Erythrocyte aggregation under high pressure studied by laser photometry and mathematical analysis

Colloids and Surfaces B: Biointerfaces 140 (2016) 189–195

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Erythrocyte aggregation under high pressure studied by laser photometry and mathematical analysis Yoshiharu Toyama ∗ , Hisashi Yoshida, Takao Yamamoto, Toshiaki Dobashi Department of Chemistry and Chemical Biology, Graduate School of Science and Technology, Gunma University, Kiryu, Gunma 376, Japan

a r t i c l e

i n f o

Article history: Received 24 September 2015 Received in revised form 30 November 2015 Accepted 19 December 2015 Available online 29 December 2015 Keywords: Erythrocyte Aggregation High pressure Laser photometry Blood Mathematical analysis

a b s t r a c t The effects of hydrostatic pressure on erythrocyte aggregation have been studied by laser photometry and analysis based on a phenomenological theory. Samples were prepared by suspending swine erythrocytes in their own plasma. A high-pressure vessel consisting of a stainless-steel block with a hole to hold a sample cell and two sapphire windows to allows the passage of a He–Ne laser beam was used in the experimental setup. The suspension was stirred at 1500 rpm to disperse the erythrocytes homogeneously. Immediately after reducing the stirring rate from 1500 rpm to 300 rpm, the transmitted light intensity (I) was recorded every 10 ms under a high pressure of 40–200 MPa. The value of I increased with time aggregation. From the phenomenological theory, the  (t) owing to erythrocyte   equation I (t) = Ieq 1 − e−Kt / 1 − B 1 − e−Kt was derived for the change in the transmitted light intensity (I) due to erythrocyte aggregation, where Ieq is the transmitted light intensity in the steady state, K is a time constant and B is a constant that represents the ratio of the number of interaction sites on erythrocyte aggregates at time t to that in the steady state. The observed time courses of I obtained at all pressures could be closely fitted to the theoretical equation. Ieq roughly increased with increasing pressure. On the other hand, K and B abruptly decreased above 120 MPa. The growth rate of aggregates decreased above 120 MPa. These results suggest a change in the mechanism of erythrocyte aggregation at approximately 120 MPa. We discuss the physical meaning of the parameters. © 2015 Elsevier B.V. All rights reserved.

1. Introduction When erythrocytes are suspended in a plasma or other macromolecular solutions, they form face-to-face aggregates called rouleaux, which are easily broken up by mechanical shearing. It has been pointed out that rouleaux formation affects in vivo blood flow [1]. There are two models for erythrocyte aggregation: the bridging model [2] and the depletion model [3]. The mechanism of erythrocyte aggregation is yet to be fully elucidated, although recent works have tended to favor the depletion model [4,5]. The degree of aggregation depends on the physical environment, such as the temperature and pressure, as well as the chemical properties of erythrocytes and their suspending medium [6–8]. There have been some reports on the effects of temperature effects on erythrocyte aggregation [9,10]. Whereas pressure together with temperature is an important thermodynamic variable for the study of erythrocyte aggregation as well as for a variety of applications, there has been insufficient study of the effects of pressure on this phenomenon

∗ Corresponding author. E-mail address: [email protected] (Y. Toyama). http://dx.doi.org/10.1016/j.colsurfb.2015.12.038 0927-7765/© 2015 Elsevier B.V. All rights reserved.

because of experimental difficulties. A high pressure can be used for the preservation and sterilization of blood. Although it is desirable to preserve blood at subzero temperatures, the process of freezing and thawing causes the hemolysis of erythrocytes. On the other hand, the freezing point of water is lowered under hydrostatic pressure to −20 ◦ C at 200 MPa [11]. Therefore, the freezing point can be depressed to enable the non-freezing preservation of blood [12]. Another potential application is the inactivation of microorganisms in blood, particularly pathogenic viruses. The infectivity of various types of viruses has been found to be greatly reduced by high-pressure treatment [13–16]. Aggregation behavior has been conventionally assessed by the erythrocyte sedimentation rate (ESR) and microscopic observation [17]. In a previous study, we found that the ESR increased with increasing hydrostatic pressure up to 200 MPa [18,19]. However, ESR measurement only provides the total amount of supernatant plasma due to the sedimentation of aggregated erythrocytes, although this is implicitly related to the aggregability of erythrocytes. Measurements of transmitted or forward-scattered light have been utilized to study the kinetics of aggregate formation [20]. In this study, we have developed a laser photometric system to investigate the aggregation kinetics under high hydrostatic

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Nomenclature I (t) Jj (t)

Transmitted light intensity at time t [V] Decrease in the number of individual erythrocytes per unit time from the jth aggregate at time t [1/s] Total decrease in the number of individual erythroJtot (t) cytes per unit time at time t [1/s] k(−) Kinetic coefficient of attachment [m/s] k(+) Kinetic coefficient of detachment [m2 /s] The number of erythrocyte aggregates at time t nag (t) n (t) The number of individual erythrocytes in the suspension at time t ntot The number of individual erythrocytes in the initial state The number of individual erythrocytes in the final neq steady state The number of erythrocytes in the j-th erythrocyte Nj (t) aggregate at time t N (t) The total number of erythrocytes making up the aggregates Sj (Nj (t), t) Attachment area of the jth aggregate at time t [m2 ] Stot (t) Total attachment area at time t [m2 ] eq Stot Total attachment area in the final steady state [m2 ] in Total attachment area in the initial state [m2 ] Stot v0 Volume of an erythrocyte [m3 ] V Volume of the suspension [m3 ]  (t) Total aggregate volume at time t [m3 ] Total aggregate volume soon after the transient in behavior has finished [m3 ] eq Total aggregate volume in the final steady state [m3 ]

pressures. Using this system, the effects of hydrostatic pressure on the erythrocyte aggregation process have been studied over a wide pressure range with pressures of up to 200 MPa. Swine blood were used in this experiments. The erythrocyte aggregation level in swine blood is known to be similar to that of normal human blood [21]. The transmitted light intensity is theoretically related to the aggregation of erythrocytes and characteristic parameters. By fitting the data to the theoretical equation, we discuss the effects of a high hydrostatic pressure on erythrocyte aggregation.

whose temperature was controlled at 25.0 ± 0.1 ◦ C. The erythrocyte suspension in the high-pressure vessel was mixed at the desired stirring rate using a strong magnetic stirrer. The transmitted light that passed through the erythrocyte suspension was amplified and then detected by a silicon photodiode. The transmitted light intensity converted into a voltage was continuously recorded by a personal computer through a digital multimeter. The erythrocyte suspension was pressurized at a rate of 20 MPa/min and then maintained at the desired pressure. To homogeneously disperse the erythrocytes in the plasma, the erythrocyte suspension was stirred at 1500 rpm for 60 s. Immediately after reducing the stirring rate from 1500 rpm to 300 rpm, the transmitted light intensity (I) was measured every 10 ms; note that when stirring at 300 rpm, neither sedimentation nor hemolysis occurs. The measurements were carried out on samples from six different individuals. 3. Relationship between transmitted light intensity and aggregation process 3.1. Application of phenomenological theory to aggregation process Let us assume that the nuclei of the erythrocyte aggregates are generated during the transient process in which the stirring rate is reduced from 1500 rpm to 300 rpm and that the aggregates grow by the attachment of individual erythrocytes to the nuclei after the short transient time. We choose the time at which the transient process is completed as the origin of the elapsed time t. We also assume that nucleation from individual erythrocytes does not occur after the transient time; the number of aggregates is changed by the fusion and division of the aggregates. Let the number of erythrocyte aggregates at time t be denoted by nag (t) and  the number of ery throcytes in the j-th erythrocyte aggregate j = 1, 2, · · ·, nag (t) at time t be denoted by Nj (t). We also assume that the area of the j-th aggregate to which individual erythrocytes can attach is a function of Nj (t). We denote the “attachment” area of the j-th aggregate by





2. Materials and method

Sj Nj (t) , t . The volume of the suspension is denoted by V and the number of individual erythrocytes in the suspension is denoted by n (t). Here we consider the decrease in the number of individual erythrocytes in the suspension. The number of individual erythrocytes is changed by their attachment to and detachment from the aggregates. The number of individual erythrocytes attaching to the

Fresh blood was obtained from healthy swine (n = 6) and anticoagulated with EDTA–2 K (1 mg/ml). The blood sample was centrifuged at 1670 × g for 10 min to collect the supernatant plasma and remove the buffy coat. Packed erythrocytes were resuspended in their own plasma at a hematocrit (Ht) of 2.0% as the final erythrocyte suspension (erythrocytes in plasma). An erythrocyte suspension in phosphate buffered saline solution (155 mM NaCl, 3.9 mM K2 HPO4 , 0.7 mM KH2 PO4 , pH 7.4) was also prepared at Ht = 2.0% as a non-aggregative control sample (erythrocytes in saline). Fig. 1 shows a diagram of the experimental setup. A 15 mW He–Ne laser beam with 0.8 mm in diameter was used as a light source. The high-pressure vessel was made of stainless steel and equipped with a rectangular hole to hold a sample cell of the dimensions 10 × 10 × 45 mm and two sapphire windows of 10 mm diameter to allow the passage of the laser beam. Hydrostatic pressure was generated through water using a screw-type pump. The erythrocyte suspension was placed in the sample cell, which had a cylindrical magnetic stirring rod in it. The sample cell was tightly sealed with a plastic film without trapping air bubbles and placed in the high-pressure vessel, which was immersed in a water bath

Fig. 1. Schematic diagram of high-pressure apparatus with a pair of sapphire windows. The transmitted laser beam passed through the erythrocyte suspension was detected by a silicon photodiode with an amplifier. The high-pressure vessel made of stainless steel was immersed in a temperature-controlled water bath.

Y. Toyama et al. / Colloids and Surfaces B: Biointerfaces 140 (2016) 189–195

j-th aggregate per unit time is expected to be proportional to the attachment area Sj and the number density n (t) /V of individual erythrocytes in the suspension. The number of erythrocytes detaching from the aggregate surface is expected to be proportional to the attachment area Sj . Therefore, by introducing the kinetic coefficients of attachment k(−) and detachment k(+) , we obtain the decrease in the number of individual erythrocytes per unit time in terms of the attachment to and detachment from the j-th aggregate as



Jj (t) = k(−)



  n (t) − k(+) Sj Nj (t) , t . V

(1)

The total decrease in the number of individual erythrocytes per unit time is given by Jtot (t) =

nag (t) 

 Jj (t) =



k(−)

n (t) − k(+) Stot (t) = (n (t) − neq ) Stot (t), V V k(−)

(2)

j=1

where

 

nag (t)

Stot (t) =

Sj Nj (t) , t



(3)

j=1

neq =

k(+) k(−)



V

k(−)

dn (t) =− V dt

(9)

neq , V

(10)

and Ieq = I0 − ˛

where ntot = n (0) is the number of individual erythrocytes in the initial state. The difference in the transparent light intensity from that in the initial state is given by ˛ I (t) ≡ I (t) − I (0) = (ntot − n (t)) = Ieq V



ın (t) 1− ın0



,

(11)

where ın0 ≡ ntot − neq is the total number of individual erythrocytes attaching to the erythrocyte aggregates during the aggregation process and Ieq ≡ Ieq − I (0) =

(4)





n (t) − neq Stot (t) .

(5)

The time development of the total attachment area Stot (t) strongly depends on details of the aggregation process such as the fusion-division process for the aggregates and the detachmentattachment process for the individual erythrocytes. Therefore, by experimentally obtaining the time development of Stot (t), we can obtain the characteristic features of the erythrocyte aggregation process. From, Eq. (5), we have



V

k(−) n (t) − neq



V dın (t) dn (t) =− , dt k(−) ın (t) dt

(6)

where

 ˛ ˛ ntot − neq = ın0 , V V

(12)

1 V dI (t) k(−) Ieq − I (t) dt

(7)

Equation (6) shows that the time development of Stot (t) can be obtained from the time development of n (t). 3.2. Transmitted light intensity

3.3. Derivation of functional form for transparent light intensity In principle, the aggregation process of the erythrocytes can be analyzed using Eq. (13). In practice, however, analysis based on the measured transparent light intensity is difficult because of the time derivative term dI (t) /dt. An analytic function form that can be fitted to the measured data is required. Here we derive the required functional form phenomenologically. To derive the function form, let us assume that Stot is expressed in terms of the total number of erythrocytes making up the aggregates,



nag (t)

N (t) =

Nj (t) .

(14)

j=1

Hence, Stot (t) = Stot (N (t)). In addition, we adopt the following linear approximation in the function form of Stot (N (t)):

n (t) , V

(8)



eq

eq

Stot (N (t)) = Stot Neq + N (t)  Stot + Atot N (t) ,

(15)

where Neq ≡ lim N (t) is the number of erythrocytes composing t→∞

the aggregates in the steady state and N (t) ≡ N (t) − Neq is the eq deviation from the number in the steady state. The quantity Stot = Stot (Ntot ) = lim Stot (t) is the attachment area in the final steady t→∞ eq

To obtain the time development of Stot (t), we derive the relationship between the transmitted light intensity and the number of individual erythrocytes. The volume of erythrocyte aggregates is much smaller than the suspension volume V . Then, we neglect absorption and/or scattering of light by erythrocyte aggregates and take into account only those by individual erythrocytes to discuss the intensity of the transparent light that passes through the erythrocyte suspension. Hence, the adsorbed light is proportional to the density of the individual erythrocytes n (t) /V and the transmitted light intensity I (t) is given by

(13)

Using this relationship, we derive the time development of the attachment area of the aggregates from that of the transparent light intensity.



ın (t) ≡ n (t) − neq

I (t) = I0 − ␣

ntot V

I (0) = I0 − ␣

Stot (t) = −

is the number of individual erythrocytes neq in the steady state. Note that the attachment and detachment process expressed by Eq. (1) does not depend on details of the attachment and detachment mechanisms. Since Jtot (t) relates to the time derivative of the number of erythrocytes n(t) in the suspension as dn (t) /dt = −Jtot , we have

Stot (t) = −

where I0 is the intensity of the incident light. The light intensities in the initial state and in the final steady state are respectively given by

From Eqs. (6) and (11), we obtain

is the total attachment area at time t, and



191





state and Atot = dStot Neq /dNeq characterizes the change in the attachment area during the growth of the aggregates. Replacing Stot (t) in Eq. (5) with Eq. (15), we have

 k(−) Stot  dn (t) n (t) − neq = V dt eq



eq

1+

Atot eq

Stot



N (t)

(16)

Using the conservation law of the erythrocyte number N (t) − N0 = ntot − n (t) ,where N0 = N (0) is the number of erythrocytes composing the aggregates in the initial state at t = 0, we can rewrite Eq. (16) as

  d␦n (t) = −Kın (t) 1 − ˇın (t) , dt

(17)

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10 8

6

4

4

2

2

10

0

1

2

3

4

5

40 MPa

8

0

4

4

2

2 0

1

2

3

4

5

80 MPa

8

0

0

10

6

4

4

2

2

0

2

3

4

5

1

2

3

4

5

2

3

4

5

200 MPa

8

6

1

160 MPa

8 6

0

0

10

6

10

120 MPa

8

6

0

ΔI / mV

10

0.1 MPa

0 0

1

2

3

4

5

0

1

t / min

Fig. 2. Typical time courses of the change in the transmitted light intensity I after decreasing the stirring rate from 1500 rpm to 300 rpm at 0.1 MPa, 40 MPa, 80 MPa, 120 MPa, 160 MPa and 200 MPa. The solid lines were regression curves using Eq. (19).



eq



eq

eq

where K = k(−1) Stot /V and ˇ = Atot /Stot . Equation (17) is easily solved under the initial condition ın (0) = ın0 = ntot − neq to give e−Kt

ın0 ın (t) = . 1 − ˇın0 + ˇın0 e−Kt

(18)

Substituting Eq. (18) into Eq. (11), we have the required function form for the transparent light intensity as



I (t) = Ieq 1 −



e−Kt



1 − B 1 − e−Kt

 .

(19)

where (20)

Using Eq. (19), we can obtain the three parameters Ieq , K and B. From the values of the three parameters and Eq. (13), the time development of the total attachment area is obtained as 1−B

eq

Stot (t) = Stot

1−B



1 − e−Kt



(21)

Here, the parameter B is expressed as B=

eq

Stot in Stot

=

1 . 1−B

(23)

Equation (23) shows that the attachment area decreases and increases with the growth of aggregates when B < 0 and B > 0 respectively. The time development of Stot from the initial state is clarified by rewriting Eq. (21) as in Stot (t) = Stot



1

1 − B 1 − e−Kt

.

(24)

The total volume of aggregates at t can be estimated as

B = ˇın0 .

eq Stot

in is the value of S in where Stot tot in the initial state; Stot ≡ Stot (0). Equation (22) is rewritten as

in − Stot eq

Stot

,

(22)

 (t)  N (t) v0 ,

(25)

where v0 is the volume of an erythrocyte. From the conservation law of erythrocyte number, and Eqs. (18) and (20), we have e−Kt  (t) − in  , =1− eq − in 1 − B 1 − e−Kt

(26)

where in =  (0) ∼ = N (0) v0 is the aggregate volume soon after the transient behavior has finished and eq ∼ = Neq v0 is that in the final steady state. Equation (26) shows that K −1 is the characteristic time of the aggregation process; large and small values of K −1

Y. Toyama et al. / Colloids and Surfaces B: Biointerfaces 140 (2016) 189–195

193

3

13 12

K / min-1

ΔIeq / mV

11 10 9 8

2

1

7 6

0

50

100

150

0

200

0

50

100

Fig. 3. Pressure dependence of Ieq determined by the least-squares method. Each datum is mean ± SE for six experiments with different individual bloods.

Fig. 4. Pressure dependence of K determined by the least-squares method. Each datum is mean ± SE for six experiments with different individual bloods.

2

respectively correspond to slow and fast aggregate growth. From Eq. (12), we have



Ieq

0



∝ eq − in .

200

P / MPa

P / MPa

˛ eq − in = V v0

150

-2

Thus, the fitting parameter Ieq represents the increase in the aggregate volume.

-4

4. Results and discussion Fig. 2 shows typical time courses of I at pressures of P = 0.1 MPa, 40 MPa, 80 MPa, 120 MPa, 160 MPa and 200 MPa. As soon as the stirring rate was reduced from 1500 rpm to 300 rpm, I increased with time owing to the development of erythrocyte aggregation. The values of the transmitted light intensity at 1500 rpm (I0 ) were almost the same for the six different individual blood samples and their average was 153 mV ± 5 mV. Measurements under the same conditions were also carried out for the control. No variation in I was observed for the control at all pressures. Thus, the initial value of I is independent of the pressures. The time courses of I for the erythrocytes in the plasma were affected by pressurization and were well expressed by Eq. (19), as shown in Fig. 2. The parameters Ieq , B and K in the equation were determined by the least-squares method. Figs. 3, 4 and 5 show the pressure dependences of Ieq , B and K, respectively. The bars in the figures represent the standard error (SE) for the experiments carried out on the six different individual blood samples. Ieq is the transmitted light intensity in the steady state, which slightly increased with increasing pressure. B is negative for all pressures. Therefore, the attachment area decreases during the aggregation process. From the values of B and eq in for the pressures of 0.1 MPa, 40 MPa, Eq. (23), the ratios Stot /Stot 80 MPa, 120 MPa, 160 MPa and 200 MPa are respectively 0.489, 0.541, 0.537, 0.141, 0.132 and 0.258. On the basis of the parameter values obtained by the measurement of I, the time developin for the six ments of the scaled total attachment area Stot (t) /Stot different pressures are shown in Fig. 6. The curves shown in Fig. 6 express the aggregation process from the viewpoint of the attacheq in and the curves in Fig. 6 show that the ment area. The ratios Stot /Stot aggregation process for the low pressure systems with P = 0.1 MPa, 40 MPa, 80 MPa (Group I) and that for the high-pressure systems with P = 120 MPa, 160 MPa and 200 MPa (Group II) are different. The curves for the systems in Group I are typified by that for atmospheric pressure P = 0.1 MPa (Hereafter referred to as the standard

B

(27)

-6 -8 -10

0

50

100

150

200

P / MPa

Fig. 5. Pressure dependence of B determined by the least-squares method. Each datum is mean ± SE for six experiments with different individual bloods.

1.2 0.1 MPa 40 MPa 80 MPa 120 MPa 160 MPa 200 MPa

1.0 0.8 0.6 0.4 0.2 0.0

0

1

2

3

4

5

6

7

8

9

10

20

t / min

in Fig. 6. Time development of the scaled total attachment area Stot (t) /Stot at six pressures. The black lines indicate the values at 0.1 MPa (solid), 40 MPa (dash), 80 MPa (dash-dot) in Group I, and the red lines indicate the values at 120 MPa (solid), 160 MPa (dash), 200 MPa (dash-dot) in Group II. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Y. Toyama et al. / Colloids and Surfaces B: Biointerfaces 140 (2016) 189–195

q / min-1

3

2

1

0

0

50

100

150

200

P / MPa

Fig. 7. Pressure dependence of q defined by Eq. (28). Each datum is mean ± SE for six experiments with different individual bloods.

system). This means that pressurization does not change or only slightly changes the aggregation process of the systems in Group I. On the other hand, the aggregation behaviors of the systems in Group II are different from that of the standard system. This means that pressurization gives rise to an irreversible change in the properties of erythrocytes. Our previous study revealed that a shape change in the erythrocytes was induced above 120 MPa and it was maintained after depressurization [19]. Furthermore, it is noticeable that the SE of the mean values of B was large in Group II. This may be related to individual differences in the resistance of erythrocytes to pressure. The curves in Fig. 6 for Group II are characterized by a small time eq in . Here we consider the ratio q constant K and a small ratio Stot /Stot between the two quantities: q≡

K eq

in Stot /Stot

= K (1 − B) =

1 (−) in in . k Stot ∝ k(−) Stot V

(28)

The pressure dependence of q is shown in Fig. 7. The quantity in , appears to be constant at all pressures. q, and therefore k(−) Stot The aggregation condition in the initial state slightly depends on the pressure since the initial light intensity I (0) is independent of in is expected to be independent of the the pressure. Therefore, Stot pressure. The initial condition and the pressure independence of in enable us to conclude that both the kinetic coefficient of k(−) Stot in in the initial the attachment k(−) and the total attachment area Stot state are independent of the pressure. The pressure independence of the initial light intensity I (0) indicates that ntot is independent of the pressure. Therefore, the pressure dependence of Ieq shown in Fig. 3 and given by Eq. (12) indicates that the values of neq for the systems in Group II are smaller than that for the standard system. From this property for Group II and the pressure independence of the kinetic coefficient of the attachment k(−) , we have the characteristic feature for the systems in Group II that the kinetic coefficient of the detachment k(+) is smaller than that for the standard system. Hence, pressurization does not change the rate of attachment of individual erythrocytes to the aggregates per unit time but lowers the rate of detachment from the aggregates. eq in for the systems in Group II The small value of the ratio Stot /Stot eq indicates that the value of Stot for these systems is less than that for the standard system. The pressure independence of the initial light intensity I (0) and the pressure dependence of Ieq shown in Fig. 3 and given by Eq. (27) indicate that the total volume of the aggregates of the systems in Group II is larger than that of the standard

system in the final steady state. Hence, the attachment area of the aggregates is small but the volume of aggregates is large in Group II in the final steady state. In the standard system, the aggregate shape is expected to be the conventional rouleau shape. A rouleautype aggregate has two attachment sites. In this picture, the ratio of the aggregate number in the initial state nag (0) to that in the eq eq eq in . final steady state nag = nag (∞) is given by nag /nag (0) = Stot /Stot eq eq ∼ in The ratio Stot /Stot for Group I is nearly 0.5. Thus, nqg = 0.5neq (0) for Group I. This means that the aggregate number in the final steady state is half of that in the initial state. Thus, we predict that an aggregate in the final steady state is formed by the fusion of the two aggregates grown by the attachment process of the individual erythrocytes and by the attachment of individual erythrocytes on the fused aggregate in Group I. On the other hand, in Group II, the eq ratio nag /nag (0) is very small. Therefore, the number of aggregates fusing together is anomalously large compared with that for the standard system. Therefore, we conclude that the aggregates in the systems in Group II do not have the rouleau shape. We observed that pressures of 160 MPa and 200 MPa induced an irreversible shape change in the erythrocytes and their aggregates. This analysis suggests that the erythrocytes transformed from a normal biconcave disk shape to a distorted spherical shape and the aggregates changed in shape from rouleaux with a characteristic face-to-face morphology to complex nonlinear three-dimensional aggregates including side-to-face structures, especially when aggregation tendency is enhanced [19]. That is, much larger attachment area of the complex nonlinear aggregates may be covered by a surface on which individual erythrocytes cannot attach and the area of attachment may be enclosed inside eq in becomes small. The small k(+) prothe aggregates. Thus, Stot /Stot motes the enclosure of the attachment area since a small k(+) hinders the reconstruction process of the aggregates. Kitajima et al. reported that a high hydrostatic pressure damages the erythrocyte membrane and that hemolysis is partially induced above the ca. 130 MPa [22]. There have been some studies reported concerning the effects of high pressure on phospholipid bilayer membranes [23–25]. The pressure-induced, interdigitated gel (L␤I) phase was found in dipalmitoylphosphatidylcholine membrane at high pressure above 100 MPa [24]. The erythrocyte shape change may be induced by high pressure closely related to the structural change in the membrane. We investigated the repeatability of the effects of pressurization on transmitted light intensity, and found that the time course was almost perfectly repeated up to 80 MPa but the repeatability gradually decreased once the sample was pressurized above 120 MPa. This can be attributed to a certain damage to the erythrocytes such as an irreversible morphological change in the plasma membrane caused by the high pressure. Care must therefore be taken in relation to this irreversibility when using a high-pressure method for the preservation and sterilization of blood, similarly to when diving to depths at which the pressure is higher than 80 MPa [26]. In conclusion, we investigated the effects of hydrostatic pressure on the erythrocyte aggregation process over a wide pressure range with pressures of up to 200 MPa by laser photometry and developed a theory relating the transmitted light intensity obtained by laser photometry and the erythrocyte aggregation process. The theoretical equation expressing the time course could be closely fitted to the experimental data. From the fitting, the three parameters in the theoretical equation were obtained. On the basis of the three parameters characterizing the aggregation process, the pressurization effects were analyzed. Pressurization effects do not appear up to pressures of approximately 120 MPa; the aggregation process in this range is roughly the same as that at atmospheric pressure P = 0.1 MPa. However, above 120 MPa, the aggregation process is different from that at atmospheric pressure. Thus, at high pressures, an irreversible change in the properties of erythrocytes is induced.

Y. Toyama et al. / Colloids and Surfaces B: Biointerfaces 140 (2016) 189–195

Acknowledgement This work was supported by JSPS KAKENHI grant number 15K05240. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

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