Membrane flickering of the human erythrocyte: constrained random walk used with Bayesian analysis

Surface model of the human red blood cell simulating changes in membrane curvature under strain

We present mathematical simulations of shapes of red blood cells (RBCs) and their cytoskeleton when they are subjected to linear strain. The cell surface is described by a previously reported quartic equation in three dimensional (3D) Cartesian space. Using recently available functions in Mathematica to triangularize the surfaces we computed four types of curvature of the membrane. We also mapped changes in mesh-triangle area and curvatures as the RBCs were distorted. The highly deformable red blood cell (erythrocyte; RBC) responds to mechanically imposed shape changes with enhanced glycolytic flux and cation transport. Such morphological changes are produced experimentally by suspending the cells in a gelatin gel, which is then elongated or compressed in a custom apparatus inside an NMR spectrometer. A key observation is the extent to which the maximum and minimum Principal Curvatures are localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. Changes on the nanometre to micro-meter scale of curvature, suggest activation of only a subset of the intrinsic mechanosensitive cation channels, Piezo1, during experiments carried out with controlled distortions, which persist for many hours. This finding is relevant to a proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. However, if the curvature that gates Piezo1 is at a very fine length scale, then membrane tension will determine local curvature; so, curvatures as computed here (in contrast to much finer surface irregularities) may not influence Piezo1 activity. Nevertheless, our analytical methods can be extended address these new mechanistic proposals. The geometrical reorganization of the simulated cytoskeleton informs ideas about the mechanism of concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.

Accelerating metabolism and transmembrane cation flux by distorting red blood cells

Under static conditions, mammalian red blood cells (RBCs) require a continuous supply of energy, typically via glucose, to maintain their biconcave disc shape. Mechanical distortion, in a complementary way, should lead to increased energy demand that is manifest in accelerated glycolysis. The experimental challenge in observing this phenomenon was met by reversibly and reproducibly distorting the cells and noninvasively measuring glycolytic flux. This was done with a gel-distorting device that was coupled with ¹³C nuclear magnetic resonance (NMR) spectroscopy. We measured [3-¹³C]l-lactate production from [1,6-¹³C]d-glucose in the RBCs suspended in gelatin gels, and up to 90% rate enhancements were recorded. Thus, for the first time, we present experiments that demonstrate the linkage of mechanical distortion to metabolic changes in whole mammalian cells. In seeking a mechanism for the linkage between shape and energy supply, we measured transmembrane cation flux with Cs⁺ (as a K⁺ congener) using ¹³³Cs NMR spectroscopy, and the cation flux was increased up to fivefold. The postulated mechanism for these notable (in terms of whole-body energy consumption) responses is stimulation of Ca-adenosine triphosphatase by increased transmembrane flux of Ca²⁺ via the channel protein Piezo1 and increased glycolysis because its flux is adenosine triphosphate demand-regulated.

Direct Cytoskeleton Forces Cause Membrane Softening in Red Blood Cells

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.

Membrane flickering of the human erythrocyte: physical and chemical effectors

Recent studies suggest a link between adenosine triphosphate (ATP) concentration and the amplitude of cell membrane flickering (CMF) in the human erythrocyte (red blood cell; RBC). Potentially, the origin of this phenomenon and the unique discocyte shape could be active processes that account for some of the ATP turnover in the RBC. Active flickering could depend on several factors, including pH, osmolality, enzymatic rates and metabolic fluxes. In the present work, we applied the data analysis described in the previous article to study time courses of flickering RBCs acquired using differential interference contrast light microscopy in the presence of selected effectors. We also recorded images of air bubbles in aqueous detergent solutions and oil droplets in water, both of which showed rapid fluctuations in image intensity, the former showing the same type of spectral envelope (relative frequency composition) to RBCs. We conclude that CMF is not directly an active process, but that ATP affects the elastic properties of the membrane that flickers in response to molecular bombardment in a manner that is described mathematically by a constrained random walk.