Thermodynamic characterization of RBCs highlights correlations between different hemoglobin types and Band 3 interactions

MOLLIQ-112070; No of Pages 12 Journal of Molecular Liquids xxx (xxxx) xxx

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Thermodynamic characterization of RBCs highlights correlations between different hemoglobin types and Band 3 interactions Francesco Farsaci a, Ester Tellone b,⁎, Annamaria Russo c, Antonio Galtieri b, Silvana Ficarra b a b c

Institute for Chemical and Physical Processes (IPCF-C.N.R.), Via Ferdinando Stagno d'Alcontres 37, Faro Superiore, 98158 Messina, Italy Department of Chemical, Biological, Pharmaceutical and Environmental Sciences, University of Messina, Viale Ferdinando Stagno d'Alcontres 31, 98166 Messina, Italy Istituto Comprensivo Primo, Milazzo, Italy

a r t i c l e

i n f o

Article history: Received 10 September 2019 Received in revised form 24 October 2019 Accepted 4 November 2019 Available online xxxx Keywords: Red blood cells Hemoglobin Non-equilibrium thermodynamics

a b s t r a c t Erythrocytes during their life in the bloodstream are subjected to continuous alterations also related to age, which alter their structure and some functional properties. Some types of erythrocytes such as fetal and sickle possesses particular characteristics both functional and structural that characterize their life. In this paper a thermodynamic characterization of fetal and sickle erythrocytes comparing to normal adults is performed. After an introduction of the Kluitenberg's non equilibrium thermodynamic theory with internal variables, the state and phenomenological coefficients are determined. The interpretation of these physical parameters and the entropy production measure highlighted interesting differences between the erythrocytes tested. This characterization accompanied by biochemical investigations on the functionality of the anion exchange led to focus to hemoglobin as the main promoter of structural and functional variations affecting the deformability of the erythrocytes. In details, fetal and sickle erythrocytes showed lower deformability and greater fragility compared to normal cells. These biophysical-thermodynamic investigations open up new perspectives for the study of blood and its characteristics that can be exploited to improve blood conservation methods through careful monitoring of blood quality control. © 2019 Published by Elsevier B.V.

1. Introduction Over the last decades, the study of dielectric properties in biological tissues has had a large development. The interpretation of dielectric phenomena in biological material in term of interaction at cellular level may be extremely significant for various bio-medical applications such as hyperthermia and non-invasive diagnosis technologies. Therefore, broadening the knowledge acquired to date on the dielectric properties of biological tissues is of great interest both as a diagnostic and therapeutic potential. In this context, blood is one of the most important human body fluid; it absolves various vital functions such as the oxygen delivery and the scoria elimination, the transport of nutrients and the defense against virus and bacteria via the immune system. Some of these physiological functionalities of the blood are susceptible of perturbations based on naturally occurring hemoglobin mutations. Hemoglobin (Hb) is the main protein inside the red blood cells (RBCs), it is a

Abbreviations: Hb, Hemoglobin; RBCs, Red Blood Cells; HbF, Fetal Hemoglobin; HbA, Human Hemoglobin; HPFH, Hereditary Persistence of Fetal Hemoglobin; SCD, Sickle Cell Anemia; 2,3-BPG, 2,3-biphosphoglycerate; HbS, Sickle hemoglobin; HbSS, Homozygous SCD patients; B3, Band 3 protein; cdb3, cytoplasmic domain of Band 3. ⁎ Corresponding author. E-mail address: [email protected] (E. Tellone).

heterotetramer composed of four subunits (two alpha and two beta globins) each associated with a heme group [1]. The major functions of Hb are to transport oxygen from the lungs to peripheral tissues and carbon dioxide from the tissues to the lungs. Therefore, Hb mutations may affect not only the protein structure and functionality but also the RBC and blood functionality and normal physiology. In details, Hb variants, caused by mutations or genetic deletions, are abnormal forms of hemoglobin in which changes occur in the amino acids that make up the globin protein. These changes, influencing the structure of hemoglobin, can affect its functionality and/or its stability. Hundreds of Hb variants are known, however only a few are common and clinically significant, between them the most significant variation is that which affects the beta globin chains. Fetal hemoglobin (HbF) is the most common variant of Hb, it is produced by erythroid precursor cells starting from the sixth week of gestation and it is the main oxygen transport protein in the human fetus during the last seven months of development in the uterus. After birth, HbF persists in the blood of newborn until roughly 2–4 months old then, its synthesis gradually decreases and HbF is replaced by adult hemoglobin A (HbA) [2]. However, HbF has been traced even in healthy adults' blood with concentrations b1% of total hemoglobin; HbF levels may enhance under some specific conditions such as in women during pregnancy or in β-thalassemia, hereditary persistence of fetal hemoglobin (HPFH) and sickle cell anemia (SCD) [3,4]. In contrast to

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the quaternary α2β2 structure of HbA, which is made up of four polypeptide chains two alpha chains of 141 amino acid residues each and two beta chains of 146 amino acid residues each, HbF is composed of two alpha and two gamma chains, commonly denoted as α2γ2. α2γ2 tetramer, while having exactly the same α-chains as HbA, has two γ polypeptide subunits that are highly homologous to the HbA β-chains but with significant structural differences. γ chains differ from β to 39 amino acids, and these substitutions affect principally the biophysical properties of the protein, such as O2 binding affinity. From a functional point of view, fetal red blood cells exhibit higher oxygen affinity than maternal ones due to poor interaction of HbF with 2,3biphosphoglycerate (2,3-BPG) because substitutions altered 2,3-BPG binding to HbF as compared to HbA. In details, differences between the β and γ chains at amino acids 1 and 143 include β1 Valine versus γ1 Glycine and β143 Histidine versus γ143 Serine, these substitutions weaken the link between 2,3-BPG and HbF [5]. During pregnancy, these differences are more important because facilitate the transport of oxygen from maternal erythrocytes to fetal ones. In addition to this role in respiration during fetal life, a variety of clinical observations have shown that HbF expression during postnatal life is beneficial to patients with beta-hemoglobinopathies. In this context, it was shown that in RBCs with HbF the polymerization of sickle cell Hb is strongly reduced, therefore HbF seems to be able to reduce the imbalances of the globin chain in beta-thalassemia erythrocytes [6–8]. β-hemoglobin disorder, known as SCD is one of the most common genetic causes of illness and death in the world [9]. Sickle hemoglobin (HbS) results from a substitution of one amino acid (Glutamic acid) for another amino acid (Valine) at position six of the β-globin polypeptide chain, which leads to a propensity of the HbS to polymerize. Homozygous SCD patients (HbSS) have two copies of this altered Hb while heterozygous HbAS individuals have only one mutated Hb, then in these last the polymerization problems are minor because the normal allele is able to produce half of the normal hemoglobin. In HbSS people, the presence of longchain polymers of HbS distorts the shape of the RBCs which can block small blood vessels, leading to impaired oxygen delivery to tissues. This can result in significant clinical complications including pain crises, respiratory complications, and organ damage. Recently, a comparative characterization on dielectric properties of normal human and pathological Hbs has been studied, in the frequency range from 0.1 to 108 Hz [10]. It was found a close relationship between structure, function and electric properties of proteins. In particular, it has been highlighted in HbS the importance of the amino acid substitution at the sixth position of beta globin chains (β6 Glu- N Val) which resulting in the replacement of two negative charges with two charge free centers may vary the dielectrical properties of the HbS compared to HbA. To verify these conclusions and in part to deepen and amplify the previous study, in this paper new dielectric characterizations on the packed human erythrocytes with hemoglobins A, AS, S and F were carried out at a frequency range of 10−1 to 102 MHz. Further studies on Band 3 protein (B3), specifically on anion flux activity in RBCs, was investigated in order to better analyze the obtained data in the light of the potential linkage existing between Hb structural alterations, B3 functionality and RBC shape. We recall, the anion exchange protein plays an important erythrocyte shape control mechanism in which the cytoplasmic domain of B3 (cdb3) plays a crucial structural role in linking bilayer with the spectrin based skeleton network [11,12]. B3 is the main integral protein of the RBC membrane, it is a multifunctional protein consisting of three domains, C- and N-terminal domains both of them cytoplasmic and a membrane spanning domain which traverses the bilayer and functions as a chloride-bicarbonate exchanger [13]. C-terminal cytoplasmic domain binds carbonic anhydrase II, while the N-terminal domain binds Hb and some glycolitic enzymes and interacts with cytoskeleton and some drugs [13–19]. Hb binding with cdb3 is mostly of electrostatic nature, the interaction causes a sort of bivalent modulation, decreasing the hemoglobin affinity for oxygen and changing the anion flux, probably due to a kind of steric hindrance exercised by Hb

on the intermembrane channel [16]. In addition, the binding of Hb with cdb3 regulates B3 interaction with ankyrin [20]. The binding between B3 and Hb occurs among the first 11 amino acid residues of the N-terminal portion of cdb3. These residues fit into the central cavity of the Hb molecule involving the residues responsible for binding with 2,3-BPG (Val1, His2, His143 and Lys 82) beyond sulphate to Arg104 residue peculiar for the binding with cdb3. Similarly to what is known for 2,3-BPG, the binding of HbF with B3 is weaker due to the substitutions present on the γ chains where in positions 1, 143 and 104 there are Gly, Ser and Lys that respectively replace Val, His and Arg on the β chains in HbA [5]. 2. Materials and methods 2.1. Remarks on Kluitenberg's theory Dielectric experimental data reported in this paper are referred to Laogun et al. (1983) studies [21]. Kluitenberg's theory is based on the idea that the usual variables of non-equilibrium thermodynamics are insufficient to describe some phenomena that occur in a medium when it is subject to perturbation [22]. In particular they are insufficient to describe relaxation dielectric phenomena in a continuous media (we neglect magnetic effects). The formalism of this theory allows to the introduction of the so called phenomenological and state equations which, in a linear approximation, are characterized by the so called phenomenological and state coefficients. These are very important since they are associated to corresponding particular phenomena. All this allows to the introduction of some field vector, depending on the phenomenological and state coefficients, which give a complete vision of the phenomena correlated to polarization and to dielectric relaxation inside the medium. In recent years the non-equilibrium thermodynamics theory formulated by Kluitenberg has been further developed by F. Farsaci et al. founding some correlations between the aforementioned coefficients and directly experimental measurable quantities when the medium is perturbed by a harmonic action; these results have been applied to some biological tissues [10,23–35]. Generally it is assumed that the specific entropy s of a dielectric is a function of the specific internal energy u and the specific polarization p:
 s ¼ s u; p

ð1Þ

Kluitenberg introduced a vector field P(1) and by postulating its independence the Eq. (1) can be re-written as [36–38]:
 s ¼ s u; p; p ð1Þ

ð2Þ

and can be defined the equilibrium electric field E ðeqÞ :

E ðeqÞ ¼ ‐T


 ∂s u; εik ; p; p ð1Þ ∂p

ð3Þ

This allows us to introduce the vector E(ir) as: E ðirÞ ¼ E‐E ðeqÞ

ð4Þ

The vector E(ir) is the irreversible electric field. The introduction of the vector field p(1) allows decomposing the polarization p as the sum of p(1) and of a vector p(0) defined as: p ð0Þ ¼ p‐p ð1Þ

ð5Þ

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and introduce the electric field correlated to P(1) as follows:

E

ð1Þ


 ∂s u; εik ; p; p ð1Þ

¼ ‐T

∂p

ð1Þ

as follows [29]:

ð6Þ

By defining: P ¼ ρp; for isotropic media one can infer the following phenomenological relationships: E ðirÞ ¼ Lð0;0Þ dP dt dP

ð1Þ

dt ¼ Lð1;1Þ E ð1Þ

E ð1Þ ¼ að0;0Þ P‐að1;1Þ P ð1Þ

ð8Þ

ð9Þ ð10Þ

where:
 ð1Þ E p ð1Þ ¼ að0;0Þ ‐að1;1Þ P ð1Þ

ð11Þ

where a(0,0) and a(1,1) are called state coefficients, which have the dimension of reciprocal dielectric constant and which are related, respectively, to elastic and inelastic processes occurring in the medium. Thus, the phenomenological and state coefficients fully characterize the medium by specifying the amount of the type of phenomena that correlate to each of them. Combining some aspects of the linear response theory with the well-known relaxation equation [36–38]: ð0Þ

χ EP E þ dE ð0Þ

ð1Þ

dtþχ

d P

dt¼χ PE P þχ PE dP ð2Þ 2

ð12Þ

PE dt2

where:

ð13Þ

að1;1Þ ðωÞ ¼

½ðΓ 2 ‐Γ 2R Þ þ Γ 1 ωσ 2 ωσ ðΓ 2 ‐Γ 2R Þð1 þ ω2 σ 2 Þ

ð16Þ

Lð1;1Þ ðωÞ ¼

1 σað1;1Þ ðωÞ

ð17Þ

Lð0;0Þ ðωÞ ¼

Γ 2R ω

ð18Þ

where: Γ1 ¼

Γ2 ¼

ε1 ‐ε0 2

ð19Þ

2

ð20Þ

ðε1 ‐ε0 Þ2 þ ε 2 ε2 ðε 1 ‐ε0 Þ2 þ ε2

Here ε1 and ε2 are real and imaginary part, respectively, of the complex dielectric constant and Γ2R is relaxed value of Γ2. It can be shown that the following relations can be obtained for the functions P(0), P(1). E(eq), E(1), and the entropy s(s) [29]: E ðeqÞ Γ1P ¼ að0;0Þ að0;0Þ

ð21Þ

  Γ1 P ð1Þ ¼ P‐P ð0Þ ¼ P 1‐ ð0;0Þ a

ð22Þ

EðeqÞ ¼ Γ 1 P

ð23Þ

P ð0Þ ¼

Eð1Þ ¼

  ð1Þ 1 dP P 0 ω cos ωt Γ1 ¼ 1‐ að0;0Þ Lð1;1Þ dt Lð1;1Þ

σ ð sÞ ¼

! ð1Þ Γ2 P 20 ωLð0;0Þ þ ω cos2 ωt T ð1 þ ω2 σ 2 Þ

ð24Þ

ð25Þ

2.2. Reagents and compounds All reagents were purchased from Sigma-Aldrich (St. Louis, MO, USA). Citrate fresh human blood was obtained from informed healthy donors who declared that they had abstained from all drug treatment for at least one week prior to sample collection, in accordance with the principles outlined in the Declaration of Helsinki.

Citrate blood samples were washed three times with an isoosmotic NaCl solution and treated as previously reported [17]. 2.4. Anion exchanger activity determination: sulphate transport measurement

ð1Þ

χ PE ¼ að0;0Þ þ að1;1Þ Lð0;0Þ Lð1;1Þ ¼ h1 ð2Þ

χ PE ¼ Lð0;0Þ ¼ h2 assuming that P vary as: P ¼ P 0 sin ωt

ð15Þ

2.3. Preparation of erythrocytes

ð0Þ

cEP ¼ að1;1Þ Lð1;1Þ ¼ K 0
 ð0Þ χ PE ¼ að0;0Þ að1;1Þ ‐að0;0Þ Lð1;1Þ ¼ h0

að0;0Þ ðωÞ ¼ Γ 2 þ Γ 1 ωσ ‐Γ 2R ωσ

ð7Þ

where possible cross-effects among dielectric relaxation and other irreversible phenomena were neglected, and it is assumed that the mass density r is constant. The coefficient L(0.0) has the dimension of a resistance and it is connected to irreversible processes related to change of p; while L(1.1) has the dimension of a conductibility and it is related to change of P(1) and of the corresponding intensive variable E(1). However, both (7) and (8) are connected with irreversible changes in the polarization and they give no information on conservative processes. By defining the fields P ð0Þ ¼ ρp ð0Þ, P ð1Þ ¼ ρp ð1Þ one can obtain the following further linear relationships: E ðeqÞ ¼ að0;0Þ P ð0Þ

3

ð14Þ

and by introducing some appropriate approximations, phenomenological and state coefficients can be expressed as functions of the frequency

Cells were incubated in the incubation buffer containing sulphate at 25 °C. At specified intervals 10 μmol of 4-acetamido-4′isothiocyanostilbene-2,2′-disulfonic acid (SITS) stopping medium was added to each test tube containing the RBC suspension. Cells were separated from the incubation medium by centrifugation (J2-HS Centrifuge, Beckman, Palo Alto, CA, USA) and washed three times at 4 °C with a -free medium. After the final washing, the packed cells were lysed with perchloric acid (4%) and distilled water and centrifuged at

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4 °C. Sulphate ions in the supernatant were precipitated by adding glycerol and distilled water (1:1), 4 M NaCl and 1 M HCl solution, and 1.23 M BaCl2·2H2O to obtain a homogeneous barium sulphate precipitate. The intracellular sulphate concentration was measured by spectrophotometry at 425 nm wavelength as reported previously [39]. Using a calibrated standard curve, obtained by measuring the absorbance of suspensions obtained from solutions containing known sulphate amounts, the sulphate concentration was determined [40]. Experimental data of sulfate concentration as a function of time incubation were analyzed by best fitting procedures according to the following equation: C∞(1-e-kt), where C(t) represents sulphate concentration at time t, C∞ intracellular sulphate concentration at equilibrium, and k the rate constant of sulphate influx. 2.5. Statistical analysis

Referring to the Debye model we recall that P(0) is the deformation polarization and P(1) is the orientation polarization. Observing this sector in Fig. 1, we notice a decrease of P(0) trend for the four RBC solutions that reach a minimum at different frequencies, in order: ω F bωS bωAS bωA

ð29Þ

with:

ω F ≅2  106 Hz

ωS ≅6  106 Hz

Differences were analyzed with a two-tailed Student's t-test for unpaired data. The results are expressed as means ±S.D. Probabilities less than or equal to 0.05 were considered as statistically significant. 3. Results 6

8

The frequency range from 10 Hz to 4 ∗ 10 Hz has been investigated and three sectors were identified. These sectors allow to group phenomena with very specific trends in the thermodynamic functions spectra. We indicate the three sectors with A, B and C and define them in the following way:

ð30Þ

107 HzbωAS bωA b2  107 Hz therefore, there is a frequency shift of the minimum values of P(0), with normal RBCs (containing HbA) on the highest frequency. In details, for frequencies below 3 ∗ 106 Hz, P(0) values will be distributed as (see Fig. 1): ð0Þ

ð0Þ

ð0Þ

ð0Þ

P F bP S bP AS bP A

ð31Þ

n
o A Sector ¼ ω : 106 bωb2  107 Hz

ð26Þ

n
o B Sector ¼ ω : 2  107 bωb108 Hz

this relation changes when ω increases until its trend inverts, as we will see in B and C sectors. P(0) minimum values follow these relations:

ð27Þ


 ð0Þ PS

min

n o C Sector ¼ ω : ω N 108 Hz

ð28Þ

We now study the thermodynamic functions in the three sectors:
 A SECTOR 106 bωb2  107 Hz

min


 ð0Þ b P AS

min


 ð0Þ b PA

min

107

9.5x10-1

ð33Þ

108

P(0)AA P(0)AS P(0)F P(0)SS

1.0x100

1.0x100

9.5x10-1

9.0x10-1

9.0x10-1

8.5x10-1

8.5x10-1

8.0x10-1

8.0x10-1 106

ð32Þ

With respect to (31) there is only an exchange of position between RBCs containing HbS (sickle RBCs) and those containing HbF (fetal RBCs), respectively. The description of the curves reported in Fig. 2 is connected to the above, because: Pð1Þ ¼ P−Pð0Þ

106

P(0)


 ð0Þ b PF

107

108

(Hz) Fig. 1. Comparison between normal RBCs AA (black line), RBCsAS (red line), fetal RBCs F (blue line) and sickle RBCs SS (purple line) of deformation polarization P(0) calculated by Eq. (21) as a function of frequency.

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106

107

108

P(1)AA P(1)AS P(1)F P(1)SS

-1

2.0x10

P(1)

5

1.0x10-1

2.0x10-1

1.0x10-1

0.0

0.0

106

107

108

(Hz) Fig. 2. Comparison between normal RBCs AA (black line), RBCsAS (red line), fetal RBCs F (blue line) and sickle RBCs SS (purple line) of orientation polarization P(1) calculated by Eq. (22) as a function of frequency.

Plotting P(0)/P, from (33) follows:

the relation, Inertia I is minor:

Pð1Þ =P ¼ 1−Pð0Þ =P

ð34Þ

therefore, where P(0)/P grows, P(1)/P decreases and vice versa if P N 0. Furthermore, the minimums for P(0)/P become maximum for P(1)/P, the order relation (29) is preserved. While the (31) and (32) relations become: ð1Þ

ð1Þ

ð1Þ

ð1Þ

P A bP AS bP S bP F

ð35Þ

for frequencies lower than 3 ∗ 106 Hz. Also in this case the relation (35) changes as ω increases until it reverses in B and C sectors. Considering relation (32), the minimums become maximum for relation (34) and therefore:
 ð1Þ PA

Max


 ð1Þ b P AS

Max


 ð1Þ b PF

Max


 ð1Þ b PS

Max

ð36Þ

After analyzing Figs. 1 and 2 and from what has been previously discussed, it is highlighted that RBCs with less deformation polarization show orientation polarization greater than the others. A decrease of P(0) values indicates that the number of elements that undergo deformation polarization decreases. Furthermore, RBCs with P(0) values less than other have fewer elements undergoing deformation polarization. An increase of P(1) values means that the elements undergoing orientation polarization increase and similarly, what has been discussed for P(0) is valid. A P (0) decrease may be interpreted as an inability of the cells to follow the trend of the field when frequency increases. In this case, the inertia of the RBC components does not allow their elongation, or rather limits their relative displacements if these are imposed at a certain frequency. The higher the frequency at which they decrease the less inertia (massivity) they have. Instead, the P(0) increase can be ascribed to less and less massive cells (they could be smaller) that manage to follow the variation (always faster) of the field. The curves of Fig. 1 have a very similar trend but shifted in frequency. At low frequencies according to relation (30), in the normal RBCs there are more elements that oscillate deforming compared to the other RBCs. According to

IðRBCA ÞbIðRBCAS ÞbIðRBCS ÞbIðRBC F Þ

ð37Þ

Generally, the frequency shift of curves indicates a massive variation. Similarly Fig. 2 shows the P(1) trend. In this sector P(1) values grow for the four RBCs, until reaching maximum values for frequencies given by the relation (30). Also in this case, there is a shift in frequency of the maximums; P(1) ω b 3 ∗ 106 Hz. P(1) values are distributed according to the relation (35), which changes as the frequency increases until it is reversed in B and C sectors. P(1) values follow the relation (36). Recalling the meaning of P(1), as ω increases an increase of P(1) values indicate an increase of the number of polar molecules following the field, until a maximum value is reached for a certain frequency. As shown in Fig. 2, sickle RBCs have the largest number of polar molecules and then, in decreasing sequence there are those containing HbF, HbAS and HbA. The P(1) maximum value is different for each RBC solution and depends from the frequency value ω, each shift from this maximum results in a P(1) decrease because the polar molecules in RBC solution begin not to follow the course of the field. The RBC solutions for which this occurs at lower frequencies are those with a greater inertia (inertia moment). Then, indicating with I the average moment of inertia for each solution (see Fig. 2): IðAÞ bIðASÞ bIðSÞ bIð FÞ

ð38Þ

Figs. 3, 4, 5, 6 show the a(0,0) and a(1,1) state coefficients for the four solutions. In A sector we note a similar trend for each solution; in detail, a(0,0) values are increasing and a(1,1) values are decreasing. We want to highlight the shift of the intersection point between a(0,0) and a(1,1) for the four solutions at different frequencies according the follow relation: ωS bωAS bω F bωA

ð39Þ

For each solution there is a frequency at which a(0,0) and a(1,1) intersect, i.e. a ωι for which: að0;0Þ ðω1 Þ ¼ að1;1Þ ðω1 Þ

ð40Þ

Since this intersection occurs at different frequencies depending on the considered RBC solution, we can consider this ωι value as a

Please cite this article as: F. Farsaci, E. Tellone, A. Russo, et al., Thermodynamic characterization of RBCs highlights correlations between different hemoglobin types an..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.112070

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106

107

108

8x108

8x108

7x108

7x108

AA

6x108

a(0.0),a(1.1)

5x108

6x108 5x108

a(0.0) a(1.1)

4x108

4x108

3x108

3x108

2x108

2x108

1x108

1x108

0

0

-1x108

-1x108 6

10

7

8

10

10

(Hz) Fig. 3. Comparison between state coefficients a(0,0) (black line) and a(1,1) (red line) calculated by Eqs. (15) and (16) as a function of frequency for normal RBCs AA.

distinctive parameter of the RBC type. Fig. 7 shows the L(1,1) displacement conductivity coefficient associated with the displacement current generated by a change in the P(1) orientation polarization shown in Fig. 8. In A sector, there is a L(1,1) increasing trend for the four RBC solutions, with values clearly higher for the fetal RBCs, according to the relation: ð1;1Þ

LA

ð1;1Þ

bLS

ð1;1Þ

ð1;1Þ

bLAS bL F

ð41Þ

even if L(1,1) and L(1,1) cross in two points. Also in Fig. 8, the displacement S AS current shows an increasing trend for the four solutions. However we observe that, the dP(1)/dt value of the fetal RBCs is initially greater, but at the end of the A sector (i.e. at ω ≅ 2 ∗ 107 Hz) it is smaller than the other RBCs. That is, while the values of RBCs containing HbA, HbAS and HbS grow assuming a trend with the same concavity, (dP(1)/dt)F assumes a different concavity so as to intersect the other curves, starting

7x108

106

from higher values. Fig. 9 shows values for the field E(1); it is possible to observe a regular trend throughout the A sector for the four RBC solutions, curves grow with a change in concavity at the end of the sector: ð1Þ

ð1Þ

ð1Þ

ð1Þ

E F bEA bEAS bES

Fig. 10 shows the values for the EP(1)(1) field associated with orientation polarization P(1). It has a growing trend in the A sector for the four solutions, with a relation: EP Að1Þ ð1ÞbEP ASð1Þ ð1ÞbEP Sð1Þ ð1ÞbEP F ð1Þ ð1Þ

ð43Þ

while EP(1)(1) starting from values higher than the other three solutions intersects them becoming the minor for ω ≅ 2 ∗ 107 Hz. Finally, Fig. 11 shows the production of entropy (or rather the trend of entropy). It is practically the same for the four RBC types in the A sector.

107

108

6x108

7x108 6x108

a(0.0) a(1.1)

5x108 4x108

a(0.0),a(1.1)

ð42Þ

5x108

AS 4x108

3x108

3x108

2x108

2x108

1x108

1x108

0

0 106

107

108

(Hz) Fig. 4. Comparison between state coefficients a(0,0) (black line) and a(1,1) (red line) calculated by Eqs. (15) and (16) as a function of frequency for RBCs AS.

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106

107

108

5x108

5.00E+008

4x108

a(0.0),a(1.1)

7

4.00E+008

a(0.0) a(1.1)

F

3x108

3.00E+008

2x108

2.00E+008

1x108

1.00E+008

0

0.00E+000 106

107

108

(Hz) Fig. 5. Comparison between state coefficients a(0,0) (black line) and a(1,1) (red line) calculated by Eqs. (15) and (16) as a function of frequency for fetal RBCs F.

B SECTOR (2 ∗ 107 b ω b 108) Hz This is the sector in which all the RBC types studied show increasing values of P(0) (see Fig. 1) and decreasing values of P(1) (see Fig. 2). Obviously, the considerations made above on the meaning of P(0) and P(1) and their link with inertia and the inertial moment of the molecules, also apply here. Therefore, molecules with minor inertia and with increasing inertial moments begin to feel the effects of the field as the frequencies increase. The curves intersect and a state is reached where the relations hold (see Figs. 1 and 2): ð0Þ

ð0Þ

ð0Þ

ð0Þ

P A bP AS bP F bP S ð1Þ

ð1Þ

ð1Þ

ð44Þ

ð1Þ

P S bP F bP AS bP A

ð45Þ

106

In other words analyzing the trend of deformation polarization P(0), we can say that when the frequency increases, the number of molecules with lower inertia values following the course of the field increases. While, analyzing P(1) trend we see that, the number of polar molecules following the field decreases because the inertial moment does not allow them to follow quickly enough the field; that is, the field changes direction before the molecule “rotation”. Therefore we can state that, concerning P (0) and P (1) trends the B sector is a “transition” towards a state identified in the C sector. In C sector the molecules of the system are no longer affected by the field which varies too quickly to be followed by them. In this sector, Figs. 3, 4, 5 and 6 show a similar trend both for a(0,0) and a(1,1) coefficients, for the four solutions analyzed; in detail, there is a growth for a (0,0) coefficient and a decrease for a (1,1) coefficient.

107

108

8x108

8x108

7x108

SS

6x108

a(0.0),a(1.1)

a(0.0) a(1.1)

7x108 6x108

5x108

5x108

4x108

4x108

3x108

3x108

2x108

2x108

1x108

1x108

0

0 106

107

108

(Hz) Fig. 6. Comparison between state coefficients a(0,0) (black line) and a(1,1) (red line) calculated by Eqs. (15) and (16) as a function of frequency for sickle RBCs SS.

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106

107

108

L(1,1)

100

100

10-1

L(1,1) AA L(1,1) AS L(1,1) F L(1,1) SS

10-2

10-1

10-2

106

107

108

(Hz) Fig. 7. Comparison between normal RBCs AA (black line), RBCs AS (red line),fetal RBCs F (blu line) and sickle RBCs SS (purple line) of state coefficient L(1,1) calculated by Eq. (17) as a function of frequency.

The displacement conductivity coefficient grows in this sector with the following relation (see Fig. 7): ð1;1Þ

ð1;1Þ

LAS bLA

ð1;1Þ

bL F

ð1;1Þ

bLS

ð46Þ

The displacement current values analyzed for the RBCs show a similar growth trend (see Fig. 8), in this case the differences found are minimal and not significant. However, it is possible to appreciate these

dP(1)/dt

106

differences in A sector, as can be seen from relation (41). The E(1) field grows for the four solutions and it is possible to notice some differences: E1F bE1A ≅E1AS bE1S

ð47Þ

Fig. 10 shows the trend of the E(1) P(1) field associated with the orientation polarization P(1). In this sector (2 ∗ 107 b ω b 6 ∗ 107 Hz) the

107

108

109

109

108

108

107

107

dP(1)/dt AA dP(1)/dt AS dP(1)/dt F dP(1)/dt SS

106

105

104

106

105

104 106

107

108

(Hz) Fig. 8. Comparison between normal RBCs AA (black line), RBCs AS (red line), fetal RBCs F (blu line) and sickle RBCs SS (purple line) of the variation of P(1) calculated by Eq. (8) as a function of frequency perturbation.

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F. Farsaci et al. / Journal of Molecular Liquids xxx (xxxx) xxx

106 109

107

9

108 109

(1)

E AA E(1) AS E(1) F E(1) SS

108

E(1)

108

107

107

106

106 106

107

108

(Hz) Fig. 9. Comparison between normal RBCsAA (black line), RBCsAS (red line), fetal RBCsF (blu line) and sickle RBCsSS (purple line) of the field E(1) calculated by Eq. (24) as a function of frequency of perturbation.

shown in Fig. 11, in this sector there is the relation:

functions are growing, with a relation of the type:

σ F bσ AS bσ AA bσ SS

EP F ð1Þ ð1ÞbEP Að1Þ ð1ÞbEP ASð1Þ ð1Þb EP Sð1Þ ð1Þ

ð48Þ

In detail, the values of sickle RBCs grow up to about ω where the maximum is found; normal RBCs and those containing HbAS grow up to about ω ≅ 6 ∗ 107 Hz where the maximum is equal for both, but lower than that of the sickle RBCs. Fetal RBCs also have a maximum value around ω ≅ 9 ∗ 107 Hz but less than all other maxima found. As

2x107

106

ð49Þ

C SECTOR (ω N108 Hz) In this sector, the increasing values of P(0) indicate an increase in the number of molecules (with less inertial moment) that follow the field. The field acts by polarizing the molecules through deformation as shown in Fig. 1: ð0Þ

ð0Þ

ð0Þ

ð0Þ

P A bP AS bP F bP S

107

108

1x107

ð50Þ

2x107

1x107

0

0

E(1) AA p E(1) p

(1)

(1)

E(1) AS p (1)

-1x107

E E

-2x107

(1) p(1) (1) p(1)

-1x107

F SS

-3x107

-2x107

-3x107 106

107

108

n (1) Fig. 10. Comparison between normal RBCsAA (black line), RBCsAS (red line), fetal RBCsF (green line) and sickle RBCsSS (blue line) of the field E(1) and P(1) associated to the polarization P calculated by Eq. (11) as a function of frequency perturbation.

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F. Farsaci et al. / Journal of Molecular Liquids xxx (xxxx) xxx

0 1.5x1016

1x108

2x108

3x108

4x108

5x108 1.5x1016

(s)

AA AS (s) F (s) SS (s)

1.0x1016

(s)

1.0x10

16

5.0x1015

5.0x1015

0.0

0.0

0

1x108

2x108

3x108

4x108

5x108

(Hz) Fig. 11. Comparison between normal RBCsAA (black line), RBCsAS (red line), fetal RBCsF (blu line) and sickle RBCsSS (purple line) of the trend of entropy production σ(s) calculated by Eq. (21) as a function of frequency perturbation.

Sickle RBCs have the highest number of molecules that polarize by deformation (they are less “massive”). In this sector P(1) has an opposite trend (see Fig. 2), it decreases indicating that the number of polar molecules following the field decreases; in other words, the moment of inertia does not allow the molecules to oscillate at those frequencies and is: ð1Þ

ð1Þ

ð1Þ

ð1Þ

P S bP F bP AS bP A

ð51Þ

Figs. 3, 4, 5 and 6 show an almost constant trend of the values of a(1,1) and a strongly increasing trend of the values of a(0,0). Recalling that a(0,0) has the dimensions of the reciprocal of the dielectric constant, we can state that an increase of a(0,0) favors the determination of the electric field associated with it, i.e. of E(eq) = a(0,0)P(0). In this sector the displacement conductivity reaches a maximum value for the RBCs around ω = 2 ∗ 108 Hz (the same for all) and then decreases (see Fig. 7). ð1;1Þ

LS

ð1;1Þ

ð1;1Þ

bLAS bLA

ð1;1Þ

bL F

ð52Þ

In other words, fetal RBCs have a coefficient of displacement conductivity greater than the others (see Fig. 7). Fig. 8 shows no significant differences in the values of the displacement current between the RBCs, therefore we can consider this value almost the same for all the solution tested. While, Fig. 9 shows clear differences in E(1) values, detectable through the relation: ð1Þ

ð1Þ

ð1Þ

ð1Þ

E F bEA bEAS bES

ð53Þ

the associated physical meaning will be confined to the same sector, making the exposure more synthetic. The same is true for P(1) and the maximum values achieved for the four types of RBC tested. They coincide in frequency with the minima found for P(0). Moreover, in this sector there is the intersection of a(0,0) and a(1,1) whose frequency shift may be considered as a peculiar phenomena for each RBC. The B sector can be considered a transition towards the sector where the intersection is between the field and the RBC fades (see Figures) except for the production of entropy which shows considerable differences between the RBC types. Fig. 12 shows the measures of anion flux activity in fetal, sickle and adult normal RBCs. The anion exchange was studied evaluating spectrophotometrically the B3 functionality in each type of RBC studied. B3 is one of the most abundant RBC membrane proteins, carries out the electrically neutral exchange of chloride and bicarbonate anions between the inside and the outside of the RBC. Fig. 12 shows an increase of anion exchanger of about double in fetal RBCs and sickle RBCs (rate constant: 0.03 and 0.025 min−1, respectively) compared to normal RBCs (rate constant: 0.012 min−1). In this context, the different B3 functionality observed may be due to the different amino acidic structure of the Hbs inside the RBCs tested. In other words, HbF and HbS partially replaced in amino acid beta chains, may in some way differently modulate

0.04 0.03

The values of the electric field EP(1)1 associated with P(1) are decreasing functions, we have the following relation (see Fig. 10):

0.02

EP F ð1Þ ð1Þb EP ASð1Þ ð1Þ≅EP Að1Þ ð1ÞbEP Sð1Þ ð1Þ

0.01

ð54Þ

The entropy production represented in Fig. 11 shows a substantial difference for ω N 2 ∗ 108 Hz in which range we have a relation equal to (49). Now let's summarize the results obtained in the three sectors. The choice to divide the frequency range studied in three sectors was guided by the trend of the polarization P(0) and P(1). In fact, in A sector the values of P(0) reach minimums and the frequency ωΜ was chosen as the upper end of the interval of ωΜ = 2 ∗ 107 Hz and the minimum is that of the normal RBCs. In doing so, all the minimums for P(0) and

0

Normal RBCs

Fetal RBCs

Sickle RBCs

Fig. 12. Rates of anion influx determined in human Normal, Fetal and Sickle RBCs. For experimental conditions see Materials and methods. Rates are reported in min−1. Data were obtained by fitting experimental data with the equation: C(t) = C∞(1 − e-kt). See Materials and methods for further experimental details.

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F. Farsaci et al. / Journal of Molecular Liquids xxx (xxxx) xxx

the B3 anion flux. In details, B3 functionality in fetal RBCs is certainly affected by the Hb replacement in the binding pocket with cdb3. In this case the weakness of the Hb-B3 bond would promote a different anion exchanger functionality less modulated by Hb. This finding suggests that the fine regulatory mechanism for the anion transport developed at the early stages of life, when HbF is substituted by HbA in adult human RBCs. A different discussion is made for HbS, in this case the replacement is limited at the beta 6 position of Hb (beta6 Glu- N Val) which results in the creation of a hydrophobic patch (Val6) on the protein surface. This condition leads to the aggregation of Hbs into long fibers which are the main cause of the hemolytic anemia. Polymerization occurs prevalently at low oxygen pressure but polymerization of Hbs is found also in partially oxygenated sickle cells. We attribute the alteration of the anion flux to this anomaly. Partially polymerized Hb loses its capacity to modulate the B3 protein flux. In detail, Hb mutated under hypoxic conditions promotes its polymerization and premature denaturation during circulation. This condition leads to the formation of hemicromes which, having a great affinity for the cdb3, cluster on the membrane near the B3. This immobile fraction of B3, interacting with the hemicromes, makes the RBCs more rigid and dense, with a reduction in the duration of the sickle RBCs [41]. By a biophysical point of view, the different anion flux measured may be explained looking to L(1,1) values. In detail, the RBC membrane generates a potential difference between the inside and the outside of the RBC indicated by V. The cytosolic side of the membrane is negatively charged while the outside is positive. The membrane is therefore associated with a set of capacitors of C capacity. Indicating Q the charge on the surface, there will be [34]: C ¼ Q =V it follows that, a change of Q or V implies a change in C. Recalling that in previous papers the relation: Lð1;1Þ ðmeterÞ ¼ ωC was introduced [34]. It is easy to deduce that, a change of L(1,1) leads to a change in C and consequently also of Q and V. Since L(1,1) is different for each RBC, we conclude that there is a variation of Q and V for each RBC tested. In other words, there is a potential difference V between the outside and the inside of the membrane which contributes to the variation of the anionic flux measured for each RBC. 4. Conclusions The kinetic anion analysis and the thermodynamic characterization of the different types of RBCs have revealed interesting differences due to the presence of different Hb variants into the cells studied. Let us recall in this regard the massive and dominant presence of Hb in RBCs (300–380,000,000 molecules per RBC) and the high number B3 of copies on the erythrocyte membrane (1.200.000 copies per RBC). We hypothesize that the differences found certainly attributable to Hbs may have a more complex impact on the entire cell, in particular on the elasticity and deformability of RBC. Wong 1994 proposed a dynamic role for B3 in controlling the form of erythrocytes [42]. Jiang 2013 shows that the cdb3 do not occupy stable positions in the protein, but instead can move relative to each other. These movements influence the control of the erythrocyte shape [43]. Stefanovic et al. 2013 demonstrated that deoxygenation of RBC results in displacement of Ankyrin from B3 with release of the Spectrin/Actin cytoskeleton from the membrane [20]. All this leads to weakening of the membrane-cytoskeletal interactions when Hb is deoxygenated. Our results support what was demonstrated by Stefanovic 2013 and underline the importance of the Hb structure in the modulation of the deformability of the RBC membrane. Particularly in fetal RBCs, HbF binds more weakly to cdb3 and this at a structural level involves a lower deformability of the whole

11

erythrocyte accompanied by greater fragility in respect to normal adult RBCs (adult RBC lifespan is of 120 days, the lifespan of the neonatal erythrocyte is only 60 to 90 days [44]). Different is the situation for sickle RBCs, HbS in fact has an altered structure causing the generation of hemoglobin fibers. These contribute to an alteration of the Hb-cdb3 binding which has long-term repercussions on the deformability of the RBC. These hypotheses are strongly supported by the thermodynamic results that show a change in surface charge density. Huang et al. 2011 found a close correlation between the surface charge density on an aging RBC and its structure and functions from the morphology and the membrane deformability to the intracellular Hb structure and oxidation ability [45]. Our new biophysical-thermodynamic approach provides new answers on RBC functionality and can help improve blood conservation methods through careful monitoring of blood quality control. A broader view of the electrical phenomena manifesting in these samples could derive from measurements at lower frequencies. In this case, with a technique introduced in previous work [27], phenomena of electrical conductivity could be investigated with extrapolations from dielectric measurements. Further thermodynamic developments in these investigations could be obtained by considering the various samples as mixtures [46,47]. Declaration of competing interest The authors declare that there are no conflicts of interest and that the manuscript has neither been published nor is it currently under consideration for publication either in whole or in part, by any other journal. References [1] M.F. Perutz, M.G. Rossmann, A.F. Cullis, H. Muirhead, G. Will, A.C. North, Structure of haemoglobin: a three-dimensional Fourier synthesis at 5.5-A. resolution, obtained by X-ray analysis, Nature 185 (4711) (1960) 416–422. [2] O. Hofmann, T. Brittain, Ligand binding kinetics and dissociation of the human embryonic haemoglobins, Biochem. J. 315 (1) (1996) 65–70. [3] B.G. Forget, Molecular basis of hereditary persistence of fetal hemoglobin, Ann. N. Y. Acad. Sci. 850 (1998) 38–44. [4] M.G. Olsson, M. Centlow, S. Rutardóttir, I. Stenfors, J. Larsson, B. Hosseini-Maaf, M.L. Olsson, S.R. Hansson, B. Akerström, Increased levels of cell-free hemoglobin, oxidation markers, and the antioxidative heme scavenger alpha(1)-microglobulin in preeclampsia, Free Radic. Biol. Med. 48 (2) (2010) 284–291. [5] L. Manca, B. Masala, Disorders of the synthesis of human fetal hemoglobin, IUBMB Life 60 (2) (2008) 94–111. [9] D.J. Weatherall, Genetic variation and susceptibility to infection: the red cell and malaria, Br. J. Haematol. 141 (2008) 276–286. [10] F. Farsaci, E. Tellone, A. Galtieri, S. Ficarra, A new model with internal variables for theoretical thermodynamic characterization of hemoglobin: entropy determination and comparative study, J. Mol. Liq. 279 (2019) 2–639. [11] V. Bennett, P.J. Stenbuck, Association between ankyrin and the cytoplasmic domain of band 3 isolated from the human erythrocyte membrane, J. Biol. Chem. 255 (13) (1980) 6424–6432. [12] J.A. Walder, R. Chatterjee, T.L. Steck, P.S. Low, G.F. Musso, E.T. Kaiser, P.H. Rogers, A. Arnone, The interaction of hemoglobin with the cytoplasmic domain of Band 3 of the human erythrocyte membrane, J. Biol. Chem. 259 (1984) 10238–10246. [13] M.J. Tanner, Band 3 anion exchanger and its involvement in erythrocyte and kidney disorders, Curr. Opin. Hematol. 9 (2) (2002) 133–139. [14] D. Zhang, A. Keyatkin, J.T. Bolin, P.S. Low, Blood 96 (2000) 2925–2933. [15] D. Sterling, R.A. Reithmeier, J.R. Casey, A transport metabolon: functional interaction of carbonic anhydrase II and chloride/bicarbonate exchangers, J. Biol. Chem. 276 (2001) 47886–47894. [16] A. Galtieri, E. Tellone, L. Romano, F. Misiti, E. Bellocco, S. Ficarra, A. Russo, D. Di Rosa, M. Castagnola, B. Giardina, I. Messana, Band-3 protein function in human erythrocytes: effect of oxygenation-deoxygenation, Biochim. Bioph. Acta 1564 (2002) 214–218. [17] E. Tellone, S. Ficarra, B. Giardina, R. Scatena, A. Russo, M.E. Clementi, F. Misiti, E. Bellocco, A. Galtieri, Oxidative effects of gemfibrozil on anion influx and metabolism in normal and beta-thalassaemic erythrocytes, physiological implications, J. Memb. Biol 224 (1–3) (2008) 1–8. [18] E. Tellone, S. Ficarra, R. Scatena, et al., Influence of gemfibrozil on sulfate transport in human erythrocytes during the oxygenation-deoxygenation cycle, Physiol. Res. 57 (4) (2008) 621–629. [19] D. Sterling, R.A. Reithmeier, J.R. Casey, A transport metabolon. Functional interaction of carbonic anhydrase II and chloride/bicarbonate exchangers, J. Biol. Chem. 276 (51) (2001) 47886–47894.

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