Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering

Abstract

Red blood cells (RBCs) present unique reversible shape deformability, essential for both function and survival, resulting notably in cell membrane fluctuations (CMF). These CMF have been subject of many studies in order to obtain a better understanding of these remarkable biomechanical membrane properties altered in some pathological states including blood diseases. In particular the discussion over the thermal or metabolic origin of the CMF has led in the past to a large number of investigations and modeling. However, the origin of the CMF is still debated. In this article, we present an analysis of the CMF of RBCs by combining digital holographic microscopy (DHM) with an orthogonal subspace decomposition of the imaging data. These subspace components can be reliably identified and quantified as the eigenmode basis of CMF that minimizes the deformation energy of the RBC structure. By fitting the observed fluctuation modes with a theoretical dynamic model, we find that the CMF are mainly governed by the bending elasticity of the membrane and that shear and tension elasticities have only a marginal influence on the membrane fluctations of the discocyte RBC. Further, our experiments show that the role of ATP as a driving force of CMF is questionable. ATP, however, seems to be required to maintain the unique biomechanical properties of the RBC membrane that lead to thermally excited CMF.

Figure 1. PCA Results.

Normalized PCA modes (A) of a single cell (B) of a paraformaldehyde fixed cell (C) of a group of n = 198 cells. The spatial distribution of the normalized mode amplitude is color coded. (D) Phase image of erythrocyte with typical ROI for PCA analysis (E) Eigenvalues of PCA modes of A,B,C (Log Scale). Standard deviations of the values are indicated by error bars.

Figure 2. RBC Equilibrium Shape.

Straigth line: Equilibrium shape that arises from bending energy minimization (see Text S1) and which was used in the calculations to derive eigenmodes of the bending deformation energies depicted in Figure 3B,C. Dashed line: Shape of deformed cell.

Figure 3. Experimental and Theoretical Comparison.

(A) Degeneracy free representation of PCA modes. The separable modes 7 (degeneracy of 2) and 9 in this representation are obtained from an appropriate linear combination of the degenerate modes 12,13 and 14 of Figure 1C. Both representations are equivalent, because they span the same subspace. (B) Eigenmodes that minimize Laplace deformation energy shown in the ROI. Eigenmodes are plotted as functions (C) Eigenmodes that minimize BCH Deformation Energy shown only in the ROI (D) Comparison of theoretical and measured fluctuation amplitudes.

Figure 4. ATP Depletion in RBC.

(A) Fluctuation amplitudes of the first six PCA modes in a population of n = 198 (no ATP depletion), 43 (1 h ATP depletion), 47 (2 h ATP depletion), 36 (4 h ATP depletion) cells. (B) Assessment of intracellular ATP level at different instants of incubation time in depletion medium through the measurement of chemiluminescence intensity of luciferin luciferase assay in RBC cell solution.