Effective Temperature of Red-Blood-Cell Membrane Fluctuations

Abstract

Biologically driven nonequilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures theoretically by examining a randomly kicked particle, with a variable number of kicking motors, and show how these two indicators of nonequilibrium behavior can contradict. Our results are compared with new experiments on shape fluctuations of red-blood cell membranes, and demonstrate how the physical nature of the motors in this system can be revealed using these global measures of nonequilibrium.

Direct Cytoskeleton Forces Cause Membrane Softening in Red Blood Cells

“…3 D). The two characteristics that support an active nature (see Section SI3 in the Supporting Material) are 1) a single-exponential decay, ACF (act)~e xp(Àt/t), compatible with shot-noise correlations; and 2) a nondispersive q-dependence, t z u act À1~q0 , indicative of a direct force (26,27) with a given characteristic timescale independent of the spatial scale probed. These features could represent the dynamical signature of the reaction cycle of a metabolic process producing nonequilibrium membrane forces of average duration t. The observed correlation bump may be related to a force applied by kicking active elements on the membrane, similar to the correlation effect of pumping activity described in Bouvrais et al (44).…”

“…It is noteworthy that the direct-force model in Eq. 8 (25,27) is able to describe the experimental PSDs of healthy cells taking the values n m (F/4h) 2 ¼ 2.5 Â 10 5 nm 2 s À2 and t ¼ 0.1 s. If these parameters are related to the structural model, and assuming a maximal areal density of potentially active elements (kickers) of n m z 5 Â 10 À4 nm À2 , one gets F z 5 Â 10 À4 pN (taking h ¼ 6 cP). This value could become even higher if a lower density of membrane active sites is assumed at the equatorial cell site: F z 2 Â 10 À3 pN assuming n m z 2.5 Â 10 À5 nm À2 (for a z L z 200 nm).…”

“…Recently, the RBC flickering phenomenon has been revisited (6,7,(22)(23)(24), providing an accurate catalog of static-averaged mechanical properties measured at different physiological conditions. The renewed interest in its metabolic causes and the possible functional consequences for RBC dynamics have motivated theoretical efforts hypothesizing the existence of ATP-dependent cytoskeleton forces (14,(25)(26)(27)). An adequate understanding of this hypothesis requires that a distinction be made between the active contribution of the cytoskeleton and passive thermal fluctuations, a problem that awaits definite experimentation.…”

Equilibrium physics breakdown reveals the active nature of red blood cell flickering

“…The effective energy coincides with the thermal energy at high frequency for all conditions, but it increases up to 23kBT at low frequencies for fresh RBCs (ref 27 ). Integrating this deviation over the full spectrum gives an estimate of the power Pf ~0.025 fW used for driving the membrane fluctuations.…”

“…However, an equilibrium fluctuations distribution is also likely to exhibit non-Gaussian tails, as soon as anharmonicities are present in the membrane 25,26 . On the other hand, the fluctuations distribution of a nonequilibrium system can be perfectly Gaussian 25,27 . As a consequence, the observation of Gaussian fluctuation distributions 6,9,11,12 does not necessarily imply that RBC flickering is purely thermal.…”