Cornelis Storm

Accurate Determination of Elastic Parameters for Multicomponent Membranes

Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line tension and the bending moduli, are crucially involved in the kinetics and the asymptotic behavior of phase separation. In this Letter we present a combined analytical and experimental approach to determine the properties of phase-separated vesicle systems. First we develop an analytical model for the vesicle shape of weakly budded biphasic vesicles. Subsequently experimental data on vesicle shape and membrane fluctuations are taken and compared to the model. The parameters obtained set limits for the size and stability of nanodomains in the plasma membrane of living cells.

Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems

We study the coupled complex Ginzburg–Landau (CGL) equations for traveling wave systems, and show that sources and sinks are the important coherent structures that organize much of the dynamical properties of traveling wave systems. We focus on the regime in which sources and sinks separate patches of left and right-traveling waves, i.e., the case that these modes suppress each other. We present in detail the framework to analyze these coherent structures, and show that the theory predicts a number of general properties which can be tested directly in experiments. Our counting arguments for the multiplicities of these structures show that independently of the precise values of the coefficients in the equations, there generally exists a symmetric stationary source solution, which sends out waves with a unique frequency and wave number. Sinks, on the other hand, occur in two-parameter families, and play an essentially passive role, being sandwiched between the sources. These simple but general results imply that sources are important in organizing the dynamics of the coupled CGL equations. Simulations show that the consequences of the wavenumber selection by the sources is reminiscent of a similar selection by spirals in the 2D complex Ginzburg–Landau equations; sources can send out stable waves, convectively unstable waves, or absolutely unstable waves. We show that there exists an additional dynamical regime where both single- and bimodal states are unstable; the ensuing chaotic states have no counterpart in single amplitude equations. A third dynamical mechanism is associated with the fact that the width of the sources does not show simple scaling with the growth rate e. This is related to the fact that the standard coupled CGL equations are not uniform in e. In particular, when the group velocity term dominates over the linear growth term, no stationary source can exist; however, sources displaying nontrivial dynamics can often survive here. Our results for the existence, multiplicity, wavelength selection, dynamics and scaling of sources and sinks and the patterns they generate are easily accessible by experiments. We therefore advocate a study of the sources and sinks as a means to probe traveling wave systems and compare theory and experiment. In addition, they bring up a large number of new research issues and open problems, which are listed explicitly in the concluding section.

Membrane-Mediated Interactions Measured Using Membrane Domains

Cell membrane organization is the result of the collective effect of many driving forces. Several of these, such as electrostatic and van der Waals forces, have been identified and studied in detail. In this article, we investigate and quantify another force, the interaction between inclusions via deformations of the membrane shape. For electrically neutral systems, this interaction is the dominant organizing force. As a model system to study membrane-mediated interactions, we use phase-separated biomimetic vesicles that exhibit coexistence of liquid-ordered and liquid-disordered lipid domains. The membrane-mediated interactions between these domains lead to a rich variety of effects, including the creation of long-range order and the setting of a preferred domain size. Our findings also apply to the interaction of membrane protein patches, which induce similar membrane shape deformations and hence experience similar interactions.

Soft glassy rheology of supercooled molecular liquids

We probe the mechanical response of two supercooled liquids, glycerol and ortho-terphenyl, by conducting rheological experiments at very weak stresses. We find a complex fluid behavior suggesting the gradual emergence of an extended, delicate solid-like network in both materials in the supercooled state—i.e., above the glass transition. This network stiffens as it ages, and very early in this process it already extends over macroscopic distances, conferring all well known features of soft glassy rheology (yield-stress, shear thinning, aging) to the supercooled liquids. Such viscoelastic behavior of supercooled molecular glass formers is difficult to observe because the large stresses in conventional rheology can easily shear-melt the solid-like structure. The work presented here, combined with evidence for long-lived heterogeneity from previous single-molecule studies [Zondervan R, Kulzer F, Berkhout GCG, Orrit M (2007) Local viscosity of supercooled glycerol near Tg probed by rotational diffusion of ensembles and single dye molecules. Proc Natl Acad Sci USA 104:12628–12633], has a profound impact on the understanding of the glass transition because it casts doubt on the widely accepted assumption of the preservation of ergodicity in the supercooled state.

Theory of unstable laser modes : edge waves and fractality

Abstract For large Fresnel numbers N , unstable laser modes are highly irregular and resemble fractals. To explore this, we derive an explicit formula for the lowest-loss mode of a one-dimensional laser (i.e. where the cavity is two dimensional) in terms of edge-diffracted waves, and demonstrate its accuracy for large N . Between the size a of the mirror (outer scale), and the inner scale a / N , there is no distinguished scale, and the graph of mode intensity has a fractal dimension close to 2. Near the inner scale, the scaling is scale dependent, and the crossover is described by an explicit formula for a `local fractal dimension D ( K ), describing the mode on scales near Δx = a /(2 πNK ). As K increases through the inner scale K =1, D ( K ) decreases from 2 when K ≪1 to 1 when K ≫1 (reflecting the smoothness of the mode on fine scales).

Bidirectional membrane tube dynamics driven by nonprocessive motors

In cells, membrane tubes are extracted by molecular motors. Although individual motors cannot provide enough force to pull a tube, clusters of such motors can. Here,weinvestigate, using a minimal in vitro model system, how the tube pulling process depends on fundamental properties of the motor species involved. Previously, it has been shown that processive motors can pull tubes by dynamic association at the tube tip. We demonstrate that, remarkably, nonprocessive motors can also cooperatively extract tubes. Moreover, the tubes pulled by nonprocessive motors exhibit rich dynamics as compared to those pulled by their processive counterparts. We report distinct phases of persistent growth, retraction, and an intermediate regime characterized by highly dynamic switching between the two. We interpret the different phases in the context of a single-species model. The model assumes only a simple motor clustering mechanism along the length of the entire tube and the presence of a length-dependent tube tension. The resulting dynamic distribution of motor clusters acts as both a velocity and distance regulator for the tube. We show the switching phase to be an attractor of the dynamics of this model, suggesting that the switching observed experimentally is a robust characteristic of nonprocessive motors. A similar system could regulate in vivo biological membrane networks.

Monte Carlo study of multiply crosslinked semiflexible polymer networks

We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their persistent directionality through the crosslinks. A Monte Carlo scheme is employed to obtain isotropic, homogeneous networks that minimize the free energy and for which all of the relevant parameters can be varied: the persistence length and the contour length as well as the crosslinking length may be chosen at will. We also provide an initial survey of the mechanical properties of our networks subjected to shear strains, showing them to display the expected nonlinear stiffening behavior. Also, a key role for nonaffinity and its relation to order in the network is uncovered.

Universal algebraic relaxation of velocity and phase in 'pulled' fronts generating periodic or chaotic states

We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state, and generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts that generate periodic or even chaotic states. A surprising feature is that such fronts also exhibit a universal algebraic phase relaxation. For fronts that generate a periodic state, like those in the Swift-Hohenberg equation or in a Rayleigh-Benard experiment, this implies an algebraically slow relaxation of the pattern wavelength just behind the front, which should be experimentally testable.

Evidence for slow velocity relaxation in front propagation in Rayleigh-Bénard convection

Recent theoretical work has shown that so-called pulled fronts propagating into an unstable state always converge very slowly to their asymptotic speed and shape. In the light of these predictions, we reanalyze earlier experiments by Fineberg and Steinberg on front propagation in a Rayleigh–Benard cell. In contrast to the original interpretation, we argue that in the experiments the observed front velocities were some 15% below the asymptotic front speed and that this is in rough agreement with the predicted slow relaxation of the front speed for the time scales probed in the experiments. We also discuss the possible origin of the unusually large variation of the wavelength of the pattern generated by the front as a function of the dimensionless control parameter.