ATP-dependent mechanics of red blood cells

Abstract

Red blood cells are amazingly deformable structures able to recover their initial shape even after large deformations as when passing through tight blood capillaries. The reason for this exceptional property is found in the composition of the membrane and the membrane-cytoskeleton interaction. We investigate the mechanics and the dynamics of RBCs by a unique noninvasive technique, using weak optical tweezers to measure membrane fluctuation amplitudes with μs temporal and sub nm spatial resolution. This enhanced edge detection method allows to span over >4 orders of magnitude in frequency. Hence, we can simultaneously measure red blood cell membrane mechanical properties such as bending modulus κ = 2.8 ± 0.3 × 10⁻¹⁹J = 67.6 ± 7.2 k_BT, tension σ = 6.5 ± 2.1 × 10⁻⁷N/m, and an effective viscosity η_eff = 81 ± 3.7 × 10⁻³ Pa s that suggests unknown dissipative processes. We furthermore show that cell mechanics highly depends on the membrane-spectrin interaction mediated by the phosphorylation of the interconnection protein 4.1R. Inhibition and activation of this phosphorylation significantly affects tension and effective viscosity. Our results show that on short time scales (slower than 100 ms) the membrane fluctuates as in thermodynamic equilibrium. At time scales longer than 100 ms, the equilibrium description breaks down and fluctuation amplitudes are higher by 40% than predicted by the membrane equilibrium theory. Possible explanations for this discrepancy are influences of the spectrin that is not included in the membrane theory or nonequilibrium fluctuations that can be accounted for by defining a nonthermal effective energy of up to E_eff = 1.4 ± 0.1 k_BT, that corresponds to an actively increased effective temperature.

The extraordinary deformability of RBCs is vital for their proper function, as it enables the cells to be elongated by more than twice their size when passing through μm-sized capillaries. The elastic properties of RBCs are dominated by the interaction between the cell membrane and the underlying cytoskeleton, mainly consisting of spectrin, a long heterodimer that aligns tail to tail forming a 200-nm-long tetramer. Each spectrin filament interconnects to up to 5 other spectrins and is bound to the cell membrane via a protein complex consisting of protein 4.1R, actin, and glycophorin C (1). The plasma membrane fluctuations are related to RBCs' mechanical properties that have been extensively studied over the past three decades (2–6). It is well known that fluctuations of the membrane depend on its bending rigidity κ and its membrane tension σ (7). Furthermore, RBCs gain their elasticity from the elastic shear modulus of the cytoskeletal spectrin network (8, 9). Recent theoretical analysis (10) suggest that the spectrin cytoskeleton acts as a steric barrier restricting membrane undulations toward the network.

Experiments by Tuvia and coworkers showed an ATP dependent effect by monitoring the static fluctuation amplitude of RBCs under normal and ATP-depletion conditions (11). In these measurements, the fluctuation amplitude (the root mean square displacement; rmsd), was found to decrease substantially under ATP depletion. This was interpreted as a sign for activity-dependent fluctuations. However, a recent report did not confirm this decrease (6), arguing that the fluctuations are purely thermally driven. Additionally to the fluctuation decrease under ATP depletion, Tuvia et al. found a fluctuation decrease upon increase of the external medium viscosity, in disagreement with thermodynamics, which predicts that all equilibrium quantities are independent of transport coefficients such as the viscosity. This suggested an active, energy-consuming process, depending on phosphorylation of the 4.1R protein or erythrocyte myosin motors. Subsequent theoretical studies argue that the viscosity dependence of static fluctuations could be explained by the ATP-dependent phosphorylation of the 4.1R protein (12), which controls the spectrin-membrane connection (1). This phosphorylation is catalyzed by protein kinase C (PKC) (13), which disassembles the 4.1R/spectrin/actin trimer, thus leading to a decreased overall stability of the RBC membrane.

Previous measurements to determine membrane fluctuations suffer from the restricted time resolution of camera acquisition (6), or can only detect relative and uncalibrated fluctuation amplitudes (5, 11). To overcome both limitations we used a unique approach to monitor the time-dependent fluctuation of the RBC membrane at a single point with sub nm spatial and μs time resolution (14). Our measurements are in excellent agreement with the theory of fluctuating membranes at frequencies >10Hz and enable us to simultaneously measure the membrane bending modulus κ, the tension σ, and an effective viscosity η_eff of RBCs, thereby showing that the external viscosity has no effect on the time averaged fluctuation amplitudes.

Results

Interferometric Fluctuation Detection.

The method used to measure RBC membrane fluctuations is an extension of well-known interferometric particle detection using optical tweezers (15). However, the laser is operated at minuscule powers (≈50 μW) at the sample, too small to create a trapping potential. In the experiments, a volume of 15 μL of a RBC suspension was sealed between two coverslips, and cells were allowed to weakly attach on the substrate for 30 min. Only discocyte-shaped RBCs with diameters varying from 6 to 8 μm were used. Weak attachment of the RBCs to the coverslip was checked by reflection interference contrast microscopy (RICM) (SI Appendix and Fig. S1). The infra-red (λ = 1064 nm) laser was positioned at the edge of the cell, and a calibration curve (line scan) was acquired by moving the RBC through the laser with a step size of 4 nm using a piezoelectric stage and recording the signal with a quadrant photodiode (QPD) at the condenser‘s back focal plane as shown in Fig. 1. The method is based on a difference in refractive index, thus detecting the plasma membrane at the interface between the cell and the medium. Each data point of the calibration curve represents an average of 500 recordings taken at a sampling rate of 100 kHz. The acquired calibration curve shows a linear regime, which was used to convert between QPD voltage and edge position in nm by determining the slope. To record the fluctuations, the edge of the RBC was positioned at the center of the linear regime (called the working point WP, Fig. 1). To measure the membrane fluctuations, the QPD voltage was recorded in 10 subsequent measurements of 10 seconds each and converted to nm using the previously determined linear slope of the calibration curve. After each recording, the line scan was repeated to ensure that the cell's properties and position did not change during the experiment. From each time series, the power spectral density (PSD) was calculated (see SI Appendix) and filtered using log binning. For further evaluation of the data, the mean PSD of the 10 recordings was used. To ensure that the laser did not interfere with the measurements, we recorded the PSD as a function of the applied power and found no dependence for laser powers smaller than 1 mW (see Fig. S1), thus confirming that the used power of 50 μW does not influence the measurement.

Fig. 1.

Schematics of the setup used to detect the RBC edge fluctuations. Infra-red (λ = 1064 nm) laser light is emitted from a fiber laser and intensity-controlled using an acousto-optical modulator (AOM). Five percent of the light is projected on a photodiode (PD) as intensity reference. A 10× telescope increases the beam diameter to 14 mm. The beam is coupled in the optical path of an inverted microscope using a dichroic mirror and focused on the sample by a water-immersion objective (O). At the sample the light is partially scattered off the cell edge. Scattered and unscattered light are collected by a water-immersion condenser (C) and imaged on a QPD. Before digitalization (DAQ), the data are amplified and filtered using custom made low-noise hardware (AMPL). Round Inset 1 shows a detailed view of the experiment. Part of the laser interacts with the cell by light scattering, which is monitored by the QPD. A calibration curve is recorded by moving the RBC through the laser focus using a 3D piezoelectric stage (3D-PZ) and determining a linear regime as shown in the plot. The center of this linear regime is used as the working point (WP) of the experiment. A camera images the position of the cell using white light (WL). Round Inset 2 sketches the interaction between the membrane and the spectrin network, which is maintained by the protein 4.1 forming a trimer with spectrin and a short actin filament.

Mechanics of Normal RBCs.

The PSD in Fig. 2 represents mean and standard error (n = 210) of 21 normal RBCs. A theoretical description of the PSD has been established previously (16) (SI Appendix, Calculations). In the limit of a flat membrane the PSD decays at high frequencies with a theoretical predicted power law of PSD_HF ∝ f^−5/3, illustrated by the dashed line in Fig. 2. At low frequency the curve levels off because of the finite size of the RBC and membrane tension. The theoretical description (SI Appendix, Calculations) provides an excellent fit in both regimes (Fig. 2) (r² = 1−Σ (PSD_exp−PSD_model)²/Σ PSD_model² = 0.98), which allows us to measure the RBCs mechanical properties of bending rigidity κ^dy = 2.8 ± 0.3 × 10⁻¹⁹J, surface tension σ = 6.5 ± 2.1 × 10⁻⁷N/m, and effective viscosity η^eff = 81 ± 3.7 × 10⁻³Pa s (Table 1). The used fit function has three independent parameters, each changing the curve in a characteristic way, which ensures that all parameters can be determined simultaneously. The bending modulus and the tension are both consistent with literature values that have been measured with other methods (3–6).

Fig. 2.

Fluctuation spectra of normal RBC under various medium viscosities. (A) Mean PSD of 21 normal RBCs. The presented error (at the center of the diamond data) is the standard error for the 210 individual PSDs. The fit provides an excellent explanation for the data over four decades. The theoretical slope of (-5/3) is shown presented as an eye-guide (dashed line). (Inset) Static fluctuations histogram of a normal RBC. (B) PSD of RBCs immersed in media of increasing viscosities, and the corresponding fluctuation histogram in the Inset. Although the PSD differ significantly, the fluctuation histogram remains almost independent of the viscosity.

Table 1.

Collection of mechanical parameters of RBCs under various conditions, compared with previous findings by Evans et al. (6) and Strey et al. (4)

	Normal	ATP-depl.	PKC
rmsdex [nm]	33.0 ± 1.3	22.3 ± 0.6	36.7 ± 2.8
rmsdth [nm]	36.3 ± 12	24.0 ± 9.0	47.2 ± 13
κSPSstat [10−19J]	2.8 ± 0.2	6.1 ± 0.3	2.3 ± 0.4
κdyn [10−19J]	2.8 ± 0.3	3.9 ± 0.3	2.6 ± 0.2
σ [10−7 N/m]	6.5 ± 2.1	19 ± 1	2.7 ± 1.1
ηeff [10−3Pa s]	81 ± 3.7	118 ± 11.8	57 ± 2.4
rmsdEvans [nm]	23.6 ± 0.6	22.8 ± 1.0	—
rmsdStrey [nm]	30.0 ± 5	—	—

Furthermore, for a consistency check, we determined the mechanics of hypertonic swollen cells (see Fig. S2) and found an increase in tension and a decrease in viscosity as expected (6). Previous work estimated κ by measuring the rmsd of edge fluctuations (4, 6), which is equivalent to the standard deviation of the Gaussian distributed histogram of the fluctuation amplitude (Fig. 2, Insets). For normal RBCs we find a rmsd value of Δh = 33.0 ± 1.3 nm, consistent with literature (4, 14, 17). The rmsd is a static measurement that averages the fluctuation amplitudes over time and is independent of the viscosity in equilibrium systems. Its measurement enables us to crosscheck our results in two ways. First, we can show the consistency of the measured rmsd with the theoretical static fluctuation amplitude rmsd_th = 36 ± 11 nm, which is calculated using the mechanical parameters determined from the dynamic measurements (Table 1). Additionally, in the literature the rmsd has been used to determine the bending stiffness by assuming a tensionless limit and accounting for the shear modulus on the first fluctuation mode. Strey, Peterson, and Sackmann (SPS) established an approximation to calculate a bending modulus from the rmsd (4): κ^stat_SPS = (6 × 10⁻⁶)k_BT R²/(Δh_{l = 1})² = 2.8 ± 0.2 × 10⁻¹⁹J, where R denotes the cell radius, and k_B the Boltzmann constant. This approximative static bending modulus is an alternative method, and in the case of normal RBCs it agrees well with the dynamic bending modulus obtained from the PSD (see Table 1). We furthermore checked the dependence of the fluctuation on the viscosity of the external medium. We increased the medium viscosity by the addition of 75 mg/mL (η₇₅ = 2.4 ± 0.1 × 10⁻³Pa s), 135 mg/ml (η₁₃₅ = 4.4 ± 0.2 × 10⁻³Pa s), and 200 mg/mL (η₂₀₀ = 10.9 ± 0.9 × 10⁻³Pa s) of Dextran 41000. In all cases fluctuation histograms were well Gaussian distributed, but did not depend on the external viscosity (Fig. 2B), as expected from equilibrium statistical mechanics. Furthermore, we used the PSD of RBC immersed in solvents of different viscosities to determine the effective viscosity as a function of external viscosity. The resulting dependence (SI Appendix and Fig. S3) can be well fitted with a linear function η_eff = a×η_ext+b, yielding fit parameters of a = 8.3 ± 2.3 and b = 53 ± 11 × 10⁻³Pa s.

PSD of ATP-Depleted Cells.

To investigate the effect of ATP on membrane mechanics, we removed ATP from the RBCs by applying an ATP depletion medium for 3 h and then measured the resulting PSD. As presented in Fig. 3A (green, n = 200, fit quality: r² = 0.85) the fluctuation amplitude was significantly smaller than for the normal RBCs over the full frequency spectrum, showing a strong dependence of the membrane fluctuations on ATP. We measured a slightly increased bending rigidity, and dynamic measurements showed that the effective viscosity was also increased by ≈50% (Table 1). The effect of ATP-depletion was additionally reflected in the static measurement of the rmsd, which was strongly decreased compared with normal cells (Table 1). Interestingly, removing ATP led to a strong increase of tension, which explains the discrepancy between the dynamic bending modulus presented in this work and the static bending modulus which assumes a vanishing tension (4) (Table 1).

Fig. 3.

Absolute and normalized fluctuation spectra. (A) Mean PSD of 21 normal RBCs (n = 210, black) and 20 ATP-depleted (n = 200, green) and 21 PKC-activated (n = 210, red). The solid lines show the fit. (Inset) Semilog plot of the same data for the marked frequency range showing that the ATP-depleted cells have the smallest amplitude. (B) Semi logarithmic representation of the fluctuation amplitudes normalized by the ATP-depleted PSD, which can be considered to be a purely thermally driven system because of the lack of the energy source ATP.

PSD of PKC-Activated Cells.

The fluctuation decrease in ATP-depleted cells might be because of an inhibition of the phosphorylation of the 4.1R protein, which connects the spectrin to the membrane in its unphosphorylated state (13). To investigate the influence of this connection we activated PKC, an enzyme that had been shown to phosphorylate 4.1R, thus resulting in an increased dissociation of the spectrin network and unbinding of spectrin from the membrane (13). The resulting PSD of 21 PKC activated cells is presented in Fig. 3A (red, n = 210, fit quality: r² = 0.97). Fluctuations increased over the accessible frequency range compared with the normal RBCs. The analysis of the data yields static and dynamic bending rigidities consistent with the bending rigidity measured on normal RBCs (Table 1). However, our results showed that over-activation of PKC decreases membrane tension by ≈50% and resulted in a slight decrease of the effective viscosity (Table 1). DMSO control experiments showed no difference with the normal cells. Additionally, we checked the effect of cells treated with the actin depolymerizing drug latrunculin A (SI Appendix and Fig. S4). The data are similar to the PKC activated cells (SI Appendix and Fig. S5), however, our controls show that F-actin in RBCs was not affected by latrunculin A (SI Appendix and Fig. S6), which indicates that there is no actin dynamics in RBCs. Our experiments suggest a yet unknown effect of LA on the cytoskeleton membrane interaction.

Relative Fluctuation Amplitudes.

To investigate the effect of nonthermal contributions, we normalized the fluctuations of normal and PKC-activated cells by the PSD of ATP-depleted cells (Fig. 3B). A striking result of this normalization arose at frequencies >10Hz, where all relative amplitudes level off to plateaus. Here, the fluctuations for PKC-activated cells level to a value of approximately twice the fluctuation of ATP-depleted cells, and the amplitude of normal cells was ≈30% higher than in ATP-depleted cells. However, <10 Hz we found relative amplitudes peaking at 6.5 ± 0.3 (PKC-activated) and 3.6 ± 0.2 (normal cells), all in arbitrary units.

Discussion

The presented results allow us to investigate membrane dynamics with millisecond time and sub nm spatial resolution, using a standard optical tweezers setup equipped with a QPD. In contrast to previous fluctuation analysis which mostly used video microscopy, our method provides great advantages in terms of spatial and temporal resolution, which is not restricted by camera properties and image analysis. In contrast, the presented method is easy to implement, only limited by fundamental signal to noise ratio and does not require complex image analysis. Using the theory of membrane fluctuations, we can extract the mechanical parameters of RBCs under various conditions. The high reproducibility of the experiments and the data quality also allow us to explore the limitations of the applied equilibrium model.

RBC Viscosity.

As presented in Table 1, we discover surprisingly high values for the effective viscosity (≈100 × 10⁻³ Pa s) compared with literature values for RBC viscosity, which was reported to be approximately η_RBC ≈10 × 10⁻³ Pa s (18). Such an increase of the effective viscosity at the membrane was predicted to be a confinement effect caused by close association of the spectrin to the membrane, providing a steric obstacle for the fluid flow (19). Hence, our measurements confirm these predictions. To gain further insight into the effective viscosity, we varied the external viscosity as presented in the results section: The effective viscosity depends linearly on the external viscosity, with a slope of a = 8.3 ± 2.3 (SI Appendix and Fig. S3). This phenomenological dependence can be used to extract a RBC viscosity of η_RBC = 6.4 ± 1.9 Pa s (see SI Appendix), which is consistent with previously reported values (18).

Comparison with the Literature.

Our results confirm previous reports by Tuvia et al. (11) of decreased static fluctuation amplitudes under ATP-depletion conditions that were put into question recently by Evans et al. (6) (see Table 1). Because the rmsd presents the integral over the PSD, it is dominated by the low frequency domain. The low frequency part depends on tension, whereas the high frequency part is dominated by the bending modulus. This allows us to give a mechanical reason for the fluctuation decrease in ATP-depleted cell, which is more pronounced in the low frequency part (see Fig. 3). We identify an increase in tension as reason for these decreased fluctuations, as discussed in the next paragraph (see also Table 1). It should be mentioned that our measurements of the rmsd is consistent with several previous reports (4, 14, 17), but not with Evans et al. A possible explanation for the difference is the duration of drug application. Evans et al. reported having applied the ATP-depletion medium for 1 h. Although we can measure already a slight decrease in the rmsd after 1 h, we found that the rmsd stabilized to a lower value only after 3 h (see Fig. S7 and Fig. S8).

Besides the effect of ATP-depletion Tuvia et al. (11) also report a decreased static fluctuation amplitude if the external viscosity is increased. However, our measurements do not confirm this (Fig. 2B), as we see no dependence of the static fluctuation amplitudes for external viscosities in the range of 1−10 × 10⁻³ Pa s. This lack of viscosity dependence has been predicted to happen if the characteristic time of membrane relaxation on length scales of the spectrin-membrane connections (≈0.1 − 1 ms) is faster than the timescale of activity (≈100 ms) (12), as observed in this work. Furthermore, we tested recent theoretical considerations predicting an additional spring like interaction between the spectrin cytoskeleton and the membrane (10). Including the respective term in our fit function hardly altered the other fit parameters, which remained essentially constant (SI Appendix and Table S1). Hence, our data can be well explained without these additional terms.

ATP-Depletion Effects.

Our measurements can give insight into the longstanding question why ATP depletion has such a strong effect on RBC fluctuation histograms. We can identify a partial mechanical reason for these reduced membrane fluctuations because we measure an increase in membrane bending modulus and surface tension, which decreases the rmsd of the measured histograms. We can explain these findings by a stronger association between the spectrin and the membrane, as ATP depletion prevents the phosphorylation of the 4.1R protein. In its unphosphorylated state, the 4.1R protein strongly couples the spectrin to the membrane, which has important implications for membrane fluctuations. As the persistence length of spectrin is short compared with its contour length and end-to-end distance, the spectrin should be considered to be an entropic spring under tension even in the relaxed state of the RBCs (12, 20). Hence, the measured tension in normal and ATP-depleted cells might be mostly because of the underlying spectrin cytoskeleton. As the presented measurements cannot distinguish between membrane and spectrin tension, we suspect that we effectively detect spectrin tension, which is in turn related to an effective shear modulus (9). The fact that the shear modulus of the spectrin network might show up as an additional tension was recently proposed theoretically by Auth et al. (10). We furthermore attribute the increased effective viscosity in the ATP-depleted cells to the same stronger spectrin-membrane interaction. As suggested, the effective viscosity might be dominated by a yet unknown mechanism, and the continuous association and dissociation of the spectrin under shear could be a molecular reason for an additional dissipative process.

Decreasing the Spectrin-Membrane Interaction.

In contrast to ATP depletion, PKC activation is believed to weaken the spectrin-membrane interaction, as PKC phosphorylates the 4.1R protein (13), thereby dissolving the binding complex. This detachment of the spectrin from the membrane can account for the measured decrease in tension, whereas the bending modulus remains almost unaffected. Furthermore, the decrease of the effective viscosity is consistent with the idea that an additional and dominating dissipative process depends on the spectrin-membrane interaction. In fact, after the model proposed by Gov et al. (12) for the nonequilibrium energy production via the phosphorylation of the 4.1R protein, activation of PKC should not only detach the membrane from the spectrin but also increase the amount of chemical energy used to drive the membrane fluctuations. Because PKC activation implies higher energy consumption, the increase in fluctuations at small frequencies might be because of active ATP-dependent energy injection.

Limitations of the Equilibrium Membrane Description.

Let us analyze the higher relative fluctuation amplitudes in the low frequency regime as shown in (Fig. 3B). The low frequency part of the spectrum is dominated by tension, which varies considerably between the different conditions (Table 1). Because we have used a passive membrane theory, the ratio:

is equal to one if E_eff = k_BT, which we expect for a purely passive system. Here, the membrane mechanics is completely described by the g function (defined in SI Appendix Calculations, N: Normal, P:PKC), which depends on the mechanical parameters (κ, σ, η) and the frequency f. Experimentally, this ratio equals one for the high frequency domain (f >10Hz) in all RBC conditions. Hence, in this regime the passive equilibrium membrane theory seems to be a correct description. However, we observe for the low frequency part a deviation from one, leaving up to 40% of the fluctuations unaccounted for (Fig. 4A). This discrepancy can be potentially explained in two ways. First, at low frequency the simple membrane description of the complex RBC membrane yielding the function g might break down. Hence, it would be necessary to extend the model, for example to composite membrane systems explicitly including the spectrin. A second possible explanation is the breakdown of the equilibrium description, leading to a frequency-dependent effective energy E_eff(f) that becomes important at frequencies <10Hz. This energy term corresponds to a frequency-dependent “effective temperature” T_eff(f) = E_eff(f)/k_B. At high frequencies (>10Hz) T_eff ≈300K, whereas at low frequencies T_eff > 300K, indicating that the system behaves as if its temperature was increased. Such frequency dependence resembles the results of recent experiments on the nonequilibrium behavior of cytoskeleton-motor systems (21) and the oscillation of hair cells (22), where at high frequency equilibrium thermodynamics dominates whereas at frequencies <10Hz, the nonequilibrium effects become apparent.

Fig. 4.

Effective energy and membrane model. (A) Frequency-dependent energy for the various cells. At high frequencies, the fluctuations are driven by thermal activation shown by the value of 1 k_BT, whereas for low frequencies the maximal effective energy is, E_N^max = 1.43 ± 0.09 k_BT for normal cells and E_P^max = 1.32 ± 0.08 k_BT for the PKC-activated cells. (B) Model to explain the measured mechanical differences (17). The fluctuations depend on the membrane properties and on the integrity of the underlying spectrin cytoskeleton, connected to the membrane by actin, glycophorin C (GPC), and protein 4.1R. In normal cells, a continuous de-and reattachment of the spectrin results in a certain net tension. ATP depletion increases the spectrin-membrane connection and the integrity of the spectrin network, leading to an increased tension. In contrast, disrupting the spectrin-membrane interaction by PKC activation weakens the spectrin network and hence decreases the measured tension.

Our finding is of great importance for the theoretical description of RBCs, because our results define a regime in which it is reasonable to apply standard thermodynamics of a single membrane, and one where either out-of-equilibrium phenomena must be taken into account or an extended description of the composite membrane has to be developed. In previous experiments on RBCs such observations were experimentally inaccessible, because their detection requires the knowledge of the full mechanics and access to high-frequency fluctuations, which is generally restricted by the camera acquisition rate of usually 25Hz. However, it should be noted that the current analysis only shows that a passive membrane model does not explain the behavior at low frequencies, and further experiments are required to prove whether this is because of an active process or requires a more complex description of the composite membrane.

Model.

A possible model accounting for the data are sketched in Fig. 4B (17). Note that the presented data reflect the fluctuation of the membrane but does not give direct information about the cytoskeleton, which consists of the floppy spectrin network. This model is based on theoretical suggestions by Gov et al. (12, 23). We attribute the physical origin of the drug dependence to the dissociation of the spectrin-membrane connection. In the context of the 4.1R/spectrin binding, this means that depleting the ATP pool forces the 4.1R protein to be in the unphosphorylated state, which favors the 4.1R/spectrin/actin binding (13, 24). If bound to the membrane, the spectrin cytoskeleton acts like a network of entropic springs, thus imposing a tension that partially compresses the membrane (Fig. 4B) (23). Upon phosphorylation of the 4.1R the spectrin-membrane connection is released and the compressed membrane can relax. The schematics can explain the measured tensions by changes in the spectrin network integrity and variations in the spectrin-membrane interactions, thus leading to modified shear of the spectrin network upon membrane fluctuations. The tension of the spectrin network depends strongly on the network integrity and its association with the membrane. It was already predicted theoretically that at the percolation transition a strong change in tension should be observed (12, 23), which our measurements confirm when modifying the spectrin network by PKC activation or ATP depletion. Increasing the spectrin-membrane connection for ATP-depleted cells leads to an increase in tension, whereas weakening the connection alters the network integrity and hence results in a decrease of tension in PKC-activated cells. As the membrane bending modulus is unaffected by the drugs used, the proposed model predicts that the membrane bending modulus stays constant, as confirmed in our measurements. An additional consequence of the presented model is a nonlinear response to strong deformations caused by a breakdown of the spectrin cytoskeleton at large strains, previously proposed by several authors (25, 26).

The continuous phosphorylation and dephosphorylation of the 4.1R protein is believed to inject mechanical energy in the system. The time scales involved in this binding/unbinding have not yet been determined, but our results indicate that this cycling is slower than 100 ms. In the case of PKC-activation the phosphorylation is favored, however, the cyclic binding/unbinding is not affected, hence energy injection is not perturbed and we measure approximately the same effective energy. The suggested additional dissipative process because of the spectrin-membrane binding might also explain the found increase of effective viscosity in ATP-depleted cells, and its decrease in PKC-activated cells.

Conclusion

In this article we report on a unique, efficient, and fast measurement to detect RBC viscosity, membrane tension, and membrane bending modulus. We confirm theoretical predictions for membrane fluctuations over a wide range of frequencies. The application of ATP-depletion medium and PKC-activation drugs clearly confirms the ATP-dependence of the membrane fluctuations and suggests that the fluctuations might be partially nonthermal in the low frequency domain (f <10Hz) or that an alternative more complex composite membrane model should be developed for this regime. At high frequencies the system is well described by an equilibrium single membrane theory. Depending on the applied drug, we detect changes in tension, which we attribute to the coupling of the membrane to the tense spectrin cytoskeleton. The changes in tension might have a role in unfolding the spectrin to expose hidden binding sites in the spectrin which could act as mechanosensors (27). The presented results are also important in the context of other cell organelles, because the spectrin network can be found to be attached to most cell membrane systems, like Golgi membranes, lysosomal membranes, and intracellular vesicles in cerebella neurons, as well as on the plasma membrane (28). Based on previous work by Gov et al. (12), we suggest a model in which the effective energy is provided by a continuous phosphorylation/dephosphorylation of the 4.1R protein, which also alters the spectrin network. The current data does not allow us to decide whether RBC fluctuations are active processes or should be described by a more refined membrane-spectrin interaction. It is also possible that both explanations are required for a full understanding of the RBCs fluctuations.

Materials and Methods

Preparation of RBCs.

Human RBCs were freshly prepared before each experiment by finger pricking of a healthy donor. Twenty microliters of blood were diluted in 250 μL of a PBS solution containing 130 mM NaCl, 20 mM K/Na phosphate buffer, 10 mM glucose, and 1 mg/mL BSA. RBCs were washed twice in the described PBS buffer by centrifugation (2 min, 200 g) and aspiration of the supernatant. Cells were diluted 1:12 in the final experimental buffers. Before the experiment was started, the slight attachment of the cells was checked by RICM microscopy. If not stated otherwise, all materials were purchased at Sigma–Aldrich, France.

Drug Application.

We tested RBCs under ATP depletion, PKC activation and LA. ATP depletion was performed by incubating the cells for 3 h at 37 °C in a PBS solution deficient, of Glucose containing 6 mM iodoacetamide and 10 mM inosine, as described previously (11). We found that only 1 h incubation under this condition was not sufficient to significantly reduce the fluctuation amplitudes. Cells were stored in the ATP depletion medium during the experiments. PKC activation was achieved as described previously (13). Briefly, cells were incubate for 30 min at 37 °C with 0.02 μM calyculin A solved in DMSO (0.2% final concentration) and subsequently for 90 min at 37 °C with 2 μM phorbol 12-myristate 13-acetate (PMA). LA was applied at a concentration of 20 μM LA for 30 min at 37 °C. In the control experiment 0.4% DMSO was applied for 1 h at 37 °C.

Experimental Setup.

To measure the fluctuation amplitude of the RBCs edge, we use a technique recently described (14), and summarized in Fig. 1. Laser light from a 1 Watt Ytterbium fiber laser (YLM-1–1064-LP, IPG Photonics, Germany) with a wavelength of 1064 nm is collimated and subsequently intensity controlled by a acousto optical modulator (MT80-A1,5–1064 nm, AA Opto Electronic, France), to reduce the power to 50μW at the sample. Up to laser powers of 1mW, no effect of trapping the RBC was observed (SI Appendix and Fig. S1). A 10× telescope increases the diameter of the beam to 14 mm before it is introduced in the beam path of the microscope with an dichroic mirror. The laser is focused in the sample by a 60× water objective (UPLSAPO 60XW/IR, NA 1.2). To control the focus and the imaging position the samples are mounted on a 3D piezoelectric stage (Tritor 102 SG, Piezosystem-Jena, Germany). The scattered light is collected by a long distance water-immersion objective (U LUMPL FL 60XW/IR NA 0.9), and projected on a InGaAs QPD (G6849, Hamamatsu, France) by imaging the back focal aperture of the collecting objective on the QPD. The signal was preamplified and finally amplified and anti-alias filtered by a custom made amplification and filtering electronics (Oeffner Electronics, Germany). The signal was digitized at 100 kHz with a 16 bit AD converter card (PCIE-6259, National Instruments, France), and analyzed using LabView (National Instruments) and Matlab (Mathworks, France).

If operated with higher laser power (5 mW), the setup can also be used as an optical tweezer. By trapping 1 μm beads and recording the PSD of the bead's position we determined the friction coefficient, which is proportional to the medium viscosity (29). For the different media prepared with Dextran 41000 concentrations of 75 mg/mL, 135 mg/mL, and 200 mg/mL we measured the viscosities to be 2.4 ± 0.1 × 10⁻³Pa s, 4.4 ± 0.2 × 10−³Pa s, and 10.9 ± 0.9 × 10−³ Pa s, respectively.