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Mechanical properties of the human red blood cell membrane at −15 °C
Cryobiology 59 (2009) 24–27
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Cryobiology journal homepage: www.elsevier.com/locate/ycryo
Mechanical properties of the human red blood cell membrane at 15 °C q Fritz Thom Institute for Transfusion Medicine, Charité –Universitätsmedizin Berlin, 10115 Berlin, Germany
a r t i c l e
i n f o
Article history: Received 24 October 2008 Accepted 2 April 2009 Available online 9 April 2009 Keywords: Human red blood cell membrane Subzero temperature Shear modulus Isotropic tension AC electrical field
a b s t r a c t The most common method for measuring the mechanical behavior of the human red blood cell (RBC) membrane is micropipette aspiration, because it can be used to apply both a low uniaxial stress at a small part of the membrane or high two-axial stresses to the whole membrane [E.A. Evans, R.E. Waugh, Mechano-chemical study of red cell membrane structure in situ, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 31–56 (Chapter 3); H.J. Meiselman, Measures of blood rheology and erythrocyte mechanics, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 75–117 (Chapter 5)]. The elastic shear moduli and area changes of the human RBC published to date were calculated by means of this technique. However, a main drawback of the method is its impracticability at subzero temperatures. Experiments at below 0 °C are of interest because it is at these temperatures that RBC lysis occurs during freezing and thawing after cryopreservation, via a mechanism that may be mechanical. A method for circumventing this limitation is deforming the cell membranes by applying an electric ac field to a supercooled suspension. In a previous study, we applied this technique to human RBCs down to 15 °C [M. Krueger, F. Thom, Deformability and stability of erythrocytes in high-frequency electric fields down to subzero temperatures, Biophys. J. 73 (1997) 2653–2666]. In this technique, the electrical dimensions must be translated into those of mechanics. We provided a formula for these calculations, which demonstrated excellent concordance with known mechanical measurements at room temperature [F. Thom, H. Gollek, Calculation of mechanical properties of human red cells based on electrically induced deformation experiments, J. Electrostat. 64 (2006) 53–61]. Using this formula, we have now calculated the shear moduli and stress–strain diagram for our deformation experiments at 15 °C and present the results below. Ó 2009 Elsevier Inc. All rights reserved.
Introduction During cryopreservation, biological cells can become damaged by a variety means. One type of cryodamage is cytolysis, i.e. rupturing of the membrane causes the cytoplasm to burst out. Human red blood cells (RBC) exhibit such membrane damage during slow freezing and/or thawing. During the latter, when cells are visible within channels of the residual ice matrix, the process is easily observable by means of phase contrast microscopy. Human RBC are also a simple and therefore expedient model for studying this type of cryodamage. LOVELOCK’s experiments [5] show that this destruction of cell integrity may be caused by an increased concentration of salt during freezing followed by a decrease to isotonic concentration during thawing. Thus, cells experience irreversible damage if they remain for more than few seconds within a critical temperature range of between 3 and 40 °C, with the lower limit corresponding to the eutectic point of the salt solution. Cells q This research was sponsored by the Charité, Clinical Department of the Humboldt-University. E-mail address: [email protected]
0011-2240/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.cryobiol.2009.04.001
within this temperature range are also extremely sensitive to the mechanical and thermal stresses inherent in the process of freezing suspensions. Furthermore, it was found that external ice itself does not damage the cell. Studies conducted using rabbit blood at temperatures down to 10 °C by Nei [8] supported the results of LOVELOCK by microscopic observations and demonstrated that RBC hemolysis occurs during freezing, as well as thawing. These results suggest that damage to RBC after freezing may be caused by concentrated salts in combination with mechanical damage. Moreover, Mazur et al. [6] conclude from experiments on human RBC using a slow freezing process that cells are subjected to forces in unfrozen channels, cell to cell interactions and osmotic pressure. They assumed that some of the cells also exhibited brittleness of the membrane below 0 °C (further hypotheses are summarized in [9]). Together, these results suggest mechanical damage to the RBC membrane by an as yet unknown mechanism. Generally we can assume that a better understanding of the mechanisms underlying cell damage is fundamental to optimizing cell protection. Our investigation into the mechanical behavior of the native RBC membrane at subzero temperatures began as early as the 1980s [9].
F. Thom / Cryobiology 59 (2009) 24–27
25
discocytic cell in one direction. Here, the RBC becomes increasingly ellipsoidale, while decreasing in biconcavity (Fig. 1). In our experiments, the cell is stretched by means of an external electrical couple of forces (F and F) generated by Maxwell–Wagner polarization at the membrane within an AC electrical field. This polarization occurs at the border (membrane) of two media with different permittivities and conductivities. Our method is described in detail in [9,4] and represents the unique technique for deforming an object (cell) in a watery suspension that is supercooled, i.e. the temperature range of Nei’s experiments. The technique was first developed by Engehardt et al. [1] for cells above 0 °C and was modified for subzero temperatures in our laboratory. The experimental set-up of the AC field and cell parameters is shown in Fig. 2. Only the elastical deformation of each part of the membrane can be described by stretching a square element x02 into a rectangle (x1 x2) with the parameter k = x0/x1 = x2/x0. k will be measurable at the whole cell within a virtual yz-cut (with axes b and c) by the circumferences of the membrane in the undeformed and deformed state. Because the semi-axis c is small and nearly constant during the whole stretching the non-deformed circumference is approximately 4b0 and the deformed 4b, if b is the semi-axis b of the cell (cf. [11] for details). During deformation, the whole elastic membrane tension in x-direction acting at the yz-cut, called Sx, will be counterbalanced by the external force Fx, which is electrically induced in the field direction, fulfilling the equation:
F x ¼ Sx 4b;
Fig. 1. Stand stills from the video sequence of the stretching experiment on the RBCs. The cells in LIS solution were attracted towards the electrode (dark region at the top) through forces by the inhomogeneity of the electric field. Field strengths at x = 0: (A) 249, (B) 1361 and (C) 5445 V/cm.
To prepare the cell deformation, we follow the ‘‘whole cell deformation concept” of HOCHMUTH [3] by stretching a single
where F is a vector. The force Fx is given by a function of Maxwell’s stress tensor and the challenge now lies in calculating Fx using mechanical units. This is possible for an ellipsoidale cell shape by numerical integration and is described in detail in [11]. The latter paper discusses the mathematical and physical approximations, and describes the application of the method to cells at room temperature. However, all semi-axes must be measured in this calculation. While this is easily performed for the a- and c- axes, the b-axis is only accurately measurable if it is parallel to the coverslide of the specimen and not oscillating. Only seven cells matched these conditions for this paper.
Fig. 2. Scheme of the experimental configuration as it was used. The cell at one electrode (gold wire, r = 10 lm) with view from top (a) corresponding to the one obtained through the microscope and with such parallel to the coverslide representing the cell model used (b). X represents the direction of the semi-axis ‘‘a” of the cell and of the force F also. The electrical field with strength E acts in direction of the wire radius around the cell.
26
F. Thom / Cryobiology 59 (2009) 24–27
Experimental
Results
Human red blood cells were deformed at 15 °C by stretching the cell in a 1-MHz electric field by means of Maxwell–Wagner polarization, as described previously for 15 cells [4]. The cells are the upper 10% (young cells) gained by density separation before washing. This procedure was used to limit the dispersion of the stretching results by excluding the cells with higher density. Briefly, cells were resuspended in a low-ionic-strength (LIS) solution using a very low hematocrit. Cryomicroscopy was used to observe and shoot the time-dependent deformation procedure (for details see [4]). The human RBC represents a system of a viscoelastic membrane and viscose cytoplasm which has a whole relaxation time of nearly 2 s at room temperature (RT). At 15 °C the cells were more viscose and the relaxation time increased to 25 s. Membrane damage due to application of abrupt high-field strengths was prevented; the membrane polarization was increased in steps (nearly 10) of field strength up to high stretching, i.e. to high final field strength. In Fig. 3, the stress–strain diagram shows points of cell-stretching after 25 s at each given field strength, which is the point at which the membrane enters the equilibrium state Fx = Sx 4b (see [4,11]). Thus, it follows the diagram characterizes the mechanical behavior of the cell membrane only. At these points of cell-stretching after 25 s the cell parameters (semi-axes a and b) will be measured using video sequences like that in Fig. 1. The semi-axis c seldom can be observed in the same stress condition at separate cells but it will be small and nearly constant at different cells as well as during stretching (cf. [11]). The membrane itself contains the lipid-bilayer in combination with the protein-skeleton, with the latter dominating the mechanical property.
Using each set of cell parameters (a-, b-, c-axes) and corresponding field strengths, we calculated the external mechanical stresses Fx/4b in x-direction acting at the imaginary cut of the membrane in the b- to c-plane (see Introduction) using Eq. (6), in connection with Eqs. (8) and (17) (described in [11]) for seven young human RBCs of different sex deformed at 15 °C. For instance, Fig. 3 plots the stresses Fx/4b (in N cm1) for Cell No. 51c (Table 2) in dependence of a function of the strain (k2 k2). Here, k = x0/x = b/b0 is the stretching parameter of a square element x02 of the membrane, while b is the b-axis of the cell. The stress Fx/4b is acting in the direction of the a-axis and is induced by the field strength in the same direction. The stepwise increase in field strength at 15 °C used in Fig. 3 is shown in Table 1. To demonstrate the influence of the decreasing temperature on the mechanical behavior of the red cell membrane Fig. 3 also demonstrates the deformation curve of a RBC at RT (from [11]). The shear moduli of the membranes are given by the slopes at small deformations (see [11]). These shear moduli and maximum stresses, as well as the averages of the seven cells as a group, determined by our experimental procedure at 15 °C [4] are shown in Table 2. A systematic error of these measurements is caused by the bvalues because the cells slowly rotate around the a-axis, such that the observed b-axis value may differ from the actual value during measurement. Two experiments were performed, in which the supercooled state reached 18 °C. While these results are not demonstrated here, they are in close concordance with those of the experiments at 15 °C. Discussion
51c, -15°C
30
54, 24°C after (25) + 9 sec. at 7.9 kV/cm
25 20
15 10
5 0 0
1
2
4
3
5
6
7
Fig. 3. Membrane external stress Fx/4b versus strain-parameter (k2 k2) of Cell No. 51c (15 °C, this paper) in comparison with Cell No. 54 (24 °C, see [11]).
Table 1 Steps of field strength E (5 lm from the electrode, see [4], in V/cm) during stretching of Cell No. 51c. Cell No. 51c/15 °C 0 k2 k2 0 E (V cm1) 2 2 1.08 k k 1 3045 E (V cm ) 3.06 k2 k2 6852 E (V cm1)
0.092 634 1.36 3426 2.77 7359
0.28 1015 1.69 3807 3.06 7867
0.28 1269 1.87 4314 3.39 8374
0.49 1523 2.51 4822 3.39 8882
0.59 1903 2.77 5329 3.39 9389
0.95 2284 3.06 5837 3.39 9897
1.08 2665 3.06 6344 3.39 10404
The stress–strain curve at 15 °C (Fig. 3) demonstrates qualitatively equal behavior in comparison to RT. However the uniaxial stress at the beginning of the curve delivers a shear modulus l of 0.99 106 N cm1 in comparison to 0.15 106 N cm1 at RT (single cell values). This relation is comparable with that of the averaged values (Table 2 and at RT [11]). It demonstrates a sevenfold higher value for l at 15 °C compared to that at RT and indicates a decrease in membrane elasticity by the same factor. The isotropic stress condition clearly indicated in the final section of the stress–strain curve at 15 °C as shown in Fig. 3 was true of all cells tested at this temperature and begins to form near a shear-strain of (k2 k2) 3. This corresponded to a field strength of between 6 and 8 kV/cm (Table 1). At RT the corresponding values were determined to be reached at 5 and a field strength of 4.3 kV/cm [11]. After this point, the strain increase was minimal and, in comparison to RT, the stress rose to higher values without breakdown of the membrane. That demonstrates that the membrane is very stable at 15 °C and does not display brittleness.
Table 2 Shear modulus l and isotropic tension Tx at maximal elongation (k2 k2)max of seven hRBC, deformed at 15 °C. Cell No./sex 51a/f 51b/f 51c/f 58/m 59a/m 59b/m 591/f Averaged value :
Temp. (°C)
l
Tx (106 N cm1)
(k2 k2)max
(106 N cm1)
15 15 15 15 15 15 15
1.026 0.535 0.992 0.405 0.54 0.57 0.992
32.464 33.479 25.042 23.907 23.58 9.742 20.518
3.09 3.75 3.39 3.95 3.09 3.75 4.55
0.72
26.5
F. Thom / Cryobiology 59 (2009) 24–27
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However, the area dilatation by isotropic stresses at the upper stress value is not calculable because the elastic modulus of the membrane’s area compressibility at 15 °C is unknown. These results demonstrate that the RBC membrane continues to have elastic deformability at 15 °C. Whether all deformability of the cell as well as the membrane would be lost with further decreases in temperature is unknown and cannot be measured using currently available experimental techniques. Measurements at unprotected heart tissue of the rat show rigidity at 30 °C [10], however, ice had formed in the tissue in this case. At high final deformation at 15 °C, and after switching of the field strength application and subsequent relaxation, a small non-reversibility of cells was observed, indicating that some of the deformation was ‘‘plastic”. However, the non-relaxed part of the cells was merely a result of damage to the membrane structure rather than a cause of a breakdown. Furthermore we speculated that a membrane damage may be due to the high relaxation time at 15 °C. To clarify this question, we applied a one step increase to high-field strength, i.e. a short-time overstrain on several cells, however the result did not differ from that of the stepwise regime.
Appendix
Conclusions
References
At 15 °C, the hRBC membrane shows a decreased viscoelastic deformability up to higher isotropic tension in comparison to RT but without breakdown. This clearly demonstrates that no brittleness (i.e. elastic deformation with direct connection of a breakdown/bursting) of the membrane occurs down to 15 °C. High relaxation time (25 s) of the whole cell and short-time overstrain of the membrane does not appear to influence a breakdown of the membrane. The observed irreversibility after high deformation is not a source of cell lyses. Human RBCs do not become rigid down to 18 °C because viscoelasticity of the membrane was observed down to this temperature (observed but not demonstrated here). More information is required now about the viscoelasticity and stability of the RBC membrane during or after exposure of the cells to strong salt solutions at subzero temperatures.
[1] H. Engelhardt, H. Gaub, E. Sackmann, Viscoelastic properties of erythrocyte membranes in high frequency electric fields, Nature 307 (1984) 378–380. [2] E.A. Evans, R.E. Waugh, Mechano-chemical study of red cell membrane structure in situ, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 31–56 (Chapter 3). [3] R.M. Hochmuth, Viscoelastic solid behavior of red cell membrane, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 57–73. [4] M. Krueger, F. Thom, Deformability and stability of erythrocytes in highfrequency electric fields down to subzero temperatures, Biophys. J. 73 (1997) 2653–2666. [5] J.E. Lovelock, The haemolysis of human red blood-cells by freezing and thawing, Biochim Biophys Acta 10 (1953) 414–426. [6] P. Mazur, F. Rall, N. Rigopoulos, Relative contributions of the fraction of unfrozen water and of salt concentration to the survival of slowly frozen human erythrocytes, Biophys. J. 36 (1981) 653–675. [7] H.J. Meiselman, Measures of blood rheology and erythrocyte mechanics, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 75–117 (Chapter 5). [8] T. Nei, Mechanism of hemolysis of erythrocytes by freezing at near-zero temperatures. I. Microscopic observation of hemolysing erythrocytes during the freezing and thawing process, Cryobiology 4 (1967) 153–156. [9] F. Thom, G. Matthes, Deformation of the cell membrane at low temperatures. I. A cryomicroscopical technique, Cryo Letters 9 (1988) 300–307. [10] F. Thom, G. Matthes, E. Richter, H.A. Hackensellner, The ductility of mammalian tissue in dependence on the deformation temperature, CryoLett. 4 (1983) 341–348. [11] F. Thom, H. Gollek, Calculation of mechanical properties of human red cells based on electrically induced deformation experiments, J. Electrostat. 64 (2006) 53–61.
Acknowledgment The author thank Dr. Hubert Gollek for preparing the numerical integration and numerical calculation of the electrical forces.
With the results discussed in this paper I am, at the age of 78, concluding my biophysical research in the field of cryobiology. Thank you for your attention. Understanding the mechanism of cryodamage to the RBC membrane is a key interest in the future overall theory of cryopreservation. Therefore, I should like to suggest some possibilities for an eventual continuation of my contribution in this field: (I) deformation of whole single RBC’s by stretching as like my own experiments but instead first suspending them in strong salt solutions, followed by decreasing the salt to isotonic concentration with one group of cells not subject to the decrease (as in LOVELOCK’s experiments). This would provide insight into the elasticity and stability of the membrane under these conditions at subzero temperatures. Young and old cells should be tested separately. Here, stretching should be carried out using a micropipette (cf. [2,3]), which will be possible because the freezing point in this case is markedly lowered. (II) The results of this should be discussed in relation to shear stresses in the streaming of the liquid regions (cf. [7]) and other forces in freezing suspensions.
Contents lists available at ScienceDirect
Cryobiology journal homepage: www.elsevier.com/locate/ycryo
Mechanical properties of the human red blood cell membrane at 15 °C q Fritz Thom Institute for Transfusion Medicine, Charité –Universitätsmedizin Berlin, 10115 Berlin, Germany
a r t i c l e
i n f o
Article history: Received 24 October 2008 Accepted 2 April 2009 Available online 9 April 2009 Keywords: Human red blood cell membrane Subzero temperature Shear modulus Isotropic tension AC electrical field
a b s t r a c t The most common method for measuring the mechanical behavior of the human red blood cell (RBC) membrane is micropipette aspiration, because it can be used to apply both a low uniaxial stress at a small part of the membrane or high two-axial stresses to the whole membrane [E.A. Evans, R.E. Waugh, Mechano-chemical study of red cell membrane structure in situ, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 31–56 (Chapter 3); H.J. Meiselman, Measures of blood rheology and erythrocyte mechanics, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 75–117 (Chapter 5)]. The elastic shear moduli and area changes of the human RBC published to date were calculated by means of this technique. However, a main drawback of the method is its impracticability at subzero temperatures. Experiments at below 0 °C are of interest because it is at these temperatures that RBC lysis occurs during freezing and thawing after cryopreservation, via a mechanism that may be mechanical. A method for circumventing this limitation is deforming the cell membranes by applying an electric ac field to a supercooled suspension. In a previous study, we applied this technique to human RBCs down to 15 °C [M. Krueger, F. Thom, Deformability and stability of erythrocytes in high-frequency electric fields down to subzero temperatures, Biophys. J. 73 (1997) 2653–2666]. In this technique, the electrical dimensions must be translated into those of mechanics. We provided a formula for these calculations, which demonstrated excellent concordance with known mechanical measurements at room temperature [F. Thom, H. Gollek, Calculation of mechanical properties of human red cells based on electrically induced deformation experiments, J. Electrostat. 64 (2006) 53–61]. Using this formula, we have now calculated the shear moduli and stress–strain diagram for our deformation experiments at 15 °C and present the results below. Ó 2009 Elsevier Inc. All rights reserved.
Introduction During cryopreservation, biological cells can become damaged by a variety means. One type of cryodamage is cytolysis, i.e. rupturing of the membrane causes the cytoplasm to burst out. Human red blood cells (RBC) exhibit such membrane damage during slow freezing and/or thawing. During the latter, when cells are visible within channels of the residual ice matrix, the process is easily observable by means of phase contrast microscopy. Human RBC are also a simple and therefore expedient model for studying this type of cryodamage. LOVELOCK’s experiments [5] show that this destruction of cell integrity may be caused by an increased concentration of salt during freezing followed by a decrease to isotonic concentration during thawing. Thus, cells experience irreversible damage if they remain for more than few seconds within a critical temperature range of between 3 and 40 °C, with the lower limit corresponding to the eutectic point of the salt solution. Cells q This research was sponsored by the Charité, Clinical Department of the Humboldt-University. E-mail address: [email protected]
0011-2240/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.cryobiol.2009.04.001
within this temperature range are also extremely sensitive to the mechanical and thermal stresses inherent in the process of freezing suspensions. Furthermore, it was found that external ice itself does not damage the cell. Studies conducted using rabbit blood at temperatures down to 10 °C by Nei [8] supported the results of LOVELOCK by microscopic observations and demonstrated that RBC hemolysis occurs during freezing, as well as thawing. These results suggest that damage to RBC after freezing may be caused by concentrated salts in combination with mechanical damage. Moreover, Mazur et al. [6] conclude from experiments on human RBC using a slow freezing process that cells are subjected to forces in unfrozen channels, cell to cell interactions and osmotic pressure. They assumed that some of the cells also exhibited brittleness of the membrane below 0 °C (further hypotheses are summarized in [9]). Together, these results suggest mechanical damage to the RBC membrane by an as yet unknown mechanism. Generally we can assume that a better understanding of the mechanisms underlying cell damage is fundamental to optimizing cell protection. Our investigation into the mechanical behavior of the native RBC membrane at subzero temperatures began as early as the 1980s [9].
F. Thom / Cryobiology 59 (2009) 24–27
25
discocytic cell in one direction. Here, the RBC becomes increasingly ellipsoidale, while decreasing in biconcavity (Fig. 1). In our experiments, the cell is stretched by means of an external electrical couple of forces (F and F) generated by Maxwell–Wagner polarization at the membrane within an AC electrical field. This polarization occurs at the border (membrane) of two media with different permittivities and conductivities. Our method is described in detail in [9,4] and represents the unique technique for deforming an object (cell) in a watery suspension that is supercooled, i.e. the temperature range of Nei’s experiments. The technique was first developed by Engehardt et al. [1] for cells above 0 °C and was modified for subzero temperatures in our laboratory. The experimental set-up of the AC field and cell parameters is shown in Fig. 2. Only the elastical deformation of each part of the membrane can be described by stretching a square element x02 into a rectangle (x1 x2) with the parameter k = x0/x1 = x2/x0. k will be measurable at the whole cell within a virtual yz-cut (with axes b and c) by the circumferences of the membrane in the undeformed and deformed state. Because the semi-axis c is small and nearly constant during the whole stretching the non-deformed circumference is approximately 4b0 and the deformed 4b, if b is the semi-axis b of the cell (cf. [11] for details). During deformation, the whole elastic membrane tension in x-direction acting at the yz-cut, called Sx, will be counterbalanced by the external force Fx, which is electrically induced in the field direction, fulfilling the equation:
F x ¼ Sx 4b;
Fig. 1. Stand stills from the video sequence of the stretching experiment on the RBCs. The cells in LIS solution were attracted towards the electrode (dark region at the top) through forces by the inhomogeneity of the electric field. Field strengths at x = 0: (A) 249, (B) 1361 and (C) 5445 V/cm.
To prepare the cell deformation, we follow the ‘‘whole cell deformation concept” of HOCHMUTH [3] by stretching a single
where F is a vector. The force Fx is given by a function of Maxwell’s stress tensor and the challenge now lies in calculating Fx using mechanical units. This is possible for an ellipsoidale cell shape by numerical integration and is described in detail in [11]. The latter paper discusses the mathematical and physical approximations, and describes the application of the method to cells at room temperature. However, all semi-axes must be measured in this calculation. While this is easily performed for the a- and c- axes, the b-axis is only accurately measurable if it is parallel to the coverslide of the specimen and not oscillating. Only seven cells matched these conditions for this paper.
Fig. 2. Scheme of the experimental configuration as it was used. The cell at one electrode (gold wire, r = 10 lm) with view from top (a) corresponding to the one obtained through the microscope and with such parallel to the coverslide representing the cell model used (b). X represents the direction of the semi-axis ‘‘a” of the cell and of the force F also. The electrical field with strength E acts in direction of the wire radius around the cell.
26
F. Thom / Cryobiology 59 (2009) 24–27
Experimental
Results
Human red blood cells were deformed at 15 °C by stretching the cell in a 1-MHz electric field by means of Maxwell–Wagner polarization, as described previously for 15 cells [4]. The cells are the upper 10% (young cells) gained by density separation before washing. This procedure was used to limit the dispersion of the stretching results by excluding the cells with higher density. Briefly, cells were resuspended in a low-ionic-strength (LIS) solution using a very low hematocrit. Cryomicroscopy was used to observe and shoot the time-dependent deformation procedure (for details see [4]). The human RBC represents a system of a viscoelastic membrane and viscose cytoplasm which has a whole relaxation time of nearly 2 s at room temperature (RT). At 15 °C the cells were more viscose and the relaxation time increased to 25 s. Membrane damage due to application of abrupt high-field strengths was prevented; the membrane polarization was increased in steps (nearly 10) of field strength up to high stretching, i.e. to high final field strength. In Fig. 3, the stress–strain diagram shows points of cell-stretching after 25 s at each given field strength, which is the point at which the membrane enters the equilibrium state Fx = Sx 4b (see [4,11]). Thus, it follows the diagram characterizes the mechanical behavior of the cell membrane only. At these points of cell-stretching after 25 s the cell parameters (semi-axes a and b) will be measured using video sequences like that in Fig. 1. The semi-axis c seldom can be observed in the same stress condition at separate cells but it will be small and nearly constant at different cells as well as during stretching (cf. [11]). The membrane itself contains the lipid-bilayer in combination with the protein-skeleton, with the latter dominating the mechanical property.
Using each set of cell parameters (a-, b-, c-axes) and corresponding field strengths, we calculated the external mechanical stresses Fx/4b in x-direction acting at the imaginary cut of the membrane in the b- to c-plane (see Introduction) using Eq. (6), in connection with Eqs. (8) and (17) (described in [11]) for seven young human RBCs of different sex deformed at 15 °C. For instance, Fig. 3 plots the stresses Fx/4b (in N cm1) for Cell No. 51c (Table 2) in dependence of a function of the strain (k2 k2). Here, k = x0/x = b/b0 is the stretching parameter of a square element x02 of the membrane, while b is the b-axis of the cell. The stress Fx/4b is acting in the direction of the a-axis and is induced by the field strength in the same direction. The stepwise increase in field strength at 15 °C used in Fig. 3 is shown in Table 1. To demonstrate the influence of the decreasing temperature on the mechanical behavior of the red cell membrane Fig. 3 also demonstrates the deformation curve of a RBC at RT (from [11]). The shear moduli of the membranes are given by the slopes at small deformations (see [11]). These shear moduli and maximum stresses, as well as the averages of the seven cells as a group, determined by our experimental procedure at 15 °C [4] are shown in Table 2. A systematic error of these measurements is caused by the bvalues because the cells slowly rotate around the a-axis, such that the observed b-axis value may differ from the actual value during measurement. Two experiments were performed, in which the supercooled state reached 18 °C. While these results are not demonstrated here, they are in close concordance with those of the experiments at 15 °C. Discussion
51c, -15°C
30
54, 24°C after (25) + 9 sec. at 7.9 kV/cm
25 20
15 10
5 0 0
1
2
4
3
5
6
7
Fig. 3. Membrane external stress Fx/4b versus strain-parameter (k2 k2) of Cell No. 51c (15 °C, this paper) in comparison with Cell No. 54 (24 °C, see [11]).
Table 1 Steps of field strength E (5 lm from the electrode, see [4], in V/cm) during stretching of Cell No. 51c. Cell No. 51c/15 °C 0 k2 k2 0 E (V cm1) 2 2 1.08 k k 1 3045 E (V cm ) 3.06 k2 k2 6852 E (V cm1)
0.092 634 1.36 3426 2.77 7359
0.28 1015 1.69 3807 3.06 7867
0.28 1269 1.87 4314 3.39 8374
0.49 1523 2.51 4822 3.39 8882
0.59 1903 2.77 5329 3.39 9389
0.95 2284 3.06 5837 3.39 9897
1.08 2665 3.06 6344 3.39 10404
The stress–strain curve at 15 °C (Fig. 3) demonstrates qualitatively equal behavior in comparison to RT. However the uniaxial stress at the beginning of the curve delivers a shear modulus l of 0.99 106 N cm1 in comparison to 0.15 106 N cm1 at RT (single cell values). This relation is comparable with that of the averaged values (Table 2 and at RT [11]). It demonstrates a sevenfold higher value for l at 15 °C compared to that at RT and indicates a decrease in membrane elasticity by the same factor. The isotropic stress condition clearly indicated in the final section of the stress–strain curve at 15 °C as shown in Fig. 3 was true of all cells tested at this temperature and begins to form near a shear-strain of (k2 k2) 3. This corresponded to a field strength of between 6 and 8 kV/cm (Table 1). At RT the corresponding values were determined to be reached at 5 and a field strength of 4.3 kV/cm [11]. After this point, the strain increase was minimal and, in comparison to RT, the stress rose to higher values without breakdown of the membrane. That demonstrates that the membrane is very stable at 15 °C and does not display brittleness.
Table 2 Shear modulus l and isotropic tension Tx at maximal elongation (k2 k2)max of seven hRBC, deformed at 15 °C. Cell No./sex 51a/f 51b/f 51c/f 58/m 59a/m 59b/m 591/f Averaged value :
Temp. (°C)
l
Tx (106 N cm1)
(k2 k2)max
(106 N cm1)
15 15 15 15 15 15 15
1.026 0.535 0.992 0.405 0.54 0.57 0.992
32.464 33.479 25.042 23.907 23.58 9.742 20.518
3.09 3.75 3.39 3.95 3.09 3.75 4.55
0.72
26.5
F. Thom / Cryobiology 59 (2009) 24–27
27
However, the area dilatation by isotropic stresses at the upper stress value is not calculable because the elastic modulus of the membrane’s area compressibility at 15 °C is unknown. These results demonstrate that the RBC membrane continues to have elastic deformability at 15 °C. Whether all deformability of the cell as well as the membrane would be lost with further decreases in temperature is unknown and cannot be measured using currently available experimental techniques. Measurements at unprotected heart tissue of the rat show rigidity at 30 °C [10], however, ice had formed in the tissue in this case. At high final deformation at 15 °C, and after switching of the field strength application and subsequent relaxation, a small non-reversibility of cells was observed, indicating that some of the deformation was ‘‘plastic”. However, the non-relaxed part of the cells was merely a result of damage to the membrane structure rather than a cause of a breakdown. Furthermore we speculated that a membrane damage may be due to the high relaxation time at 15 °C. To clarify this question, we applied a one step increase to high-field strength, i.e. a short-time overstrain on several cells, however the result did not differ from that of the stepwise regime.
Appendix
Conclusions
References
At 15 °C, the hRBC membrane shows a decreased viscoelastic deformability up to higher isotropic tension in comparison to RT but without breakdown. This clearly demonstrates that no brittleness (i.e. elastic deformation with direct connection of a breakdown/bursting) of the membrane occurs down to 15 °C. High relaxation time (25 s) of the whole cell and short-time overstrain of the membrane does not appear to influence a breakdown of the membrane. The observed irreversibility after high deformation is not a source of cell lyses. Human RBCs do not become rigid down to 18 °C because viscoelasticity of the membrane was observed down to this temperature (observed but not demonstrated here). More information is required now about the viscoelasticity and stability of the RBC membrane during or after exposure of the cells to strong salt solutions at subzero temperatures.
[1] H. Engelhardt, H. Gaub, E. Sackmann, Viscoelastic properties of erythrocyte membranes in high frequency electric fields, Nature 307 (1984) 378–380. [2] E.A. Evans, R.E. Waugh, Mechano-chemical study of red cell membrane structure in situ, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 31–56 (Chapter 3). [3] R.M. Hochmuth, Viscoelastic solid behavior of red cell membrane, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 57–73. [4] M. Krueger, F. Thom, Deformability and stability of erythrocytes in highfrequency electric fields down to subzero temperatures, Biophys. J. 73 (1997) 2653–2666. [5] J.E. Lovelock, The haemolysis of human red blood-cells by freezing and thawing, Biochim Biophys Acta 10 (1953) 414–426. [6] P. Mazur, F. Rall, N. Rigopoulos, Relative contributions of the fraction of unfrozen water and of salt concentration to the survival of slowly frozen human erythrocytes, Biophys. J. 36 (1981) 653–675. [7] H.J. Meiselman, Measures of blood rheology and erythrocyte mechanics, in: Kroc Foundation Series, vol. 13, Erythrocyte Mechanics and Blood Flow, Alan R. Liss. Inc., New York, 1980, pp. 75–117 (Chapter 5). [8] T. Nei, Mechanism of hemolysis of erythrocytes by freezing at near-zero temperatures. I. Microscopic observation of hemolysing erythrocytes during the freezing and thawing process, Cryobiology 4 (1967) 153–156. [9] F. Thom, G. Matthes, Deformation of the cell membrane at low temperatures. I. A cryomicroscopical technique, Cryo Letters 9 (1988) 300–307. [10] F. Thom, G. Matthes, E. Richter, H.A. Hackensellner, The ductility of mammalian tissue in dependence on the deformation temperature, CryoLett. 4 (1983) 341–348. [11] F. Thom, H. Gollek, Calculation of mechanical properties of human red cells based on electrically induced deformation experiments, J. Electrostat. 64 (2006) 53–61.
Acknowledgment The author thank Dr. Hubert Gollek for preparing the numerical integration and numerical calculation of the electrical forces.
With the results discussed in this paper I am, at the age of 78, concluding my biophysical research in the field of cryobiology. Thank you for your attention. Understanding the mechanism of cryodamage to the RBC membrane is a key interest in the future overall theory of cryopreservation. Therefore, I should like to suggest some possibilities for an eventual continuation of my contribution in this field: (I) deformation of whole single RBC’s by stretching as like my own experiments but instead first suspending them in strong salt solutions, followed by decreasing the salt to isotonic concentration with one group of cells not subject to the decrease (as in LOVELOCK’s experiments). This would provide insight into the elasticity and stability of the membrane under these conditions at subzero temperatures. Young and old cells should be tested separately. Here, stretching should be carried out using a micropipette (cf. [2,3]), which will be possible because the freezing point in this case is markedly lowered. (II) The results of this should be discussed in relation to shear stresses in the streaming of the liquid regions (cf. [7]) and other forces in freezing suspensions.