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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 8 — Aug. 1, 2011
  • pp: 2126–2143
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Hypochromicity in red blood cells: an experimental and theoretical investigation

Akihisa Nonoyama, Alicia Garcia-Lopez, Luis H. Garcia-Rubio, German F. Leparc, and Robert L. Potter  »View Author Affiliations


Biomedical Optics Express, Vol. 2, Issue 8, pp. 2126-2143 (2011)
http://dx.doi.org/10.1364/BOE.2.002126


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Abstract

Multiwavelength UV-visible transmission spectrophotometry is a useful tool for the examination of micron-size particle suspensions in the context of particle size and chemical composition. This paper reports the reliability of this method to characterize the spectra of purified red blood cells both in their physiological state and with modified hemoglobin content. Previous studies have suggested the contribution of hypochromism on the particle spectra caused by the close electronic interaction of the encapsulated chromophores. Our research shows, however, that this perceived hypochromism can be accounted for by considering two important issues: the acceptance angle of the instrument and the combined scattering and absorption effect of light on the particles. In order to establish these ideas, spectral analysis was performed on purified and modified red cells where the latter was accomplished with a modified hypotonic shock protocol that altered the hemoglobin concentration within the cells. Moreover, the Mie theory was used to successfully simulate the spectral features and trends of the red cells. With this combination of experimental and theoretical exploration, definition of hypochromism has been extended to two subcategories.

© 2011 OSA

1 Introduction

Multiwavelength ultraviolet-visible (UV-vis) spectrophotometry is a rapid, reliable and effective tool for the qualitative and quantitative characterization of macroscopic particles in suspension [1

1. B. A. Seiber and P. Latimer, “Extinction efficiencies of large latex spheres,” J. Colloid Interface Sci. 23(4), 509–512 (1967). [CrossRef]

5

5. Y. Mattley, G. Leparc, R. Potter, and L. García-Rubio, “Light scattering and absorption model for the quantitative interpretation of human blood platelet spectral data,” Photochem. Photobiol. 71(5), 610–619 (2000). [CrossRef] [PubMed]

]. The optical density (OD) spectrum of turbid systems depends on both its absorption and scattering components [6

6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

,7

7. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, NY, 1981)

]. While an OD transmission spectrum of a small chromophore in solution is composed mainly of absorption, large particles in a suspension exhibit more pronounced scattering along with absorption [6

6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

8

8. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, NY, 1969)

]. Such properties make suspended particle systems more complex to model in terms of their physical attributes and make interpretation of the spectrum equally problematic. The light scattering theory of electromagnetic radiation has been shown to provide an effective approach to examining the particle suspensions including polymers [9

9. L. H. Garcia-Rubio and N. Ro, “Detailed copolymer characterization using ultraviolet spectroscopy,” Can. J. Chem. 63(1), 253–263 (1985). [CrossRef]

], molecular aggregates [10

10. V. A. Bloomfield, “Static and dynamic light scattering from aggregating particles,” Biopolymers 54(3), 168–172 (2000). [CrossRef] [PubMed]

12

12. L. H. Garcia-Rubio, “Characterization of proteins during aggregation using turbidimetry,” Chem. Eng. Commun. 80(1), 193–210 (1989). [CrossRef]

], and microorganisms [13

13. A. A. Kokhanovskii, “Absorption and scattering of light by large layered ellipsoidal particles,” Opt. Spektrosk. 71(2), 351–354 (1991).

15

15. A. L. Koch and E. Ehrenfeld, “Th size and shape of bacteria by light scattering measurements,” Biochim. Biophys. Acta 165(2), 262–273 (1968). [PubMed]

]. Successful use of the theory to model multiwavelength spectra of particles requires the knowledge of several important parameters including the chemical composition, particle number, particle size, and particle size distribution (PSD), all of which can be acquired experimentally.

From a clinical standpoint, a rapid and dependable blood screening method for determining hematologic parameters and detecting abnormalities that surpasses current technology would be medically useful. Accurately interpreted multiwavelength UV-vis technology shows the promise of providing such improvements. Whole blood is a complex particle suspension with erythrocytes (red blood cells [RBC]) being the major particle component (~45% v/v) [16

16. E. Beutler, M. A. Lichtman, B. S. Coller, and T. J. Kipps, Williams Hematology. Fifth Ed. (McGraw-Hill, Inc., New York, NY 1995).

]. The erythrocytes contain mainly hemoglobin, a strongly chromophoric protein that constitutes approximately 98% (w/w) of the total encapsulated protein [16

16. E. Beutler, M. A. Lichtman, B. S. Coller, and T. J. Kipps, Williams Hematology. Fifth Ed. (McGraw-Hill, Inc., New York, NY 1995).

]. The optically dense nature and the abundance of erythrocytes make it the focus for the spectral characterization of whole blood.

In order to obtain a more comprehensive understanding of whole particle absorption and scattering on a macroscopic level, a combination of experimental techniques and mathematical modeling was used to examine data on the spectral characteristics of erythrocytes. Studies had indicated the significance of hemoglobin concentration on the red cell spectrum [17

17. M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37(31), 7410–7418 (1998). [CrossRef] [PubMed]

,18

18. A. N. Yaroslavsky, A. V. Priezzhev, J. Rodriguez, I. V. Yaroslavsky, and H. Battarbee, Handbook of Optical Biomedical Diagnostics, Ch 2, Edited by Tuchin, V. V. (SPIE Press, Bellingham, WA 2002).

]. Thus, the strategy of this research has been to explore the optical behavior of dilute isolated red cells not only at physiological hemoglobin levels (33% w/v), but as cells modified to contain reduced hemoglobin concentrations. Modeling the red cell spectra using the theory of electromagnetic radiation to account for the combined absorption and scattering components of the spectra provides the ability to predict qualitative spectral changes by manipulating important parameters such as the hemoglobin concentration and particle size to successfully estimate a spectrum that is in good agreement with experimental data [6

6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

,8

8. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, NY, 1969)

]. In order to achieve this level of realization, it is important to understand both how the data is obtained and processed, and to make informed assumptions about the intermolecular interactions of the hemoglobin under physiologically concentrated conditions. Hence, two important issues have been considered in this investigation: 1) hypochromism and 2) instrumental setup.

Hypochromism, or more appropriately observed hypochromism is a general term used to describe the attenuation of the absorption component (and hence that of the observed extinction coefficient) typically associated with the presence of a chromophore in high concentrations [19

19. V. I. Danilov and S. N. Volkov, “Quantum-mechanical study of the hypochromic effect in polynucleotides. Intra- and interstrand interaction contributions,” Biopolymers 14(6), 1205–1212 (1975). [CrossRef] [PubMed]

,20

20. M. Weissbluth, “Hypochromism,” Q. Rev. Biophys. 4(01), 1–34 (1971). [CrossRef] [PubMed]

]. Historically, certain strongly absorbing chromophores capable of close association have been shown to exhibit molecular hypochromism, a reduction in the absorption when the molecules are in close proximity of one another [20

20. M. Weissbluth, “Hypochromism,” Q. Rev. Biophys. 4(01), 1–34 (1971). [CrossRef] [PubMed]

]. The phenomenon has been suggested to be present in strongly absorbing biological constituents such as chlorophyll [21

21. L. N. M. Duyens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19(1), 1–12 (1956). [CrossRef] [PubMed]

,22

22. P. Latimer, “The deconvulation of absorption spectra of green plant material-improved corrections for the sieve effect,” Photochem. Photobiol. 38(6), 731–734 (1983). [CrossRef]

], polynucleotides [23

23. I. Tinoco Jr., “Hypochromism in polynucleotides,” J. Am. Chem. Soc. 82(18), 4785–4790 (1960). [CrossRef]

], and hemoglobin [24

24. R. A. Macrae, J. A. McCLURE, and P. Latimer, “Spectral transmission and scattering properties of red blood cells,” J. Opt. Soc. Am. 51(12), 1366–1372 (1961). [CrossRef] [PubMed]

,25

25. N. L. Vekshin, “Screening hypochromism in molecular aggregates and biopolymers,” J. Biol. Phys. 25(4), 339–354 (1999). [CrossRef]

]. In the most well studied system, polynucleotides, the molecular hypochromic effect has been explained in terms of absorptive distortions due to molecular dipolar interactions [21

21. L. N. M. Duyens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19(1), 1–12 (1956). [CrossRef] [PubMed]

] or the physical overlap of π orbitals of stacked chromophores [26

26. T. A. Hoffmann and J. Ladik, “Some remarks on the hypochromicity of polynucleotides,” J. Theor. Biol. 6(1), 26–32 (1964). [CrossRef] [PubMed]

]. It has also been attributed to the screening of radiation by adjacent molecules [27

27. N. L. Vekshin, “Screening hypochromism of biological macromolecules and suspensions,” J. Photochem. Photobiol. B 3(4), 625–630 (1989). [CrossRef]

]. Regardless of the mechanism, the fundamental cause of the hypochromism of the polynucleotides stems from their close, stacked nature. This fixed juxtaposition of the nucleotide bases has been shown to evoke a hypochromic effect of up to 28% (λmax = 260 nm) for an oligoadenine [28

28. N. L. Vekshin, “Screening hypochromism of chromophores in macromolecular biostructures,” Biofizika 44(1), 45–55 (1999).

] or up to 60% for a helical polynucleotide [29

29. H. DeVoe and I. Tinoco Jr., “The hypochromism of helical polynucleotides,” J. Mol. Biol. 4(6), 518–527 (1962). [CrossRef] [PubMed]

]. For hemoglobin in erythrocytes, Vekshin (1999) reported a decrease in absorption of up to 70% (λmax ~415nm) [24

24. R. A. Macrae, J. A. McCLURE, and P. Latimer, “Spectral transmission and scattering properties of red blood cells,” J. Opt. Soc. Am. 51(12), 1366–1372 (1961). [CrossRef] [PubMed]

]. Contrary to the closely packed and relatively fixed nucleotides of a double helix where the partially stacked bases are in Van der Waals contact [30

30. D. Voet and J. G. Voet, Biochemistry, 3rd ed. (Wiley, Hoboken, NJ 2004), Vol. 1.

], hemoglobin encapsulated in red blood cells presumably exist as independent proteins with their intermolecular distance estimated to be 62–75 Å (approximately the width of one molecule) [31

31. J. Bateman, S. S. Hsu, J. P. Knudsen, and K. L. Yudowitch, “Hemoglobin spacing in erythrocytes,” Arch. Biochem. Biophys. 45(2), 411–422 (1953). [CrossRef] [PubMed]

]. Under such conditions, random collisions are prevalent but the effect of organized molecular hypochromism is perhaps questionable.

1.1. Experimental approach

A protocol for the red cell permeabilization (by hypotonic shock) experiments was established where the conditions of the modifications were controlled in such a manner so that the resulting concentration of the encapsulated hemoglobin could be manipulated as desired. Similar methods have been reported of using hypotonic exchange to render red blood cells transiently permeable to enable the passing of high-molecular weight molecules across the membrane [36

36. R. F. Baker, “Entry of ferritin into human red cells during hypotonic haemolysis,” Nature 215(5099), 424–425 (1967). [CrossRef] [PubMed]

39

39. G. P. Sartiano and R. L. Hayes, “Hypotonic exchange-loading of erythrocytes. II. introduction of hemoglobins S and C into normal red cells,” J. Lab. Clin. Med. 89(1), 30–40 (1977). [PubMed]

]. In contrast, the aim of our modified protocol was to allow the hemoglobin to permeate out of the cells to different degrees, achieving resealed cell samples over a range hemoglobin mass fractions. While the erythrocytes are suspended in an isotonic phosphate buffered saline (PBS), the internal osmotic pressure (Pi) is constant with that of the external medium (Pe). When a hypotonic buffer is introduced to the cells (Pi > Pe), basic colligative property states that the water will flow into the cell to achieve equilibrium. If the buffer is sufficiently hypotonic, the force of the expanding cell membrane will initiate transient pores of 200–500 Å to allow the hemoglobin to pass out of the cell [39

39. G. P. Sartiano and R. L. Hayes, “Hypotonic exchange-loading of erythrocytes. II. introduction of hemoglobins S and C into normal red cells,” J. Lab. Clin. Med. 89(1), 30–40 (1977). [PubMed]

]. In order to reseal the cells, the osmotic pressure of the medium is reversed such that the pores are closed and the system returns to osmotic equilibrium. The resulting encapsulated hemoglobin concentration of the resealed cells is controlled by the volume of the administered hypotonic buffer and the duration of the hypotonic shock. It has been suggested that of the initial cell population, approximately 45–60% of the permeabilized cells maintain the capability reseal depending on the temperature of the experiment [40

40. H. Bodemann and H. Passow, “Factors controlling the resealing of the membrane of human erythrocyte ghosts after hypotonic hemolysis,” J. Membr. Biol. 8(1), 1–26 (1972). [CrossRef] [PubMed]

]. The ability obtain encapsulated hemoglobin concentrations from physiological values (~0.33 mass fraction) down to very low mass fractions of ~0.05 provides a valuable opportunity for the fundamental investigation of hypochromism.

2. Materials and methods

2.1. Erythrocyte harvesting

EDTA-treated whole blood units from human donors were obtained by gracious contribution from the Florida Blood Services (St. Petersburg, FL). Typically, the blood samples were used for experiments within 48 hours of the donation. The erythrocytes were isolated from each unit by a standard two-step protocol performed by blood bank personnel. The first was a leukocyte depletion step in which the whole blood unit was passed through a standard leuko-reducing filter (Sepacell Pre-Storage Leukocyte Reduction Set for Red Cells, Baxter Healthcare Corp., Fenwal Division, IL). The second step was a thorough washing that removed platelets and replaced the plasma and its components with isotonic (0.9%, pH 7.0-7.2) phosphate buffered saline (PBS) (Nerl Diagnostics, RI) by employing cycles of centrifugation (1500 x g) and re-suspension in PBS.

2.2. Hypotonic modification of erythrocytes

Hypotonic permeation/restoration of red cells was accomplished using a modified version of previously published procedures [40

40. H. Bodemann and H. Passow, “Factors controlling the resealing of the membrane of human erythrocyte ghosts after hypotonic hemolysis,” J. Membr. Biol. 8(1), 1–26 (1972). [CrossRef] [PubMed]

,41

41. J. F. Hoffman, “Physiological characteristics of human red blood cell ghosts,” J. Gen. Physiol. 42(1), 9–28 (1958). [CrossRef] [PubMed]

]. Briefly, the washed red cells (~5 ml) were gently packed by centrifugation for approximately 5 minutes. The packed cells were then carefully aliquotted to varying volumes of hypotonic 7 mM PB (phosphate buffer (pH 7.2)). For example the ratios of hypotonic buffer volume to packed cell volume ranged from 0.75:1 to 8:1. The higher the hypotonic buffer volume, the lower the resulting concentration of the hemoglobin was in the resealed cells. In order to obtain the most dilute hemoglobin concentrations, the packed cells were treated with large amounts of hypotonic buffer and kept in ice for 20 minutes. Following the permeation and equilibration of the cells, a high concentration PBS (typically 1.0–2.0%) was used to adjust the sample tonicity back to 0.9% and the cells were allowed to reseal for 45 minutes in 37°C. The restored cells were harvested via centrifugation and washing (three cycles). After the third washing, the packed cells were re-suspended in isotonic PBS to an approximate volume ratio of 1:1 and kept at room temperature during the spectrophotometric analysis. The samples were typically analyzed within an hour post-preparation. Spectral reproducibility of the samples was confirmed by performing replicates of the resealing experiment in parallel reaction vessels.

2.3. Spectrophotometric analysis of whole blood and resealed cells

Multiwavelength UV-visible spectrophotometric data (190–1100 nm) were collected for whole blood and washed red cell samples which were diluted to 4000 cells/μl in isotonic PBS. This is a concentration that was determined to give the maximum intensity for the optical density without departing from the linear range of the instrument (upper OD limit ~1.2). The Agilent 8453 diode array spectrophotometer was used to acquire a majority of the data and has an acceptance angle of approximately 2°. The integration time (time of scan) was adjusted to 15 seconds with spectra being acquired 10 times in one second, hence the resulting spectra was an average of 150 scans. Samples were read in a standard 3.5 ml quartz cuvette with a 1 cm pathlength (Starna Cells Inc., CA) at room temperature. Prior to sampling, the spectrophotometer was first blanked to correct for ambient light conditions. The sample was then solvent-corrected by taking a spectrum of approximately 2 ml of the solvent and programming the software to subtract this solvent spectrum from each scanned sample. Suspensions of resealed red cells were treated in the same manner as unmodified red cells for consistency.

2.4. Diffuse transmission spectra

Diffuse spectra were obtained using the Perkin-Elmer Lambda 900 (Perkin-Elmer, CT) spectrophotometer. The sample cuvette was placed in front of an integrating sphere module and the diffuse spectra was acquired by the light being transmitted across the sphere (acceptance angle > 2°). The Perkin-Elmer Lambda 18 fitted with an integrating sphere module (RSA-PE-18, Labsphere, NH) was used to collect all of the scattered light by the cell suspension. The spectra acquired by the three modes of data collection were compared and analyzed for a better understanding of instrumental configuration.

2.5. Standard hematology analysis

Blood samples were also examined using a hematology analyzer model 9010+ (Serono-Baker, PA) for corroboration with spectral data. The instrument uses an impedance based technology for cell counting and provides parameters such as red blood cell counts, mean corpuscular volume (MCV), hematocrit (HCT), and mean corpuscular hemoglobin concentration (MCHC). The hematology analyzer provides independent corroborating data for the spectroscopy methods.

3. Theory

3.1. Angular scattering predictions

  • Macroscopic hypochromicity which is due to changes in scattered light and as consequence is proportional to the size of the scattering elements.
  • Microscopic or molecular hypochromicity which is due to the electronic interactions resulting from close proximity of chromophoric groups and therefore a function of the chromophore concentration within the particle.

Based on the above definitions, a chromophoric group within a particle (i.e., hemoglobin in red blood cells) will experience hypochromicity when the observed absorption coefficient of the encapsulated chromophore is smaller than the absorption coefficient of the same chromophore in dilute solution. The implication of dilute solution is that, statistically, the likelihood of one molecule screening other molecules is negligible. Given that finite acceptance angle detectors admit a considerable amount of scattered light, to assess hypochromicity the interpretation of the spectral data should be done within the context of a scattering model.

3.2. Mie theory

First published in 1907, Mie theory provides an exact solution to Maxwell’s equations for spherical particles [6

6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

8

8. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, NY, 1969)

] and contains information on the refractive index and the absorption coefficient of the materials constituting the particles, as well as, on the absorption and scattering components of the transmitted light. The material properties are defined through the complex index of refraction m(λ) such that:

m(λ)=n(λ)+iκ(λ)n0(λ)
(1)

where n(λ) is the refractive index of the particle, n0(λ) is the refractive index of the medium, and κ(λ) is the absorption coefficient of the particle; n(λ) and κ(λ) constitute the optical properties of the particle. The equation that relates the particle size and the complex refractive index to the absorption and scattering components of the transmitted light at a given wavelength (τ(λ)) is given by:

τ=Np0π4D2Qsca(α,m(λ))f(D)dD+Np0π4D2Qabs(α,m(λ))f(D)dD
(2)

3.3. Simulations of erythrocytes

The Mie-based turbidity calculations described in Eq. (2) (and assuming a 2° acceptance angle) were implemented as a computer program capable of predicting the multiwavelength spectrum of red cells as well as the resealed cells. The simulation model required inputs for parameters that describe the red cell suspension including the cell volume fraction, the cell concentration in the cuvette, the equivalent sphere diameter of the cell, the mass fraction of the protein component, the optical properties (complex refractive index) of the protein component, and the refractive index of the medium. Where applicable, the simulations (as well as experimental data) were normalized by dividing through the entire wavelength range by the area under the curve. The benefits of normalization were to eliminate the effects of concentration on the spectra, and to visually elucidate features of spectra (in comparison to each other) that are not readily apparent on a linear scale.

3.4. Estimation of optical properties

Since hemoglobin is the dominant chromophore in red cells, it was important to obtain reliable optical properties for the protein. Absorption spectra of oxyhemoglobin (Sigma-Aldrich, Inc., St. Louis, MO) were obtained across a broad wavelength range (190–1100 nm) in numerous replicates. Statistical analysis ensured a small standard deviation of the samples (within 1–2% error) and the generated extinction coefficient (ε(λ)) was found to be in good agreement with published data [42

42. UV Atlas of Organic Compounds, (Plenum, New York, NY., 1966), Vol. II.

]. The experimentally obtained ε(λ) was converted to (κ(λ)) (using Bouger’s Law) which was then was used to calculate the refractive index (n(λ)) part of m(λ) (Eq. (1) using the Kramers-Kronig transform [6

6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

] to give the complete optical properties of hemoglobin. Figure 3
Fig. 3 Optical properties of oxyhemoglobin and the medium. Plot of the contents of an optical properties file for oxyhemoglobin over the wavelength range of 190-1100 nm. Plots include the absorption coefficient (κ(λ)) and refractive index (n(λ)) of hemoglobin and the refractive index (n0(λ)) of water.
illustrates the two components of the complex refractive index of hemoglobin as well as the refractive index of water. The latter was obtained from values reported by Thormaehlen et al. (1985) [43

43. I. Thormählen, J. Straub, and U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14(4), 933–945 (1985). [CrossRef]

].

3.5. Sensitivity analysis: varying MCV

The theoretical calculations based on Mie theory were used to examine the sensitivity of the spectra to changes in the cell size (MCV). The simulation varied the MCV over the physiological range of 80–100 fl [44

44. S. B. McKenzie, Textbook of hematology, (Williams and Wilkins, Baltimore, MD, 1996)

]. The MCHC (0.33 mass fraction) and the hematocrit (0.45 volume fraction) were both held constant throughout the simulations. The MCV were represented using the diameters of spheres of equivalent volume (e.g. 80 fl has a spherical diameter of 5.35 x 104 cm). Figure 4
Fig. 4 Simulated spectra of erythrocytes at varying MCV at constant high MCHC (0.33 mass fraction). The MCV was varied in the physiological range of 80–100 fl. The volumes were expressed in the model as the equivalent sphere diameter. The spectra were normalized to eliminate the effects of number based cell concentration.
shows the result of the simulation, normalized to eliminate effects due to particle concentration differences. As the sizes increased, the trend in the optical density showed a flattening of the spectra. The overall features stayed the same but the region above 600 nm showed small but consistent decreases in the slope with increasing particle size. In the 190–600 nm region, the larger cells exhibited a lower OD than the smaller cells. Thus, changes in the MCV within the physiological range had a detectable impact on the simulated spectra when the hemoglobin concentration was high (0.33 mass fraction). Varying the MCV at low MCHCs in the low range of ~0.05 mass fraction (Fig. 5
Fig. 5 Simulated spectra of erythrocytes at varying MCV at constant low MCHC (0.05 mass fraction). The MCV was varied in the physiological range of 80–100 fl. The volumes were expressed in the model as the equivalent sphere diameter. The spectra were normalized to eliminate the effects of number based cell concentration.
) showed smaller changes in the overall spectra compared to the changes seen in Fig. 4. The hemoglobin peaks were well defined with the low MCHC. Overall, the spectra of the different MCVs overlapped across the entire wavelength range with the exception of the two large peaks at 223 and 417 nm. The intensity of these peaks increased with smaller particle sizes, however, the differences were slight.

3.6. Sensitivity analysis: varying MCHC

It was also of interest to examine how variations in the encapsulated hemoglobin concentration would affect the spectra as the MCV was held constant at 80 fl and the MCHC value was varied from the high physiological mass fraction (0.33) down to a mass fraction of 0.05 (Fig. 6
Fig. 6 Simulated spectra of erythrocytes at varying MCHC and constant MCV. The MCV was held constant at 80 fl and the hematrocrit at 0.45 mass fraction. The MCHC was varied from the physiological value of 0.33 (high range) and decreased to medium and low ranges. The spectra are expressed per unit cell.
). The hematocrit value was also held constant at the physiological volume fraction of 0.45 thus the cell number was invariant throughout the simulation. The most compelling trend was the overall increase in the intensity the spectra across the entire wavelength range as the MCHC increased. At the low MCHC values (0.05 and 0.09), the characteristic spectral features of free hemoglobin were visible [singlet at (417 nm) and the doublet (500~600 nm)] (compare to spectrum of free hemoglobin in solution in Figs. 79). Even a small difference in mass fractions between 0.05 and 0.09 lead to a substantially elevated spectrum for the 0.09 mass fraction. The features of the simulated spectrum were markedly affected as the mass fraction hemoglobin was increased from 0.09 to 0.20 with the hemoglobin peaks becoming less prominent. At physiological MCHC (0.33 mass fraction) the overall optical density was increased and further masked the characteristic hemoglobin peaks.

4. Results

4.1. Effects of instrumental setup on the spectra of erythrocytes and hemoglobin

In combination with the simulations, the effect of changes in the MCV and MCHC was also examined experimentally. To this end, it was necessary to first study the effects on the spectrum of spectrophotometer systems that captured different amounts of scattered light. Three commercially available instruments were examined: 1) the Agilent 8453 diode array spectrophotometer captured the transmitted light at a small (2°) acceptance angle, 2) the Perkin-Elmer Lambda 900 spectrophotometer acquired data at larger (> 2°) angles (referred to as diffuse transmission spectra), and 3) the Perkin-Elmer Lambda 18 spectrophotometer was fitted with an integrating sphere module to collect light scattered at all angles by the sample. Figure 6 shows a solid curve representing a spectrum of purified, diluted red cells (4000 cells/μl) containing a physiological hemoglobin concentration (33% w/v) taken with an Agilent spectrophotometer. The dashed curve shows the spectrum of a free hemoglobin solution obtained by lysing the same concentration of red cells in a hypotonic buffer (7mM phosphate buffer), thus the total mass of the hemoglobin was constant between the two samples. All the spectra presented in this section were obtained in replicates of three with good reproducibility. The spectrum of the encapsulated hemoglobin exhibits a significantly greater OD throughout the entire wavelength range compared to the spectrum of the hemoglobin solution, however it lacks the prominent absorption peaks that define free hemoglobin (characteristic hemoglobin peaks at 270, 337, 417, 547, and 575 nm).

Figure 9 represents spectra acquired with an integrating sphere. In this arrangement, essentially all of the scattered light was collected, hence the resulting transmission spectrum reflected solely the absorption component (hence it can be referred to as an absorption spectrum). The baseline of the absorption spectrum of the red cells overlapped that of the spectrum of the true hemoglobin solution, contrary to the elevated nature of the diffuse transmission spectrum shown in Fig. 7. As expected, the hemoglobin peaks of the red cell absorption spectrum were more pronounced with the integrating sphere in comparison to the diffuse red cell spectrum, however, the peaks at 270, 337 and 417 nm were less intense than the peaks of the hemoglobin solution. The doublet at 547 and 575 nm showed good overlap between the whole and lysed red cell spectra. The differences in intensity have been attributed to molecular hypochromicity by several authors [24

24. R. A. Macrae, J. A. McCLURE, and P. Latimer, “Spectral transmission and scattering properties of red blood cells,” J. Opt. Soc. Am. 51(12), 1366–1372 (1961). [CrossRef] [PubMed]

,25

25. N. L. Vekshin, “Screening hypochromism in molecular aggregates and biopolymers,” J. Biol. Phys. 25(4), 339–354 (1999). [CrossRef]

].

4.2. Comparisons of spectra between experimental and simulated data

As indicated in the theory section, Mie theory has no limitations relative to the size of the particles and no constraints relative to the magnitude of the optical properties. Given the size of the red blood cells and that that hemoglobin is a strong chromophore, Mie theory has been used as an effective tool to examine the relationship between the spectral features and the physical parameters of the experimental red cell data. The experimental system was composed of spectra of purified, unmodified red blood cells as well as red cells containing hypotonically altered hemoglobin concentrations. The data was obtained using the 2° acceptance angle to maximize information content of the spectra relative to the absorption and scattering components of the red blood cells. The experimental and simulated spectra were compared closely for consistencies in features and trends. Moreover, replicates of the resealed cells samples indicated reproducibility of relevant hematologic parameters (MCV, MCHC) and the features of the accompanying spectra.

Figure 10
Fig. 10 Experimental data set of purified red cells in the high MCHC range with varying MCV values. The data set is normalized in the 230-900 nm range using the area under the curve method. The MCHC is expressed in mass fractions and the MCV in fl. The free hemoglobin solution spectrum is included as a reference.
is a summary of experimental spectra of purified red blood cells selected for similar MCHCs in the physiological range, but with varying MCVs. The spectra were normalized to eliminate effects due to particle concentration. A free hemoglobin spectrum scaled to fit the normalized plot was included as a reference for comparison of the features. For comparison with the experimental data, the same MCHC/MCV values were simulated using the Mie theory (Fig. 11
Fig. 11 Simulated spectra mimicking the experimental data set from Fig. 6, normalized on a per cell basis. The MCHC is expressed in mass fractions and the MCV in fl. The free hemoglobin solution spectrum is included as a reference.
).

5. Discussion

Historically, hypochromicity has been defined by electronic molecular interactions [21

21. L. N. M. Duyens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19(1), 1–12 (1956). [CrossRef] [PubMed]

,23

23. I. Tinoco Jr., “Hypochromism in polynucleotides,” J. Am. Chem. Soc. 82(18), 4785–4790 (1960). [CrossRef]

] and it has been hypothesized that the same effect is significant in encapsulated systems such as red cells [24

24. R. A. Macrae, J. A. McCLURE, and P. Latimer, “Spectral transmission and scattering properties of red blood cells,” J. Opt. Soc. Am. 51(12), 1366–1372 (1961). [CrossRef] [PubMed]

,25

25. N. L. Vekshin, “Screening hypochromism in molecular aggregates and biopolymers,” J. Biol. Phys. 25(4), 339–354 (1999). [CrossRef]

]. Our study approached this question from the perspective of instrumental configuration and a theoretical interpretation of the combined absorption and scattering phenomenon. It is generally accepted in optics that the angle of acceptance of the detector contributes significantly to the outcome of the spectral features when particles, the size of red blood cells or mitochondria, are present [2

2. G. Crawley, M. Cournil, and D. Di Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91(3), 197–208 (1997). [CrossRef]

,6

6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

,21

21. L. N. M. Duyens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19(1), 1–12 (1956). [CrossRef] [PubMed]

,35

35. P. Latimer, “The influence of photometer design on optical-conformational changes,” J. Theor. Biol. 51(1), 1–12 (1975). [CrossRef] [PubMed]

,45

45. A. L. Koch, “Some calculations on the turbidity of mitochondria and bacteria,” Biochim. Biophys. Acta 51(3), 429–441 (1961). [CrossRef] [PubMed]

]. Although the importance of the detector aperture has been recognized it has not been incorporated as a key parameter in the interpretation of hypochromicity. The comparison of acceptance angles presented herein shows clear differences in the spectra of red cells resulting from the amount of scattered light acquired by the detector. A configuration that collects a large amount of scattered light loses scattering information in the transmission spectrum because the intensities of the scattered light are averaged over the angles accepted by the detector. In contrast, small acceptance angle transmission spectra contain a better balance of absorption and scattering information.

Acknowledgments

The authors would like to acknowledge the Florida Blood Services, St. Petersburg, FL for their resources and expertise in hematology, the University of South Florida Department of Chemistry (Tampa, FL), the Engineering Research Center (ERC) for Particle Science and Technology at the University of Florida (NSF grant #EEC-94-02989), and Los Alamos National Laboratory (contract #W-7406-ENG-36).

References and links

1.

B. A. Seiber and P. Latimer, “Extinction efficiencies of large latex spheres,” J. Colloid Interface Sci. 23(4), 509–512 (1967). [CrossRef]

2.

G. Crawley, M. Cournil, and D. Di Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91(3), 197–208 (1997). [CrossRef]

3.

A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, and V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38(1), 230–235 (1999). [CrossRef] [PubMed]

4.

S. Narayanan, S. Orton, G. F. Leparc, L. H. Garcia-Rubio, and R. L. Potter, “Ultraviolet and visible light spectrophotometric approach to blood typing: objective analysis by agglutination index,” Transfusion 39(10), 1051–1059 (1999). [CrossRef] [PubMed]

5.

Y. Mattley, G. Leparc, R. Potter, and L. García-Rubio, “Light scattering and absorption model for the quantitative interpretation of human blood platelet spectral data,” Photochem. Photobiol. 71(5), 610–619 (2000). [CrossRef] [PubMed]

6.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).

7.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, NY, 1981)

8.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, NY, 1969)

9.

L. H. Garcia-Rubio and N. Ro, “Detailed copolymer characterization using ultraviolet spectroscopy,” Can. J. Chem. 63(1), 253–263 (1985). [CrossRef]

10.

V. A. Bloomfield, “Static and dynamic light scattering from aggregating particles,” Biopolymers 54(3), 168–172 (2000). [CrossRef] [PubMed]

11.

M. Kunitani, S. Wolfe, S. Rana, C. Apicella, V. Levi, and G. Dollinger, “Classical light scattering quantitation of protein aggregates: off-line spectroscopy versus HPLC detection,” J. Pharm. Biomed. Anal. 16(4), 573–586 (1997). [CrossRef] [PubMed]

12.

L. H. Garcia-Rubio, “Characterization of proteins during aggregation using turbidimetry,” Chem. Eng. Commun. 80(1), 193–210 (1989). [CrossRef]

13.

A. A. Kokhanovskii, “Absorption and scattering of light by large layered ellipsoidal particles,” Opt. Spektrosk. 71(2), 351–354 (1991).

14.

C. E. Alupoaei, J. A. Olivares, and L. H. García-Rubio, “Quantitative spectroscopy analysis of prokaryotic cells: vegetative cells and spores,” Biosens. Bioelectron. 19(8), 893–903 (2004). [CrossRef] [PubMed]

15.

A. L. Koch and E. Ehrenfeld, “Th size and shape of bacteria by light scattering measurements,” Biochim. Biophys. Acta 165(2), 262–273 (1968). [PubMed]

16.

E. Beutler, M. A. Lichtman, B. S. Coller, and T. J. Kipps, Williams Hematology. Fifth Ed. (McGraw-Hill, Inc., New York, NY 1995).

17.

M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37(31), 7410–7418 (1998). [CrossRef] [PubMed]

18.

A. N. Yaroslavsky, A. V. Priezzhev, J. Rodriguez, I. V. Yaroslavsky, and H. Battarbee, Handbook of Optical Biomedical Diagnostics, Ch 2, Edited by Tuchin, V. V. (SPIE Press, Bellingham, WA 2002).

19.

V. I. Danilov and S. N. Volkov, “Quantum-mechanical study of the hypochromic effect in polynucleotides. Intra- and interstrand interaction contributions,” Biopolymers 14(6), 1205–1212 (1975). [CrossRef] [PubMed]

20.

M. Weissbluth, “Hypochromism,” Q. Rev. Biophys. 4(01), 1–34 (1971). [CrossRef] [PubMed]

21.

L. N. M. Duyens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19(1), 1–12 (1956). [CrossRef] [PubMed]

22.

P. Latimer, “The deconvulation of absorption spectra of green plant material-improved corrections for the sieve effect,” Photochem. Photobiol. 38(6), 731–734 (1983). [CrossRef]

23.

I. Tinoco Jr., “Hypochromism in polynucleotides,” J. Am. Chem. Soc. 82(18), 4785–4790 (1960). [CrossRef]

24.

R. A. Macrae, J. A. McCLURE, and P. Latimer, “Spectral transmission and scattering properties of red blood cells,” J. Opt. Soc. Am. 51(12), 1366–1372 (1961). [CrossRef] [PubMed]

25.

N. L. Vekshin, “Screening hypochromism in molecular aggregates and biopolymers,” J. Biol. Phys. 25(4), 339–354 (1999). [CrossRef]

26.

T. A. Hoffmann and J. Ladik, “Some remarks on the hypochromicity of polynucleotides,” J. Theor. Biol. 6(1), 26–32 (1964). [CrossRef] [PubMed]

27.

N. L. Vekshin, “Screening hypochromism of biological macromolecules and suspensions,” J. Photochem. Photobiol. B 3(4), 625–630 (1989). [CrossRef]

28.

N. L. Vekshin, “Screening hypochromism of chromophores in macromolecular biostructures,” Biofizika 44(1), 45–55 (1999).

29.

H. DeVoe and I. Tinoco Jr., “The hypochromism of helical polynucleotides,” J. Mol. Biol. 4(6), 518–527 (1962). [CrossRef] [PubMed]

30.

D. Voet and J. G. Voet, Biochemistry, 3rd ed. (Wiley, Hoboken, NJ 2004), Vol. 1.

31.

J. Bateman, S. S. Hsu, J. P. Knudsen, and K. L. Yudowitch, “Hemoglobin spacing in erythrocytes,” Arch. Biochem. Biophys. 45(2), 411–422 (1953). [CrossRef] [PubMed]

32.

J. M. Steinke and A. P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt. 27(19), 4027–4033 (1988). [CrossRef] [PubMed]

33.

D. H. Tycko, M. H. Metz, E. A. Epstein, and A. Grinbaum, “Flow-cytometric light scattering measurement of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24(9), 1355–1365 (1985). [CrossRef] [PubMed]

34.

A. G. Borovoi, E. I. Naats, and U. G. Oppen, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998). [CrossRef]

35.

P. Latimer, “The influence of photometer design on optical-conformational changes,” J. Theor. Biol. 51(1), 1–12 (1975). [CrossRef] [PubMed]

36.

R. F. Baker, “Entry of ferritin into human red cells during hypotonic haemolysis,” Nature 215(5099), 424–425 (1967). [CrossRef] [PubMed]

37.

G. M. Ihler, R. H. Glew, and F. W. Schnure, “Enzyme loading of erythrocytes,” Proc. Natl. Acad. Sci. U.S.A. 70(9), 2663–2666 (1973). [CrossRef] [PubMed]

38.

N. V. B. Marsden and S. G. Ostling, “Accumulation of dextran in human red cells after haemolysis,” Nature 184(4687), 723–724 (1959). [CrossRef] [PubMed]

39.

G. P. Sartiano and R. L. Hayes, “Hypotonic exchange-loading of erythrocytes. II. introduction of hemoglobins S and C into normal red cells,” J. Lab. Clin. Med. 89(1), 30–40 (1977). [PubMed]

40.

H. Bodemann and H. Passow, “Factors controlling the resealing of the membrane of human erythrocyte ghosts after hypotonic hemolysis,” J. Membr. Biol. 8(1), 1–26 (1972). [CrossRef] [PubMed]

41.

J. F. Hoffman, “Physiological characteristics of human red blood cell ghosts,” J. Gen. Physiol. 42(1), 9–28 (1958). [CrossRef] [PubMed]

42.

UV Atlas of Organic Compounds, (Plenum, New York, NY., 1966), Vol. II.

43.

I. Thormählen, J. Straub, and U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14(4), 933–945 (1985). [CrossRef]

44.

S. B. McKenzie, Textbook of hematology, (Williams and Wilkins, Baltimore, MD, 1996)

45.

A. L. Koch, “Some calculations on the turbidity of mitochondria and bacteria,” Biochim. Biophys. Acta 51(3), 429–441 (1961). [CrossRef] [PubMed]

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.1470) Medical optics and biotechnology : Blood or tissue constituent monitoring

ToC Category:
Cell Studies

History
Original Manuscript: May 26, 2011
Revised Manuscript: June 30, 2011
Manuscript Accepted: June 30, 2011
Published: July 1, 2011

Citation
Akihisa Nonoyama, Alicia Garcia-Lopez, Luis H. Garcia-Rubio, German F. Leparc, and Robert L. Potter, "Hypochromicity in red blood cells: an experimental and theoretical investigation," Biomed. Opt. Express 2, 2126-2143 (2011)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-8-2126


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References

  1. B. A. Seiber and P. Latimer, “Extinction efficiencies of large latex spheres,” J. Colloid Interface Sci. 23(4), 509–512 (1967). [CrossRef]
  2. G. Crawley, M. Cournil, and D. Di Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91(3), 197–208 (1997). [CrossRef]
  3. A. N. Shvalov, J. T. Soini, A. V. Chernyshev, P. A. Tarasov, E. Soini, and V. P. Maltsev, “Light-scattering properties of individual erythrocytes,” Appl. Opt. 38(1), 230–235 (1999). [CrossRef] [PubMed]
  4. S. Narayanan, S. Orton, G. F. Leparc, L. H. Garcia-Rubio, and R. L. Potter, “Ultraviolet and visible light spectrophotometric approach to blood typing: objective analysis by agglutination index,” Transfusion 39(10), 1051–1059 (1999). [CrossRef] [PubMed]
  5. Y. Mattley, G. Leparc, R. Potter, and L. García-Rubio, “Light scattering and absorption model for the quantitative interpretation of human blood platelet spectral data,” Photochem. Photobiol. 71(5), 610–619 (2000). [CrossRef] [PubMed]
  6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, NY, 1983).
  7. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, NY, 1981)
  8. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, NY, 1969)
  9. L. H. Garcia-Rubio and N. Ro, “Detailed copolymer characterization using ultraviolet spectroscopy,” Can. J. Chem. 63(1), 253–263 (1985). [CrossRef]
  10. V. A. Bloomfield, “Static and dynamic light scattering from aggregating particles,” Biopolymers 54(3), 168–172 (2000). [CrossRef] [PubMed]
  11. M. Kunitani, S. Wolfe, S. Rana, C. Apicella, V. Levi, and G. Dollinger, “Classical light scattering quantitation of protein aggregates: off-line spectroscopy versus HPLC detection,” J. Pharm. Biomed. Anal. 16(4), 573–586 (1997). [CrossRef] [PubMed]
  12. L. H. Garcia-Rubio, “Characterization of proteins during aggregation using turbidimetry,” Chem. Eng. Commun. 80(1), 193–210 (1989). [CrossRef]
  13. A. A. Kokhanovskii, “Absorption and scattering of light by large layered ellipsoidal particles,” Opt. Spektrosk. 71(2), 351–354 (1991).
  14. C. E. Alupoaei, J. A. Olivares, and L. H. García-Rubio, “Quantitative spectroscopy analysis of prokaryotic cells: vegetative cells and spores,” Biosens. Bioelectron. 19(8), 893–903 (2004). [CrossRef] [PubMed]
  15. A. L. Koch and E. Ehrenfeld, “Th size and shape of bacteria by light scattering measurements,” Biochim. Biophys. Acta 165(2), 262–273 (1968). [PubMed]
  16. E. Beutler, M. A. Lichtman, B. S. Coller, and T. J. Kipps, Williams Hematology. Fifth Ed. (McGraw-Hill, Inc., New York, NY 1995).
  17. M. Hammer, D. Schweitzer, B. Michel, E. Thamm, and A. Kolb, “Single scattering by red blood cells,” Appl. Opt. 37(31), 7410–7418 (1998). [CrossRef] [PubMed]
  18. A. N. Yaroslavsky, A. V. Priezzhev, J. Rodriguez, I. V. Yaroslavsky, and H. Battarbee, Handbook of Optical Biomedical Diagnostics, Ch 2, Edited by Tuchin, V. V. (SPIE Press, Bellingham, WA 2002).
  19. V. I. Danilov and S. N. Volkov, “Quantum-mechanical study of the hypochromic effect in polynucleotides. Intra- and interstrand interaction contributions,” Biopolymers 14(6), 1205–1212 (1975). [CrossRef] [PubMed]
  20. M. Weissbluth, “Hypochromism,” Q. Rev. Biophys. 4(01), 1–34 (1971). [CrossRef] [PubMed]
  21. L. N. M. Duyens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19(1), 1–12 (1956). [CrossRef] [PubMed]
  22. P. Latimer, “The deconvulation of absorption spectra of green plant material-improved corrections for the sieve effect,” Photochem. Photobiol. 38(6), 731–734 (1983). [CrossRef]
  23. I. Tinoco., “Hypochromism in polynucleotides,” J. Am. Chem. Soc. 82(18), 4785–4790 (1960). [CrossRef]
  24. R. A. Macrae, J. A. McCLURE, and P. Latimer, “Spectral transmission and scattering properties of red blood cells,” J. Opt. Soc. Am. 51(12), 1366–1372 (1961). [CrossRef] [PubMed]
  25. N. L. Vekshin, “Screening hypochromism in molecular aggregates and biopolymers,” J. Biol. Phys. 25(4), 339–354 (1999). [CrossRef]
  26. T. A. Hoffmann and J. Ladik, “Some remarks on the hypochromicity of polynucleotides,” J. Theor. Biol. 6(1), 26–32 (1964). [CrossRef] [PubMed]
  27. N. L. Vekshin, “Screening hypochromism of biological macromolecules and suspensions,” J. Photochem. Photobiol. B 3(4), 625–630 (1989). [CrossRef]
  28. N. L. Vekshin, “Screening hypochromism of chromophores in macromolecular biostructures,” Biofizika 44(1), 45–55 (1999).
  29. H. DeVoe and I. Tinoco., “The hypochromism of helical polynucleotides,” J. Mol. Biol. 4(6), 518–527 (1962). [CrossRef] [PubMed]
  30. D. Voet and J. G. Voet, Biochemistry, 3rd ed. (Wiley, Hoboken, NJ 2004), Vol. 1.
  31. J. Bateman, S. S. Hsu, J. P. Knudsen, and K. L. Yudowitch, “Hemoglobin spacing in erythrocytes,” Arch. Biochem. Biophys. 45(2), 411–422 (1953). [CrossRef] [PubMed]
  32. J. M. Steinke and A. P. Shepherd, “Comparison of Mie theory and the light scattering of red blood cells,” Appl. Opt. 27(19), 4027–4033 (1988). [CrossRef] [PubMed]
  33. D. H. Tycko, M. H. Metz, E. A. Epstein, and A. Grinbaum, “Flow-cytometric light scattering measurement of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24(9), 1355–1365 (1985). [CrossRef] [PubMed]
  34. A. G. Borovoi, E. I. Naats, and U. G. Oppen, “Scattering of light by a red blood cell,” J. Biomed. Opt. 3(3), 364–372 (1998). [CrossRef]
  35. P. Latimer, “The influence of photometer design on optical-conformational changes,” J. Theor. Biol. 51(1), 1–12 (1975). [CrossRef] [PubMed]
  36. R. F. Baker, “Entry of ferritin into human red cells during hypotonic haemolysis,” Nature 215(5099), 424–425 (1967). [CrossRef] [PubMed]
  37. G. M. Ihler, R. H. Glew, and F. W. Schnure, “Enzyme loading of erythrocytes,” Proc. Natl. Acad. Sci. U.S.A. 70(9), 2663–2666 (1973). [CrossRef] [PubMed]
  38. N. V. B. Marsden and S. G. Ostling, “Accumulation of dextran in human red cells after haemolysis,” Nature 184(4687), 723–724 (1959). [CrossRef] [PubMed]
  39. G. P. Sartiano and R. L. Hayes, “Hypotonic exchange-loading of erythrocytes. II. introduction of hemoglobins S and C into normal red cells,” J. Lab. Clin. Med. 89(1), 30–40 (1977). [PubMed]
  40. H. Bodemann and H. Passow, “Factors controlling the resealing of the membrane of human erythrocyte ghosts after hypotonic hemolysis,” J. Membr. Biol. 8(1), 1–26 (1972). [CrossRef] [PubMed]
  41. J. F. Hoffman, “Physiological characteristics of human red blood cell ghosts,” J. Gen. Physiol. 42(1), 9–28 (1958). [CrossRef] [PubMed]
  42. UV Atlas of Organic Compounds, (Plenum, New York, NY., 1966), Vol. II.
  43. I. Thormählen, J. Straub, and U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14(4), 933–945 (1985). [CrossRef]
  44. S. B. McKenzie, Textbook of hematology, (Williams and Wilkins, Baltimore, MD, 1996)
  45. A. L. Koch, “Some calculations on the turbidity of mitochondria and bacteria,” Biochim. Biophys. Acta 51(3), 429–441 (1961). [CrossRef] [PubMed]

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