Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of ATP dependence

Abstract

We have analyzed the fluctuations of the red blood cell membrane in both the temporal ((omega(s(-1))) and spatial (q(m(-1))) frequency domains. The cells were examined over a range of osmolarities leading to cell volumes from 50% to 170% of that in the isotonic state. The fluctuations of the isotonic cell showed an approximately q(-3)-dependence, indicative of a motion dominated by bending, with an inferred bending modulus of approximately 9 x 10(-19) J. When the cells were osmotically swollen to just below the point of lysis (166% of physiological volume), a q(-1)-dependence of the fluctuations supervened, implying that the motion was now dominated by membrane tension; estimated as approximately 1.3 x 10(-4) nm(-1). When, on the other hand, the cells were osmotically dehydrated, the fluctuation amplitude progressively decreased. This was caused by a rise in internal viscosity, as shown by measurements on resealed ghosts containing a reduced hemoglobin concentration, which displayed no such effect. We examined, in addition, cells depleted of ATP, before the onset of echinocytosis, and could observe no change in fluctuation amplitude. We conclude that the membrane fluctuations of the red cell are governed by bending modulus, membrane tension, and cytosolic viscosity, with little or no dependence on the presence or absence of ATP.

FIGURE 1

Membrane edge location procedure. An initial spline giving the approximate edge of the cell is obtained by a simple thresholding method (datum line). Using this as a starting point, strips perpendicular to the cell edge are generated for each video frame around the entire periphery at 1° intervals. These are then used to locate the edge position with the aid of a subpixel algorithm. The process is repeated for each video image, and results for multiple videos are combined to generate statistically meaningful results.

FIGURE 2

Images of cells in differing osmotic conditions. (a and d) Cells under hypertonic conditions in bright-field (hemoglobin Soret-band filter) and reflection interference contrast. (b and e) Equivalent images of cells under isotonic conditions. (c and f) Equivalent images for hypotonic cells. For the RIC images, due to the π phase shift at the interface, the contact region is dark and can be readily distinguished from the other dark bands, since these show clear thermal fluctuations. Arrows indicate the contact regions for the three conditions, and it can be seen that in the hypotonic state this is restricted to the center of the cell. The spacing of the other rings is closest in the hypertonic condition, representing the relatively steep angle of the membrane where it nears the central dimple. Images in the top row, which represent hemoglobin absorption, are consistent with these qualitative observations. The schematic diagrams (g–i) are the corresponding inferred cross sections.

FIGURE 3

Modal decomposition of cell edge movement. (a) Contributions of successive modes (squares of amplitudes) to the spatial power spectrum, P_φ, of the edge fluctuation for the first 11 modes (schematic representations are shown for the first four modes). (b) Autocorrelation functions of membrane fluctuations measured before, and after, subtraction of the centroid movement, with schematic insets showing the dominant mode in each case.

FIGURE 4

Space and time power spectra for a typical single cell in isotonic and hypotonic conditions. (a) The space power spectrum displays a power-law relationship in the midregion (6 < q < 20 cell⁻¹) giving 2.85 and 0.87 for the exponent, μ, in isotonic and hypotonic conditions, respectively. Mean values for different cells are close to 3 and 1, respectively. (b) The time power spectrum follows a power-law relationship, with exponents, γ, of 0.91 and 0.28 in the isotonic and hypotonic states.

FIGURE 5

Relation between projected cell diameter and medium tonicity. Measured diameters, averaged over 15 cells, are shown as a function of medium osmolality. Tonicity was altered in successive steps (•), and brought back to isotonic and reanalyzed (○) between changes. Cells were measured first in the hypotonic and then in the hypertonic range in the sequence indicated by arrowheads joining the points. The osmolality, C, and the corresponding volume, V, relative to that in the isotonic state (22), and cytosolic viscosity, η (23), at each tonicity are tabulated, expressed relative to the values C₀ (300 mOsm kg⁻¹), V₀ (unity), and η₀ (10 cP) in the isotonic state. Note the sharp rise in viscosity at the highest tonicities.

FIGURE 6

Effect of reduced hemogloblin concentration on fluctuations. Fluctuation amplitudes are shown for the first four modes of an intact cell (a) and for cells (resealed ghosts) containing ∼⅓ of the normal hemoglobin concentration (b) for different cell volumes.

FIGURE 7

Decomposition of fluctuations into space and time components for different cell volumes. (a) Fluctuation amplitudes of low- and high-mode-number components (q ≤ 10 cell⁻¹ and q > 10 cell⁻¹, respectively). (b) Low- and high-frequency fluctuation amplitudes (ω < 2 s⁻¹ and ω > 2 s⁻¹, respectively).

FIGURE 8

Dependence of the power-law exponents of the time and space power spectra on cell volume, and the derived values of membrane bending stiffness. (a) Exponents of the power-law relations of the time power spectrum (γ) and the space power spectrum (μ) as a function of cell volume. (b) Bending stiffness, κ, calculated by the methods of Strey et al. (10)) and Pécréaux et al. (24). (See text for explanation.)