 0.01 Å. In this work,
we developed an approach to estimate the influence of several
factors on the precision of these distance determinations and
comparisons.
In fluorescence mode, the main factor limiting the precision
of distance determination is the noise level of the data.
Consequently, the most suited methods for estimating the
precision and analyzing comparisons in such experimental
conditions are statistical methods, including analysis of Monte
Carlo simulation results.
In transmission mode, however, noise level of the data is
much less important, leading to statistical estimates of distance
precision almost ten times smaller than the 0.01 Å rule of
thumb. However, as was shown, under these conditions, the
choice of the initial value in the fit procedure and the
limitations of the model used to fit the data lead to important
bias in the results. The influence of initial values may depend
on the specific choice of the algorithm used to minimize the
data. As was exemplified, analysis of the repartition of Monte
Carlo simulation results around the minimum may help to
distinguish the true minimum from spurious ones. Model
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