8
Biomechanical Characterization of Human Red Blood Cells with Optical Tweezers
Youhua Tan and Dong Sun
City University of Hong Kong Hong Kong, China
Wenhao Huang
University of Science and Technology of China Hefei, China
CONTENTS
8.3 Cell Manipulation with Optical Tweezers
8.3.2 Experimental Materials Preparation
8.3.4 Robotic Manipulation of Microbeads
Abstract
Human red blood cells (RBCs) are essential for transportation of oxygen and carbon dioxide for human bodies The mechanical properties of cells are crucial to the exercise of normal cellular functions Abnormity of cell mechanics may cause disorders In this chapter, the biomechanical properties of human RBCs in hypotonic conditions are investigated using robotic manipulation technology with optical tweezers to understand the correlation between cell mechanics and osmotic environments Optical traps serve as end-effectors to manipulate micro-beads attached to the cell surface The cell is stretched by progressively increasing the distance between the bead and the binding site, where the induced deformation responses are recorded for analysis To extract the mechanical properties from the obtained force-deformation relationship, a cell mechanical model is developed from our previous work This model is based on membrane theory and adopts a hyperelastic material to represent the deformation behavior of RBC membranes. By fitting the modeling results to the experimental data, the area compressibility modulus and elastic shear modulus are characterized as 0. 29 ± 0. 05 N/m and 6. 5 ± 1.0 uN/m, respectively, which are less than the reported results of natural RBCs in isotonic conditions This study indicates that hypotonic stress has a significant effect on the biomechanical properties of human RBCs, providing insight into the pathology of some human diseases and disease therapy.
8.1 Introduction
Human red blood cells (RBCs) are responsible for transportation of oxygen and carbon dioxide, which are crucial for maintaining normal physiological functions of human bodies It is well known that RBCs have the ability to withstand large passive deformation when traversing narrow capillaries during microcirculation An RBC mainly includes a liquid drop (hemoglobin) and a biomembrane, in which a lipid bilayer membrane is attached to a two-dimensional cytoskeletal network through some transmembrane proteins (Mohandas and Gallagher 2008). Compared to the biomembrane, the resistance of the inner fluid to stress is small and negligible. The deform-ability of human RBCs is thus dominated by the mechanical properties of biomembranes.
Cell mechanics is essential in maintenance and regulation of the physiological functions of biological cells Abnormity of cell mechanics, especially biomechanical properties, may reflect microstructural alterations of the cyto-skeleton and may lead to some disorders. Therefore, cell mechanics of human RBCs has received considerable attention in recent years Accumulating evidence has reported that alterations of the mechanical properties of RBCs may be associated with the onset and progression of some diseases For example, mechanical properties of oxygenated RBCs in sickle cell disease are significantly different from those of healthy RBCs (Nash, Johnson, and Meiselman 1984). RBCs parasitized by malaria virus, namely, Plasmodium falciparum, become rigid and poorly deformable and show abnormal circulatory behavior (Glenister et al. 2002; Shelby et al. 2003; Suwanarusk et al. 2004). The shear modulus of these infected RBCs was found to increase up to tenfold during parasite development (Suresh et al 2005) Additionally, the cell mechanics of RBCs is related to some other disorders, such as diabetes mellitus (Tsukada et al 2001), sepsis (Baskurt, Gelmont, and Meiseliman 1998), and chronic renal failure (Meier et al 1991).
The cell mechanics of RBCs has been extensively investigated It has been reported that several factors may regulate the cell properties of RBCs, such as chemical or drug treatment by thyroxine (Baskurt et al 1990), nitric oxide (Bor-Kucukatay et al. 2003), and lanthanum (Alexy et al. 2007) and the effect of pH (Kuzman et al. 2000), temperature (Mills et al. 2007), and cell age (Sutera et al 1985) An important physiological condition, osmotic stress has been found to have great influence on the biomechanical properties of some other types of cells; for example, articular chondrocytes (Guilak, Erickson, and Ting-Beall 2002), human neutrophils (Ting-Beall, Needham, and Hochmuth 1993), and Madin-Darby canine kidney cells (Steltenkamp et al 2006) However, little attention has been paid to its effect on human RBCs.
To investigate the influence of osmotic stress on the mechanical properties of RBCs, robotic manipulation technology with optical tweezers is utilized to study the cell mechanics of human RBCs in hypotonic solutions Increasing demands for both high precision and high throughput in cell manipulation highlights the need for automated processing with robotics technology. Benefiting from great advances such as visual servoing (Feddema and Simon 1998; Huang et al 2009a, 2009b), microforce sensing and control (Wejinya, Shen, and Xi 2008; Xie et al. 2009), motion control (Sun and Mills 2002), microfabrication techniques (Zhang et al. 2004), and image processing (Li, Zong, and Bi 2001), robotic manipulation of biological objects has been achieved (Huang et al 2009a, 2009b; Xie et al 2009) In parallel, optical tweezer technology is known for its ability to impose force and deformation on a microscaled object on the order of piconewtons (pN, 10-12 N) and nanometers (nm, 10-9 m), respectively, in noncontact and noninvasive manners Combining these two advanced techniques, biological cells can be manipulated with high precision and good controllability.
In this chapter, a cell mechanical model is developed from our previous work (Tan, Sun, and Huang 2010; Tan et al. 2008, 2009, 2010a, 2010b) to model the deformation behavior of human RBCs in optically induced cell stretching Equilibrium equations are adopted to represent the force balance of the biomembrane; a hyperelastic constitutive material, namely, Evans-Skalak material, is utilized to describe the material characteristics of RBC membranes According to the mechanical model, the relationship between the stretching force and the induced deformation can be established To investigate the osmotic effect on the mechanical properties of human RBCs, robotic manipulation technology with optical tweezers is used to stretch human RBCs in hypotonic conditions RBCs are stretched to different levels of deformation at various trapping forces. By fitting the modeling results to the experimental data, the area compressibility modulus and the shear elastic modulus of RBCs are obtained, which are less than the reported results of the natural RBCs in isotonic conditions. This indicates the significant effect of osmotic stress on the mechanical properties of human RBCs but also can be used to shed light on the therapy and pathology of some human diseases.
8.2 Cell Mechanical Modeling
In our previous work (Tan, Sun, and Huang 2010; Tan et al 2008), we proposed a theoretical model to interpret the deformation response of biological cells in microinjection This model was based on membrane theory and unitized a hyperelastic material to describe the deformation behavior of cell membranes In this chapter, according to the practical conditions of RBCs stretching experiments by optical tweezers, the mechanical model is modified and extended to extract the mechanical properties of RBC membranes.
The experimental conditions of RBCs stretching meet the prerequisite and restriction of the mechanical model developed in our previous work. First, human RBCs in hypotonic solutions appear to be spherical or spheroidic; that is, rotationally symmetric Second, RBC biomembranes are usually treated as incompressible homogeneous isotropic materials (Henon et al 1999; Mills et al 2004) Third, during the deformation process of RBCs, their internal volumes are generally considered to stay constant; that is, cytoplasm is incompressible (Dao, Lim, and Suresh 2003; Mills et al. 2007).
According to the shell theory of Landau and Lifshitz (1986), the contribution of the bending rigidity can be neglected due to the small thickness of biomembrane Then, the deformation behavior of RBCs in optical stretching is mainly determined by membrane theory. Quasistatic equilibrium equations are used to describe the force balance in the meridian tangential and normal directions of the cell membrane, which are expressed by (Feng and Yang 1973; Tan, Sun, and Huang 2010; Tan et al. 2008, 2009):
(8.1)
(8.2)
where T1 and T2, À1 and À2, and K1 and K2 are the principal tensions, stretch ratios, and curvatures, respectively The indices 1 and 2 refer to the corresponding component in the meridian and circumferential directions of the deformed membrane, respectively P is the external pressure acting on the membrane in the normal direction. p and n are the coordinates after deformation as shown in Figure 8.1. The prime denotes the derivative with respect to the angle |/.
The principal tensions T1 and T2 are calculated according to the strain energy function of the chosen membrane material Because the constitutive material proposed by Evans and Skalak (1980; ES material) is usually used to represent the deformation behavior of RBC membranes, it is adopted here to model the stretching deformation T1 and T2 can be derived from the strain energy function as follows:
FIGURE 8.1
Coordinates definition before and after optical stretching. Image courtesy of Y. Tan, used with permission from IEEE (Tan et al. 2009).
(8.3)
where k and u are the area compressibility modulus and shear modulus, respectively
There are two contact areas between an RBC and its exterior. One is between the bead and the RBC, and the other is between the glass surface and the other side of the cell. Because it is difficult to define the interactions in the contact areas, we simplify this problem by assuming that the interactions in both the contact areas are similar This approximation is consistent with the treatment method reported previously (Mills et al. 2007). As shown in Figure 8.1, due to dual symmetry, only a quarter of the deformed cell shape is needed for analysis According to the experimental conditions in cell stretching, appropriate boundary conditions are used, which are given as follows:
At point
At point
At point
where rcontact is the contact radius between the cell and the bead.
To solve the equilibrium Equations (8.1) and (8.2), the volume conservation constraint is imposed (Dao, Lim, and Suresh 2003; Mills et al. 2004; Tan, Sun, and Huang 2010; Tan et al. 2008, 2009, 2010a, 2010b). Moreover, the contact radius between beads and RBCs must be known prior by image processing. In the coordinates defined in Figure 8.1, K1, K2, p, and n can all be expressed as a function of X1 and X2, respectively (see more details in Tan et al. 2008). With the five equations, that is, Equations (8.1)-(8.3) and the volume conservation constraint, five unknowns X^ X^ T1, T2, and P can be solved. The deformed cell shapes are then determined as shown in Figure 8.2. The axial deformation d (along the stretching direction) is thus obtained. In parallel, the stretching force is acquired from the force balance in the equatorial plane Therefore, the force and the induced deformation can be expressed as follows:
(8.4)
(8.5)
FIGURE 8.2
Calculated deformed cell shapes after optical stretching.
As stated above, the force-deformation relationship is determined when the area compressibility modulus k and the shear modulus u are given in Equation (8.3) Different mechanical properties lead to different force-deformation curves. By minimizing the deviation between the modeling results and the experimental data, the biomechanical properties of RBCs can be characterized.
8.3 Cell Manipulation with Optical Tweezers
To study the cell mechanics of human RBCs, experiments of robotic cell manipulation with optical tweezers were conducted Human RBCs are stretched at different levels of trapping forces Through force calibrations and image processing, the relationship between the stretching forces and the induced deformations is established, from which the mechanical properties of RBCs can be characterized based on the cell mechanical model.
8.3.1 Optical Tweezer System
Figure 8.3 shows a schematic diagram of our optical tweezer system, which mainly consists of a single laser trap. The 808-nm diode laser source has a maximum power of 2.0 W. The laser beam is reflected by a dichroic mirror into a 40x objective and focused on the observation plane. To minimize the possible optical damage to living cells, the laser beam is focused on the attached polystyrene beads instead of RBCs The biological sample is placed on a two-dimensional motorized stage that is driven by two DC motors with a positioning accuracy of 50 nm (PI M-111.1DG, Physik Instrumente Co., Shanghai, China) The cell manipulation process is guided by visual feedback provided by a CCD camera, from which the positions of cell and beads are obtained as well as the cell deformation All of the mechanical components were supported on an antivibration table.
The mixture of RBCs and beads was contained in a home-built chamber, which was assembled with microscopic slides and coverslips conglutinated by super glue All slides and coverslips were cleaned using ethanol The coverslips were glued to the slide with super glue and sealed at the corners with nail polish In cell stretching experiments, the surfaces of the chamber were bare glass. Once adhesion between cells and beads was confirmed, the diluted mixture was injected into the chamber from an open end, which was then sealed with a coverslip The chamber was then reversed for about 10 minutes to let the cells settle down and adhere Most RBCs were attached to the sidewall surface of the chamber, and unattached cells sank to the slide after inverting the chamber back to its original position Then the chamber was ready for robotic manipulation experiments It should be noted that all of the glass surfaces of the chamber were treated with 100 mg/mL bovine serum albumin (BSA, Sigma, St. Louis, MO, USA) to prevent the beads from sticking for microbead manipulation experiments (Tan et al 2009, 2010b)
FIGURE 8.3
Robotic optical tweezer system: (a) experimental setup of optical tweezer system and (b) schematic diagram of optical tweezer system.
8.3.2 Experimental Materials Preparation
Fresh blood was drawn from healthy donors by fingertip prick. A small portion of blood was suspended in phosphate-buffered saline (PBS, Sigma) and then washed three times by centrifugation. A dense RBC sample was obtained after discarding the top layer of blood after rinsing In parallel, streptavi-din-coated polystyrene beads with a radius of 1.5 um (Bangs Laboratories, Fishers, IN) were centrifuged three times in 0. 1 mg/mL PBS-BSA solution. The washed beads were incubated with 1 mg/mL biotin-conjugated concana-valin A (Con A, Sigma) at 4°C for 40 minutes. The beads were then rinsed three more times in 0. 1 mg/mL PBS-BSA and stored in 0. 1 mg/mL PBS-BSA solution with Ca2+ and Mn2+. The prepared polystyrene beads were added to the RBC suspension and incubated at 25°C for one hour to allow the adhesion between beads and RBCs. Once the adhesion was confirmed under an optical microscope, the mixture was diluted in 0. 7% hypotonic sodium chloride buffer to allow RBCs to become swollen.
8.3.3 Force Calibration
To acquire the optical trapping force at a certain laser power, it is necessary to perform force calibration experiments because the trapping force cannot be measured directly The usual viscous drag force calibration method was used here (Henon et al 1999; Mills et al 2004; Tan et al 2010a) A polystyrene bead was trapped at the same separation distance h as that used in cell stretching experiments As the chamber was driven to move via the motorized stage, the fluid flow exerted a viscous drag force on the trapped bead. When the flow velocity increased up to a critical value beyond which the bead just escaped the laser trap, the bead achieved equilibrium; that is, the trapping force equaled the viscous drag force. According to Stokes' law, the viscous drag force is expressed as (Svoboda and Block 1994)
(8.6)
where R is the radius of the trapped bead, n0 is the fluid viscosity (n0 = 1.01 x 10-3 Pa. s at 25°C), v0 is the critical velocity, and h is the separation distance of the bead below the coverslip surface Throughout calibration and cell stretching experiments, h was kept at 5 um
FIGURE 8.4
Optical force calibration versus various laser powers by trapping a polystyrene bead with radius of 1. 5 urn at the separation depth h = 5 um from the coverslip.
The force calibration results are shown in Figure 8.4 over a range of laser power. At each level of laser power, five separate measurements were conducted and the results were averaged. All data can be fitted by a straight line, which is consistent with the results reported by Svoboda and Block (1994) and Mills et al (2004).
8.3.4 Robotic Manipulation of Microbeads
Robotic manipulation of biological cells has been reported in mechanical contacts (Huang et al. 2009a, 2009b; Li, Zong, and Bi 2001; Sun and Mills 2002; Wejinya, Shen, and Xi 2008; Xie et al. 2009). In many noninvasive cell manipulation applications (Arai et al. 2001; Gu, Kuriakose, and Gan 2007), cells were held and manipulated by laser traps directly. In this study, microbeads were attached to the cell surface, serving as handles to stretch the RBCs The laser beam was focused on the attached bead instead of the cell to minimize the potential optical damage Microbeads were manipulated by optical traps directly in RBC stretching experiments. Here, we first demonstrate the efficiency of bead manipulation by optical tweezers. Figure 8.5 illustrates the manipulation process When the moving velocity of the motorized stage is lower than the critical value calculated from Equation (8.6), the trap holds the bead tightly, as shown in Figures 8.5a-c. As the velocity increases beyond this critical value, the bead escapes the trap, as shown in see Figure 8.5d. During cell manipulation, the centroids of microbeads can be obtained through image processing Because the position of the trap is fixed, bead escape is detected when the centroid of the bead deviates from the trap position with a certain distance
FIGURE 8.5
Robotic manipulation process of microbeads by optical tweezers: the large cross denotes the initial position of the manipulated bead, while the small cross denotes the position of the optical trap. The black circle and dot indicate the contour and the center of the microbeads, respectively. Scale bar is 10 um. Reprinted with permission from IEEE (Tan et al. 2009).
8.3.5 Optical Stretching of Human RBCs
Because our optical tweezer system consists of a single laser trap, a small portion of an RBC was required to be anchored to the side wall of the cham-ber while the attached bead on the opposite side was grasped by an optical trap, as shown in Figure 8.6 (Mills et al. 2007). As the chamber was driven to move by the motorized stage, the anchored side of the cell was moved with the stage. Because the trapped bead was kept fixed in the optical trap, the RBC was stretched until the trapped bead escaped from the trap. Note that the moving direction of the stage was determined along the line passing through the bead's centroid and the binding site of the cell. Figure 8.7 shows the cell stretching process.
FIGURE 8.6
A schematic graph of cell stretching experiments, where one side of an RBC is fixed onto the glass surface and the other side is held by a laser trap Reprinted with permission from IEEE (Tan et al 2009).
FIGURE 8.7
Stretching process of a swollen RBC: (a) before stretching, (b) during stretching, (c) stretched to the maximum deformation, and (d) the bead escapes the laser trap. Scale bar is 5 um. Reprinted with permission from IEEE (Tan et al 2009).
For each stretching experiment, RBCs were stretched to different levels of deformation over a range of laser powers, which were recorded by the CCD camera for image analysis The image at the moment when the trap could not hold the bead any longer was captured for cell deformation estimation The trapping force can be acquired from the calibrated relationship between trapping force and laser power. Figure 8.8 shows the stretched cell shapes under a series of trapping forces To obtain the deformations of RBCs, the digital image was processed by a home-built program to detect the edges of the stretched RBCs as shown in Figure 8.9. Then the axial deformation was measured.
8.4 Results and Discussion
Cell deformation was measured at each laser power Then the relationship between the stretching force and the induced axial deformation was established for cell stretching experiments, which is shown in Figure 8.10. For each data point, ten separate tests were conducted and the obtained results were averaged It was found that RBCs tend to become stiff after repetitive stretching. To eliminate the influence of stretching-induced cell stiffening, we used the results from the first stretch for each cell for analysis. The error bar in Figure 8.10 represents the standard deviation of the measured cell deformation. According to Equations (8.4) and (8.5), the modeling relation between force and deformation can be obtained once the mechanical properties of RBCs are prescribed. The contact radius between the beads and RBCs rconnect was measured as 0. 8 um. It was found that the experimental data agreed well with the modeling results when the area compressibility modulus and shear modulus were given as k = 0. 29 ± 0.95 N/m and u = 6. 5 ± 1. 0 uN/m. The mechanical properties were determined through an identification procedure as reported in Tan, Sun, and Huang (2010). When the deviation between the experiments and the cell modeling was minimized, the most appropriate values of k and u were obtained. The acquired mechanical properties of swollen RBCs are consistent with the reported values; for example, the area compressibility modulus of RBCs in hypotonic conditions is on the order of 0. 2-0.45 N/m (Evans, Waugh, and Melnik 1976), and the elastic shear modulus is in the range of 2.5-10 uN/m (Dao, Lim, and Suresh 2003; Henon et al. 1999; Mills et al. 2004) but less than the elastic shear modulus of natural RBCs in isotonic conditions, which is reported to be 13 uN/m (Dao, Lim, and Suresh 2003). The results indicate that cell softening in hypotonic conditions may be related to the significant effect of osmotic stress on RBCs. Under hypotonic conditions, the osmotic pressure causes water influx from the exterior of the cell, which leads to the inflation of cytosol and the cyto-skeleton The decrease of cell stiffness is attributed to the fact that the phos-pholipids bilayer membrane swells faster than the cytoskeleton (Steltenkamp et al. 2006). As a consequence, the volume inflation leads to either rupture of cytoskeleton or its detachment from the lipid membrane Moreover, the osmosis-induced increase of cell deformability has some potential biomedical significance and can provide a reasonable explanation for the observations reported previously RBCs from sickle cell anemia patients appear to be much stiffer and less deformable than healthy RBCs (Nash, Johnson, and Meiselman 1984). It has been observed that treatment using hypotonic saline solution can reverse the sickling of the sickled RBCs, which may be beneficial in emergency therapy for painful sickle cell crises (Guy, Gavrilis, and Rothenberg 1973; McManus, Churchwell, and Strange 1995) This phenomenon can be explained by the outcome of this study in that the hypotonic solution makes the sickled RBCs much softer and more deformable, which may be beneficial in the alleviation of sickle cell disease. However, excessively hypotonic conditions will swell RBCs to an extreme extent and may cause hemolysis (Braasch 1971)
FIGURE 8.8
Deformed cell shapes of a swollen RBC at different levels of stretching forces: (a) 0 pN, (b) 8 pN, (c) 12 pN, and (d) 17. 5 pN. Scale bar is 5 um. Reprinted with permission from IEEE (Tan et al 2009).
FIGURE 8.9
Image analysis for cell deformation estimation: (a) original image and (b) processed image Reprinted with permission from IEEE (Tan et al 2009).
FIGURE 8.10
Comparison of experimental data and modeling results. Reprinted with permission from IEEE (Tan et al. 2009).
Additionally, the results show that the relation between the stretching force and the axial deformation is quasilinear, which is consistent with the results reported in Henon et al. (1999) and Mills et al. (2004). This finding indicates that when the stretching force is low enough (less than 18 pN), the swollen RBC behaves like a linear elastic spring, which reflects the intrinsic membrane deformation characteristics in this force range and sheds light on the study of the microstructures of RBC biomembranes
8.5 Summary
In this chapter, mechanical characterization of human RBCs was successfully achieved through robotic manipulation with optical tweezers. A cell mechanical model was developed based on membrane theory, in which Evans-Skalak material was utilized to represent the deformation behavior of RBC biomembranes. To investigate the influence of osmotic stress on the mechanical properties of human RBCs, robotic manipulation technology with optical tweezers was used to stretch RBCs in hypotonic conditions The linear relationship between the stretching force and the axial deformation was obtained in experiments Comparing the experimental data to the modeling results, the mechanical properties of RBCs, for example, the area compressibility modulus and the elastic shear modulus, were characterized, which were lower than the counterpart RBCs in isotonic conditions This preliminary study not only helps in understanding the significant effect of osmotic stress on human RBCs but provides insight into the pathology of some human diseases and disease therapy.
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