Improved chitosan-mediated gene delivery based on easily dissociated chitosan polyplexes of highly defined chitosan oligomers.

Nonviral gene delivery systems based on conventional high-molecular-weight chitosans are efficient after lung administration in vivo, but have poor physical properties such as aggregated shapes, low solubility at neutral pH, high viscosity at concentrations used for in vivo delivery and a slow dissociation and release of plasmid DNA, resulting in a slow onset of action. We therefore developed highly effective nonviral gene delivery systems with improved physical properties from a series of chitosan oligomers, ranging in molecular weight from 1.2 to 10 kDa. First, we established structure-property relationships with regard to polyplex formation and in vivo efficiency after lung administration to mice. In a second step, we isolated chitosan oligomers from a preferred oligomer fraction to obtain fractions, ranging from 10 to 50-mers, of more homogeneous size distributions with polydispersities ranging from 1.01 to 1.09. Polyplexes based on chitosan oligomers dissociated more easily than those of a high-molecular-weight ultrapure chitosan (UPC, approximately a 1000-mer), and released pDNA in the presence of anionic heparin. The more easily dissociated polyplexes mediated a faster onset of action and gave a higher gene expression both in 293 cells in vitro and after lung administration in vivo as compared to the more stable UPC polyplexes. Already 24 h after intratracheal administration, a 120- to 260-fold higher luciferase gene expression was observed compared to UPC in the mouse lung in vivo. The gene expression in the lung was comparable to that of PEI (respective AUCs of 2756+/-710 and 3320+/-871 pg luciferase x days/mg of total lung protein). In conclusion, a major improvement of chitosan-mediated nonviral gene delivery to the lung was obtained by using polyplexes of well-defined chitosan oligomers. Polyplexes of oligomer fractions also had superior physicochemical properties to commonly used high-molecular-weight UPC.

Macromolecular triplex zipping observed in derivatives of fungal (1 --> 3)-beta-D-glucan by electron and atomic force microscopy.

Scleroglucan, a comb-like branched (1 --> 3)-beta-D-glucan, dissolves in water as a stiff, triple-helical structure with the single glucose branches extending from the surface. The aim of this study is to investigate structural changes in the triple-helical structure associated with selective chemical modification of the side chains. Electron and atomic force microscopy, respectively, were used to investigate the macromolecular structures of aldehyde and carboxylated derivatives of scleroglucan-namely, scleraldehyde and sclerox-with different degrees of substitution. Scleraldehyde was observed to have structures resembling the triplex of the unmodified scleroglucan for all degrees of substitution up to 1.0. Additionally, an increasing tendency to aggregate for the higher degrees of substitution was observed. Fully carboxylated scleroglucan, sclerox(1.0), prepared from solutions at ionic strengths below 1.0M, revealed dispersed, flexible, coil-like structures. This indicates an electrostatic-driven strand separation of the scleroglucan triple-helical structure occurring concomitant with an increasing fraction of the side chains bearing carboxylate groups. Annealed sclerox(1.0) samples in aqueous 1.0 and 1.5M NaCl exhibited partly, or completely, reassociated triplex ensembles, with species ranging from apparently fully zipped linear and circular topologies, partly zipped structures with triplex strand separation occurring at the ends, to dispersed single-strands with random coil-like appearance. This study shows that periodate oxidation of the scleroglucan side chains is not a sufficient modification of the side chains to induce dissociation of the triple-helical structure, whereas further oxidation of the side chains to carboxylic groups dissociates the triple-helical structure when the degree of substitution is above 0.6.

The cytokine stimulating activity of (1-->3)-beta-D-glucans is dependent on the triple helix conformation.

The immunomodulating properties of comb-like branched (1-->3)-beta-D-glucans scleroglucan, schizophyllan and lentinan depend on branching pattern, molecular weight and higher-order structure. The effect of weight average molecular weight Mw and higher order structure of scleroglucan, on stimulation of human monocytes cultured in vitro to secrete tumor necrosis factor-alpha (TNF-alpha) was investigated. The higher order structures of the scleroglucan samples were determined by electron microscopy. The data showed that the samples with a linear wormlike, triple helical structure with Mw less than 50 x 10(4) g/mol or larger than 110 x 10(4) g/mol stimulated the monocytes more efficiently than samples with Mw in the range (67-110) x 10(4) g/mol. The denaturation of the linear triple helices by NaOH (> 0.25 M), followed by neutralization yielded blends of linear and macrocyclic topologies with concomitant irreversible reduction of the cytokine inducing activity compared with the untreated scleroglucans. The dose-dependent ability to activate monocytes to cytokine production was not restored following annealing of the denatured-renatured samples, despite the fact that electron micrographs revealed similar structures of these annealed samples to the starting material. Pre-incubation of monocytes with antibodies against cluster of differentiation antigens CD14 or CD11b reduced the scleroglucan potency to stimulate TNF-alpha secretion mainly for mAb against CD14 in the presence of serum.

The recombinant Azotobacter vinelandii mannuronan C-5-epimerase AlgE4 epimerizes alginate by a nonrandom attack mechanism.

The Ca2+-dependent mannuronan C-5-epimerase AlgE4 is a representative of a family of Azotobacter vinelandii enzymes catalyzing the polymer level epimerization of beta-D-mannuronic acid (M) to alpha-L-guluronic acid (G) in the commercially important polysaccharide alginate. The reaction product of recombinantly produced AlgE4 is predominantly characterized by an alternating sequence distribution of the M and G residues (MG blocks). AlgE4 was purified after intracellular overexpression in Escherichia coli, and the activity was shown to be optimal at pH values between 6.5 and 7.0, in the presence of 1-3 mM Ca2+, and at temperatures near 37 degrees C. Sr2+ was found to substitute reasonably well for Ca2+ in activation, whereas Zn2+ strongly inhibited the activity. During epimerization of alginate, the fraction of GMG blocks increased linearly as a function of the total fraction of G residues and comparably much faster than that of MMG blocks. These experimental data could not be accounted for by a random attack mechanism, suggesting that the enzyme either slides along the alginate chain during catalysis or recognizes a pre-existing G residue as a preferred substrate in its consecutive attacks.

Determination of enzymatic hydrolysis specificity of partially N-acetylated chitosans.

A new method for determining the specificity of hydrolysis of the linear binary heteropolysaccharide chitosan composed of (1-->4)-linked 2-acetamido-2-deoxy-beta-D-glucopyranose (GlcNAc; A-unit) and 2-amino-2-deoxy-beta-D-glucopyranose (GlcN; D-unit) residues is described. The method is based on the assignments of the 13C chemical shifts of the identity (A- or D-units) of the new reducing and non-reducing ends and the variation in their nearest neighbours, using low molecular weight chitosans with known random distribution of A- and D-units as substrate. A highly N-acetylated chitosan with fraction of acetylated units (FA) of 0.68 and a number-average degree of polymerization (DPn) of 30 was hydrolysed with hen egg-white lysozyme, showing that both the new reducing and non-reducing ends consisted exclusively of A-units, indicating a high specificity for A-units in subsites DL and EL on lysozyme. Our data suggests that the preceding unit of the reducing A-units, is invariable, and based on earlier studies, most probably an A-unit, while the unit following the non-reducing A-units can be either an A- or a D-unit. A more detailed study of the specificity of lysozyme at subsite DL was performed by hydrolyzing a more deacetylated chitosan (FA = 0.35 and DPn of 20) to a DPn of 9, showing that even for this chitosan more than 90% of the new reducing ends were acetylated units. Thus, lysozyme depolymerizes partially N-acetylated chitosans by preferentially hydrolyzing sequences of acetylated units bound to site CL, DL and EL of the active cleft, while there is no specificity between acetylated and deacetylated units to site FL. In addition, a moderately N-acetylated chitosan with fraction of acetylated units (FA) of 0.35 and a DPn of 20 was hydrolysed with Bacillus sp. No. 7-M chitosanase, showing that both the new reducing and non-reducing ends consisted exclusively of D-units. Our data suggests that the nearest neigbour to the D-unit at the reducing end is invariable, and based on earlier studies, most probably a D-unit, while the unit following the non-reducing D-units can be either an A- or a D-unit. We conclude that the Bacillus chitosanase hydrolyzes partially N-acetylated chitosan by preferentially attacking sequences of three consecutive deacetylated units, hypothetical subsites CC, DC and EC, where the cleavage occur between sugar units bound to subsites DC and EC. A hypothetical subsite FC on the chitosanase show no specificity with respect to A- and D-units. The new NMR method described herein offers a time and labour-saving alternative to the procedure of extensive hydrolysis of the binary heteropolysaccharide chitosan and subsequent isolation and characterization of the oligosaccharides.

Conformation of (2-->1)-beta-D-fructan in aqueous solution.

The conformation and dilute solution properties of (2-->1)-beta-D-fructan in aqueous solution were studied by gel permeation chromatography, low-angle laser light-scattering photometry, viscometry, small-angle X-ray scattering and electron microscopy. Fractions covering a broad range of weight-average molecular weights (Mw) from 1.49 x 10(4) to 5.29 x 10(6) were obtained from a native sample by ultrasonic degradation and fractional precipitation. For Mw < 4 x 10(4), the intrinsic viscosity [eta] varies with Mw0.71, indicating that the fructan chain behaves as a random coil expanded by an excluded-volume effect in this molecular weight region. For Mw > 10(5), [eta] exhibits an unusually weak dependence on Mw and finally becomes almost independent of molecular weight. This behaviour is interpreted in terms of a globular conformation of the high-molecular-weight fructan molecules. Small-angle X-ray-scattering measurements and electron microscopic observations support this interpretation of the values of [eta] observed.

An antitumor, branched (1-->3)-beta-D-glucan from a water extract of fruiting bodies of Cryptoporus volvatus.

A water-soluble, (1-->6)-branched (1-->3)-beta-D-glucan (H-3-B) was isolated from a hot-water extract of the fruiting bodies of the fungus, Cryptoporus volvatus (Basidiomycetes). Enzymatic analysis using exo-(1-->3)-beta-D-glucanase and methylation analysis indicated that this polysaccharide has a main chain composed of beta-(1-->3)-linked D-glucopyranosyl residues, and single, beta-(1-->6)-linked D-glucopyranosyl residues attached as side chains to, on average, every fourth sugar residue of the main chain. This structure was confirmed by 13C NMR spectra of the glucan in Me2SO-d6. The weight-average molecular weight (Mw) of H-3-B was determined to be 44.0 x 10(4) by gel permeation chromatography equipped with a low-angle laser-light-scattering photometer. The electron microscopic observations showed that H-3-B and its sonicated sample (S-H-3-B, Mw = 13.7 x 10(4)) can be described as linear worm-like chains. The mass per unit length for native and sonicated H-3-B was determined to be 1750 and 1780 g mol-1 nm-1, respectively, from the contour lengths obtained by electron microscopy and the molecular weights. These values are in good agreement with that expected for the triple stranded structure. A sample denatured in 0.1 M NaOH and subsequently renatured by neutralization showed a mixture of linear and cyclic structures, and larger aggregates with less well-defined morphology. The H-3-B and S-H-3-B had antitumor activity against the Sarcoma 180 tumor.

Conformation, order-disorder conformational transitions and gelation of non-crystalline polysaccharides studied using electron microscopy.

Direct imaging of polysaccharides using transmission electron microscopy (EM) is an important alternative to physical characterization of non-crystalline polysaccharides in solution. The polymer nature of stiff-chain polysaccharides is quite apparent from direct visualization of the electron micrographs, despite the fact that commonly employed preparation techniques reduce the resolution limit to about 1-2 nm. Electron microscopy has recently been used to study polysaccharides with emphasis both on quantitative properties like contour length, end-to-end distance and chain stiffness, and on qualitative structural features such as cyclization at the macromolecular level. The structural richness observed for polysaccharides of the beta-D0glucan family after a denaturation-renaturation treatment of the specimen, in particular, illustrates the unique potential of EM as a tool for obtaining conformational information about carbohydrate macromolecules. Examples of the latter also include the recent discoveries of cyclic beta-D-glucan and l-carrageenan structures. The EM technique provides information that is not only complementary to what can be obtained using other physical techniques, but also offers important insight otherwise masked by the averaging implicit in most physical techniques used to study aqueous polysaccharide solutions.

Physicochemical properties of (1-->6)-branched (1-->3)-beta-D-glucans. 1. Physical dimensions estimated from hydrodynamic and electron microscopic data.

The physical dimensions of several (1-->6) branched (1-->3)-beta-D-glucan samples obtained from different organisms and their derivatives have been studied by electron microscopy, light scattering measurements, viscometry, and gel permeation chromatography. The electron micrographs indicate that in most samples these biopolymers are adequately described as linear worm-like coils. A sample reconstituted from alkaline media appeared as a blend of the linear, circular, and aggregated polymer morphologies. The average mass per unit length, ML = Mw/Lw for the macroscopically linear samples, was estimated to be 2100 +/- 200 g mol-1 nm-1. The parameter ML was determined from the contour lengths obtained by electron microscopy and the molecular weight by light scattering measurements. The observed ML was consistent with the triple-helical structure reported from x-ray diffraction studies and observed degree of side-chain substitution. From the molecular snapshots shown in the electron micrographs, the persistence lengths of these beta-D-glucans were determined to be 140 +/- 30 nm. The experimentally determined intrinsic viscosities were consistent with these estimates of ML and persistence length. Comparison of the molecular weight distributions obtained from gel permeation chromatography and those deduced from the electron micrographs indicates that number and weight average contour lengths are more reliable than z and z + 1 averages.

Macrocyclization of polysaccharides visualized by electron microscopy.

Topological features of the polysaccharides schizophyllan, l-carrageenan and gellan gum were studied using electron microscopy. Electron micrographs of schizophyllan not subjected to any thermal or solvent composition history destabilizing the triple helix, show stiff, linear chains consistent with the structure being triple helical and with contour length proportional to the molecular weight in solution. A blend of linear, cyclic and hairpin topologies and higher molecular weight clusters were observed after renaturation, i.e. return to conditions favouring the triple helical structure, from solvent conditions dissociating the triple helix. Electron micrographs of l-carrageenan in salt-free solution reveal linear extended structures. Addition of 0.15 M LiI to the solution before preparation for electron microscopy, i.e. salt conditions that favour ordering but not gelation, yields a large fraction of cyclic structures with circumference of different lengths. Likewise, adding KCl to aqueous gellan gum changes their appearance from dispersed polymers to suprastrands with several associated chains. Macrocyclic species can also be observed in gellan gum after the addition of a gel-promoting salt. The tendency to form macrocyclic structures in competition with intermolecular aggregates is determined by the three factors: (1) chain stiffness relative to overall length; (2) parallel or antiparallel alignment of interacting chain segments; and (3) polymer concentration. The present study indicates that electron microscopy provides information about the topology adopted by polysaccharides.

Thermally induced conformational transition of double-stranded xanthan in aqueous salt solutions.

The thermally induced conformational transition of double-stranded xanthans (degree of pyruvate substitution, DSp = 0.45) having Mw = 3.1, 5.7, and 20.3 x 10(5) has been studied in aqueous salt solutions by high-sensitivity differential scanning calorimetry (DSC). The double strandedness of these samples in the ordered conformation was ascertained by the value of mass per unit length, ML = 2090 +/- 270 g mol-1 nm-1, which was determined from the contour length obtained by electron microscopic observations and the molecular weight by light scattering measurements. The temperature at half completion of the transition T 1/2 for these samples increased linearly with the logarithm of the cation (Na+, K+) concentration. The plot of 1/T1/2 vs the natural logarithm of cation (Na+) concentration in mM for the sample with Mw = 5.7 x 10(5) (15-SX) yielded the equation 10(3)/T1/2 = 3.45-0.159 ln [Na+]. The specific enthalpy delta hcal for 15-SX, essentially independent of salt concentration above 20 mM, was 8.31 +/- 0.39 J/g (SD, n = 6). No systematic dependence of molecular weight on the transition temperature and the enthalpy was observed. Application of the Manning polyelectrolyte theory to the system using the DSC data suggested that the separation of the double strand of xanthan into two single chains was not completed at the temperature where the endothermic peak was finished. This suggestion is consistent with recent findings by light scattering measurements as a function of temperature. Our DSC study was extended to include four other samples from various sources. It was found that T1/2 and delta hcal depend on the pyruvate contents of the samples. For example, the t1/2 (t1/2/degrees C = T1/2/K - 237.15) values for samples with high pyruvate content (DSp = 0.9) and depyruvated (DSp = 0.14) in 20 mM aqueous NaCl were 48.8 and 85.3 degrees C, respectively. Two other samples showed relatively broad DSC curves having shoulders, which were resolved into two independent components. Thermodynamic parameters for each component were examined as a function of salt concentration, and the results obtained were interpreted in terms of the heterogeneity of the pyruvate content of the samples.

The reliability of wormlike polysaccharide chain dimensions estimated from electron micrographs.

Electron micrographs of alginate, xylinan, xanthan, and scleroglucan were prepared by vacuum-drying aqueous glycerol-containing solutions, and then heavy-metal, low-angle rotary replicated. Quantitative methods for excluding streamlining effects and deformation artifacts were developed and applied to the digitized polymer contours prior to analysis of stiffness. The apparent macromolecular dimensionalities were not obtainable on the basis of the change in the scaling coefficient alpha relating the rms end-to-end distance and the contour length, mean value of r2(1/2) approximately L alpha, for chains subject to the excluded volume effect in two and three dimensions. Using a two-dimensional model, the persistence length of these molecules was estimated to be (9 +/- 1) nm (alginate), (25 +/- 4) nm (xylinan), (30 +/- 4) nm (single-stranded xanthan), (68 +/- 7) nm (double-stranded xanthan), and (80 +/- 10) nm (scleroglucan). Monte Carlo calculations for wormlike chains close to an interacting surface or confined to the region between two surfaces showed that (1) strongly adsorbed molecules are essentially two-dimensional and (2) molecules restricted to the space between two surfaces separated by a distance less than 20% of the persistence length are two-dimensional in their directional correlation. The somewhat low estimates of the persistence lengths obtained from the electron micrographs compared with those reported from solution measurements can be accounted for by the adoption of a strictly two-dimensional model in the analysis, whereas the absorbed polymers are most likely intermediate between the two-and three-dimensional cases. The model calculations and the analysis of the electron micrographs suggest that stiffness parameters are obtainable from the electron micrographs when the proper theoretical description are used in the analysis.

Long-term storage of xanthan in seawater at elevated temperature: physical dimensions and chemical composition of degradation products.

Commercial xanthan and xanthan from Xanthomonas strain 646 produced in the laboratory have been subjected to heat treatment for various periods of time in oxygen depleted, high salinity, aqueous solutions. Both the viscosity and the carbohydrate content decreased with increasing incubation time at a specified temperature. The losses increased with increasing temperature. Data from electron micrographs and dialysable sugar content indicate that random cleavage of the double-stranded xanthan chain is the main mechanism responsible for the decreasing viscosity. Removal of pyruvate and acetate substituents on the side chains was apparently not related to the change in physical dimensions. The mannose/glucose ratio in the non-diffusible fraction decreased with incubation time, apparently not related to change in physical dimensions. Electron micrographs showed that one of the samples appeared as highly aggregated in the native condition. After 1 month at 80 degrees C, we observed that the aggregates had dissolved and that the viscosity had increased fivefold. This suggests that heat treatment can be used to avoid microgels and to obtain higher viscosifying power of the native xanthan.

The molecular size and shape of xanthan, xylinan, bronchial mucin, alginate, and amylose as revealed by electron microscopy.

Electron microscopy of some selected, vacuum-dried and rotary-shadowed, polyelectrolytic polysaccharides and glycoproteins adsorbed to mica indicates that this technique can yield reliable information about polymer conformation for chains with persistence lengths q exceeding about 10 nm. Statistical analyses of the local polymer tangent-direction yield q = 150 nm for double-stranded xanthan, q = 60 nm for single-stranded xanthan, q = 45 nm for xylinan, q = 16 nm for alginate (90% beta-D-mannuronic acid), and q = 15 nm for human-bronchial mucin. These values are all in adequate agreement with values of q obtained by using other techniques. Amylose, on the other hand, appears as non-randomly aligned chains. The observed contour lengths of amylose indicate a mass per unit length of 1440 dalton/nm, consistent with a pseudo-helical conformation.

The molecular basis of erythrocyte shape.

Recent discoveries about the molecular organization and physical properties of the mammalian erythrocyte membrane and its associated structural proteins can now be used to explain, and may eventually be used to predict, the shape of the erythrocyte. Such explanations are possible because the relatively few structural proteins of the erythrocyte are regularly distributed over the entire cytoplasmic surface of the cell membrane and because the well-understood topological associations of these proteins seem to be stable in comparison with the time required for the cell to change shape. These simplifications make the erythrocyte the first nonmuscle cell for which it will be possible to extend our knowledge of molecular interactions to the next hierarchical level of organization that deals with shape and shape transformations.

The human erythrocyte membrane skeleton may be an ionic gel. III. Micropipette aspiration of unswollen erythrocytes.

We have carried out a theoretical analysis of micropipette aspiration of unswollen erythrocytes using the protein-gel-lipid-bilayer membrane model and taking into account that the modulus of area compression of the membrane skeleton may depend on the environmental conditions. Our analysis shows that the aspiration pressure needed to obtain a certain membrane projection length is strongly dependent on the ratio between the membrane skeleton modulus of area compression and the elastic shear modulus. Our analysis therefore predicts that micropipette aspiration of unswollen erythrocytes may be a sensitive method for detection of changes in this ratio. The analysis thus also shows that micropipette aspiration of unswollen erythrocytes can not be used to determine the membrane shear modulus unless something is known about the membrane skeleton modulus of area compression.

Spectrin, human erythrocyte shapes, and mechanochemical properties.

Physical studies of human erythrocyte spectrin indicate that isolated spectrin dimers and tetramers in solution are worm-like coils with a persistence length of approximately 20 nm. This finding, the known polyelectrolytic nature of spectrin, and other structural information about spectrin and the membrane skeleton molecular organization have lead us to the hypothesis that the human erythrocyte membrane skeleton constitutes a two-dimensional ionic gel (swollen ionic elastomer). This concept is incorporated in what we refer to as the protein gel-lipid bilayer membrane model. The model accounts quantitatively for red elastic shear modulus and the maximum elastic extension ratio reported for the human erythrocytes membrane. Gel theory further predicts that depending on the environmental conditions, the membrane skeleton modulus of area compression may be small or large relative to the membrane elastic shear modulus. Our analyses show that the ratio between these two parameters affects both the geometry and the stability of the favored cell shapes and that the higher the membrane skeleton compressibility the smaller the values of the gel tension needed to induce cell shape transformations. The main virtue of the protein gel-lipid bilayer membrane model is that it offers a novel theoretical and molecular basis for the various mechanical properties of the membrane skeleton such as the membrane skeleton modulus of area compression and osmotic tension, and the effects of these properties on local membrane skeleton density, cell shape, and shape transformations.

The human erythrocyte membrane skeleton may be an ionic gel. I. Membrane mechanochemical properties.

Biochemical and biophysical observations indicate that the erythrocyte membrane skeleton is composed of a swollen network of long, flexible and ionizable macromolecules located at the cytoplasmic surface of the fluid membrane lipid bilayer. We have analyzed the mechanochemical properties of the erythrocyte membrane assuming that the membrane skeleton constitutes an ionic gel (swollen ionic elastomer). Using recently established statistical thermodynamic theory for such gels, our analysis yields mathematical expressions for the mechanochemical properties of erythrocyte membranes that incorporate membrane molecular parameters to an extent not achieved previously. The erythrocyte membrane elastic shear modulus and maximum elastic extension ratio predicted by our membrane model are in quantitative agreement with reported values for these parameters. The gel theory predicts further that the membrane skeleton modulus of area compression, KG, may be small as well as large relative to the membrane elastic shear modulus, G, depending on the environmental conditions. Our analysis shows that the ratio between these two parameters affects both the geometry and the stability of the favoured cell shapes.

The human erythrocyte membrane skeleton may be an ionic gel. II. Numerical analyses of cell shapes and shape transformations.

In the first paper in this series (Stokke et al. Eur Biophys J 1986, 13:203-218) we developed the general theory of the mechanochemical properties and the elastic free energy of the protein gel--lipid bilayer membrane model. Here we report on an extensive numerical analysis of the human erythrocyte shapes and shape transformations predicted by this new cell membrane model. We have calculated the total elastic free energy of deformation of four different cell shape classes: disc-shaped cells, cup-shaped cells, crenated cells, and cells with membrane invaginations. We find that which of these shape classes is favoured depends strongly on the spectrin gel osmotic tension, IIGu, and the surface tensions, IIEu and IIPu, of the extracellular and protoplasmic halves of the membrane lipid bilayer, respectively. For constant ratio IIEu/IIPu greater than O large negative or positive values of IIGu favour respectively the crenated and invaginated cell shape classes. For small absolute values of IIGu, IIEu, and IIPu, biconcave or cup-shaped cells are the stable ones. Our numerical analysis shows that the higher the membrane skeleton compressibility is, the smaller are the values of IIGu needed to induce cell shape transformation. We find that the stable and metastable shapes of discocytes and stomatocytes generally depend both on the shape of the stressfree membrane skeleton and the membrane skeleton compressibility.