Red cell membrane crenation: A macromodel of the echinocyte I

theor BioL (1989) 140, 185-192

Red Cell Membrane Crenation: A Macromodel of the Echinocyte I DANIEL H. ALDANAt, J. DOUGLAS BRAILSFORD~ AND BRIAN S. BULLt

~School of Allied Health Professions and tSchool of Medicine, Loma Linda University, Loma Linda, California 92354, U.S.A. (Received 22 November 1988, and accepted in revised form 15 March 1989) A physical macromodel of the erythrocyte membrane was constructed to investigate the effect of intrinsic membrane precurvature on a unique non-isotropic, composite material that dissipated shear energy but stored bending energy. The intrinsic precurvature of the material could be modified from strong positive precurvature through neutral to strong negative precurvature. A spherical shell constructed of the negatively precurved variant of this non-isotropic material spontaneously assumed the characteristic shape of the echinocyte I.

1. Introduction The mechanism that causes the membrane of a red blood cell to crenate is not completely understood. One proposal is that crenations arise through the effect of pharmacological agents that selectively perturb either the inner or the outer layer of the membrane (Deuticke, 1968; Evans, 1974; Sheetz & Singer, 1976; Matayoshi, 1980). This proposal, commonly known as the coupled-bilayer hypothesis, suggests that an expansion of the inner half of the bilayer favors cupping, while crenation results if the pharmacological agent selectively expands the outer half of the bilayer. Insertion into the inner layer results in negative intrinsic precurvature. Insertion into the outer layer results in positive intrinsic precurvature. A piece of membrane detached from an intact sphered cell would, if negatively precurved, tend to curve in the opposite direction from the membrane on the sphered cell. The coupled-bilayer hypothesis provides a satisfactory explanation for the tip of a crenation: it does not, however, fare as well in explaining the genesis o f a crenation when applied to the whole cell membrane surface. Under these conditions, the positively curved regions are offset by the negatively curved regions at the base of the crenation. An alternative view of the mechanism by which crenations arise was advanced by Brailsford et al. (1980). Computer iteration was used to determine the minimum energy configurations for a crenation arising out of the rim of a biconcave red blood cell. Negative intrinsic precurvature in the mathematically simulated membrane caused it to buckle into a low, rounded, b u m p y profile that was very reminiscent of the surface configuration of an echinocyte I. Single crenations are axisymmetrical and thus, tractable candidates for mathematical modelling. A crenated red cell has a more complicated shape, as a result, it is considerably more difficult to model. It would be reassuring if the validity of the 185 0022-5193/89/180185+08 $03.00/0

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above mathematical analysis and other similar analyses could be checked by reference to the behavior of a physical model, it was for these reasons that the present study was undertaken. The material devised for the construction o f the model is anisotropic, and can be fabricated to maintain positive, negative, and neutral precurvature as desired. The material can also be formed into a spherical shell. The effects o f varying precurvature on the m i n i m u m energy configuration of an intact shell can be determined. Thus, the difficult mathematical modelling procedures can be checked directly.

2. Materials MODEL

The anisotropic m e m b r a n e material represents a further development of a previously employed, composite structure (Brailsford & Bull, 1973). The earlier version of the material was constructed with neutral precurvature and proved useful for an investigation of the m i n i m u m bending energy hypothesis of C a n h a m (1970) as an explanation for the biconcave resting shape o f the normal red blood cell. The present material is constructed out o f unclenched p a p e r staples held together in polygonal units by silicone rubber tubing, small retaining washers, and 1 cm diameter polyacrylic disks (Fig. 1). The purpose of the polyacrylic disks is to restrict the m o v e m e n t of the staple legs so that the polygons do not become re-entrant and in doing so absorb surface area.

FIG. 1. A small section of the model showing five hexagonal subunits arranged around one pentagonal unit.

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A neutral (no intrinsic precurvature) surface results if the legs of the unclenched staples are left in their normal, right angle configuration. Positive or negative intrinsic precurvature can be produced in the material by bending the staple legs inward or outward and upon assembly, holding adjacent staple legs parallel by means of a sleeve of silicone rubber. A 15 degree bend inwards or outwards (producing an angle between the leg and the cross-piece of the staple of 75 or 105 degrees respectively) results in an appropriate amount of intrinsic precurvature. The elasticity of the silicone rubber tubing allows the staple legs to diverge when the membrane deforms, yet exerts a force along their whole length that attempts to keep them parallel. The effectiveness of this force is enhanced by the small retaining washers which ensure that the bases of the legs are kept tightly together and that any separation between the legs takes place with the brass washer serving as a fulcrum. As a result, the three dimensional deformability and precurvature persist in the fully assembled model. 3. Methods

A flat sheet of the material with neutral precurvature was made. It was suspended from its four corners and the symmetry of its bending resistance was determined. Weights were added to the center of the suspended sheet and the amount of deflection for a given weight was determined. The sheet was then turned upside down and the procedure was repeated. From this data, plots of deflection against weight for both sides of the material were prepared. A second sheet with intrinsic precurvature was constructed. The stresses required to raise a crenation were investigated by draping the sheet over a hemisphere to give it a strong tendency to buckle upwards. A lasso of fine string around the perimeter of the hemisphere applied hoop stress to the sheet when it was constricted (Fig. 2). The relationship between the height of the "crenation" and the force required to produce it was recorded. The sheet was then inverted to give it precurvature of the opposite sign but of the same degree and the experiment repeated. Finally, a closed spherical shell was constructed out of precurved material. This shell was formed from 490 hexagonal subunits arranged symmetrically around 12 pentagonal units placed at the vertices of an icosahedron. First, the shell was closed with the material precurved positively and subsequently collapsed into a biconcave discoid shape for dimensional analysis. It was then opened, turned inside-out to give the membrane shell negative intrinsic precurvature, and closed once more. The closed shell was then collapsed in biconcave discoid shape and reanalyzed. 4. Results

The deformation experiments performed with the flat sheet of material confirmed that it was equally deformable in both directions regardless of whether the staple legs were being bent towards or away from the cross piece. In Fig. 3 the plots of force vs. deflection are seen to have equal slopes regardless of the material's orientation. Thus, the neutral staple lattice did not exhibit a preferential direction

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FIG. 2. Series of three representations showing hoop stress as a crenation inducer; (upper left) anisotropic sheet over a hemisphere; (upper right) string laid in the form of a lasso around the circumference of a future crenation; (lower center) crenation formed as a result of a decrease in circumference.

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for bending. The noncoincidence of the two lines is a result of the staple leg play within the retaining washers. The negatively curved sheet was substantially easier to "crenate" than the positively curved one. Less force was required to produce a low rounded protuberance characteristic of crenations on an echinocyte I (Fig. 4). The spherical shell was first completed with the material oriented so as to produce positive intrinsic precurvature. When this spherical shell was collapsed into an appropriately shaped biconcave discoid shape it showed the characteristic behavior predicted by Canham. The girth increased by 15-20%, the meridians bisecting the concavities shortened by a similar amount. The surface of the biconcave discoid shape was smooth [Figs 5(a, b)]. The shell was then opened, everted and reclosed forming a spherical shell with strong negative intrinsic precurvature. When this shell was collapsed into a biconcave disk it too showed appropriate expansion of the girth with contraction of the meridianal dimensions. However, rather than the smooth surface previously exhibited, the negatively precurved shell displayed six to eight low, rounded bumps. As is the case with the echinocyte I, these bumps were located on the upper and lower surfaces of the rim of the disk [Figs 6(a, b)]. 5. Discussion

The behavior of this physical red cell membrane macromodel confirms the earlier mathematical conclusions that crenations will arise more readily from a negatively

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FIG. 5. The mechanical model was split in half and mounted as a biconcave hemisphere on a polyacrylic board. Each half was put through a CAT scan and a three-dimensional analysis of the radiographsproduced. (a) A radiograph showing the lattice with positive precurvature viewed directly from above; (b) the same lattice tilted 30 degrees.

precurved than from a positively precurved surface. It should be emphasized, however, that both the mathematical analysis and the behavior of the model account only for the initial stages of crenation--the low, rounded bumps characteristic o f an echinocyte I. At no point in the experiments with the precurved sheet or with the macromodel itself did the crenations progress to anything similar to those displayed by a fully developed echinocyte III. An echinocyte Ill shows 15-30 cylindrical crenations with hemispherical tips. These protuberances are evenly spaced around a central spherical body. To transform the few large low protuberances typical of an echinocyte I into the.many high protuberances of an echinocyte III requires, mathematically at least, an additional source of energy beyond that available from the negatively precurved membrane itself. Furthermore, the impressive amount of work done on the effects of the cationic and anionic phenothiazines cannot be ignored. The evidence from experiments with these and similar agents strongly suggests that insertion of foreign molecules into the outer half-leaflet of thelipid bilayer results in positive precurvature and in crenation. We will return to these observations in a moment after considering the effects of two other agents capable of affecting red cell shape. These agents are albumin and pH. The extensive experiments of Ponder (1940) on the effect of albumin on red cell shape showed it to be a most effective antiechinocytogenic agent. Albumin is known

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FIG. 6. (a) A radiograph showing the lattice with negative precurvature viewed directly fro above; (b) the same lattice tilted 30 degrees.

not to penetrate the red cell membrane, but to bind strongly to the red cell surface. In this position it must either expand the outer part of the red cell membrane or exert no effect--there is no evidence to suggest that the albumin would shrink the outer half leaflet as it would be expected to do if crenation and positive membrane precurvature were related as effect-to-cause. Jay (1975) have extended the observations of Ponder on albumin and red cell shape. These workers demonstrated that albumin added in excess actually exerted a stomatocytogenic effect. This is most unexpected, as experiments with phenothiazine derivatives have been interpreted to show that expansion of the inner half-leaflet (negative precurvature) resulted in the production of stomatocytes. Helfrich (1973, 1974), for other reasons, had earlier emphasized the theoretical importance of spontaneous negative membrane precurvature. He calculated axisymmetric shapes for red blood cells and other bilayer vesicles and noted that intrinsic negative precurvature would ensure the basic flattened discoid form of the red cell. Otherwise, both his mathematical models and those of Jenkins (1977) predicted a variety of equilibrium shapes for the red cell; shapes which did not, in fact, occur. This thesis was further developed with Deuling, (Helfick & Deuling, 1975). The experiments of Elgsaeter et al. (1986) identified a mechanical element of the red cell membrane capable of undergirding intrinsic negative precurvature while simulataneously lending support to the notion that negative precurvature rather than positive precurvature facilitates crenations. These workers, drawing upon the

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insights o f Tanaka et al. (1980) on ionic gels have proposed that the spectrin submembrane skeleton behaves as an ionic gel. Such a gel would expand as the pH rose; red cells crenate in an environment of high pH, circumstances where the membrane would be expected to acquire negative intrinsic precurvature as a result of expansion of the spectrin ionic gel layer on the inside of the plasma membrane. What then of the data on the membrane effects of cationic phenothiazines, which crenate red cells and are thought to insert themselves into the outer half leaflet? Several possibilities exist for the apparent discrepancy. It is possible that the cationic phenothiazines do not insert themselves uniformly into the outer leaflet but are preferentially concentrated over the tips of the crenations. It is intuitively obvious that positive membrane precurvature over the tips of the crenations would be strongly supportive of the crenation process. The notion that there may exist preferential insertion in the tips of crenations appears to be supported by the experiment performed by Bessis & Prenant (1972) where a glass rod was brought into the immediate environment of a cell caught on the tip of a micropipette. The alkalinity of the glass caused the cell to crenate: removal of the glass rod reverted the cell to a biconcave disk. This cycle could be repeated over and over without apparent fatigue of the membrane. On each occasion, the crenations arose in the same locations on the membrane. This can be explained if certain molecules insert at the tips of the crenations thereby making those areas more susceptible to crenation. On the other hand, the phenothiazine derivatives may exert their effects at a different locus within the membrane complex than albumin or pH. It is clear that more information will be needed before a completely inclusive theory o f red cell membrane crenation can be constructed. In the meanwhile, the notion that crenations start more readily from a negatively precurved surface has been supported from two independent approaches. These are the theoretical minimum energy calculations and the physical macromodel constructed out of material that exhibits the low shear, high bending resistance posited for the red cell membrane itself. REFERENCES BESSIS, M. & PRENANT, M. (1972). Nouv. Rev. Franc. D'Hem. 12, 351. BRAILSFORD, J. D. & BULL, B. S. (1973). J. theor. Biol. 39, 325. BRA|LSFORD, J. D., KORPMAN, R. A. & BULL, B. 5..(1980). J. theor. Biol. 86, 513. CANHAM, P. B. (1970). J. theor. Biol. 26, 61. DEUTICKE, B. (1968). Biochim. Biophys. Acta 163, 494. ELGSAETER, A., STOKKE, MIKKELSEN, A. & BRANTON, D. (1986). Science, N.Y. 234, 1217. EVANS, E. A. (1974). Biophys. J. 14, 923. HELFRICH, W. (1973). Z Naturforsch 28, 693. HELFRICH, W. (1974). Z Natuororsch 29c, 510. HELFRICH, W. & DEUL1NG, H. J. (1975). J. Phys. 36, 327. JAY, A. W. L. (1975). Biophys. J. 15, 205. JENKINS, J. T. (1977). J. math. Biol. 4, 149. MATAYOSHI, E. D. (1980). Biochemistry 19, 3414. PONDER, E. (1940). In: Hemolysis and Related Phenomena. p. 39. New York: Waverly Press Inc. SHEETZ, M. P. & SINGER, S. J. (1976). J. Cell Biol. 70, 247. TANAKA, Z., FILLMORE, D., SUN, S. T., NISHIO, I., SWISLOW, G. & SHAH, A. (1980). Phys. Rev. Left. 45, 1636.