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A two-component network is studied by Monte Callo simulation to model the lipid/spectrin membrane of red blood cells. The model predicts that the shear modulus decreases rapidly with the maximum length of the model spectrin lind shou ld be in the 10 -7 11m 2 range for human red blood cells. A simplified model for the isolated spectrin network shows a negative Lame coefficient i... Transverse fluctuations of the dual membrane are found to be fl uidlike over the range of wavelengths investigated.PACS numbm: 87.12. BI. 05.40.+;, Erythrocytes are rem arkab le e lastic bodies Ill. They are stiff enough to recover t heir biconcave equilibrium shape after being squeezed through narrow capillaries on ly t of their diameter. Yet they a re soft enough to a llow for thermally excited shape fluctuations as seen in the flicker phenomenon [21. Their basic membrane architecture is essen tia lly a three-component system. The lipid bilayer provides a relatively la rge area compression modulus and high flex ibility for bending deformations. The cytoskeleton on the cytoplasmatic side of this bilayer consists mainly of spectrin let ramers linked together at junctional complexes to form a quasi hexagonal network. The spect ri n network and its junctional complexes are attached to the bilayer by integral membrane proteins. The third component, the glycoca li x, controls the interact ion with the extracellu la r ma trix or other cells.Understanding how the mechanica l properties of the red blood cell (RBC) membrane arise from its st ructural composition remains a sign ifican t cha llenge. While equ ilibrium shapes. shape transformations, and fluctuations of giant lipid bilayer vesicles are now understood on the basis of cont inuum elastic models for the bending energy I3J. it is not yet fully clear whether and how the cytoskeleton affects the equilibrium shape of the erythrocyte and its fluctuations. Recently, analysis of the flicker spect ru m revealed a wavelengt h dependence characteristic of fluid membranes and , thus. no effect of the spect rin network for wavelengths less than 1.5 pm [41. Likewise. direct measu rement of the mean-square thickness fluctuations (51. which are dominated by the long -wavelength shape fl uctuat ions, seems to suggest that the shea r modu lus for sma ll fluctuations is much less than the one obtained from the micromechanica l experiments 161. A possible explanation for such a discrepancy might be a non linear behavior of the network with respect to shea r distortions. If the spectrin tethers can be expanded to a certain lengt h with almost no cost in energy. then one might expect that small flu ctuations basically do not involve the network, whereas larger distortions as measured by micromechanical experiments involve shea r of this network. These effects a re difficult to model within a conti nuum mechanical model.In this paper, we present a mod~l for RBC membranes which draws its inspiration from computer simulations developed for both polymerized [7,81 and fluid 191 membranes. We capture what we be...

SUMMARY It is generally agreed that surface‐tension forces and the direct interaction between the specimen and either the air‐water interface or the water‐substrate interface can influence significantly the preparation of biological materials for electron microscopy. Even so, there is relatively little systematic information available that would make it possible to control surface‐tension forces and interfacial energies in a quantitative fashion. The main objective in undertaking the present work has been to understand somewhat better the factors that influence the degree of specimen flatness of large, monolayer crystals of biological macromolecules. However, the data obtained in our work should be useful in understanding the preparation of specimens of biological macromolecules in general. Data collection by electron diffraction and electron microscopy at high resolution and high tilt angles requires thin crystals of biological macromolecules that are flat to at least 1°, and perhaps less than 0·2°, over areas as large as 1 μm2 or more. In addition to determining empirically by electron diffraction experiments whether sufficiently flat specimens can be prepared on various types of modified or unmodified carbon support films, we have begun to use other techniques to characterize both the surfaces involved and the interaction of our specimen with these surfaces. In the specific case of large, monolayer crystals of bacteriorhodopsin prepared as glucose‐embedded specimens on hydrophobic carbon films, it was concluded that the initial interfacial interaction involves adsorption of the specimen to the air‐water interface rather than adsorption of the specimen to the substrate. Surface‐tension forces at the air‐water interface and an apparently repulsive interaction between the specimen and the hydrophobic carbon seem to be major factors influencing the specimen flatness in this case. In the more general case it seems likely that interfacial interactions with either the substrate or the air‐water interface can be variously manipulated in the search to find desirable conditions of specimen preparation.

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