Frequency spectrum of the flicker phenomenon in erythrocytes

Abstract

Red blood cells show a remarkable flicker phenomenon under physiological conditions. We have studied experimentally the correlations functions G(R12, ω) for the flicker intensities measured at two different points r 1 r2 on the cell surface, at various filtering frequencies ω. We find that the shape of G is universal and involves only one characteristic length λ(ω) varying like ω-n, where 0.12 < n < 0.19. Measurements of G(0, ω) (i.e. at a single point) show an ω-m dependence, where 1.30 < m < 1.45. These results are then interpreted theoretically in term of thermal fluctuations of the cell thickness. In physiological conditions the membrane surface tension vanishes exactly and the resistance to deformation is mainly due to curvature energy. In this approximation : a) the fluctuations are of very large amplitude (a fraction of a micron) as required by the observations ; b) the detailed shape of the correlations is in rather good agreement with the theory ; c) the scaling length λ(ω) is expected to vary like ω-1/6; d) the single point spectrum G(0, ω) should go like ω-4/3. The approximation involves the neglect of some non linear effects related to surface tension and to the Evans elastic energy. We show that the inclusion of non linear terms leads to a problem related to the critical point of a (special) two dimensional magnetic system. Our approximation (equivalent to a mean field theory) essentially ignores the exponent correction η introduced by Fisher for phase transitions. Thus, the experimental evidence favours a rather small η. We conclude that a purely physical interpretation of the flicker effect is sufficient, but that rather stringent physiological conditions are required to maintain the zero surface tension which is crucial to the effect.