Direct Cytoskeleton Forces Cause Membrane Softening in Red Blood Cells

Abstract

Erythrocytes are flexible cells specialized in the systemic transport of oxygen in vertebrates. This physiological function is connected to their outstanding ability to deform in passing through narrow capillaries. In recent years, there has been an influx of experimental evidence of enhanced cell-shape fluctuations related to metabolically driven activity of the erythroid membrane skeleton. However, no direct observation of the active cytoskeleton forces has yet been reported to our knowledge. Here, we show experimental evidence of the presence of temporally correlated forces superposed over the thermal fluctuations of the erythrocyte membrane. These forces are ATP-dependent and drive enhanced flickering motions in human erythrocytes. Theoretical analyses provide support for a direct force exerted on the membrane by the cytoskeleton nodes as pulses of well-defined average duration. In addition, such metabolically regulated active forces cause global membrane softening, a mechanical attribute related to the functional erythroid deformability.

Figure 1

Characteristic membrane-fluctuation time traces tracked at an arbitrary (real-space) point in the equatorial profile of RBCs (both global variations in the cell radius (cell swelling) and net displacements of the cell center (cell translation) have been subtracted from the data). The data correspond to RBCs with a discocyte shape (dys) at different activity states, as shown in the micrographs (left). (A) A healthy flicker (dys_h) upon cytoskeleton activity. (B and C) Passive cases (h-scale magnified by a factor of 2 with respect to (A)) included drugged RBCs (dys_d) after ATP depletion in PBS(−) buffer (B) and cells fixed with glutaraldehyde (dys_f) (C). Although most RBCs in the passive conditions appeared as nonfluctuating speckled echinocytes, some retained their discocyte shape and continued to fluctuate (dys_d and dys_f). The normalized histograms at right represent the probability distributions of the membrane displacements averaged over all the points in the equatorial profile (σ_h is the standard deviation). The line envelopes correspond to the normal distribution. To see this figure in color, go online.

Figure 2

(A) Experimental static spectra calculated from the time-averaged amplitudes of the equatorial modes, P(qR) = <h_q²>, of discocytes at different states (see Materials and Methods). In the active case (red), the variance band represents data obtained over different healthy cells (N = 40). In passive cases, blue- and black-outlined circles represent the average spectra measured for drugged and fixed discocytes, respectively. Lines represent the fits to the MS spectrum using Eqs. 1 and 2, with bending modulus κ_eff as defined in Eq. 2. For the healthy RBCs (dashed yellow line), in the low-q region dominated by membrane tension, the MS spectrum predicts smaller fluctuations than can be registered experimentally. (B) Statistics for the mechanical parameters as obtained from the fits to the P(qR) spectra (see Table 1 for numerical data). (C) Effective temperature, defined as T_eff/T = P_h/P_d (from the data in A) and plotted as a function of the fluctuation wavenumber, m = qR. The dashed yellow line represents the trend expected for a direct force (the black dashed line indicates limiting behavior, T_eff ∼ 1/q at low q and T_eff ∼ 1/q² at high q (at γ ≠ 0); see Gov (38)). (D) Inactivation kinetics for RBCs treated with KF. The different curves correspond to the P(qR) spectra recorded at increasing KF incubation times. (E) Time dependence of the mechanical parameters along the inactivation process in (D) (open circles); the solid circles correspond to a passive limit represented by the mechanical parameters of the fixed discocytes with a cross-linked cytoskeleton after treatment with glutaraldehyde. To see this figure in color, go online.

Figure 3

(A) Experimental autocorrelation functions of the RBC flicker in the passive (drugged, left) and active (healthy, right) cases; wave numbers m = qR = 4 (blue), 5 (green), 6 (red), and 7 (black). Solid lines correspond to fits of the experimental data to the stretched exponential model in Eq. 4 for the thermal modes in passive cells (left) and to the bimodal function in Eq. 6 for the healthy cells (right). (B) Relaxation rates in the passive (left) and active (right) cases, with open circles corresponding to thermal modes, ω_q, and solid circles to the active component, ω_act. MS frequencies were fitted using Eq. 5 with η = 6 cP and κ_eff from Eq. 2, taking values from Table 1 (dotted line, tensionless membrane, Σ = 0; solid line, tensioned membrane, Σ > 0; dashed line: tensioned and viscous membrane, Σ > 0, γ > 0, with L_C = 260 ± 80 nm). (C) Comparison between autocorrelation (m = 4) in passive cells with Eq. 4 (blue) and in healthy cells with Eq. 6 (red). (D) Relative amplitudes of the active component decaying according to the direct-force model (red line, Eq. 7) and the curvature-force model (black dashed line). To see this figure in color, go online.

Figure 4

(A) PSDs of the RBC flickers using the fast-Fourier transform (FFT) algorithm, PSD(ω) = {FFT[h(t)]}², for healthy cells (dys_h) (red region), drugged cells (dys_d) (blue region), and fixed cells (cyan region). Vertical bars correspond to experimental data; lines indicate theoretical predictions (see Eqs. S3.3 and S3.4 for the pure thermal spectrum (dashed lines) and the thermal spectrum plus the active component arising from direct cytoskeletal forces (with 5% residual activity in the passive case) (solid lines)). (B) Time evolution of the experimental PSDs of RBC flickers under KF treatment. (C) KF-passivation kinetics measured as the decrease in effective temperature calculated from the data in (B) interpolated at different frequencies. To see this figure in color, go online.

Figure 5

(A) Cartoon of the molecular structure of the RBC cytoskeleton in which we explain our dynamical model. A near-hexagonal spectrin network is assembled by means of multiprotein junctional complexes (see details in the text), which act as primary attachments to the plasma membrane via a specific membrane domain of band 4.1 protein that reversibly interacts with glycophorin C in an ATP-dependent manner. Secondary attachment is provided by ankyrin, which interacts with transmembrane band 3 dimers. (B) Pinning model of cytoskeleton activity at junctional nodes. Complete membrane attachment to a rigid cytoskeleton causes effective stiffening, shown as low-amplitude fluctuations, Δh (upper). Node phosphorylation causes the membrane to pinch off from the cytoskeleton, resulting in an effective kicking force of amplitude f₀ in the membrane, which undergoes a normal displacement, δ (lower). In this case, the membrane experiences larger fluctuations of average amplitude Δh + δ. To see this figure in color, go online.