Yulia M. Serebrennikova and Luis H. Garcia-Rubio, "Modeling and interpretation of extinction spectra of oriented nonspherical composite particles: application to biological cells," Appl. Opt. 49, 4460-4471 (2010)
The majority of cells and microorganisms have a nonspherical shape and complex structure that challenge the interpretation of their spectral features. To address this issue, two approximations to the core-shell Mie theory were proposed. These included the approximation of light extinction by an ellipsoid with representation of the extinction by an equivalent sphere and representation of the extinction by a population of ellipsoidal particles with those of two weighted particle orientations. These hypotheses were first tested through numerical interpretation of the theoretical extinction spectra of prolate nucleated ellipsoids mimicking biological cells generated with anomalous diffraction approximation used as a reference method. Theoretical cases of fixed and random particle orientations demonstrated excellent capabilities of the proposed approach to retrieve the size, shape, and composition parameters of the model particles. Second, the UV–visible spectra of Leishmania species, promastigotes, elongated cells with prominent nuclei, were interpreted. The retrieved estimates of the protozoa size, shape, nucleus size, and nucleotide composition were in agreement with the corresponding microscopy estimates and literature values. Both theoretical tests and experimental results illustrated that the proposed approach can be successfully applied to estimate the structural and compositional parameters of cells from spectroscopic measurements.
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Comparison Between Known (Anomalous Diffraction Approximation) and Estimated (Modified Mie Theory) Parameters of Prolate Nucleated Ellipsoids at Fixed Orientations Including Particle Volume (V), Length (L), Width (W), Nucleus Volume (), Fraction of Nucleotides in Nucleus (), and Relative Contribution of First Orientation (; Contribution of Second Orientation was ), and Rotation Angles a
Estimated Parameter
Known
A
B
Known
C
D
;
;
;
;
20.5
23.0
18.5
20.5
15.3
12.3
10.0
9.7
9.9
5.0
4.8
4.8
2.0
2.1
1.9
2.8
2.5
2.2
1.57
1.50
1.4
1.57
0.64
0.50
0.20
0.17
0.19
0.20
0.17
0.20
1.0
0.86
0.93
0.72
72, 3
32, 88
85, 24
2, 70
76, 22
54, 90
79, 90
RSSQ
0.003
0.02
0.002
0.08
The RSSQ values of the fit between the original ADA and the MMT reconstructed extinction spectra are also included. The nucleus position was in the center of the host particles [Fig. 1a]. The test cases A–D correspond to those in Fig. 4.
Table 2
Comparison Between Known (Anomalous Diffraction Approximation) and Estimated (Modified Mie Theory) Parameters of Randomly Oriented Prolate Nucleated Ellipsoids Including Particle Volume (V), Length (L), Width (W), Nucleus Volume (), Fraction of Nucleotides in Nucleus (), Relative Contribution of First Orientation (; Contribution of Second Orientation was ), and Rotation Angles a
Estimated Parameter
A
B
C
D
E
Known
Estimated
Known
Estimated
Known
Estimated
Known
Estimated
Known
Estimated
20.5
20.5
20.5
20.5
20.5
10.0
10.0
10.0
10.0
10.0
2.0
2.0
2.0
2.0
2.0
1.57
1.57
1.57
1.05
2.1
0.20
0.10
0.05
0.10
0.20
,
,
,
,
,
,
,
,
,
,
RSSQ
The RSSQ values of the fit between the original ADA and the MMT reconstructed extinction spectra are also included. The average [ deviation (S.D.)] estimates were obtained from the interpretation of nine spectra (three replicates for each of the three nucleus positions within the host particle).
Table 3
Comparison Between Known (Anomalous Diffraction Approximation) and Estimated (Modified Mie Theory) Parameters of Randomly Oriented Prolate Nucleated Ellipsoids with Different Aspect Ratios Including Particle Volume (V), Length (L), Width (W), Nucleus Volume (), Fraction of Nucleotides in Nucleus (), Relative Contribution of First Orientation (; Contribution of Second Orientation was ), and Rotation Angles a
Parameter
A
B
C
D
Known
Estimated
Known
Estimated
Known
Estimated
Known
Estimated
20.5
20.5
20.5
20.5
5.0
6.0
7.0
8.0
2.8
2.55
2.4
2.2
1.05
1.05
1.05
1.05
0.10
0.10
0.10
0.10
,
,
,
,
,
,
,
,
RSSQ
The RSSQ values of the fit are also included. The average () values of the parameters were obtained from the interpretation of three replicate spectra for the nucleus position in the center of the host particle [Fig. 1a].
Table 4
Estimates of Structural and Compositional Parameters of Leishmania Major and Leishmania Amazonensis Promastigotes Obtained from Modified Mie Theory Interpretation of Measured UV–Visible Spectra and from Full Ranges of Those Obtained from Microscopy Evaluation of Giemsa-Stained Smearsa
Parameter
(%)
RSSQ
Leishmania major
MMT
,
,
Microscopy
Leishmania amazonensis
MMT
,
,
Microscopy
The estimated parameters were cell volume (V), length (L), width (W), nucleus volume (), total amount of nucleotides in nucleus (), relative contribution of the first orientation (; the contribution of the second orientation was ), and the rotation angles []. The average () values of the parameters were obtained from the interpretation of four replicate spectra for each species. The RSSQ values of the fit between the measured and the MMT reconstructed spectra are also included.
Tables (4)
Table 1
Comparison Between Known (Anomalous Diffraction Approximation) and Estimated (Modified Mie Theory) Parameters of Prolate Nucleated Ellipsoids at Fixed Orientations Including Particle Volume (V), Length (L), Width (W), Nucleus Volume (), Fraction of Nucleotides in Nucleus (), and Relative Contribution of First Orientation (; Contribution of Second Orientation was ), and Rotation Angles a
Estimated Parameter
Known
A
B
Known
C
D
;
;
;
;
20.5
23.0
18.5
20.5
15.3
12.3
10.0
9.7
9.9
5.0
4.8
4.8
2.0
2.1
1.9
2.8
2.5
2.2
1.57
1.50
1.4
1.57
0.64
0.50
0.20
0.17
0.19
0.20
0.17
0.20
1.0
0.86
0.93
0.72
72, 3
32, 88
85, 24
2, 70
76, 22
54, 90
79, 90
RSSQ
0.003
0.02
0.002
0.08
The RSSQ values of the fit between the original ADA and the MMT reconstructed extinction spectra are also included. The nucleus position was in the center of the host particles [Fig. 1a]. The test cases A–D correspond to those in Fig. 4.
Table 2
Comparison Between Known (Anomalous Diffraction Approximation) and Estimated (Modified Mie Theory) Parameters of Randomly Oriented Prolate Nucleated Ellipsoids Including Particle Volume (V), Length (L), Width (W), Nucleus Volume (), Fraction of Nucleotides in Nucleus (), Relative Contribution of First Orientation (; Contribution of Second Orientation was ), and Rotation Angles a
Estimated Parameter
A
B
C
D
E
Known
Estimated
Known
Estimated
Known
Estimated
Known
Estimated
Known
Estimated
20.5
20.5
20.5
20.5
20.5
10.0
10.0
10.0
10.0
10.0
2.0
2.0
2.0
2.0
2.0
1.57
1.57
1.57
1.05
2.1
0.20
0.10
0.05
0.10
0.20
,
,
,
,
,
,
,
,
,
,
RSSQ
The RSSQ values of the fit between the original ADA and the MMT reconstructed extinction spectra are also included. The average [ deviation (S.D.)] estimates were obtained from the interpretation of nine spectra (three replicates for each of the three nucleus positions within the host particle).
Table 3
Comparison Between Known (Anomalous Diffraction Approximation) and Estimated (Modified Mie Theory) Parameters of Randomly Oriented Prolate Nucleated Ellipsoids with Different Aspect Ratios Including Particle Volume (V), Length (L), Width (W), Nucleus Volume (), Fraction of Nucleotides in Nucleus (), Relative Contribution of First Orientation (; Contribution of Second Orientation was ), and Rotation Angles a
Parameter
A
B
C
D
Known
Estimated
Known
Estimated
Known
Estimated
Known
Estimated
20.5
20.5
20.5
20.5
5.0
6.0
7.0
8.0
2.8
2.55
2.4
2.2
1.05
1.05
1.05
1.05
0.10
0.10
0.10
0.10
,
,
,
,
,
,
,
,
RSSQ
The RSSQ values of the fit are also included. The average () values of the parameters were obtained from the interpretation of three replicate spectra for the nucleus position in the center of the host particle [Fig. 1a].
Table 4
Estimates of Structural and Compositional Parameters of Leishmania Major and Leishmania Amazonensis Promastigotes Obtained from Modified Mie Theory Interpretation of Measured UV–Visible Spectra and from Full Ranges of Those Obtained from Microscopy Evaluation of Giemsa-Stained Smearsa
Parameter
(%)
RSSQ
Leishmania major
MMT
,
,
Microscopy
Leishmania amazonensis
MMT
,
,
Microscopy
The estimated parameters were cell volume (V), length (L), width (W), nucleus volume (), total amount of nucleotides in nucleus (), relative contribution of the first orientation (; the contribution of the second orientation was ), and the rotation angles []. The average () values of the parameters were obtained from the interpretation of four replicate spectra for each species. The RSSQ values of the fit between the measured and the MMT reconstructed spectra are also included.