Anisotropic mechanical properties of magnetically aligned fibrin gels measured by magnetic resonance elastography

The anisotropic mechanical properties of magnetically aligned fibrin gels were measured by magnetic resonance elastography (MRE) and by a standard mechanical test: unconfined compression. Soft anisotropic biomaterials are notoriously difficult to characterize, especially in vivo. MRE is well-suited for efficient, non-invasive, and non-destructive assessment of shear modulus. Direction-dependent differences in shear modulus were found to be statistically significant for gels polymerized at magnetic fields of 11.7 and 4.7 T compared to control gels. Mechanical anisotropy was greater in the gels polymerized at the higher magnetic field. These observations were consistent with results from unconfined compression tests. Analysis of confocal microscopy images of gels showed measurable alignment of fibrils in gels polymerized at 11.7 T. This study provides direct, quantitative measurements of the anisotropy in mechanical properties that accompanies fibril alignment in fibrin gels.     

The reinforcement of gellan gel network by the immersion into salt solution

The effect of immersion into salt solutions on rheological properties of gellan gels was investigated. The storage Young's modulus of gellan gels increased with time during the immersion into salt solutions. The increase of the storage Young's modulus can not be explained solely by change in the concentration of gellan. The ellipticity at 202 nm decreased by the immersion, suggesting the formation and aggregation of gellan helices. It was considered that during immersion cations penetrated into gellan gels to induce the formation and aggregation of gellan helices in gels, resulting in reinforcement of the gel network.     

Sickle cell trait human erythrocytes are significantly stiffer than normal

Atomic force microscopy (AFM) allows for high-resolution topography studies of biological cells and measurement of their mechanical properties in physiological conditions. In this work, AFM was employed to measure the stiffness of abnormal human red blood cells from human subjects with the genotype for sickle cell trait. The determined Young's modulus was compared with that obtained from measurements of erythrocytes from healthy subjects. The results showed that Young's modulus of pathological erythrocytes was approximately three times higher than in normal cells. Observed differences indicate the effect of the polymerization of sickle hemoglobin as well as possible changes in the organization of the cell cytoskeleton associated with the sickle cell trait.     

Geometric confinement influences cellular mechanical properties I -- adhesion area dependence

Interactions between the cell and the extracellular matrix regulate a variety of cellular properties and functions, including cellular rheology. In the present study of cellular adhesion, area was controlled by confining NIH 3T3 fibroblast cells to circular micropatterned islands of defined size. The shear moduli of cells adhering to islands of well defined geometry, as measured by magnetic microrheometry, was found to have a significantly lower variance than those of cells allowed to spread on unpatterned surfaces. We observe that the area of cellular adhesion influences shear modulus. Rheological measurements further indicate that cellular shear modulus is a biphasic function of cellular adhesion area with stiffness decreasing to a minimum value for intermediate areas of adhesion, and then increasing for cells on larger patterns. We propose a simple hypothesis: that the area of adhesion affects cellular rheological properties by regulating the structure of the actin cytoskeleton. To test this hypothesis, we quantified the volume fraction of polymerized actin in the cytosol by staining with fluorescent phalloidin and imaging using quantitative 3D microscopy. The polymerized actin volume fraction exhibited a similar biphasic dependence on adhesion area. Within the limits of our simplifying hypothesis, our experimental results permit an evaluation of the ability of established, micromechanical models to predict the cellular shear modulus based on polymerized actin volume fraction. We investigated the "tensegrity", "cellular-solids", and "biopolymer physics" models that have, respectively, a linear, quadratic, and 5/2 dependence on polymerized actin volume fraction. All three models predict that a biphasic trend in polymerized actin volume fraction as a function of adhesion area will result in a biphasic behavior in shear modulus. Our data favors a higher-order dependence on polymerized actin volume fraction. Increasingly better experimental agreement is observed for the tensegrity, the cellular solids, and the biopolymer models respectively. Alternatively if we postulate the existence of a critical actin volume fraction below which the shear modulus vanishes, the experimental data can be equivalently described by a model with an almost linear dependence on polymerized actin volume fraction; this observation supports a tensegrity model with a critical actin volume fraction.     

Free Heme and the Polymerization of Sickle Cell Hemoglobin

In search of novel control parameters for the polymerization of sickle cell hemoglobin (HbS), the primary pathogenic event of sickle cell anemia, we explore the role of free heme, which may be excessively released in sickle erythrocytes. We show that the concentration of free heme in HbS solutions typically used in the laboratory is 0.02-0.04 mole heme/mole HbS. We show that dialysis of small molecules out of HbS solutions arrests HbS polymerization. The addition of 100-260 μM of free heme to dialyzed HbS solutions leads to rates of nucleation and polymer fiber growth faster by two orders of magnitude than before dialysis. Toward an understanding of the mechanism of nucleation enhancement by heme, we show that free heme at a concentration of 66 μM increases by two orders of magnitude the volume of the metastable clusters of dense HbS liquid, the locations where HbS polymer nuclei form. These results suggest that spikes of the free heme concentration in the erythrocytes of sickle cell anemia patients may be a significant factor in the complexity of the clinical manifestations of sickle cell anemia. The prevention of free heme accumulation in the erythrocyte cytosol may be a novel avenue to sickle cell therapy.     

Mechanism of inhibition of sickling by dimethyl adipimidate. Effects of intertetramer cross-linking

Dimethyl adipimidate (DMA), an effective antisickling agent in vitro, reacts with free amino groups producing chemically modified and cross-linked molecules. In this report, we have investigated the effect of cross-linked hemoglobin tetramers on sickle hemoglobin polymerization. Since the extent of cross-linking is pH-dependent, we first compared the solubilities of deoxygenated hemolysates prepared from sickle cells previously treated with dimethyl adipimidate at either pH 7.4 or 8.4. The solubility of the hemolysate increased from 18.6 +/- 0.8 g/dl in the untreated sample to 20.9 +/- 1.5 g/dl (pH 7.4) and to 25.4 +/- 3.0 g/dl (pH 8.4) after dimethyl adipimidate treatment. Removal of cross-linked hemoglobin tetramers from hemolysate obtained from dimethyl adipimidate-treated cells abolished part of this effect; at pH 7.4, the solubility decreased from 20.9 +/- 1.5 to 19.4 +/- 0.2 and at pH 8.4 from 25.4 +/- 3.0 to 21.0 +/- 1.5. However, the ratio of [14C]DMA-labelled hemoglobin in the sol phase to that in the gel phase in the unfractionated hemolysate was 1.17 at pH 7.4 and 1.25 at pH 8.4, suggesting that part of the cross-linked hemoglobin tetramers was incorporated into the gel. In order to further investigate the effect of cross-linked hemoglobin tetramers on sickle hemoglobin polymerization, we separated cross-linked hemoglobin tetramers on a gel-filtration column, prepared mixtures of untreated sickle hemoglobin and cross-linked hemoglobin tetramers and studied the polymerization of these mixtures. The Csat of the untreated hemolysate increased progressively from 18.6 +/- 0.8 to 22.5 +/- 0.8 g/dl with 33% cross-linked hemoglobin tetramers. The hemoglobin concentration in the gel decreased from 43 +/- 1.0 to 33.8 +/- 1.0 g/dl with 33% cross-linked hemoglobin tetramers, while the pellet volume fraction, phi p, increased with and almost approached 1 at 50% cross-linked hemoglobin tetramers. In addition, the sol phase contained a higher molecular weight distribution of cross-linked hemoglobin tetramers than the gel phase. These observations suggest that a loose polymer was formed in the gel phase with a hemoglobin concentration much lower than that of the control. Thus, polymerization of sickle hemoglobin is inhibited by: (1) exclusion of higher molecular weight cross-linked hemoglobin tetramers from the gel, and (2) loose incorporation of cross-linked hemoglobin tetramers into the gel, perhaps preventing lateral packing and formation of tightly ordered fibers.     

Shear creep of gelatin gels from mammalian and piscine collagens.

This paper describes new measurements on the creep rheological behaviour of gelatin gels from both traditional mammalian and piscine sources. Measurements on a series of concentrations of gels were obtained using a high-precision controlled stress rheometer. Results for the concentration dependence of compliance are close to those expected from dynamic oscillatory measurements of gel modulus, assuming ideal elasticity. The concentration dependence of viscosity approximates power law behaviour, with eta~C( approximately 2-3), lower than the exponent expected for semi-dilute solutions. The apparent contradiction implied by this is discussed and a novel gel viscosity versus concentration state diagram presented.     

Viscoelastic properties of the oxygenated sickle erythrocyte membrane

Although most apparent in permanently misshapen irreversibly sickled erythrocytes (ISC), biochemical and structural alterations are present in the majority of sickle cell membranes. The relationship of membrane rigidity to cell shape and its dependence upon the internal hemoglobin cytosol are not clarified. We therefore examined the frequency dependent viscoelasticity of oxygenated, packed sickle red cell and ghost suspensions and hemoglobin solutions prepared from density gradient separated ISC and reversibly sickled cell (RSC) fractions. Low amplitude, oscillatory shear was applied in a Weissenberg cone and plate viscometer and the resultant viscoelastic signals provided a dynamic viscosity (eta') and elastic storage modulus (G') which varied with frequency of deformation. The viscoelastic response of the cell and ghost suspensions reflected the material properties of the membrane over most of the frequency range tested. Sickle erythrocyte, red ghost, and white ghost suspensions demonstrated greater viscocoelasticity than comparable normal suspensions. The viscoelastic magnitude of ISC was several-fold greater than normal, with little variation of viscoelasticity with frequency. RSC samples which were characterized by normal shape, size, and internal hemoglobin concentration were also significantly harder than normal, although similar in frequency dependence. Red ghosts prepared from ISC manifested 80% of the viscoelasticity of intact ISC despite diminution of the internal hemoglobin concentration by 90%. Under conditions of low amplitude shear, the behavior of the RSC membrane is compatible with a cytoskeleton possessing an increased number of molecular associations. The mechanical stability of the ISC membrane is related to a substantial, intrinsic reorganization of the cytoskeleton.     

Gelling properties of apohemoglobin S alone and in mixtures with hemoglobin S

Apohemoglobin S formed a gel in the cold (5 degrees C) with a protein concentration in the supernatants after centrifugation of the gels (Csat) near 27 g/dl, in 0.02 M phosphate buffer at pH 7.2. Under the same experimental conditions in mixtures of apohemoglobin S and deoxyhemoglobin S the solubility of hemoglobin S in the cold was decreased from Csat greater than 40 g/dl in the absence to about 18 g/dl in the presence of apohemoglobin S. Conversely, in the same mixture, Csat of apohemoglobin S was decreased to about 5 g/dl. Also, gelling occurred in mixtures of oxyhemoglobin S and its apoderivative. Apohemoglobin A alone did not form gels; however, it induced fiber formation in deoxyhemoglobin S in the cold; unlike apohemoglobin S, it was not included in the precipitate. Gels of apohemoglobin S were not birefringent, and inspection at the electron microscope failed to show the presence of organized structures. Excluded volume effects were probably at the origin of the decreased solubility of hemoglobin S and apohemoglobin S in the presence of each other.     

Universal metastability of sickle hemoglobin polymerization

Sickle hemoglobin (HbS) polymerization occurs when the concentration of deoxyHbS exceeds a well-defined solubility. In experiments using sickle hemoglobin droplets suspended in oil, it has been shown that when polymerization ceases the monomer concentration is above equilibrium solubility. We find that the final concentration in uniform bulk solutions (i.e., with negligible boundaries) agrees with the droplet measurements, and both exceed the expected solubility. To measure hemoglobin in uniform solutions, we used modulated excitation of trace amounts of CO in gels of HbS. In this method, a small amount of CO is introduced to a spatially uniform deoxyHb sample, so that less than 2% of the sample is liganded. The liganded fraction is photolyzed repeatedly and the rate of recombination allows the concentration of deoxyHbS in the solution phase to be determined, even if polymers have formed. Both uniform and droplet samples exhibit the same quantitative behavior, exceeding solubility by an amount that depends on the initial concentration of the sample, as well as conditions under which the gel was formed. We hypothesize that the early termination of polymerization is due to the obstruction in polymer growth, which is consistent with the observation that pressing on slides lowers the final monomer concentration, making it closer to solubility. The thermodynamic solubility in free solution is thus achieved only in conditions with low polymer density or under external forces (such as found in sedimentation) that disrupt polymers. Since we find that only about 67% of the expected polymer mass forms, this result will impact any analysis predicated on predicting the polymer fraction in a given experiment.     

Rheological properties of mixtures of protein-polysaccharide-dynamic viscoelasticity of blend gels of acylated gelatin, kappa-carrageenan, and agarose

Complex Young's modulus of blend gels of gelatin and kappa-carrageenan or agarose has been measured in order to clarify the protein-polysaccharide interaction in biological systems. The mixture of gelatin and kappa-carrageenan showed phase separation in the intermediate volume fraction of gelatin, and it formed a homogeneous gel when the volume fraction of gelatin is very large or very small. Since the dynamic Young's modulus for blend gels of kappa-carrageenan and gelatin was larger than the calculated one from a theory for dispersed systems, some structural reinforcing must occur. The mixture of agarose and gelatin showed the inverse tendency. It was concluded that the role of electrolytic groups was dominant in dilute gels, while molecular entanglement became more important in concentrated gels.     

Net charge and oxygen affinity of human hemoglobin are independent of hemoglobin concentration

The dependence of net charge and oxygen affinity of human hemoglobin upon hemoglobin concentration was reinvestigated. In contrast to earlier reports from various laboratories, both functional properties of hemoglobin were found to be independent of hemoglobin concentration. Two findings indicate a concentration-independent net charge of carbonmonoxy hemoglobin at pH 6.6: (A) The pH value of a given carbonmonoty hemoglobin solution remains constant at 6.6 when the hemoglobin concentration is raised from 10 to 40 g/dl, indicating that there is no change in protonation of titratable groups of hemoglobin: (b) the net charge of carbonmonoxy hemoglobin as estimated from the Donnan distribution of 22Na+ shows no dependence on hemoglobin concentration in this concentration range. The oxygen affinity of human hemoglobin was determined from measurements of oxygen concentrations in equilibrated samples using a Lex-O2-Con apparatus (Lexington Instruments, Waltham, Mass.). P50 averaged 11.4 mm Hg at 37 degrees C, pH = 7.2, and ionic strength approximately 0.15. Neither P50 nor Hill's n showed any variation with hemoglobin concentrations increasing from 10 to 40 g/dl.     

Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation.

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.     

Interpretation of the osmotic behavior of sickle cell hemoglobin solutions: Different interactions among monomers and polymers

It has long been known that a simple hard particle model quantitatively explains the osmotic properties of monomeric hemoglobin near its isoelectric point. However, we find that a hard particle model is not consistent with the osmotic properties of polymerized hemoglobin and that substantial soft repulsions are indicated. With allowance for different interactions among monomers and among polymers, a self-consistent quantitative fit to the experimental data is obtained. The results suggest that the decreasing “solubility” of deoxy sickle cell hemoglobin with increasing temperature from 20 to 37°C is due to weaker repulsions between polymers at higher temperatures rather than stronger polymerization. The temperature dependence of these variables indicates that the aggregation of monomers is enthalpically and entropically driven (the latter effect being stronger), while the approach of polymers toward each other is enthalpically disfavored and entropically favored (with the former dominating). In both cases, the entropic contribution suggests that water is released. © 1998 John Wiley & Sons, Inc. Biopoly 45: 299–306, 1998     

Cardiac Myosin Binding Protein-C Is Essential for Thick-Filament Stability and Flexural Rigidity

Using atomic force microscopy, we examined the contribution of cardiac myosin binding protein-C (cMyBP-C) to thick-filament length and flexural rigidity. Native thick filaments were isolated from the hearts of transgenic mice bearing a truncation mutation of cMyBP-C (t/t) that results in no detectable cMyBP-C and from age-matched wild-type controls (+/+). Atomic force microscopy images of these filaments were evaluated with an automated analysis algorithm that identified filament position and shape. The t/t thick-filament length (1.48 ± 0.02 μm) was significantly (P < 0.01) shorter than +/+ (1.56 ± 0.02 μm). This 5%-shorter thick-filament length in the t/t was reflected in 4% significantly shorter sarcomere lengths of relaxed isolated cardiomyocytes of the t/t (1.97 ± 0.01 μm) compared to +/+ (2.05 ± 0.01 μm). To determine if cMyBP-C contributes to the mechanical properties of thick filaments, we used statistical polymer chain mechanics to calculate a per-filament-specific persistence length, an index of flexural rigidity directly proportional to Young's modulus. Thick-filament-specific persistence length in the t/t (373 ± 62 μm) was significantly lower than in +/+ (639 ± 101 μm). Accordingly, Young's modulus of t/t thick filaments was ∼60% of +/+. These results provide what we consider a new understanding for the critical role of cMyBP-C in defining normal cardiac output by sustaining force and muscle stiffness.     

Elastic properties of deoxy hemoglobin S (deoxy-HbS) gels

Equilibrium shear moduli for deoxyhemoglobin S(HbS) gels were measured as a function of HbS concentration. The modulus was found to depend approximately on the 18th power of the HbS concentration. Deoxy-HbS gels were found at HbS concentration as low as 10 g/dl.     

Thermodynamic study of the crystallization of sickle-cell deoxyhemoglobin (hemoglobin S solubility/saturation concentration/enthalpy of crystallization/entropy of crystallization).

The solubility of crystalline deoxygenated sickle-cell hemoglobin has been determined by a new turbidometric technique. In the absence of the allosteric effector, inositol hexaphosphate, the solubility of sickle deoxyhemoglobin crystals is about 30% less than that of gels. The dependence of the solubility of crystals on temperature at pH 7.1 is very much the same as that of gels at pH 6.48. The change in Van't Hoff enthalpy with crystallization is positive but small (3.11 kcal mol^?1) and essentially independent of temperature below 30 °C. The presence of inositol hexaphosphate cuts the solubility almost in half. The entropy change when crystals form, just under 40 cal K^?1 mol^?1, is larger than the values of ΔS ° found for gels. None of the measurements reported required the estimation of pellet volumes and compositions.     

Enzyme-ligand complexes of pyridoxine 5'-phosphate synthase: implications for substrate binding and catalysis

Pathogenesis in sickle cell disease depends on polymerization of deoxyhemoglobin S into rod-like fibers, forming gels that rigidify red cells and obstruct the systemic microvasculature. Fiber structure, polymerization kinetics and equilibria are well characterized and intimately related to pathogenesis. However, data on gel rheology, the immediate cause of obstruction, are limited, and models for structure and rheology are lacking. The basis of gel rheology, micromechanics of individual fibers, has never been examined. Here, we isolate fibers by selective depolymerization of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal fluctuations in fiber shape to obtain bending moduli (kappa) and persistence lengths (lambda(p)). Some fibers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of fiber midpoints from mean positions. Serial deviations, sufficiently separated to be independent, exhibit Gaussian distributions and provide mean-squared fluctuation amplitudes from which kappa and lambda(p) can be calculated. Lambda(p) ranges from 0.24 to 13 mm for the most flexible and stiffest fibers, respectively. This large range reflects formation of fiber bundles. If the most flexible are single fibers, then lambda(p) =13 mm represents a bundle of seven single fibers. Preliminary data on the bending variations of frozen, hydrated single fibers of HbS obtained by electron microscopy indicate that the value 0.24 mm is consistent with the persistence length of single fibers. Young's modulus is 0.10 GPa, less than for structural proteins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macroscopic rheology of hemoglobin S gels. This new technique, combining isolation of hemoglobin S fibers and measurement of micromechanical properties based on thermal fluctuations and midpoint deviations, can be used to study fibers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S.     

Effect of dehydration on the viscoelastic behavior of red cells.

Dehydration of red cells alters their rheological behavior and may contribute to the pathology of disorders such as sickle cell disease. We have measured the viscoelastic properties of individual human HbAA red cells after graded dehydration induced by incubation with valinomycin at different external K levels. With dehydration, the cells underwent progressive reduction in their rate of extensional shape recovery (i.e., after elongation by micropipette manipulation). Their rigidity remained unaffected until the mean cell hemoglobin concentration (MCHC) rose above 50 g/dl, but then increased about 100% as judged from the response of membrane tongues drawn into micropipettes. There was also a marked reduction in the shape recovery rate at this level of dehydration, and the cells no longer behaved elastically but rather showed unrecoverable residual deformation. Additionally, the cytoplasm took on solid-like properties. Changes in cell rigidity and shape recovery rate have been previously demonstrated for dense sickle cells; our results indicate that normal red cells can be induced to behave similarly, but that a greater degree of dehydration is required.     

Rheological characterization and dissolution kinetics of fibrin gels crosslinked by a microbial transglutaminase

Various fibrin gels were prepared with a microbial transglutaminase under miscellaneous conditions. The gels were characterized through their rheological properties. The influence of fibronectin addition and that of covalent bonding on the viscoelastic characteristics were evaluated. Gel elasticity is proportional to fibrinogen concentration but shows a nonlinear dependence on transglutaminase concentration. Additional crosslink of fibronectin in fibrin gels has no effect on the rheological character of the matrix. Dissolution kinetics in concentrated urea solutions evidences the role of covalent bonds on gel stability. The rheological properties and gel stability are discussed in relation with the enzyme-catalyzed covalent bonding. The microbial enzyme reactions are compared to those of FXIII and tissue transglutaminases.