Arne Mikkelsen

Inhomogeneous alginate gel spheres: An assessment of the polymer gradients by synchrotron radiation-induced x-ray emission, magnetic resonance microimaging, and mathematical modeling

It has been previously demonstrated that calcium alginate gels prepared by dialysis often exhibit a concentration inhomogeneity being the polymer concentration considerably lower in the center of the gel than at the edges. Inhomogeneity may be a preferred structure in microcapsules due to low porosity and higher stability so that it is interesting to evaluate the polymer gradient in spherically symmetrical small alginate beads (1.0-0.7 mm diameter) obtained in different conditions. In this paper, two complementary techniques have been used to investigate this aspect. The concentration gradient of alginate has been analyzed by measuring both the spatial distribution of calcium ions in sections of alginate gel spheres, by means of x-ray fluorescence spectroscopy, and the T2 relaxation behavior on intact gel beads using magnetic resonance microimaging. The experimentally determined gradients from three-dimensional gels provide data to reevaluate the parameter estimates in the recently reported mathematical model for alginate gel formation (A. Mikkaelsen and A. Elgsaeter, Biopolymers, 1995, Vol. 36, pp. 17-41). The model may account for the gels being less inhomogeneous when nongelling sodium or magnesium ions are added during gelation.

The human erythrocyte membrane skeleton may be an ionic gel

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.

Human erythrocyte spectrin dimer intrinsic viscosity: Temperature dependence and implications for the molecular basis of the erythrocyte membrane free energy

We have determined experimentally the temperature dependence of human erythrocyte spectrin dimer intrinsic viscosity at shear rates 8-12 s-1 using a Cartesian diver viscometer. We find that the intrinsic viscosity decreases from 43 +/- 3 ml/g at 4 degrees C to 34 +/- 3 ml/g when the temperature is increased to 38 degrees C. Our results show that spectrin dimers are flexible worm-like macromolecules with persistence length about 20 nm and that the mean square end-to-end distance for this worm-like macromolecules decreases when the temperature is increased. This implies that the spectrin dimer internal energy decreases when the end-to-end distance is increased and that the free energy increase associated with making the end-to-end distance longer than the equilibrium value for the free molecules is of entropic origin. The temperature dependence of the erythrocyte membrane shear modulus reported previously in the literature therefore appears mainly to be due to temperature dependent alterations in the membrane skeleton topology.

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.

Brownian dynamics simulation of needle chains

Polymers consisting of rigid segments connected by flexible joints (needle chains) constitute an important class of biopolymers. Using kinetic theory as a starting point, we first derive the generalized coordinate–space diffusion (Fokker–Planck) equation for the needle chain polymer model. Next, the equivalent generalized coordinate Ito stochastic differential equation is established. Nonlinear transformations of variables finally yield a stochastic differential equation for the needle chain spatial coordinates in the laboratory coordinate system where the coefficients are expressed in terms of the chain constraint conditions. This latter equation constitutes the basis for our needle chain Brownian dynamics (BD) algorithm. The used needle chain model includes needle translation–translation and rotation–rotation hydrodynamic interactions, a homogeneous solvent flow field, external forces, excluded volume effects, and bending and twisting stiffness between nearest neighbor segments. For this chain model we ...

Human spectrin. V. A comparative electro-optic study of heterotetramers and heterodimers

The electrically induced birefringence of human spectrin heterotetramer and heterodimer solutions at 5 degrees C has been studied. 1. The steady-state birefringence, delta, was found to be approximately proportional to the electric field strength, E, when E greater than or equal to 0.2 kV/mm. For spectrin solutions the specific linear coefficient, delta/(E x c), therefore is a more relevant parameter for describing birefringence saturation behavior when E greater than or equal to 0.2 kV/mm than the commonly used Kerr constant. At 5 degrees C were measured delta/(E x c) = (27 +/- 5) x 10(-8)m4 x V(-1) x kg(-1) for heterodimers and heterotetramers. 2. At 5 degrees C both heterotetramers and heterodimers exhibited more than one birefringence relaxation time and the shortest of these was for both molecules found to be 4.2 +/- 1.0 microseconds. This indicates that the spectrin molecules are highly flexible. The birefringence build-up time for heterotetramers and heterodimers was found to be 20 +/- 7 microseconds and 15 +/- 5 microseconds, respectively.

Brownian dynamics simulation of needle-spring chains

Chains consisting of rigid segments connected by flexible joints constitute an important class of polymers. The joints may be modeled as rigid constraints (the needle chain polymer model) or as springs interconnecting the ends of nearest neighbor segments where both the equilibrium length and stiffness of each spring are selectable parameters (the needle–spring polymer model). Using kinetic theory as the starting point we have derived the theoretical foundation for a Brownian dynamics algorithm for needle-spring polymer chains. The employed polymer model is valid for some Reynolds numbers and includes needle translational–translational, translational–rotational and rotational–rotational hydrodynamic interactions, external forces, excluded volume effects, and bending and twisting stiffness between nearest neighbor needles. Studies reported in the literature on other polymer models show that polymer chain dynamics may depend significantly on whether the constraints are rigid or spring-like. It is therefore expected that the dynamics of some biopolymers may be more accurately modeled by the needle–spring rather than the needle-chain polymer model.

An electro-optic study of human erythrocyte spectrin dimers the presence of calcium ions does not alter spectrin flexibility

In order to determine whether the presence of Ca2+ increases the stiffness of the highly elongated and flexible spectrin molecules, we have carried out a birefringence relaxation study of isolated human erythrocyte spectrin dimers. Our measurements indicate no significant change in the flexibility of spectrin in solutions containing 0-10(-3) M Ca2+. This finding indicates that decreased spectrin flexibility is not the major functional mechanism underlying the decreased erythrocyte deformability reported as result of elevated intracellular levels of Ca2+. We find that the persistence length of spectrin dimers is less than 20 nm and is not dependent on the Ca2+ concentration.

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.

Brownian dynamics simulation of rigid bodies and segmented polymer chains. Use of Cartesian rotation vectors as the generalized coordinates describing angular orientations

The three Eulerian angles constitute the classical choice of generalized coordinates used to describe the three degrees of rotational freedom of a rigid body, but it has long been known that this choice yields singular equations of motion. The latter is also true when Eulerian angles are used in Brownian dynamics analyses of the angular orientation of single rigid bodies and segmented polymer chains. Starting from kinetic theory we here show that by instead employing the three components of Cartesian rotation vectors as the generalized coordinates describing angular orientation, no singularity appears in the configuration space diffusion equation and the associated Brownian dynamics algorithm. The suitability of Cartesian rotation vectors in Brownian dynamics simulations of segmented polymer chains with spring-like or ball-socket joints is discussed.