Forty-Percent Area Strain in Red Cell Membranes?—Doubtful

I am writing to take issue with the conclusions of the recent article in the August issue of the Biophysical Journal by Li, Chan, and Ohl entitled “Yield Strength of Human Erythrocyte Membranes to Impulsive Stretching” (1xYield strength of human erythrocyte membranes to impulsive stretching. Li, F., Chan, C.U., and Ohl, C.D. Biophys. J. 2013; 105: 872–879Abstract | Full Text | Full Text PDF | PubMed | Scopus (19)See all References1). Having studied red cell membrane mechanics since 1974, I was very much intrigued by the title. It is well known that the red cell membrane is viscoelastic, and most of its properties have been characterized at timescales of tens of milliseconds to many seconds. To be able to assess properties at a microsecond timescale would be an important breakthrough. However, the content of the article fell far short of the title’s promise. My main concerns have to do with the authors’ definition and method of measurement of area strain. Their definition is based on measurements of projected cell area in high-speed imaging frames. This quantity is not the area strain of the membrane, nor is it a particularly good approximation of it.Without information about deformation in the direction normal to the image plane, it is impossible to make a reliable determination of the membrane area, much less how much it is altered during μs-scale impulses. The problem with the definition can be illustrated with a simple example. Consider a red cell with the average dimensions determined by Fung et al. (2xHigh-resolution data on the geometry of red blood cells. Fung, Y.C., Tsang, W.C.O., and Patitucci, P. Biorheology. 1981; 18: 369–385PubMedSee all References2): area = 130 μm2, volume = 98 μm3, and cell radius = 3.82 μm. If this cell was to be pressed flat against a surface, it should assume the shape of two circular disks bounded by a hemispherical torus. Such a shape would have a diameter of 3.98 μm, and have exactly the same area and volume as it had originally. In this case, the authors would calculate an area strain of >8% by their definition, but in fact, the area strain for this deformation is zero.The problem is compounded by the challenges of imaging cells at such high rates and the extreme elongation of the cells. Although it may be possible to repeat measurements for different pixel sizes of the same image to within 6%, as is shown in the article, the potential for systematic error in the measurements is much larger. Under the best of circumstances the resolution of light microscopy has an uncertainty of roughly half a micron, and in the challenging imaging conditions of these experiments, errors at least this large might be expected. Furthermore, inspection of their Figs. S4 and S5 appears to show a systematic difference in how the automated algorithm has chosen the cell edge in the two cases (inside the white diffraction band in Fig. S5, outside the white diffraction band in Fig. S4). This difference could lead to errors as large as the total change in surface area that is described. For the elongated cells shown in Fig. 1, which appear to have perimeters of ∼50 μm in length, overestimating the location of the cell boundary by half a micron would lead to a 25-μm2 overestimation of the area. This is ∼40% of the projected area of the cell. Thus, not only is the definition of area strain incorrect, but the potential error in the measurements is as large as the changes in area that have been determined.Another issue relates to the argument that changes in cell thickness are unlikely to lead to substantial errors in calculating area strain. The assertion that changes in cell thickness are likely to be minimal because the shear stress is only applied in the stretching direction disregards the fact that the cell volume is incompressible. Incompressibility requires that a 40% increase in area be accompanied by a 40% decrease in thickness. For a cell with a 50-μm perimeter, a 40% reduction in cell thickness would correspond to a reduction of the area at the cell edge of ∼16 μm2, roughly 60% of the area changes that have been estimated. The assertion that changes in cell thickness do not occur implies that the cell volume must increase by 40% over the time of the deformation (a few tens of microseconds). This is not physically reasonable, particularly in light of the fact that cell elongations of the magnitude they observe would tend to pressurize the cell interior, potentially causing the volume to decrease, not increase.Others have considered the possibility that rapid membrane loading (albeit at rates much smaller than those applied in this recent report) could lead to higher force resultants (3xDynamic strengths of molecular anchoring and material cohesion in fluid biomembranes. Evans, E. and Ludwig, F. J. Phys. Condens. Matter. 2000; 12: A315–A320CrossrefSee all References3) or larger strains (4xAdhesively-tensed cell membranes: lysis kinetics and atomic force microscopy probing. Hategan, A., Law, R...., and Discher, D.E. Biophys. J. 2003; 85: 2746–2759Abstract | Full Text | Full Text PDF | PubMed | Scopus (118)See all References4) at lysis, but in both cases the strains at lysis under rapid loading were calculated to be ∼5–6%. Although it is conceivable that the ultra-high loading rates applied in the recent report could lead to even larger strains, the conclusion that a bilayer membrane can undergo area strains of up to 40% is inconsistent with understanding of bilayer membrane structure and mechanics that is based on >30 years of careful research in this area, and should be accepted only after scrupulous examination of the evidence. The erroneous definition of strain, the uncertainty of the measurements, and the physically unreasonable arguments made to justify disregarding confounding factors raises significant doubts about the authors’ interpretation of their observations. Thus, the conclusions of the article are not well supported by the evidence, and likely serve to foster confusion, not enlightenment, among the readership.