The bending rigidity of mitotic chromosomes

The bending rigidities of mitotic chromosomes isolated from cultured N. viridescens (newt) and Xenopus epithelial cells were measured by observing their spontaneous thermal bending fluctuations. When combined with simultaneous measurement of stretching elasticity, these measurements constrain models for higher order mitotic chromosome structure. We measured bending rigidities of B approximately 10(-22) N. m(2) for newt and approximately 10(-23) N. m(2) for Xenopus chromosomes extracted from cells. A similar bending rigidity was measured for newt chromosomes in vivo by observing bending fluctuations in metaphase-arrested cells. Following each bending rigidity measurement, a stretching (Young's) modulus of the same chromosome was measured in the range of 10(2) to 10(3) Pa for newt and Xenopus chromosomes. For each chromosome, these values of B and Y are consistent with those expected for a simple elastic rod, B approximately YR(4), where R is the chromosome cross-section radius. Our measurements rule out the possibility that chromosome stretching and bending elasticity are principally due to a stiff central core region and are instead indicative of an internal structure, which is essentially homogeneous in its connectivity across the chromosome cross-section.     

Dynamic tension spectroscopy and strength of biomembranes

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the kinetic pathway. Using tests on five types of giant phosphatidylcholine lipid vesicles over loading rates(tension/time) from 0.01-100 mN/m/s, we show that the kinetic process of membrane breakage can be modeled by a causal sequence of two thermally-activated transitions. At fast loading rates, a steep linear regime appears in each spectrum which implies that membrane failure starts with nucleation of a rare precursor defect. The slope and projected intercept of this regime are set by defect size and frequency of spontaneous formation, respectively. But at slow loading rates, each spectrum crosses over to a shallow-curved regime where rupture tension changes weakly with rate. This regime is predicted by the classical cavitation theory for opening an unstable hole in a two-dimensional film within the lifetime of the defect state. Under slow loading, membrane edge energy and the frequency scale for thermal fluctuations in hole size are the principal factors that govern the level of tension at failure. To critically test the model and obtain the parameters governing the rates of transition under stress, distributions of rupture tension were computed and matched to the measured histograms through solution of the kinetic master (Markov) equations for defect formation and annihilation or evolution to an unstable hole under a ramp of tension. As key predictors of membrane strength, the results for spontaneous frequencies of defect formation and hole edge energies were found to correlate with membrane thicknesses and elastic bending moduli, respectively.     

Dynamic bending rigidity of DNA

Rapidly relaxing components in the decay of the transient electric dichroism of DNA restriction fragments were reported by Diekmann et al. [(1982) Biophys. Chem. 15, 263-270] and P?rschke et al. [(1987) Biopolymers 26, 1971-1974]. These are analyzed using a new normal mode theory for weakly bending rods and assigned to bending. The longest bending relaxation times for fragments with 95-250 base pairs coincide with the theoretical curve calculated for a dynamic bending rigidity corresponding to a dynamic persistence length Pd = 2100 A. Analysis of the relative amplitudes of fast and slow components following weak orienting pulses is also consistent with a rather large dynamic persistence length. The enhancement of the relative amplitude of the fast component in large electric fields is attributed to steady-state bending of initially perpendicular DNAs by the field. Several reasons are proposed why the dynamic bending rigidity is 4 times larger than the apparent static bending rigidity inferred from equilibrium persistence length measurements on the same fragments.     

Line tension and structure of raft boundary calculated from bending,tilt, and lateral compression/stretching

Bilayer thickness in membrane domains enriched with sphingomielin and cholesterol (known as “rafts”) is bigger than thickness of neighboring membrane. Monolayers need to deform to compensate the thicknesses difference in the vicinity of the raft boundary. Line tension of the boundary of rafts associated with elastic deformations originating from the compensation of the thickness mismatch is calculated in the frame-work of the elasticity theory. In the calculations deformations of splay, tilt and lateral stretching/compression are considered. It is assumed that raft consists of two monolayer domains situated in the different membrane monolayers; it is also assumed that the boundaries of domains can shift in the lateral direction with respect to relative to each other. Dependence of the boundary energy of raft on the value of the relative shift of the boundaries is calculated. It is shown that the boundary energy is minimal when shift is equal to 4.5 nm. Dependence of the optimal shift on the mismatch of the monolayer thicknesses of raft and surrounding membrane as well as membrane shape in the vicinity of boundary are calculated. The calculated values of line tension are in a good agreement with available experimental data. Taking into account deformation of stretching/compression increases the accuracy of calculations by 30%; this exceeds the uncertainty of the line tension measurements by modern techniques.     

How sequence determines elasticity of disordered proteins

How nature tunes sequences of disordered protein to yield the desired coiling properties is not yet well understood. To shed light on the relationship between protein sequence and elasticity, we here investigate four different natural disordered proteins with elastomeric function, namely: FG repeats in the nucleoporins; resilin in the wing tendon of dragonfly; PPAK in the muscle protein titin; and spider silk. We obtain force-extension curves for these proteins from extensive explicit solvent molecular dynamics simulations, which we compare to purely entropic coiling by modeling the four proteins as entropic chains. Although proline and glycine content are in general indicators for the entropic elasticity as expected, divergence from simple additivity is observed. Namely, coiling propensities correlate with polyproline II content more strongly than with proline content, and given a preponderance of glycines for sufficient backbone flexibility, nonlocal interactions such as electrostatic forces can result in strongly enhanced coiling, which results for the case of resilin in a distinct hump in the force-extension curve. Our results, which are directly testable by force spectroscopy experiments, shed light on how evolution has designed unfolded elastomeric proteins for different functions.     

Effect of anisotropic bending rigidity and finite twisting rigidity on statistical properties of DNA model filaments

The persistence length and effective long-range bending rigidity are derived for a discrete model of an anisotropically bending filament and shown to be independent of the torsional rigidity. The twisting persistence length is found to be independent of the anisotropic bending rigidity. Other statistical properties are briefly discussed, including the dependence of tangent vector projections on contour length. The dependence of a tensor contraction on contour length is derived for an isotropically bending filament with no equilibrium twist.     

Lowering line tension with high cholesterol content induces a transition from macroscopic to nanoscopic phase domains in model biomembranes

Chemically simplified lipid mixtures are used here as models of the cell plasma membrane exoplasmic leaflet. In such models, phase separation and morphology transitions controlled by line tension in the liquid-disordered (Ld)?+?liquid-ordered (Lo) coexistence regime have been described [1]. Here, we study two four-component lipid mixtures at different cholesterol fractions: brain sphingomyelin (BSM) or 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC)/1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/cholesterol (Chol). On giant unilamellar vesicles (GUVs) display a nanoscopic-to-macroscopic transition of Ld?+?Lo phase domains as POPC is replaced by DOPC, and this transition also depends on the cholesterol fraction. Line tension decreases with increasing cholesterol mole fractions in both lipid mixtures. For the ternary BSM/DOPC/Chol mixture, the published phase diagram [19] requires a modification to show that when cholesterol mole fraction is >~0.33, coexisting phase domains become nanoscopic.     

Surface tension and the dodecahedron model for lung elasticity

Macroscopic elastic moduli governing the incremental deformations of lung parenchyma are calculated on the basis of a model for an individual lung element in the shape of a regular dodecahedron. Elastic stiffness within the element is provided by pin-jointed tension members along the edges of the dodecahedron, surface tension is incorporated into its pentagonal faces, and the influence of transpulmonary pressure is simulated by an externally applied hydrostatic tension. The analysis is based on a variational statement of nonlinear structural mechanics, and the results show how the moduli depend on the effective inflation pressure, the constitutive behavior of the idealized truss members, and the surface-area dependent surface tension. The theory is discussed in the light of available experimental information. A more general analysis is needed to account for the effects of structural as well as surface-tension hysteresis.     

Agonist-induced tension determines vascular reactivity during anoxia and reoxygenation.

To determine the influence of pre-existing pharmacologically-induced tension on vascular reactivity during anoxia and reoxygenation, rat aortic rings were contracted with norepinephrine, epinephrine, endothelin or KCl to 1, 2 or 4 g of tension. The rings were then exposed to anoxia (95% N2) for 10 min followed by reoxygenation (95% O2). The degree of anoxia-mediated contraction varied with the magnitude of tension before anoxia and resembled the length-tension relationship in myocardial fibers. The optimal agonist-induced tension for maximal anoxic contraction was approximately 1 to 2 g. This relationship between tension and anoxic contraction was observed in all but KCl-contracted rings. The agonist- as well as KCl-contracted rings showed normal relaxant response to acetylcholine, suggesting that a decrease in endothelium-derived relaxing factor (EDRF) alone cannot be the basis of anoxic contraction and release of endothelium-derived constricting factors (EDCFs) may relate to anoxic contraction in agonist-preconstricted rings. The relationship between the magnitude of agonist-induced tension and the extent of anoxia-mediated contraction may relate to the ability of endothelium to release EDRF and EDCFs as well as to the degree of phosphorylation in vascular smooth muscle cells. The reoxygenation-mediated contraction was noted to progressively increase in all experiments regardless of the pharmacologic agent used. This increase in reoxygenation-mediated contraction correlated with pre-existing pharmacologic tension, and may relate to calcium influx and restoration of ATP and other mediators in the vascular tissues during reoxygenation.     

Quinones and their interactions with enzyme complexes of energy-transducing biomembranes

The functionally essential properties of biomembrane quinones and the mechanism of their interaction with protein components are discussed. The hypotheses on the mobile quinone pool or the ability of protein-bound quinones to transfer redox equivalents in biomembranes are discussed. The idea of quinone domains is invoked, and evidence is provided for the presence of such domains in operative biomembranes.     

The influence of lysolipids on the spontaneous curvature and bending elasticity of phospholipid membranes.

The effects of lysolipids on phospholipid layer curvature and bending elasticity were examined using x-ray diffraction and the osmotic stress method. Lysolipids with two different head groups, phosphatidylcholine (PC) and phosphatidylethanolamine (PE), and differing hydrocarbon chains were mixed with the hexagonal-forming lipid, dioleoylphosphatidylethanolamine (DOPE). With up to 30 mole% lysolipid in DOPE, the mixture maintains the inverted hexagonal (H(II)) phase in excess water, where increasing levels of lysolipid result in a systematic increase in the H(II) lattice dimension. Analysis of the structural changes imposed by lysolipids show that, opposite to DOPE itself, which has an spontaneous radius of curvature (R(0)) of -30 A, PC lysolipids add high positive curvature, with R(0) = +38 to +60 A, depending on chain length. LysoPEs, in contrast, add very small curvatures. When both polar group and hydrocarbon chains of the added lysolipid mismatch those of DOPE, the structural effects are qualitatively different from otherwise. Such mismatched lysolipids "reshape" the effective combination molecule into a longer and more cylindrical configuration compared to those lysolipids with either matching polar group or hydrocarbon chain.     

The consequence of substrates of large-scale rigidity on actin network tension in adherent cells

Abstract

There is compelling evidence that substrate stiffness affects cell adhesion as well as cytoskeleton organization and contractile activity. This work was designed to study the cytoskeletal contractile activity of single cells plated on micropost substrates of different stiffness using a numerical model simulating the intracellular tension of individual cells. We allowed cells to adhere onto micropost substrates of various rigidities and used experimental traction force data to infer cell contractility using a numerical model. The model shows that higher substrate stiffness leads to an increase in intracellular tension. The strength of this model is its ability to calculate the mechanical state of each cell in accordance to its individual cytoskeletal structure. This is achieved by regenerating a numerical cytoskeleton based on microscope images of the actin network of each cell. The resulting numerical structure consequently represents pulling characteristics on its environment similar to those generated by the cell in-vivo. From actin imaging we can calculate and better understand how forces are transmitted throughout the cell.     

Cell fusion generates an inhomogeneous distribution of elasticity and rigidity in plasma membranes

The post-electrofusion oscillation cycle of human erythrocytes (doublets) was evaluated for the first four pump events in order to quantify the spectrin-network rearrangement in the fusion zone. Experiments were carried out on control cells and on cells that received a 40 degree C and a 45 degree C 20-min heat treatment. The amplitude of the geometrical changes depended on the heat-treatment procedure, whereas the roundness on entering the pump event was always identical. The rigid influence of the fusion zone prevented the doublets from adopting a spherical shape. The fusion zone was characterized by a linear elongation modulus that could be calculated from geometrical measurements and earlier findings on erythrocyte membrane mechanics, and that ranged between 1.44E6 Nm(-2) for control doublets and 0.99E6 Nm(-2) after 45 degrees C heat treatment. The membrane composition of the fusion zone differs greatly from that of the other membrane parts not involved in fusion processes and evidence is given that this inhomogeneity stems from a rearrangement of the triangulated spectrin network and other membrane skeletal proteins in the fusion zone.     

Interaction between bending and tension forces in bilayer membranes.

A theoretical analysis is presented of the bending mechanics of a membrane consisting of two tightly-coupled leaflets, each of which shears and bends readily but strongly resists area changes. Structures of this type have been proposed to model biological membranes such as red blood cell membrane. It is shown that when such a membrane is bent, anisotropic components of resultant membrane tension (shear stresses) are induced, even when the tension in each leaflet is isotropic. The induced shear stresses increase as the square of the membrane curvature, and become significant for moderate curvatures (when the radius of curvature is much larger than the distance between the leaflets). This effect has implications for the analysis of shape and deformation of freely suspended and flowing red blood cells.     

Temperature dependence of structure, bending rigidity, and bilayer interactions of dioleoylphosphatidylcholine bilayers

X-ray diffuse scattering was measured from oriented stacks and unilamellar vesicles of dioleoylphosphatidylcholine lipid bilayers to obtain the temperature dependence of the structure and of the material properties. The area/molecule, A, was 75.5 Å² at 45°C, 72.4 Å² at 30°C, and 69.1 Å² at 15°C, which gives the area expansivity α_A = 0.0029/deg at 30°C, and we show that this value is in excellent agreement with the polymer brush theory. The bilayer becomes thinner with increasing temperature; the contractivity of the hydrocarbon portion was α_Dc = 0.0019/deg; the difference between α_A and α_Dc is consistent with the previously measured volume expansivity α_Vc = 0.0010/deg. The bending modulus K_C decreased as exp(455/T) with increasing T (K). Our area compressibility modulus K_A decreased with increasing temperature by 5%, the same as the surface tension of dodecane/water, in agreement again with the polymer brush theory. Regarding interactions between bilayers, the compression modulus B as a function of interbilayer water spacing D′_W was found to be nearly independent of temperature. The repulsive fluctuation pressure calculated from B and K_C increased with temperature, and the Hamaker parameter for the van der Waals interaction was nearly independent of temperature; this explains why the fully hydrated water spacing, D′_W, that we obtain from our structural results increases with temperature.